Non-Equilibrium Dynamics of DNA Nanotube

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Non-Equilibrium Dynamics of DNA Nanotubes
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Hariadi, Rizal Fajar
(2011)
Non-Equilibrium Dynamics of DNA Nanotubes.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/6GQW-YG26.
Abstract
Can the fundamental processes that underlie molecular biology be understood and simulated by DNA nanotechnology? The early development of DNA nanotechnology by Ned Seeman was driven by the desire to find a solution to the protein crystallization problem. Much of the later development of the field was also driven by envisioned applications in computing and nanofabrication. While the DNA nanotechnology community has assembled a versatile tool kit with which DNA nanostructures of considerable complexity can be assembled, the application of this tool kit to other areas of science and technology is still in its infancy. This dissertation reports on the construction of non-equilibrium DNA nanotube dynamic to probe molecular processes in the areas of hydrodynamics and cytoskeletal behavior.
As the first example, we used DNA nanotubes as a molecular probe for elongational flow measurement in different micro-scale flow settings. The hydrodynamic flow in the vicinity of simple geometrical objects, such as a rigid DNA nanotube, is amenable to rigorous theoretical investigation. We measured the distribution of elongational flows produced in progressively more complex settings, ranging from the vicinity of an orifice in a microfluidic chamber to within a bursting bubble of Pacific ocean water. This information can be used to constrain theories on the origin of life in which replication involves a hydrodynamically driven fission process, such as the coacervate fission proposed by Oparin.
A second theme of this dissertation is the bottom-up construction of a
de novo
artificial cytoskeleton with DNA nanotubes. The work reported here encompasses structural, locomotion, and control aspects of non-equilibrium cytoskeletal behavior. We first measured the kinetic parameters of DNA nanotube assembly and tested the accuracy of the existing polymerization models in the literature. Toward recapitulation of non-equilibrium cytoskeletal dynamics, we coupled the polymerization of DNA nanotubes with an irreversible energy consumption reaction, analogous to nucleotide hydrolysis in actin and microtubule polymerization. Finally, we integrated the DNA strand displacement circuits with DNA nanotube polymerization to achieve programmable kinetic control of behavior within artificial cytoskeleton. Our synthetic approach may provide insights into natural cytoskeleton dynamics, such as minimal architectural or reaction mechanism requirements for non-equilibrium behaviors including treadmilling and dynamic instability.
The outgrowth of DNA nanotechnology beyond its own boundaries, serving as a general model system for biomolecular dynamics, can lead to an understanding of molecular processes that advances both basic and applied sciences.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
DNA, nanotechnology, nanotube, cytoskeleton, the origin of life, bond breakage, drag reduction, polymer dynamics, DNA rupture, cytoskeleton
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Winfree, Erik
Thesis Committee:
Phillips, Robert B. (chair)
Fraser, Scott E.
Elowitz, Michael B.
Yurke, Bernard
Winfree, Erik
Defense Date:
25 March 2011
Record Number:
CaltechTHESIS:06062011-122322347
Persistent URL:
DOI:
10.7907/6GQW-YG26
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
6502
Collection:
CaltechTHESIS
Deposited By:
Rizal Hariadi
Deposited On:
06 Jun 2011 20:46
Last Modified:
02 Jul 2025 20:39
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Non-equilibrium Dynamics
of DNA Nanotubes
Thesis by

Rizal Fajar Hariadi

In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy

California Institute of Technology
Pasadena, California

(Submitted March, 2011)

Rizal F. Hariadi

in loving memory of my parents

Muhammad Amin
(1940 - 2010)

Suhartati
(1944 - 2009)

whose unconditional love and altruism
kindle inspiration and motivate me in every step of my life

Acknowledgments
Having arrived at the end of my odyssey, I now take a great pleasure in thanking those
who mean a lot to me.
My advisor, Erik Winfree, has shaped my scientific philosophy and influenced my direction more than any others. He is a pioneer whose imagination and creativity lead us to a
magical endeavor in the quest of truth and beauty in science. As an advisor, he is incredibly
generous in letting me pursue my true passions with my own scientific and artistic flare,
while providing constant feedback on my growth as a scientist. He has assembled a rich
learning environment filled with brilliant and delightful people from a variety of disciplines.
It is a great privilege for me to work with a great man like him. I wish to pay his kindness
by keeping the same intellectual standards for me and for my future students.
I am one of the fortunate few who get the opportunity to learn from Bernie Yurke who
seems to be an expert in everything, including humility. As his apprentice, I have benefited
greatly from his broad expertise. He taught me theoretical physics, introduced me to the
power of craftsmanship in experimental physics, and showed me different approaches to
data analysis. He is an extraordinary example of a scientist; so much so that my wife and I
named our first daughter after him as our gesture of respect. Some of my fondest memories
are the hiking trips with him and in situ investigation of ocean bubbles on Malibu beach
with him and Damien Woods.
I am very grateful to the rest of my thesis advisory committee: Rob Phillips, Scott
Fraser, and Michael Elowitz. Rob Phillips always has wonderful comments about my
project; and his office is always open for unscheduled conversation about physics, science,
life, and surfing in Indonesia. I thank Michael Elowitz for profound comments about the
importance of nucleation in my artificial cytoskeleton project and Scott Fraser for pointing
out the interesting structural features of DNA nanotubes during my candidacy.
Within the DNA and Natural Algorithms lab, I have gotten to know and learned from
a lot of amazing people whom I will always be thankful for their scientific help and sincere
friendship. I must thank Paul Rothemund and Nick Papadakis who showed me the ropes
early on. Paul Rothemund and Georg Seelig instilled the importance of spending time on
my bench where science happens. Peng Yin filled many gaps in my science and exemplified

iii

how to be an excellent mentor for a graduate student. Damien Woods was an ideal collaborator for learning the Origin of Life, always had time to carefully read my manuscripts,
and will remain a close collaborator. My first office mate, Rebecca Schulman, taught me
about molecular self-replication, the Origin of Life theories, and a bit of computer science.
I thank Elisa Franco, my second office mate, who helped me tremendously with communicating my ideas effectively in my writings and presentations. My third office mate, Dave
Zhang, shared his expertise in entropy-driven chemical reaction networks for controlling
self-assembly of DNA nanotubes. Jongmin Kim pursued a project exploring in vitro transcription of the RNA tiles with me. Even though we did not have the opportunity to go
far with the project, the experience was critical in the catalytic self-assembly project with
Dave. I also thank Jongmin Kim for being a great real-life next-door neighbor. Constantine
Evans and Christina Wright analyzed our single molecule AFM movies, an often tedious
task, and brought the work over the publication barrier. Sungwook Woo lent his expertise
in DNA origami and often filled my role as WHYscope czar when I had to be away. Nadine
Dabby taught me about DNA walkers and co-supervised a SURF student with me. Si-Ping
Han, Rob Barish, Sungwook Woo, and Ashwin Gopinath have been great people to talk
to, fellow DNA-world-ers treading into biology. David Soloveichik, Tosan Omabegho, and
Ho-Lin Chen helped me think about my long-term plan. Paul Rothemund, Nick Papadakis,
Sung Ha Park, Nadine Dabby, Sungwook Woo, Constantine Evans, Peng Yin, Rob Barish,
Shaun Lee, and Joseph Schaeffer were excellent AFM czars and underlings; as were Rebecca Schulman, Constantine Evans, Damien Woods, and Niranjan Srinivas with the UV
Spectrophotometer. Most of all, I want to thank all past and current group members for
intellectually-engaging discussions and for entertaining Biruni during my frequent “take
your child to your lab day”.
Throughout my graduate study, I have been fortunate to have to opportunity to discuss
the cytoskeleton with a number of experts: Deborah Kuchnir Fygenson, Igor Kulic, Rob
Phillips, Chin Lin Guo, Dyche Mullins, Julie Theriot, and Ethan Garner. John Dabiri,
Sandra Troian, and Victor Beck contributed very helpful discussion about hydrodynamics
and ocean waves. I sincerely thank my undergraduate advisors, J. Tom Dickinson and
Jessica Cassleman, for nurturing my early interest in science and inspiring me to take this
path. Recently, Joel Swanson, Nils Walter and Sivaraj Sivaramakrishnan helped me finding
an ideal lab for my post-doctoral research.
The chapters in this thesis would not have been possible without the support of my
collaborators. It is a pleasure to work with Peng Yin, Sudheer Sahu, Harry Choi, Bethany
Walters, Tom LaBean, and John Reif in the characterization of a single-stranded tile con-

struct. The fragmentation and bubble bursting projects were collaborations with Bernard
Yurke and Damien Woods. Sung Ha Park, Satoshi Murata and Kenichi Fujibayashi were
great collaborators in the Sierpinski belt project. My two SURF students: Christina Wright
and Yudistira Virgus, taught me about being a better teacher and person. I also embarked
on a project in single molecule AFM and TIRF tracking of DNA walkers with Niles Pierce,
Harry Choi, Bill Dempsey, Nadine Dabby, Ruobing Zhang, Paul Selvin, Paul Rothemund,
and Erik Winfree. The project did not reach its completion but I gained a lot of knowledge
about optics from this interaction, which later proved to be very useful in my artificial
cytoskeleton projects.
For technical help in microscopy, Rob Phillips’ group has been generous with their advice
and equipment. In particular, Heun Jin Lee was instrumental in getting me over the many
obstacles that popped up in the design and construction of my microscope. David Wu,
Hernan Garcia, and Stephanie Johnson let me used their syringe pump, optical stage, and
other optical parts. Zahid Yaqoob and Michael Diehl helped me learn about optics and
parenting. Rebecca Schulman and Ann McEvoy pointed my attention to the glass capillary
chamber. Jeffry Kuhn shared his filament snapping and length measurement codes.
Karolyn Yong was a very resourceful lab administrative assistant; and more importantly,
a great friend of mine. Esthela Jalabert has been keeping the building clean and tidy. The
Applied Physics program, headed by Rob Phillips who was succeeded by Kerry Vahalla and
later Sandra Troian, has been a tremendous source of moral and technical support. John
P. Van Deusen taught me a lot of craftsmanship and supervised my machine shop time in
Jim Hall Design and Prototyping Lab (Mechanical Engineering machine shop). Saurabh
Vyawahare and Caltech Microfluidic Foundry assisted in the designing and manufacturing
process of the PDMS microfluidic chip. Grant J. Jensen allowed me to use plasma cleaner
and to have fun with his cryo-EM with supervision from Bill Tivol and Alasdair McDowall.
I thank the NSF, the NSF Molecular Programming Project (MPP), the NSF Center of
Molecular Cybernetics (CMC), Caltech Center for Biological Circuit Design (CBCD), and
NASA for funding.
Erik Winfree is an altruistic advisor who genuinely understands the importance of contributing to society; he always gave me permission to participate in outreach activities. I
thank Yohanes Surya and Srisetiowati Seiful from Surya Institute for inviting me to speak
at the 2008 Asian Science Camp in Bali. I treasure the experience. The science camp helped
me decide what I want to pursue after the thesis. Achmad Adhitya, Willy Sakareza, Mahir
Yahya Baya’sut, Teuku Reiza Yuanda and others sharpen my organizational skill during
the launch of Ikatan Ilmuwan Indonesia Internasional (International Indonesian Scholar

Society) in Jakarta and our subsequent activities. It has also been a pleasure to interact
with Johny Setiawan, Yow-Pin Lim, Nelson Tansu, Ken Soesanto, and Pak Ishadi S. K.
who share deep passion in advancing education and research in Indonesia. Two days after
the passing of my mother, I gave a talk at Universitas Paramadina in Jakarta. After introducing me as a speaker, Pak Ishadi S. K. requested the audience for a moment of silence
in remembrance of my mother. My family and I are still touched by the sincere gesture.
Throughout my time at Caltech, I have had the support of good friends at Caltech
who share passions in science and more: Akram Sadek, Aamir Ali, Mohamed Aly, Ahmed
Elbanna, Hareem Maune, Suvir Venkataraman, Gabriel Kwong, and Imran Malik. Ann
Erpino has continued to amaze me with her beautiful art. She is very generous in giving
me permission to exhibit her paintings in this thesis.
Our fellow Indonesians in weekly gathering at the Indonesian consulate in Los Angeles
have always been a source of warm comfort for my family, in particular Pak Dhe and Bu
Dhe. We are really fortunate that in a short amount of time after leaving Pasadena, we
are part of a similar community in Ann Arbor.
This thesis is dedicated to my first teachers, my parents: Muhammad Amin and Suhartati. Although neither of them has the chance to see these chapters finished and submitted,
they have the soundest perspective on the completion of this thesis. My parents inculcated
the attitude that even the largest task can be accomplished if it is done with pure intention,
carefully organized, and executed one step at a time toward perfection. My interesting sisters and caring in-laws have been my favorite counselors. This thesis is also dedicated to
my wife and daughter. My wife, Nurul Itqiyah Hariadi, has been my companion, heart,
mind, and continuous source of inspiration. When she was a pediatric resident at UCLA,
she never let her hectic schedule, ridiculously frequent on-calls, and long daily commute
preclude her from raising her two “kids” at home: my daughter and me. My daughter,
Aliyapadi Biruni Hariadi (who is currently sitting on my lap) always amazes me with her
character, curiosity, and creativity. Both of you make my life a blissful one.

Abstract
Can the fundamental processes that underlie molecular biology be understood and recapitulated by DNA nanotechnology? The early development of DNA nanotechnology by Ned
Seeman was driven by the desire to find a general solution to the protein crystallization
problem. Much of the later development of the field was motivated by envisioned applications in computing and nanofabrication. While the DNA nanotechnology community has
assembled a versatile tool kit with which DNA nanostructures of considerable complexity
can be assembled, the application of this tool kit to other areas of science and technology
is still in its infancy. This dissertation reports on the construction of DNA nanotubes with
non-equilibrium dynamics to probe molecular processes in the areas of hydrodynamics and
the physics of biopolymers.
As the first example, we used DNA nanotubes as a molecular probe for elongational
flows in different micro-scale settings. The hydrodynamic flow in the vicinity of a simple
geometrical object, such as a rigid DNA nanotube, is amenable to rigorous theoretical and
experimental investigation. We measured the distribution of elongational flows produced in
progressively more complex settings, ranging from the vicinity of an orifice in a microfluidic
chamber to within a bursting bubble of Pacific ocean water. This information can be used
to constrain theories on the origin of life in which replication involves a hydrodynamicallydriven fission process, such as the coacervate fission proposed by Oparin.
A second theme of this dissertation is the bottom-up construction of a de novo artificial cytoskeleton using DNA nanotubes. The work reported here encompasses structural,
locomotive, and control aspects of non-equilibrium cytoskeletal dynamics. We first measured the kinetic parameters of DNA nanotube assembly and tested the accuracy of the
existing polymerization models in the literature. Toward recapitulation of non-equilibrium
cytoskeletal dynamics, we coupled the polymerization of DNA nanotubes with an irreversible energy consumption reaction, analogous to nucleotide hydrolysis in actin and microtubule polymerization. Our synthetic approach may provide insights concerning natural
cytoskeleton dynamics, such as minimal architectural or reaction mechanism requirements
for non-equilibrium behaviors including treadmilling and dynamic instability.

vii

Contents
Acknowledgments

iii

Abstract

vii

1. Self-assembly: an introduction
1.1. What is self-assembly? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2. Classes of self-assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3. Non-equilibrium self-assembly to probe biomolecular processes . . . . . . .
1.4. Artificial cytoskeleton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5. Tools for studying non-equilibrium self-assembly . . . . . . . . . . . . . . .
1.6. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.7. Organization of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8. Publications outside this thesis . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
11

2. Programming DNA Tube Circumferences
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3. Concluding remarks and outlook . . . . . . . . . . . . . . . . . . . . . . . .
2.4. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13
14
15
21
23

3. Elongational-flow-induced scission of DNA nanotubes
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3. Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25
26
28
31
39
39

4. Elongational rates in bursting bubbles measured using DNA nanotubes
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41
41
43
45
50

4.5. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5. Could ocean hydrodynamic flows have driven self-replication of the protobiont? 51
5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3. Concluding remarks and outlook . . . . . . . . . . . . . . . . . . . . . . . .

52
55
57

5.3.1. What have we learned? . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2. Trip to Malibu beach . . . . . . . . . . . . . . . . . . . . . . . . . .

57
57

5.4. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6. Single molecule analysis of DNA nanotube polymerization

6.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2. Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1. Total Internal Reflection Fluorescence microscope . . . . . . . . . .

62
66
66

6.2.2. DNA tile design . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.3. Polymerization mix . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.4. Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2.5. Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1. Polymerization rate measurements . . . . . . . . . . . . . . . . . . .

75
75

6.3.2. Local and global analysis of combined polymerization data . . . . .

6.4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1. Interpretation of the measured kon and kof f rate constants . . . . .

84
85

6.4.2. Asymmetric polymerization . . . . . . . . . . . . . . . . . . . . . . .

6.4.3. Comparison with previously reported reaction rates of DNA selfassembled structures . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4. Comparison with the polymerization rates of actin and microtubules

93
95

6.5. Concluding remarks and outlook . . . . . . . . . . . . . . . . . . . . . . . .

6.6. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7. Toward de novo recapitulation of cytoskeletal dynamics with DNA nanotubes

7.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.2. The biophysics of microtubules . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.2.1. The structure of microtubules . . . . . . . . . . . . . . . . . . . . . . 102
7.2.2. GTP hydrolysis in microtubule polymerization gives rise to treadmilling and dynamic instability . . . . . . . . . . . . . . . . . . . . . 104

7.3. DNA nanotube implementation of the engineering principles of cytoskeletal
assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.4.1. The enzymatic activity of EcoRI on dsDNA with nicks . . . . . . . . 113
7.4.2. Nicking reaction of DNA nanotubes . . . . . . . . . . . . . . . . . . 115
7.4.3. Single molecule movie of DNA nanotube polymerization with nicking
reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.6. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A. Supplementary materials for Chapter 2: Programming DNA Tube Circumferences
131
A.1. DNA sequence design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.2. Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.3. AFM imaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.4. Fluorescence imaging and length measurements.

. . . . . . . . . . . . . . . 132

A.5. Thermal transition profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.6. Curvature analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
A.7. DNA sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
B. Supplementary materials for Chapter 3: Elongational-flow-induced scission of
DNA nanotubes
157
B.1. Underlying scission theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
B.2. Bayesian inference and stochastic scission simulation . . . . . . . . . . . . . 161
B.3. Best Lcrit fit by Bayesian inference . . . . . . . . . . . . . . . . . . . . . . . 162
B.4. Best Lcrit fit by Bayesian inference with truncated Gaussian noise . . . . . 162
C. Supplementary materials for Chapter 6: Single molecule analysis of DNA nanotube polymerization
167
C.1. Movie of anomalous diffusion and side-to-side joining . . . . . . . . . . . . . 168
C.2. Movie of depolymerization experiment . . . . . . . . . . . . . . . . . . . . . 169
C.3. Movie of DNA nanotube growth . . . . . . . . . . . . . . . . . . . . . . . . 170
C.4. Movie of complete depolymerization of DNA nanotubes followed by annealing of newly released free DNA tiles . . . . . . . . . . . . . . . . . . . . . . 171
C.5. AFM images of opened DNA nanotubes . . . . . . . . . . . . . . . . . . . . 173
C.6. UV absorbance of DNA nanotube . . . . . . . . . . . . . . . . . . . . . . . . 175

D. Supplementary materials for Chapter 7: Toward de novo recapitulation of cytoskeleton dynamics with DNA nanotubes
177
D.1. The spacing between neighboring DNA tiles in DNA lattice. . . . . . . . . . 177
Bibliography

xii

183

Self-assembly: an introduction

Richard Feynman’s blackboard at the time of his death. (Caltech Archive)

I started my graduate study at Caltech in the spring of 2003, just in time to celebrate
the 50th anniversary of the discovery of the molecular structure of DNA double helix [WC53].
The specificity of Watson-Crick base pairing rules (A=T and G≡C) provides the molecular
foundation of storing genetic information. Aside from its pre-conceived role as the “genetic
blueprint of life”, the simple recognition rule of Watson-Crick base pairing, in addition to
structural features of the DNA double helix, are being exploited by the emerging field of
structural DNA nanotechnology to assemble one-, two-, and three-dimensional nanostructures. Structurally, DNA is an attractive building block for synthesis of nanostructures as
the DNA double helix has a defined diameter of 2 nm and 10.5 base pairs in a full DNA
turn. An additional desirable physical attribute of DNA is its rigidity. The persistence
length of DNA is ∼150 base pairs, which implies that up to 50 nm, the DNA molecule
behaves as a rigid beam. Therefore, in the context of structural DNA nanotechnology, the
end product of molecular programming is the self-assembly of organized DNA helices in
specific spatial configurations; whereas in the context of molecular biology, the end product
is the transcription of DNA sequence into RNA molecules by cellular machinery.
Structural DNA nanotechnology offers one promising approach to constructing dynamical autonomous nanoscale systems. In this approach, the instructions for how to assemble
larger structures are coded in the DNA sequences using the specificity of canonical WatsonCrick hybridization [WLWS98]. Diverse tiling lattices have been constructed [LLRY06],
and some of these lattices are reported to form tubes [YPF+ 03,MHM+ 04,LPRL04,RENP+ 04,
RSB+ 05, LCH+ 06, KLZY06].

Recently, the DNA “origami” approach of folding viral

genomes using hundreds of synthetic oligonucleotides has provided a reliable method for
producing pseudo one-, two- and three-dimensional DNA nanostructures of length 100 nm
or larger [Rot06, DDL+ 09, ESK+ 10, LZWS10]. Furthermore, algorithmic self-assembly of
a small number of DNA tiles can give rise to complex patterns, such as Sierpinski triangles [RPW04, FHP+ 08] and binary counters [BRW05, BSRW09]. Despite the versatile
tool kit with which DNA nanostructures of considerable complexity can be assembled, the
application of this tool kit to other areas of science and technology is still in its infancy.
This dissertation reports on the construction of non-equilibrium DNA nanotube dynamics to probe molecular processes in the area of hydrodynamics and cytoskeletal behavior.
DNA nanotubes have desirable physical features such as (a) long length, (b) long persistence length and (c) inherently simple geometries, which are amenable to rigorous theoretical modelling. Inspired by analogy with the ubiquity of tubular structures in nature
and the roles of microtubules and actin filaments in living cells, this thesis reports the

Narratives for studying DNA self-assembly
There are various reasons for studying DNA self-assembly. First, humans find beauty in ordered structures. This is seen in the early years of DNA self-assembly after the publication
of the seminal paper by Winfree et al. in 1998 [WLWS98], when most of the reported constructs were two-dimensional and tubular crystalline structures that were assembled from
pre-formed multiple stranded DNA tiles [FS93]. Second, algorithmic self-assembly of a simple set of building blocks can result in complex patterned structures [RPW04, BSRW09].
Third, DNA self-assembly is an efficient bottom-up strategy for synthesizing nanostructures as first proposed in Seeman’s classic paper in 1982 [See82]. A striking example of the
efficiency of self-assembly is the construction of a 100-nm scaled map of the Americas using
a technique called DNA origami [Rot06]. In a one pot reaction, Rothemund produced more
maps than human civilizations have ever made.1 Fourth, a more recent class of DNA selfassembly incorporates non-autonomous [SP04, SS04] and autonomous [LMD+ 10, HL10]
DNA robots, thereby enriching our concept of robotics. Fifth, novel properties can be engineered into DNA self-assembly systems, such as self-healing structures [Win06, SCW08]
and reconfigurable structures that can sense the existence of molecules in their environment [GHD+ 08]. Sixth, because living systems are non-equilibrium self-assembled system,
understanding life requires understanding self-assembly [WG02].

1.1. What is self-assembly?
Before focussing further on DNA self-assembly, it is necessary to examine the definition of
self-assembly in general. Within the rich “self-assembly” literature, from the hybridization
of the DNA double helix to the formation of galaxies, one can find elastic definitions of
“self-assembly” that are typically geared toward the focus of the latest trends. In this
thesis, we restrict our definition of self-assembly to the spontaneous formation of organized
structures from many pre-existing components that can be controlled by programming the
components and reaction conditions, such as temperature and component concentrations.
Thus, self-assembly is not synonymous with crystallization or aggregation.

adapted from Erik’s blurb, www.dna.caltech.edu/DNAresearch_publications.html

Chapter 1

application of DNA nanotubes as a micro-scale fluid flow sensor and for the construction
of an artificial cytoskeleton.

In this thesis, we further limit our discussion of self-assembly within the realm of
DNA tile-based self-assembly or structural DNA self-assembly, which is a subset of a
broader field of DNA nanotechnology. The two main signatures of structural DNA selfassembly are the high order and rigidity of the final assembly. This rigidity can be inherited
from the rigid structural core of the building blocks, called DNA tiles, such as in the nanotubes of chapter 6 or can emerge from interactions between floppy building blocks during
the nucleation and growth of the end products, such as in the structures of chapters 2−5.
Since we stipulate that the end product must be rigid, we strictly exclude all of the dynamic strand-displacement reaction-based systems [YTM+ 00,SSZW06,ZW09,BT07,ZS11,
SSW10] from our definition of structural DNA self-assembly

1.2. Classes of self-assembly
Based on the definition of self-assembly above, there are two major classes of self-assembly:
equilibrium self-assembly and non-equilibrium self-assembly, which are also often referred
as static and dynamic (dissipative) self-assemblies, respectively as in refs. [WG02,FBK+ 06].
The distinction between equilibrium and non-equilibrium self-assemblies is strictly based
on the thermodynamic description of the final assemblies and not to the self-assembly
processes by which such structures are synthesized, as will be detailed below.

Equilibrium self-assembly
In equilibrium self-assembly, the final structures are at global or local minimum and do not
dissipate energy. The formation of the ordered structures often requires non-equilibrium
agitation or processing; but once the final structure is formed, it is static and stable. In
the context of chemical potential of the building blocks, each component is initially at
high chemical potential and as each component is added to the assembly, the chemical
potential goes down until reaching its equilibrium chemical potential. Most reported DNA
self-assemblies lie in this territory. One of the most celebrated example in structural DNA
nanotechnology is Rothemund’s two-dimensional DNA origami [Rot06]. The structures
are formed by equilibrium self-assembly, although the synthesis involves a non-equilibrium
step. Typically, DNA origami constructs are made by annealing a set of equimolar short
DNA strands and a substoichiometric concentration of scaffold strand from 90 ◦ C to room
temperature.

In the formation of non-equilibrium dynamic structures or patterns, one must drive the
self-assembly away from equilibrium by continuous supply of energy, which is an integral
part of the local interaction rule set between the components and with the environment.
These non-equilibrium self-assembled structures continue to consume and dissipate energy
for their survival in the form of irreversible entropy producing processes and die when the
flow of energy ceases. The study of non-equilibrium structural DNA self-assembly is still
in infancy.
We further define two subclasses of non-equilibrium self-assembly based on the energy
source. The first subclass obtains the energy from its environment. Most synthetic nonequilibrium self-assembly systems are in this subclass. As an example, Whitesides et al.
studied a variety of non-equilibrum assemblies of ferromagnetic disks, floating at the liquidair interface, under the influence of a rotating external bar magnet [GSW00]. The spinning
disks assemble into a variety of stable patterns. The second subclass of non-equilibrium
assembly consumes energy that is stored in a reservoir of fuel molecules, which are distinct
from the self-assembling components and continuously release waste molecules. My favorite
example of the fuel molecule powered assembly is the non-equilibrium polymerization of
microtubules. Detailed structural properties and non-equilibrium dynamics of microtubules
are presented in section 7.2. The energy is derived from irreversible nucleotide hydrolysis
of GTP to GDP, and used to generate physical phenomena that are only possible in nonequilibrium polymers, such as treadmilling and dynamic instability. The main thrust of
this thesis is our effort in de novo engineering of an artificial cytoskeleton using DNA
nanotubes, and which has the potential to exhibit non-equilibrium phenomena.

1.3. Non-equilibrium self-assembly to probe biomolecular
processes
From a purely scientific perspective, the most important justification for studying selfassembly is the understanding of life. Although the principles of self-assembly are applicable at all scales, the nanoscale size of the DNA tile is attractive because it lies in the length
scale at which gathering, processing, and transmission of information occurs in living systems [Man08]. The construction of non-equilibrium self-assembly systems with features as
intricate and complex as their biological counterparts satisfies Feynman’s criteria of understanding: “What I cannot create I do not understand”. These artificial systems could
provide insight to molecular structures, biological process and how dissipation of energy

Chapter 1

Non-equilibrium self-assembly

leads to the emergence of ordered structures from disordered building blocks, which are
vital in living system.

From the experimental point of view, engineering artificial systems for understanding biological systems offers three advantages. First, building simple nanoscale systems that are
easy to modify provides a platform for rigorous testing, refining, and confirming mathematical models of biomolecular processes. In the case of microtubules, a detailed understanding
of the molecular machinery of α,β-tubulin is difficult to attain because the activity of the
monomer and polymer are affected by complex systems of exogenous and endogenous cellular factors. Claiming that studying artificial system will help understanding biology is
still controversial. Not all insights obtained from artificial systems are guaranteed to have
biological relevance, as will be discussed in section 1.5. Second, the similar length scales
of the biological molecules and their technological analogs permits engineering of a more
advanced artificial system that can alter or even improve the performance of the biological system of interest. Third, for non-equilibrium self-assembly, collective behavior may
arise from simple local rules which might yield insights into the principles of self-organized
system. This set of principles could be essential for engineering materials that exhibit
novel behaviors, such as adaptive assembly [BR09, SY10], self-healing [Win06, SCW08],
and self-replication [SW05].

Advances in DNA nanotechnology and clever experimental design have led to successful construction of several artificial systems, such as artificial muscles [LYL05], artificial
ribosomes [LS04], artificial listeria [VDR+ 07], and artificial myosins [SP04, SS04, YCCP08,
GBT08, LMD+ 10]. Although these artificial constructs were inspired by natural systems,
most of them were primarily technologically-driven and made little connection to their
biological counterparts. The remainder of this chapter mostly explains our work toward
the de novo construction of an artificial cytoskeleton with DNA nanotubes. We aim to
engineer a DNA nanotube system that satisfies the structural, propulsion, and assembly
control aspects found within the biological cytoskeleton, as will be described in the next
section.

Chapter 1

1.4. Artificial cytoskeleton
In the Wright brothers’ conquest of flight2 , Orville and Wilbur Wright approached the
technical challenge as three unique engineering problems3 : (1) The structural challenge;
How do you engineer a structure that generates lift? (2) The propulsion challenge; How
do you power an airplane to move forward? (3) The control challenge; How do you adjust
the speed and navigate an airplane?
Inspired by the Wright Brothers’ approach, we divided our quest of de novo construction
of an artificial cytoskeleton into three engineering challenges:
1. Structural challenge: How can non-equlibrium polymers establish polarity for
asymmetric polymerizations, such as treadmilling and dynamic instability?
The structural challenge for an artificial cytoskeleton encompasses both (1) equilibrium selfassembly and (2) non-equilibrium self-assembly. First, biological cytoskeleton structures
are long-and-rigid polymers composed of non-covalently-bound monomers. DNA nanotubes
satisfy these criteria already, as will be described in chapter 6 and appendix C. Second, since
asymmetric polymerization requires energy source, we couple an irreversible dissipative
reaction with DNA nanotube polymerization (chapter 7). In our design, we inserted the
EcoRI restriction sequence at the two opposing sticky ends of a DNA tile, such that docking
a DNA tile to a growing polymer will complete the restriction site and will trigger the analog
of the nucleotide hydrolysis reaction. Our aim is to investigate minimal architectural or
reaction mechanism requirements for asymmetric polymerizations, such as treadmilling and
dynamic instability.
Apart from being a candidate material for an artificial cytoskeleton, we also used static
DNA nanotubes as a novel micro-scale fluid flow sensor. The simple “structural” features of
DNA nanotubes enable us to rigorously calculate a simple fluid-flow-induced tension along
an n-helix DNA nanotube (appendix B). By Bayesian inference from the nanotube length
distribution before and after being subjected to the fluid flow, we measured the strength
of elongational flows produced in progressively more complex settings, ranging from the
vicinity of an orifice in a microfluidic chamber (chapter 3), to within a bursting bubble of
DNA buffer (chapter 4) or of Pacific ocean water (chapter 5).

On a personal note, I started my graduate study 100 years after the Wright brothers’ first controlled,
powered and sustained human flight, on December 17th , 1903.
Paraphrased from Dyche Mullins’ lectures on prokaryotic and eukaryotic cytoskeleton at Caltech.

2. The propulsion challenge: What are the mechanisms by which molecular
assemblies generate the force required to apply force to other structures?
The non-equilibrium polymerization of rigid polymers has been shown to transduce chemical energy from the concentration gradient into mechanical energy [The00]. This represents
another class of molecular motor, called a polymerization motor. Rather than using a general cellular energy currency, such as ATP or GTP, the energy in a polymerization motor is
stored in the chemical potential of free monomers µs that is either higher or lower than the
chemical potential of the monomers at the tip of a polymer µp . If µs > µp , polmerization
is favored, while in the opposite case, µs < µp , depolymerization dominates. As an example of a polymerization motor, the polymerizing protein ParM [GCWM07] in prokaryotic
cells uses non-equilibrium insertional polymerization to push two chromosomes apart in a
dividing cell. Interestingly, Venkataraman et al. [VDR+ 07] devised an elegant construct
of DNA-based insertional polymers that, in principle, is capable of generating force or
transporting nanoscale objects in solution. As another example, depolymerizing microtubules in the mitotic spindle are used by eukaryotic cells to segregate their chromosomes
correctly during cell division [DKRLJ05, WWAS+ 06]. In chapter 6 and appendix C, we
demonstrated and characterized non-equilibrium polymerization and depolymerization of
isolated DNA nanotubes. In this work, similar to the biological polymerization motor, the
energy of the assembly is stored in the chemical potential of free DNA tiles.

3. The control challenge: How do alterations in the DNA tile regulate its function?
How can chemical reaction networks control when and where the polymerization of
DNA nanotubes take place?
Like a flying airplane, active polymers, such as the cytoskeleton, are inherently unstable.
The cytoskeletal monomers and cytoskeletal accessory proteins are intelligent molecules
that evaluate their environments to assemble and disassemble cytoskeletal polymers at the
right time and the right place within cells. In collaboration with Dave Zhang and Harry
Choi, I addressed the control challenge by integrating strand displacement circuitry with
DNA nanotube polymerization The interplay between chemical reaction networks and selfassembly described in this thesis is essential toward building non-equilibrium systems that
can execute tasks based on the evaluation of molecular information in its environment.

Chapter 1

1.5. Tools for studying non-equilibrium self-assembly
Continued progress in the construction of non-equilibrium DNA self-assembly as model
systems for molecular biology requires effective light microscopy assays, physical models,
computational tools, and equally important, formal criteria for assessing the biological
relevance of any insight obtained from an artificial system.

Microscopy
Open a biophysics textbook [PKTG09], you will be presented with many microscopy images
of non-equilibrium biochemical reactions that drive the essential processes of life. Light
microscopy has been the standard assay for the study of temporal evolution and spatial
organization in cells. In contrast, traditional equilibrium self-assembly typically reports the
final structures in the form of static AFM images, which provides little information about
the dynamics enroute to the end product. Compelling demonstration of non-equilibrium
engineered structures or patterns often requires continuous observation of dynamic systems
in real time. In chapter 6 and and appendix C, we use TIRF microscopy to continuously
monitor the non-equilium polymerization of self-assembled DNA structures in real time.
From a set of polymerization movies at a wide range of tile concentrations and reaction
temperatures, we were able to measure both the kinetic and thermodynamic parameters
of DNA nanotube assembly and discover the subtle features of polymerization that can be
observed with single-molecule microscopy technique.

Theories and principles of non-equilibrium self-assembly
Physical models and computational tools are central in guiding the experimental design of
DNA self-assembly as well as understanding the global behavior that emerges in these systems. In chapter 6, we report the experimental verification and refinement of the existing
kinetic Tile Assembly Model [Win98]. Measured kinetic and thermodynamic parameters
were subsequently used in the stochastic simulation of DNA nanotube polymerization at
different circumferences. In a subsequent experiment, we employed both the polymerization
model and stochastic simulation in predicting the effect of coupling irreversible chemical
reactions, analogous to nucleotide hydrolysis, with DNA nanotube polymerization (chapter 7).

Turing test analog for artificial systems
The engineering approach to studying biomolecular assemblies that is highlighted in this
chapter, is still considered controversial because of two reasons: (1) The biological insight
that one obtains from artificial systems is inherently indirect. (2) At least in DNA nanotechnology, artificial systems are much simpler than their biological counterparts. Only a
small set of primitives and a subset of features used by biomolecules of interest are embedded in an artificial system. Hence, any insight obtained from this approach does not always
carry over to meaningful insight about biological system. One way to filter the experimental results from this approach is by subjecting the artificial system to the analog of the
Turing test for artificial intelligence. Here, by looking at the behavior of the system that
we create, we judge the relevance of our study by our ability to distinguish the artificially
constructed system from the biological system [LF09].

1.6. Outlook
The field of DNA nanotechnology can offer opportunities to build artificial systems of biological assemblies. Future developments in non-equilibrium DNA nanotechnology may
lead to components for artificial life and materials with novel properties, such as adaptability, self-healing, and self-replication. However, it is unclear whether this herculean
effort will lead to an efficient way of advancing biology. We understand biological cells
are self-organized chemical systems that acquire material and information, make molecules
and decisions, and take actions that regulate their internal functions and their interactions
with the environment. Yet we know very little how simple chemical reaction networks
obtain the complexity and emergent behaviors found in living cells. We are also still learning how various artificial and natural non-equilibrium systems utilize energy dissipation in
the emergence of order from interactions of disordered components. Even modest progress
toward solving these scientific mysteries will provide sufficient justification to the study of
these artificial systems.

1.7. Organization of the thesis
The author contribution, and publication or work in preparation, associated with each
chapter are presented in the first footnote of each chapter. Other than chapter 2, I am the
first author or co-first author of the publication or manuscript in preparations in the rest
of this thesis.

The first theme of this thesis describes the elongational flow induced scission of n-helix
DNA nanotubes (chapter 2 and appendix A) in progressively more complex settings, ranging from the vicinity of an orifice in a microfluidic chamber (chapter 3 and appendix B) to
within a bursting bubble of DNA buffer (chapter 4) and Pacific ocean water (chapter 5).
This work was inspired by Rebecca Schulman’s project on engineering DNA tile-based
artificial life [SW05] and was initiated by a serendipitous observation by Harry M. T. Choi.
The second part of this thesis describes our effort toward de novo construction of an artificial cytoskeleton with DNA nanotubes. Chapter 6 and appendix C, indirectly addresses
the propulsion challenge of an artificial cytoskeleton. We demonstrated the application
of TIRF microscopy to measure the kinetic and thermodynamic parameters of DNA nanotube polymerization. The structural challenge for an artificial cytoskeleton is addressed
in chapter 7 and appendix D. Finally, in a paper that is currently in review (see below),
we integrated DNA nanotube polymerization and strand displacement circuitry to address
the control aspect for an artificial cytoskeleton.

1.8. Publications outside this thesis
During my years as a graduate student, I also embarked on these following projects:
1. Kenichi Fujibayashi, Rizal F. Hariadi, Sung Ha Park, Erik Winfree, and Satoshi
Murata, Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular
automaton pattern, Nano Letters, 2008, Vol. 8, Issue 7, 1791 - 1797.
2. Constantine G. Evans, Rizal F. Hariadi, and Erik Winfree
Direct Atomic Force Microscopy Observation of DNA Tile Crystal Growth at the
Single Molecule Level, Journal of the American Chemical Society, 2012, vol. 134,
Issue 25, 10485-10492.

∗ Authors contributed equally.

Chapter 1

For the published works, all of the the text and figures in this thesis come directly
from the published manuscripts with minor stylistic modification to match the style of the
document. The experimental work for all the results presented in the thesis are primarily
performed by me and all of the figures were mine, except where explicitly noted, such as
all of Ann Erpino’s paintings.

3. Dave Yu Zhang∗ , Rizal F. Hariadi∗ , Harry M. T. Choi, and Erik Winfree, Integrating
DNA strand displacement circuitry with DNA tile self-assembly,
Nature Communications, 2013, Vol. 4, 1965
4. Rizal F. Hariadi, Damien Woods, and Bernard Yurke,
Assessing the effectiveness with which breaking waves could have driven protobiont
replication, in preparation

∗ Authors contributed equally.

Programming DNA Tube
Circumferences
Creativity has more to do with the
elimination of the inessential than
with inventing something new.
(Helmut Jahn)

U5
U3

U4
U3
U2
U1

Image courtesy of Peng Yin

Abstract
Synthesizing molecular tubes with monodisperse, programmable circumferences is an
important goal shared by nanotechnology, materials science, and supermolecular chemistry.
We program molecular tube circumferences by specifying the complementarity relationships
between modular domains in a 42-base single-stranded DNA motif. Single-step annealing
results in the self-assembly of long tubes displaying monodisperse circumferences of 4, 5,
6, 7, 8, 10, or 20 DNA helices.

2.1. Introduction
DNA, life’s information carrier, has recently emerged as a versatile material for constructing
self-assembled synthetic molecular structures and devices [See03, FN06, BT07, See07]. The
construction of extended DNA arrays has motivated the search for rigid molecular building
blocks, as component rigidity is commonly considered necessary for the formation of wellordered DNA crystals rather than ill-defined aggregates [SWY+ 98]. A typical building
block, or tile, has a rigid structural core, and displays several “sticky ends" that allow for
specific binding with other tiles to guide lattice formation [FS93, WLWS98]. Diverse tiling
lattices have been constructed [LLRY06], and some of these lattices are reported to form
tubes [YPF+ 03, MHM+ 04, LPRL04, RENP+ 04, RSB+ 05, LCH+ 06, KLZY06]. Such DNA
nanotubes typically possess varied circumferences.
As the precise control of the structure of matter is a central goal for nanotechnology,
materials science, and supermolecular chemistry, controlling DNA tube circumferences has
attracted intense research interest. One strategy is to encode the circumferential tube geometry directly in each individual building block [MLK+ 05, PBL+ 05, WM05, SS06, DCS07,
KWSS07]: barrel/half-barrel like rigid tiles with designed tubular curvature and circumference are first assembled, and then stacked to produce tubes with prescribed circumferences. Using this strategy, researchers have successfully constructed DNA tubes containing three [PBL+ 05, WM05], six [MLK+ 05, KWSS07, DCS07], and eight circumferential
helices [KWSS07], and have proposed designs for tubes of arbitrary circumference [SS06].

This work was published in full as:
Peng Yin, Rizal F. Hariadi, Sudheer Sahu, Harry M. T. Choi, Sung Ha Park,
Thomas H. LaBean, and John H. Reif.
Programming DNA Tube Circumferences.
Science (2008) vol. 321 (5890) pp. 824-826

However, this approach requires the circumference-dependent construction of distinct building blocks that often possess complicated molecular structures. This motivates us to search
for alternative strategies that are modular and simpler.

2.2. Results
The 42-nucleotide (nt) single-stranded DNA motif has four concatenated modular domains
(Fig. 2.1A): the orange domain 1 and the blue domain 2 together contain 21 nucleotides;
the green domain 3 and the pink domain 4 together contain 21 nucleotides. By pairing up
complementary domains, the motifs can be arranged to form DNA lattices composed of
parallel DNA helices connected by single-stranded linkages (or half-crossovers1 ) (Fig. 2.1B).

The half-crossover can be viewed as a simplified Holliday-junction analog, which utilizes one strand,
rather than the normal two strands, at the crossover exchange point. A similar structure was previously
used in constructing DNA nanotubes [LCH+ 06].

Author contributions:
PY invented the SST motif, conceived and initiated the project, organized the team, and
supervised the work. The work at Duke (May 2005 - Aug. 2005) was hosted in the lab of
JHR and THL, and the work at Caltech (Sep. 2005-Aug. 2008) was hosted in the lab of
Erik Winfree. While at Duke, PY designed sequences. PY designed the experiments with
input from THL and SHP. PY and SS prepared the samples. PY and SS performed the AFM
experiments. SHP performed nanotube metalization experiments (not included). Bethany
Walters performed melting experiments (not included). PY and SS analyzed the data with
input from THL and SHP. While at Caltech, PY designed the sequences, and prepared all
the samples. PY and RFH designed the experiments with input from HMTC and SHP. PY,
RFH, SS, HMTC, and SHP performed AFM imaging. RFH acquired the high resolution
images of 5-helix ribbon. PY and RFH analyzed the data. PY and RFH run the melt
experiments. RFH imaged SST with TIRF and confocal microscopes. SHP metalized SST
nanotubes (not included). RFH and Bernard Yurke built the TIRF microscope. The figures
and the manuscript were prepared by PY, with discussion and input initially from SHP, THL,
and JHR, then primarily from RFH and Erik Winfree.

Chapter 2

We report the construction of DNA lattices using a flexible, single-stranded DNA motif,
which is substantially simpler than the current practice using multi-stranded rigid tiles.
During lattice formation, the motif configures itself into a tile-like geometry, and motifmotif interactions result in emergent rigidity along the extended growth direction of the
lattice. Importantly, this flexible motif allows us to program the tube circumference also as
an emergent property collectively defined by the modular interactions between the motifs.
In the resulting framework, simply pairing modular domains in the single motif results in
the self-assembly of monodisperse DNA tubes with designed circumferences. Additionally,
the motif-based, codified construction permits the description of a tube de sign in the form
of an abstract “molecular program", further simplifying the design process.

Motif

Domain 4

Domain 1

Domain 3
Domain 2

10
11

11
10

Port 3

Abstraction
Port 4

Port 2

Node
Port 1

D D

Figure 2.1.: (A) Motif. Colored lines represent modular domains; the arrow head indicates the 30 end. (B)
Secondary structure of DNA lattices. Short vertical bars represent base pairing. The shaded area indicates a
repeating structural unit. (C) Abstraction of the motif as a node with four ports [YCCP08]. The ports are
depicted as colored circles. The color use is consistent with A, and the ordering of the ports is specified by their
colors: orange → blue → green → pink. (D) Complementarity graph.

As the orange-blue domains and the green-pink domains in a motif each measure 21 nt, the
inter-helicial linkages are spaced periodically at every two full helical turns (i.e. 21 base
pairs). In the lattices, each non-boundary motif is configured into a rectangle-like shape,
a tile, and is termed a single-stranded tile, or SST (see Fig. A.1 for the comparison between
a traditional rigid multi-stranded tile and SST). In Fig. 2.1B, the number k associated
with a green domain indicates the number of nucleotides contained in the domain, and
determines the putative, approximate inter-helix curvature for an un-strained lattice (e.g.
not closed into tubes) through a simple formula, k × 34.3◦ − 330◦ [see Appendix A.6 for
details].
The modularity and standardization of the SST motif allows us to codify the lattice
design procedure: first “wire" together complementary domains and then assign the dimensions of the green domains2 . The codification further permits us to ignore molecular
structure details and express the lattice design in a simple abstract form. Adapting a previous notation system [YCCP08], we abstract our motif as a node with four ports, where
each port represents a modular domain (Fig. 2.1C). The lattice design is expressed as a
complementarity graph (Fig. 2.1D), where two complementary ports are connected by a
grey line, and the dimension of each green port is indicated with an associated number.
A complementarity graph represents a “molecular program" to be executed physically
by the corresponding DNA molecules. During the execution of the program through onepot annealing (see Materials and Methods in Appendix A), the specified complementarity
relationship between the modular domains of the motif directs the DNA molecules toward a
(global or local) thermodynamic minimum on the free energy landscape, where the designed
target structure resides. For example, the execution of the molecular program in Fig. 2.1D
results in the formation of the 3-helix ribbon lattice depicted in Fig. 2.1B.
The 3-helix ribbon program can be generalized to program the formation of k-helix
ribbons (Fig. 2.2A), using (k −1) full SST species (U1 , U2 , . . . , Uk−1 ) and 2 boundary halfSST species (L1 and Lk ). By executing the general program in Fig. 2.2A, we demonstrate
the experimental construction of monodisperse ribbons [SW07] with five distinct widths:
3-, 4-, 5-, 6-, and 20-helix ribbons. Fig. 2.2B depicts the secondary structure for the 5-helix
ribbon. Direct imaging of the self-assembly product by atomic force microscopy (AFM)
reveals the expected linear filament morphology (Fig. 2.2C). AFM further confirms the

Due to the modularity and standardization of the motif, assigning the dimensions of all the green domains
in the lattice also uniquely determines the dimensions of all the other domains.

Chapter 2

and is connected to four adjacent neighbors. Thus the motif implements the functionality of

Uk-1

11
10

U1
L1

L5
U4
U3
U2
L1

5-helix ribbon

3-helix ribbon

1 μm

4-helix ribbon

1 μm

5-helix ribbon

1 μm

6-helix ribbon

1 μm

20-helix ribbon

1 μm

Figure 2.2.: Monodisperse DNA ribbons with programmed widths. (A) The molecular program for assembling a
k-helix ribbon. (B) Secondary structure for the 5-helix ribbon. See figs. S3 and S4 for more structures and details.
(C) AFM images of 3-, 4-, 5-, 6-, and 20-helix ribbons. See Fig. A.5 for larger AFM images. Insets, scale bar, 50
nm. Measured ribbon widths: 9.3 ± 0.7 nm (3-helix ribbon), 12.5 ± 0.5 nm (4-helix), 14.9 ± 0.7 nm (5-helix),
18.0 ± 0.8 nm (6-helix), and 59.0 ± 1.1 nm (20-helix). See Fig. A.6 for ribbon width measurements. (D) High
resolution AFM image of the 5-helix ribbon. Left, depiction of the expected DNA structure, emphasizing bended
helices and inter-helix gaps. The color use is consistent with B. Right, AFM image revealing an alternating pattern
of four columns of inter-helix gaps, in agreement with the depiction on the left. See Fig. A.7 for details.

10 nm

designed dimensions of the ribbons: a k-helix ribbon has a measured width of ∼3 × k nm
(Fig. 2.2C insets). Further, the morphology details of the 5-helix ribbon are revealed by
high resolution AFM (Fig. 2.2D).

(Fig. 2.3A). Fig. 2.3B (left) describes the secondary structure for k = 6. The execution of
the 6-helix tube program through annealing results in linear filament products (Fig. 2.4A,
third panel from left). The mechanical force exerted by repeated AFM scanning opens these
filaments, confirming their tubular nature (Fig. A.12). Finally, AFM width measurement
of 10 random opened tubes establishes the monodispersity (i.e., no 6 × m-helix tubes
identified, for m > 1) of their circumferences (Fig. A.13).
This molecular implementation could in theory allow concatenation of multiple repeats
of U1-U2-U3-U4-U5-T6 along the tube’s circumference, resulting in poly-disperse tubes
composed of 1 × 6 circumferential helices, 2 × 6 helices, 3 × 6 helices, etc.. Further, geometric modeling [RENP+ 04] suggests that the SST domain dimensions in Fig. 2.3A would
result in an average inter-helix curvature of ∼30◦ per helix (Appendix A.6). One would
therefore expect 12-helix tubes to be less sterically strained [RENP+ 04] than 6-helix tubes
and to thus dominate at thermodynamic equilibrium. The observed monodisperse formation of 6-helix tubes suggests that the tube formation should be understood as a kinetic
process [MHM+ 04, KLZY06] and that these tubes are trapped at a local minimum on the
free energy landscape (Fig. 2.3B, right). These tubes are stable: AFM images obtained ∼6
months after sample preparation reveal monodisperse 6-helix tubes.
We next tested the general program (Fig. 2.3A) where k distinct SST species selfassemble into k-helix tubes. By choosing appropriate subsets from a common pool of 15
distinct SST species (Fig. A.9), we have engineered monodisperse tubes of 6 different circumferences: 4-, 5-, 6-, 7-, 8-, and 10-helix tubes. The generality of this strategy is further
confirmed by the successful engineering of mono-disperse 20-helix tubes. The secondary
structures of these tubes are presented in Fig. A.8. Their 3D illustrations are summarized
in Fig. 2.3A (right) and detailed in Fig. A.10. In each case, AFM imaging reveals the
formation of long tubes (Fig. 2.4A) and AFM width measurement of randomly selected,
opened tubes confirms the expected circumference monodispersity (Fig. 2.4A, insets, AFM
images. Fig. 2.4B, summary. See Fig. A.13 for details). The length of SST tubes is investigated using fluorescence microscopy (Fig. 2.4C). For 7-helix tubes, the average length is

Chapter 2

A natural strategy for constructing monodisperse k-helix SST tubes is to merge the
two boundary half SST species in the k-helix ribbon program into a full SST species

U3
11

U2
10

U5
U4
U3
U2
U1

Kinetic
trap

No 12-helix
tube formed

Monomers

6-helix tube
formed

Figure 2.3.: Monodisperse DNA tubes with programmed circumferences. (A) Molecular program (left) and 3D
illustrations (right) for assembling k-helix tubes. (B) Secondary structure (left) and putative kinetic trapping
(right) for 6-helix tubes. Asterisks denote complementarity.

∼6 µm, with some tubes reaching ∼20 µm.
Thermal formation and melting profiles of SST tubes (Fig. 2.4D) and SST ribbons
(Fig. A.15) reveal hysteresis. Such hysteresis has also been observed in DNA lattices
nealing/melting curves of SST tubes and ribbons demonstrate only one sharp transition
temperature. This is consistent with the expectation that single-stranded DNA oligonucleotides are directly assembled into the growing lattice during annealing and disassembled
from the lattice during melting. In contrast, two or more characteristic transition temperatures are commonly observed in multi-stranded rigid tile based lattices [BRW05,SW07]: the
lowest temperature corresponds to lattice formation/melting, and the others correspond to
tile formation/melting.
We suggest that the structural flexibility of SST may contribute to the success of the
putative kinetic trapping of monodisperse tubes. The long sticky ends of SST and the
flexible inter-helix single-stranded linkage points in the assembled lattice may facilitate
fast cyclization and hence trapping of the tubes with the smallest compatible number of
helices. Additionally, it is conceivable that in a nucleation-elongation model [SW07] (see
Fig. A.16 for a hypothetical assembly pathway), the nucleation barrier difference between
the k-helix tube and the 2k-helix tube may help trap the system into monodisperse khelix tubes. The observed hysteresis (Fig. 2.4D) suggests the existence of a significant
kinetic barrier during tube formation and it is conceivable that this kinetic barrier is due
to the presence of a nucleation barrier. It would be interesting to experimentally elucidate
the kinetic assembly pathways of SST tubes. It would also be interesting to test if a
similar kinetic strategy can be applied to programming the circumferences of DNA tubes
assembled from multi-stranded rigid DNA tiles [YPF+ 03, MHM+ 04, LPRL04, RENP+ 04,
RSB+ 05, LCH+ 06, KLZY06].

2.3. Concluding remarks and outlook
The ribbon/tube systems constructed here are likely to find applications ranging from
biophysics, to electronics, and to nanotechnology. In biophysics, the programmable dimensions of the ribbons/tubes and hence their programmable physical properties, e.g.
persistence length, make them attractive synthetic model systems. In electronics, metalization of DNA nanotubes [YPF+ 03, LPRL04, PBL+ 05] may result in nanowires with
controlled diameters, and hence controlled electronic properties. In nanotechnology, DNA

Chapter 2

formed from multi-stranded tiles [BRW05, SW07]. It is also worth noting that the an-

1 μm

10-helix tube

20 μm

6-helix tube

7-helix tube

20 μm

1 μm

5-helix tube

w=3×k

10
15
20
Designed helix number, k

w=6×k

4-helix tube

50 nm

40
20

1 μm

7-helix tube

60
40
20

8-helix tube

1 μm

N = 565

10
15
Length (μm)

0.14
0.12
0.10
0.08
10

20-helix tube

1 μm

Melting

50
Temperature (°C)

Annealing

1 μm

10-helix tube

Absorbance

Figure 2.4.: (A) AFM images of 4-, 5-, 6-, 7-, 8-, 10-, and 20-helix tubes. See Fig. A.11 for larger AFM images.
(B) Width plot of opened tubes. A k-helix opened tube is expected to have a width w ≈ 3 × k nm, as determined
by the width measurement of the k-helix ribbons (Fig. A.6). A 2 × k-helix opened tube, by contrast, is expected
to have w ≈ 6 × k nm. Dashed lines corresponding to w = 3 × k and w = 6 × k are plotted to facilitate tube
circumference monodispersity determination. See Fig. A.13 for a larger picture. (C) Left, fluorescence microscopy
images of 7- and 10-helix tubes decorated with Cy3 fluorophores. Right, length profile of 7-helix tubes (sample
size N = 565). See Fig. 14 for larger images and more profiles. (D) Annealing (blue) and melting (red) curves of
4-helix tubes. Each constituent DNA strand at 100 nM. Cooling/heating rate at 0.15◦ C per minute. See Fig. A.15
for more thermal profiles.

Width,w (nm)

nanotubes with programmable geometrical and mechanical properties can be used as
building blocks for more sophisticated architectures and devices (e.g. tracks for molecular motors [PTS+ 06, YCCP08, BT07]) and as templates for organization of functional

Chapter 2

groups [YPF+ 03, LLRY06].

2.4. Acknowledgements
The authors would like to thank Prof. Erik Winfree at Caltech for generously hosting the
majority part of this work in his lab. For inspiring discussions, the authors would like to
thank Erik Winfree, Paul W. K. Rothemund, Rebecca Schulman, Victor A. Beck, Jeffrey
R. Vieregg, Robert D. Barish, Bernard Yurke, David Y. Zhang, Niles A. Pierce, Shogo
Hamada, Marc Bockrath, Hareem Tariq, Y. Huang, Colby R. Calvert, Nadine L. Dabby,
and Jongmin Kim. The authors are also grateful to Prof. Niles A. Pierce at Caltech
and Prof. Jie Liu at Duke for facility support, to the Pierce group for the use of the
unpublished DNA sequence design component and DNA structure illustration component
of the NUPACK server (www.nupack.org), and to Bethany Walters for technical assistance.
The fluorescence microscope was built by Rizal Hariadi and Bernard Yurke. There is a
patent pending on this work. This work is supported by the Center for Biological Circuit
Design at Caltech, NSF grants CCF-0523555 and CCF-0432038 to John H. Reif, NSF grant
CBET-0508284 to Thomas H. LaBean, NSF grants 0622254 and 0432193 to Erik Winfree,
NSF grant 0506468 to Niles A. Pierce.

Elongational-flow-induced scission
of DNA nanotubes

Compression (Ann Erpino)
www.annerpino.com

Abstract
The length distributions of polymer fragments subjected to an elongational-flow-induced
scission are profoundly affected by the fluid flow and the polymer bond strengths. In
this paper, laminar elongational flow was used to induce chain scission of a series of
circumference-programmed DNA nanotubes. The DNA nanotubes served as a model system for semi-flexible polymers with tunable bond strength and crossectional geometry. The
expected length distribution of fragmented DNA nanotubes was calculated from first principles, by modeling the interplay between continuum hydrodynamic elongational flow and
the molecular forces required to overstretch multiple DNA double-helices. Our model has
no free parameters; the only inferred parameter is obtained from DNA mechanics literature, namely the critical tension required to break a DNA duplex into two single-stranded
DNA strands via the overstretching B-S DNA transition. The nanotube fragments were
assayed with fluorescence microscopy at the single-molecule level and their lengths are in
agreement with the scission theory.

3.1. Introduction
Elongational-flow-induced scission can break a long polymer into fragments with controlled size and is an important physical technique in genome sequencing and biopolymer science [BZK+ 04].

Elongational-flow-induced scission of genomic DNA into con-

trolled narrow distribution of short fragments, but with random break points, is a critical
preparatory technique for producing unbiased DNA libraries in shotgun genome sequencing [OHSC+ 96, THSOD98, Qua03]. The fluid-flow-induced mechanical shearing of prion
fibrils is routinely used in prion studies to replicate structural conformation of the determinant nuclei by generating new polymerizing ends [SCK+ 00, CDVW04].
Polymer scission in a strong elongational flow occurs because of the interplay between
macro-scale hydrodynamic flows and atomic-scale intramolecular interactions of the poly-

This manuscript is published as:
Rizal F. Hariadi and Bernard Yurke
Extensional-flow-induced scission of DNA nanotubes in laminar flow.
Physical Review E, 2010, 82, 046307
Author contributions:
Bernard Yurke and I conceived the idea and prepared the first draft of the paper. I carried
out the experiment, analyzed the data and wrote the first draft of this manuscript.

mer [HM84]. Substantial effort has been made toward understanding polymer scission, including elucidation of the scaling relations between key physical parameters [BD72,Dan78,
OK86, NK92, OT94, THSOD98, VCS06, LYZ+ 06] and measurement of the polymer bond
strength based on the fragment distributions. Recently, Vanapalli et al. reconciled the
scaling discrepancies between theory and scission experiments and showed the significance
of turbulent flow in polymer scission data [VCS06].

considered “extraordinarily difficult” to achieve [VCS06]. In our investigation, this long
contour length challenge was satisfied by using long DNA nanotubes. This structure selfassembles cooperatively from individual 5–15 nm size components through a nucleation
and condensation mechanism [YHS+ 08, SW07, OK62] that yields long tubular structures
on the order of 5 µm. The second ramification from the weak induced tension in laminar
flow is that for polymer scission to occur, the molecular forces between polymer subunits
must be weak enough to be broken apart by the weak flow. In contrast to the polymer
samples in previous scission studies, DNA nanotubes are held together by non-covalent
interactions between their subunits. These two properties of DNA nanotubes, namely, long
contour length and weak non-covalent intramolecular interactions, enable us to rigorously
investigate polymer scission in laminar flow.
Here we report the scission of circumference-programmed DNA nanotubes in a purely
laminar flow device. Scission is achieved when the tension along a DNA nanotube becomes
sufficient to break the non-covalent base-pair interactions holding the structure together.
In our DNA nanotube construct, breakage is expected when the tension along individual
duplex DNA strands is sufficient to induce a B-S transition from the B form of the double
helix to the S form of the DNA overstretched state [SCB96]. In a duplex DNA with two
opposite nicks, the overstretching transition disrupts base pairings along the entire length
of duplex DNA and allows the two strands to slide past each other until duplex DNA is
completely melted into two free single-stranded DNAs. To generate quantifiable fluid flows
with sufficient elongation rates, a syringe pump-driven microfluidic device was employed.
The DNA nanotube fragment size distribution was quantified using single-molecule fluorescence microscopy. We derived a model without free parameters and validated the model

Chapter 3

Despite the amenability of laminar flow in the vicinity of a rigid rod to rigorous theoretical
investigation, there have been no systematic studies of the scission of rigid polymers in the
absence of turbulence. First, because of the weak elongational flow in the laminar regime,
only long polymers on the order of a micron in length can accumulate enough tension for
polymer scission to occur. Due to this requirement, polymer scission in laminar flow is

predictions using the experimental data over nearly a decade of elongational flow rates and
for DNA nanotubes having three different tube circumferences and bond strengths.

3.2. Methods

|||||||||| |||||||||| ||||||||||

-6

|||||||||| |||||||||| ||||||||||

u7
u6
u5

-8

21 bp 〜 7 nm

t(1,7)
u1

|||||||||| |||||||||| ||||||||||

u5
u7

nanotube circumference
(# of DNA helices)

t(1,7)

u4
t(1,7)
u1
u2
u3
u4

- 10

Figure 3.1.: (Color) An 8-helix nanotube is chosen to illustrate the modular construct
of the DNA nanotube system used in this experiment adapted from [YHS+ 08]. (a)
Complementarity graph of the 8-helix DNA nanotube. Each tile has four binding
domains; each domain has a unique complement in its adjacent tile. The interaction
between complementary domains drives the assembly into the designed order. (b)
Each t(1,n-1) strand concatenates two u1 and two u(n − 1) strands, and, thus wraps
the two-dimensional crystalline structure into an n-helix nanotube. The same strategy
has been demonstrated to successfully produce DNA nanotubes up to 20 duplex helices
in circumference [YHS+ 08]. (c) Putative structures of 6-, 8-, and 10-helix nanotubes.
The DNA nanotubes used in this experiment are composed of recently devised “singlestranded-tile" structures [YHS+ 08]. These nanotube constructs are self-assembled structures that are rationally designed by encoding information in the sequence of DNA subunits
using the techniques of structural DNA nanotechnology [WLWS98, RENP+ 04, RPW04,
APS08]. Single-stranded tile-based DNA nanotubes [YHS+ 08] represent a new variant
of one-dimensional crystalline DNA nanostructures, as they are homogeneous in their circumferences. Current common model systems for semi-flexible biopolymers, such as micro-

tubules [WC93] and earlier DNA nanotube motifs [RENP+ 04, ENAF04], suffer from a circumference heterogeneity. Single-stranded tile-based DNA nanotubes can potentially serve
as a controlled model system for semi-flexible polymer physics, due to their monodispersity
and amenable physical properties, namely circumference, bond strength, and persistence
length.
In the single-stranded-tile construct, each 42-base DNA subunit binds to four of its neighbors with non-covalent base-pair interactions [Fig. 3.1(a)]. Monodisperse n-helix nanotubes
consist of n unique DNA single-stranded subunits that self-assemble according to the comflexible single-stranded DNA subunits during lattice formation yields a tubular structure
with uniform circumference and long contour length on the order of 5 µm [YHS+ 08]. The
DNA base sequence, cross-over points [FS93], and location of nicks have translational symmetries along the longitudinal axis with periodicity of 21 base pairs (∼7 nm). The rupture
is expected to occur when the drag force is sufficient to break a ring of n−DNA binding
domains along the angular axis of the n-helix nanotube.
The persistence lengths of our DNA nanotubes were calculated to be on the order of 10
µm, based on the model described in references [RENP+ 04, BCTH00]. This considerable
rigidity to nanotube bending is likely to arise collectively from the electrostatic repulsion
of charges and the steric interaction of chemical groups along a single DNA helix and
between multiple parallel DNA helices. The single-stranded tile-based DNA nanotubes
have persistence lengths that are three orders of magnitude longer than the persistence
length of their single-stranded DNA subunits (that is, less than 5 nm [TPSW97]). More
importantly, these persistence lengths are longer than their average nanotube lengths, that
is, on the order of 5 µm. Note also that in a different DNA nanotube construct [RENP+ 04],
the mean and variance of nanotube length have been observed to increase over time, due to
end-to-end joining [ENAF04]. In hydrodynamic flow analysis, the substantial persistence
length allows the treatment of the DNA nanotubes as rigid rods and allows us to neglect
polymer vibrations.
The DNA nanotubes were prepared by mixing an equimolar subunit concentration
(≤ 3 µM) of n-programmed single-stranded DNA subunits (IDT DNA) in 1× TAE [40
mM Tris-acetate and 1 mM EDTA(Ethylenediaminetetraacetic acid)] with 12.5 mM Mgacetate.4H2 O and then slowly annealing from 90 ◦ C to room temperature over the course of
a day in a styrofoam box. For fluorescence imaging, a Cy3 fluorophore is covalently linked
into the 5’ end of the single-stranded DNA subunit u1 [see Fig 1(a)], which corresponds to

Chapter 3

plementarity graph shown in Fig. 3.1(a). Remarkably, the collective interaction between

one fluorophore every ∼7 nm along the DNA nanotube.
syringe
pump

w = 30 µm
W = 740 µm

nanotube
collection

Your words here...

Figure 3.2.: (Color) (a) Schematic of the microfluidic chip used in the scission experiment. The nanotube sample was supplied via a syringe pump and collected in a vial
before deposition on a microscope slide. (b) Light microscopy image of the microfluidic chamber used to produce the laminar elongational flow field. (c) Schematic of
the putative streak lines of flow around the orifice. All scale bars are 100 µm.
The Polydimethylsiloxane (PDMS) microfluidic device [DMSW98, UCT+ 00] produces
high elongational flow at the transition volume between a wide channel and a small orifice
(Fig. 3.2). The width of the wide channel W is 740 µm and the orifice has a rectangular
cross-section with a width w of 30 µm. We estimate that the width of the orifice is larger
than the length of 84% of the DNA nanotubes in the test tube. The channel height h is
20 µm throughout the microfluidic chip.
Near the orifice, the flow is a laminar elongational flow [Fig. 3.2(c)]. At the microfluidic
device entrance [labeled “syringe pump” in Fig. 2(a)], a capillary tube feeds the DNA nanotubes into the flow channel. In this region, the nanotubes are subjected to a much weaker
elongational flow than in the area close to the orifice. This weak elongational flow is useful
for pre-conditioning DNA nanotubes into a stretched conformation before entering the zone
with high elongational flow. A control experiment involving a microfluidic chip without an

orifice shows no detectable difference between the length distributions before (in the test
tube) and after being subjected to the control microfluidic device. The large rectangular
and triangular posts [gray-shaded regions in Fig. 3.2(a)], were required to prevent chamber
deformation due to the elastomeric nature of PDMS and the relatively high pressures used
in the scission experiments. Based on the comparison between dimensions of our device
and the initial distribution of the DNA nanotubes, we claim that the presence of the posts
does not perturb the flow pattern in the vicinity of the orifice where the scission occurs.

3.3. Results and Discussions
In a scission experiment, a dilute DNA nanotube solution at ∼1 nm initial tile concentration
was injected into the microfluidic device at rates in the range 0.500–4.00 mL/hr using an
automatic syringe pump. We found that the syringe pump is a better injection method
than pressurized gas because of the absence of initial dead volume that slows down the
initial volumetric flow rate. Each nanotube was passed into the microfluidic chamber
only once. The first 50 µL sample was discarded to avoid any contamination from the
previous run and to make sure that the volumetric rate was constant during the scission
of the collected sample. Without stopping the syringe pump, the next 20 µL sample of
fragmented DNA nanotubes was collected at the outlet port in a 500 µL vial. A 5 µL drop
of this DNA solution was deposited between an RCA cleaned [BHKQ03] microscope slide
and a coverslip and placed on the microscope sample stage. The presence of divalent cations
in the buffer facilitates the formation of salt bridges between the two negatively charged
species, namely the DNA fragments and the glass surface. Once the DNA nanotubes
were immobilized on the glass coverslip, any further reaction, such as end-to-end joining,
spontaneous scission [ENAF04, RENP+ 04], and polymerization, are quenched. Thus, the
images are the record of the fragment distribution immediately after being subjected to
the elongational flow.
The nanotube fragment distribution was imaged with a home-built Total Internal Reflection Fluorescence (TIRF) microscope as previously described in [YHS+ 08] and quantified
at the single-molecule level with ImageJ (available at http://rsbweb.nih.gov/ij/). The

Chapter 3

The upper bound on the range of flow rates investigated is given by the maximum rate
at which the syringe pump can inject fluid into the microfluidic device without resulting
in noticeable deformation and mechanical failure of the device. The minimum flow rate
required to break a substantial fraction of the DNA nanotubes sets the lower limit on the
range of flow rates used in the reported experiments.

0.3

3.00

0 0
0 0

0.3 0.3

1.80

4 4
3.95

8 8

12 12

0 0
0 0

0.3 0.3

2.15

4 4
4.20

4 4
4.00 mL/h

0 0
0 0

3.70

8 8

12 12

0.3

0.2

12 12

1.80

0.2 0.2

2.80

0.3 0.3

0.2 0.2

0 0
0 0
1.50

12 12

0.2

4 4
8 8
1.41 mL/h

10 µm

0.1

4 4

8 8

0.1 0.1

0.500 mL/h

0.3 0.3

12 12

10 µm

0.1 0.1

2.70

4 4

8 8

0.1

0.3

0 0
0 0

2.45

0 0
0 0
1.50

2.70

4.00 mL/h

0.3

0.2

12
1.45

0.3 0.3

0.2 0.2

10 µm

0.2 0.2

4.85

0.2

0.3 0.30.3

0.1

4.75

0.1 0.1

2.10

0.500 mL/h

1.41 mL/h

0.1

0.30.3

0.2

8 8

1212

0.10.1
0 0
0 0

0.30.3

1.80

4 4
3.70

8 8

1212

0.1

0.3

1.75

0.2 0.2

12 12

0.2 0.20.2

4 4
8 8
fragment length [µm]

0.20.2

0 0
0 0

0.1
0 0 0
0 0 0

12 1212

2.20

0.1 0.1

1212

4 4 4
8 8 8
fragment length [µm]
4.20
2.15

0.1 0.10.1

0 0
0 0

4 4
8 8
fragment length [µm]
3.95

4 4
2.80

0.10.1

1.80

1.50

length histogram of 8-helix nanotubes
Figure 3.3.:
! (Color) Light microscopy images and fragment
! after being sub!
jected
to volumetric flow rates at 0.500 0.3
mL/hr,
1.41 mL/hr, and 4.00 mL/hr. The
0.3
0.3 mean fragment length and
0.3
0.3
Bayesian fit results are summarized in Table I. The orange solid line is the best Bayesian fit of the experimental
data. The blue and orange dots with error bars are the average fragment length and most probable inferred Lcrit ,
0.20.2
0.2
respectively.

0.20.2

0.10.1
0 0
0 0

0.30.3

normalized frequency

2.20

1.75

1.65

In Fig. 3.3 (top row), we show snapshots of 8-helix nanotube fragments imaged immediately after a scission experiment at 0.500 mL/hr, 1.41 mL/hr, and 4.00 mL/hr volumetric
flow rates V̇ . The Reynold’s number Re for the fluid flow within the orifice, at the fastest
volumetric flow rates used, was calculated to be 25, which is safely within the laminar
regime (Re < 2000). Elsewhere in the system, the fluid velocities and the corresponding
Re are smaller. The light microscopy images and the corresponding length histograms show
the dependence of fragment size on volumetric flow rate. Faster flow rates generate higher
elongational rates and shorter fragment size (Fig 3.3). The same experiment was repeated
with DNA nanotubes having different circumferences and corresponding bond strengths,
namely the 6- and 10-helix nanotubes, and the same trend was consistently observed in all
nanotubes (see Table I, Figs 3.4, B.2, and B.3).
Elongational flow induces the alignment of DNA nanotubes along the flow gradient.
According to the scission theory presented in Appendix A, the drag force experienced
by the nanotubes induces tension along the axis of the DNA nanotubes. This tension
is greatest at the midpoint of DNA nanotubes [LPSC97], and when it exceeds the tensile
strength of the nanotube, the tube fragments into two shorter tubes of approximately equal
length. In our microfluidic device, the elongational rate is proportional to the reciprocal
of the square of the distance to the orifice 1/ρ2 (Eq. B.13). Hence, after encountering
an elongation flow regime sufficient to break the nanotube in two, the fragments may
encounter a flow regime which is sufficient to break each newly generated fragment again
into two shorter fragments of approximately equal length. This process of scission will
continue until the length of the individual fragment is such that the tensions exerted in the
region of highest elongational flow is insufficient to result in chain scission. In our model,

Chapter 3

number of photons emitted by a DNA nanotube was used as a proxy for nanotube length.
In each frame, the longest nanotube whose length could be easily measured provided a
calibration for this proxy. This technique is insensitive to the curvature of DNA tubes
and how focused each fragment image is. Moreover, the photon-counting method allows
for the determination of nanotube lengths even for fragments that are not optically resolved. The single-molecule assay enables us to exclude experimental artifacts resulting
from the rare occurrence of high mass nanotube aggregates which were visually identified
and not counted. Nanotube aggregation is expected to behave differently in elongational
flow, leading to different fragment size distributions than for pristine DNA nanotubes. All
features whose maximum pixel intensities were above the saturation level of the camera
were excluded from the length measurement.

volumetric flow rate
(mL/hr)
√ −2
2 = 0.500
√ −1
2 ≈ 0.707
√ 0
2 = 1.00
√ 1
2 ≈ 1.41
√ 2
2 = 2.00
√ 3
2 ≈ 2.83
√ 4
2 = 4.00
control
(device without the orifice)
[3.65 , 4.50]
[2.80 , 3.25]
[2.45 , 2.85]
[1.95 , 2.20]
[1.70 , 2.05]
[1.40 , 1.60]
[1.25 , 1.45]

4.40 ± 0.22
4.19 ± 0.43
3.91 ± 0.38
3.13 ± 0.34
3.06 ± 0.28
2.51 ± 0.27
2.29 ± 0.22
5.70 ± 0.45

6-helix nanotube
Lcrit (µm)
Mean (µm)
3.95
3.00
2.70
2.10
1.80
1.50
1.35

[4.05 , 5.25]
[3.60 , 4.15]
[2.65 , 2.95]
[2.30 , 2.60]
[1.90 , 2.25]
[1.65 , 1.95]
[1.40 , 1.60]

5.31 ± 0.48
5.35 ± 0.53
4.10 ± 0.48
3.65 ± 0.37
3.18 ± 0.28
2.90 ± 0.28
2.43 ± 0.26
6.32 ± 0.31

8-helix nanotube
Lcrit (µm)
Mean (µm)
4.75
3.95
2.80
2.45
2.15
1.80
1.50

[4.25 , 5.25]
[3.90 , 4.95]
[3.45 , 3.95]
[2.50 , 2.85]
[2.05 , 2.30]
[1.65 , 1.90]
[1.55 , 1.75]

5.87 ± 0.22
5.47 ± 0.51
5.10 ± 0.46
4.04 ± 0.43
3.58 ± 0.34
2.95 ± 0.30
2.71 ± 0.25
6.03 ± 0.29

10-helix nanotube
Lcrit (µm)
Mean (µm)
4.85
4.20
3.70
2.70
2.20
1.75
1.65

Table 3.1.: The most probable L
√crit and mean fragment length for 6-, 8-, and 10- helix nanotubes after scission at
flow rate chosen to be powers of 2 in mL/hr. For Lcrit , the first number is the most probable value, the second and
third entries are the lower and upper bounds of the 90% confidence interval. The mean is the mean fragment length
of the sample. The uncertainty of the mean length is the standard deviation as determined by a bootstrapping
technique.

2Lcrit is defined as the length of the shortest DNA nanotube that can be broken in two
in the region of the highest elongational flow ˙max . Therefore, Lcrit is the length of the
shortest DNA nanotube that can be produced by each elongational-flow-induced scission
in our device at a particular volumetric flow rate. For a tube i of length Li , the number of
scission rounds is given by mi = bln(Li /Lcriti )/ ln(2)c, where the brackets denote rounding
down to the nearest integer (Appendix B.2). In our model, an initial tube i of length Li
yields 2mi output fragments that have identical length of Li /(2mi ).
extract Lcrit from each fragment histogram data H . The mean fragment length is not a
valid estimate for Lcrit because the mean of the fragment length distribution is affected
by the DNA nanotube distribution before being subjected to the elongational flow. The
Bayesian inference has to include the stochasticity of the scission events in our device. The
elongational flow in the device and the flux of the DNA nanotube are not uniform, but are
functions of position (xi , yi ) of DNA nanotube i within the channel. In particular, they
will be zero at the channel walls and maximum at the center of the channel. Hence, even
if we start with a population of DNA nanotubes that is monodisperse in size, the length
of the DNA nanotube fragments produced will be different at different points within the
orifice.
The results of the Bayesian inference of Lcrit are presented in Figs. 3.3–3.4, Table I,
and Appendix B.3. Table I lists the most probable Lcrit , its 90% probability interval, and
the mean DNA nanotube length for 6-, 8-, and 10-helix nanotubes for various fluid flow
rates. In Fig. 3.3 and also in Fig. B.2 of Appendix B.3, the orange circle represents the most
probable Lcrit and the orange error bar is the range where the a posteriori probability is over
90%. For comparison, the mean fragment lengths and their uncertainties are indicated in
blue. As expected, the difference between fragment mean and Lcrit is less significant when
Lcrit approaches the initial fragment mean [Fig 3.3 (left panel)], because in that regime
the elongational flow breaks only an insignificant portion of the initial nanotubes. The
Bayesian inference performs poorly when Lcrit approaches the mean of control nanotube
distribution, as illustrated by the wider 90% confidence bands in Table I and longer error
bar in Fig. 3.3 (and also in Fig. B.2 of Appendix B.3) for the slowest volumetric flow rate.
The Bayesian inferred Lcrit of the slowest volumetric flow rate experiment might be still
very good, but the data does not warrant strong conclusion.
The most probable inferred Lcrit is plotted against the volumetric flow rate in Fig. 3.4.
For comparison, the no-free-parameter theoretical prediction of Eq. (B.15) using fc = 65

Chapter 3

We employed stochastic scissions simulation and Bayesian inference (Appendix B.2) to

pN is shown as a dashed line in the figures, where fc is the critical tension required to
overstretch a single DNA double helix [SCB96, MKB+ 07]. The theoretical line has a slope
of −0.5 in these double logarithmic plots, indicating that Lcrit scales as the square root of
the flow rate. Linear fitting of the Bayesian inferred Lcrit with respect to volumetric flow
rate yields the slope to be −0.52 ± 0.06, −0.55 ± 0.07, and −0.57 ± 0.07 for 6-, 8-, and 10helix nanotubes, respectively. In all measured nanotubes, the theoretical exponent is within
the 90% confidence interval of our linear fit, giving us confidence in the −0.5 theoretical
scaling of Lcrit with the volumetric flow rate or with the elongational rate. The Lcrit /2R
term in Eq. (B.15) is on the order of 102 and its natural log was treated as constant and
absorbed by the fitted slope in the linear fit for each DNA nanotube circumference.
Having established confidence in the scaling based scission theory, we use Eq. (B.15) in
a separate Bayesian inference to obtain an experimental value of the tension required to
simultaneously break n parallel DNA helices Tcrit = n × fc (Eq. B.11). In this Bayesian
inference, the fit takes into account the probability P r(Lcrit |H ) at various volumetric flow
rates. Separate inference analysis of each nanotube yields 330 pN, 488 pN, and 590 pN as
the most probable bond strength of 6-, 8-, and 10-helix nanotubes. The 90% confidence
bands span across 282 pN to 468 pN, 376 pN to 544 pN, 500 pN to 740 pN, for 6-, 8-,
and 10-helix nanotubes, respectively. In Fig. 3.5, the linear trend of the inferred Tcrit as a
function of the number of DNA double helices in the tube circumference is in agreement
with Eq. B.11.
Finally, to extract an experimental fc , we perform a Bayesian inference on all the data,
imposing the -0.5 scaling relation between Lcrit and flow rate and the linear scaling of
Tcrit with n. The most probable fc was inferred to be 58 pN, with a 90% confidence band
spanning across 47 pN to 76 pN. Our measurement is consistent with the reported 45 65 pN as the applied tension when overstretch transition occurs in various experimental
conditions, namely ionic concentration and temperature [SCB96, MKB+ 07]. All of our
scission experiments were performed at room temperature. The striking agreement further
validates our scission model and its assumption that all the DNA helices contribute to
the total bond strength cooperatively as assumed in our model. The measured critical
tension is consistent with the notion that the elongational-flow-induced tension breaks
the non-covalent interactions, and the DNA nanotube scission occurs via a collective B-S
transition from the B-form of double helices to the S-form of the overstretched state of
DNAs at the breaking point. We note that the bond strength value for breaking a covalent
phosphodiester bond in the DNA backbone was measured and calculated to be of the order

4.4

1.5

2.0

3.0

0.50

1.0
2.0
3.0
volumetric flow rate !mL"h#
4.0

1.5

2.0

3.0

4.0

3.3
5.0

2.2

4.0

1.1

5.0

0.55

Εmax !x 105 "sec#

0.50

0.55

2.2

3.3

1.0
2.0
3.0
volumetric flow rate !mL"h#

1.1

Εmax !x 105 "sec#

8-helix nanotube

4.0

4.4

1.5

2.0

3.0

4.0

5.0

0.50

0.55

2.2

3.3

1.0
2.0
3.0
volumetric flow rate !mL"h#

1.1

Εmax !x 105 "sec#

10-helix nanotube

4.0

4.4

Figure 3.4.: Fragment length as a function of volumetric flow rate of 6-, 8-, and 10-helix nanotubes. The solid
line corresponds to the most probable of Lcrit from all data based on our theoretical model by Bayesian a priori
probability. The dashed line is the theoretical curve with fc = 65 pN [SCB96]. Note that for the same volumetric
flow rate, the most probable Lcrit (solid black circle) increases with larger nanotube circumference.

most probable Lcrit [µm]

6-helix nanotube

Chapter 3

Tcrit @pN D

590
488
330

0 Ê

n @helixD

Figure 3.5.: Inferred Tcrit as a function of nanotube circumference. The solid and
dashed lines correspond to the most probable (fc = 58 pN) and the literature value of
the critical tension required B-S DNA overstretching transition (fc = 65 pN) [SCB96],
respectively. The linear fit was constrained to intersect the point of origin (0,0). The
grey region represents the 90% confidence area for the linear fit that passes through
the point of origin. The steep dotted line illustrates the critical strength of breaking
covalent bonds in DNA backbones (fc = 2n× 5860 pN) [BSLS00, VCS06, LYZ+ 06],
which has a much steeper slope than our experimental data.
of 5 ×103 pN [BSLS00, VCS06, LYZ+ 06], which is approximately two orders of magnitude
larger than the measured fc in this work (see Fig. 5).
That fc should be the force required to overstretch DNA is based on the notion that
passage through the region of high elongational flow is fast compared to the time scale
which would allow the DNA tubes to break apart by slower, less energetic, relaxation
mechanisms, such as those involving thermal fluctuations and base-pair breathing. In
particular, the transit time of the DNA through the region of high elongational flow in
our microfluidic device ranges from 7 µs to 60 µs for the fastest and slowest flow rates
used in this experiment, respectively. These times are comparable to the 10 µs that it
takes for a branch point to move by one base position in three-strand branch migration
[RBHW77, PH94]. We note that the time scale involving rearrangement of a few bases is
already comparable to the transit times of the high flow region.
It is conceivable that each midpoint scission event will produce two fragments that are
not exactly equal in length. Based on our theory in Appendix A (Eq. B.10), the distribution
of tension along the nanotube is approximately parabolic, being maximum at the midpoint
and symmetrically dropping to zero at both ends. Thus, the applied tension reaches a
plateau at the center of the fragment in which the scission could occur anywhere due to
unmodeled physical sources of randomness, while still maintaining its midpoint as the most

probable location for scission.
In order to evaluate the effect of randomness in our experiment, we incorporated tunable
truncated Gaussian noise into the previously presented Bayesian inference to account for
other plausible sources of randomness that are unmodeled in our theory (see Appendix B.4).
The tunable parameters in this new Bayesian fit are Lcrit and the standard deviation of
the truncated Gaussian noise σi relative to the nanotube length Li . Excluding the slowest
volumetric flow rate result, the most probable Lcrit from Bayesian inference by a posteriori
probability from the same model with various Gaussian noise added agrees with the most

3.4. Concluding Remarks
In this paper, we presented the results of systematic experiments on the scission of DNA
nanotubes with well-defined circumferences in a microfluidic device with a well-defined region of laminar elongational flow. This allowed us to rigorously test the scission theory
involving no adjustable parameter, presented in Appendix B. We find that the theory accurately predicts DNA nanotube fragment size as a function of elongational rate and the
number of circumferential helices of the tube. Since fragment size is a predictor of the maximum elongation rate encountered by a DNA nanotube, we suggest that DNA nanotubes
can be used as microscopic probes to measure the maximum elongation rates encountered
in fast, small-scale, or complex hydrodynamic flow fields (chapter ??).

3.5. Acknowledgments
We are indebted to Erik Winfree for his generous support throughout the period of the
research. The authors would like to thank Erik Winfree, Rebecca Schulman, Peng Yin,
Damien Woods, Victor A. Beck, Elisa Franco, Zahid Yaqoob, Karthik Sarma, Saurabh
Vyawahare, Nadine Dabby, Tosan Omabegho, Jongmin Kim, Imran Malik, and Michael
Solomon for valuable discussions. It is our great pleasure to acknowledge the support
of the NASA Astrobiology NNG06GAOG, NSF DMS-0506468, NSF EMT-0622254, NSF
NIRT-0608889, and the Caltech Center of Biological Circuit Design grants. This work
was initiated by a serendipitous observation by Harry M. T. Choi and was inspired by

Chapter 3

probable Lcrit from inference with our simple scission theory within 5%. This insight leads
us to conclude that the noise has to be implausibly large to make a noticeable difference in
our inference and that the assummption of the absence of other plausible physical factors
which could contribute to noise in the theoretical model and Bayesian inference is justified.

Rebecca Schulman’s project on engineering DNA tile-based artificial life [SW05]. The DNA
nanotubes used in this experiment and their three-dimensional illustrations were generous
gifts from Peng Yin. The design and manufacturing process of the PDMS microfluidic chip
were assisted by the Caltech Microfluidic Foundry.

Elongational rates in bursting
bubbles measured using DNA
nanotubes

Abstract
Flow induced scission of DNA nanotubes can be used to measure elongational rates in
aqueous fluid flows [HY10]. Here we report the measurement of elongational rates generated
in bursting films within aqueous bubble foams with this technique. Elongational rates as
large as ˙ = 3.2 × 107 sec−1 are generated by the bursting of bubbles with a 9.26 mm3
volume.

4.1. Introduction
Bursting bubbles and films exhibit a rich variety of phenomena [BdRCS10,NN09,KNT+ 08,
DdGBW98, MlKS07, SCM00, ESF97, LCC96, DMBW95] that often provide keys to understanding processes that occur in environmental, industrial, and laboratory settings.

This manuscript is submitted to a journal as:
Rizal F. Hariadi, Bernard Yurke, and Erik Winfree
Elongational rates in bursting bubbles measured using DNA nanotubes.
submitted
Author contributions:
Bernard Yurke conceived the idea. Bernard Yurke and I carried out the experiment, analyzed
the data, and revised the manuscript. I assayed measured the fragment length distribution
from TIRF microscopy images.

)a(
'&%$#"!

#'$,$+$*)(

'&),$#0%'./#.$'1)0

microcentrifuge
tube

)b(

humidifier

60 mL
syringe

Figure 4.1.: (a) Schematic of apparatus. (b) Sample, housed in a microcentrifuge tube,
to which air is being delivered. For scale, the outer diameter of the upper section of the
microcentrifuge tube is 1.1 cm. (c) Bubbles and 7-helix nanotubes (not in scale) are in
the solution. (d) Schematic of the 7-helix nanotube used in this experiment [YHS+ 08].

Bursting ocean bubbles, through production of sea spray and marine aerosol, significantly
influence climate [RHF+ 10, Wu81]. Bursting bubbles also provide a means by which microorganisms become airborne [BPB77, BS70]. Many industrial and laboratory processes
involve the flow of gas bubbles through liquid columns where bubble bursting can affect the
process. For example, detrimental effects on cell lines by the gas bubbling of bioreactors
have been attributed to hydrodynamically induced death of cells caught within the films
of bursting bubbles [CH92]. Lastly, building on a suggestion by Oparin [Opa52], ocean
bubble bursting may have played a role in abiogenesis by providing fluid flows of requisite
strength to drive the fissioning of organic aggregates.
In previous work [HY10], we determined the relationship between the elongational rate
of the fluid flow encountered by DNA nanotubes and the length of the fragments produced.
This relationship allows the determination of elongational rates by measurement of tube
fragment length. This novel probe of fluid flow is particularly well-suited for the study of
small-scale flows of short duration and for situations where following tracer particles by
high-speed photography is impractical.
Here we report the use of the 7-helix DNA nanotubes [YHS+ 08] to measure elongational flow rates within bursting bubbles in a bubble foam at the surface of an aqueous

buffer solution. DNA strands self-assemble into DNA nanotubes of well-defined diameter
of ∼7 nm and tube lengths that can exceed 20 µm in length. The tubes have a theoretical persistence length of 16 µm and, for the experiments reported here, can be regarded
as rigid rods. The design and characterization of these nanotubes has been discussed by
Yin et al. [YHS+ 08] and, apart from the oligomer T7, we have employed their published
DNA sequences. The modified T7 strand (5’-GGAGGTGCAT-CATTCAAAGCT-TGGCTTAGCGTCCTAATCGCC-3’) was designed to reduce the twist energy in the 7-helix nanotube. Cy3
fluorophores were attached to the tubes for fluorescent imaging, as described in [YHS+ 08].

4.2. Materials and Methods
A stock solution of DNA nanotubes was prepared by mixing 7 DNA strands (ordered from
consisting of 1× TAE [40 mM Tris-acetate and 1 mM EDTA (Ethylenediaminetetraacetic
acid)], pH 8.3 with 12.5 mM Mg-acetate and then slowly annealing from 90o C to room
temperature over the course of a day in a styrofoam box. The nanotube stock solution was
then diluted by a factor of 20 for the experiments.
A schematic of the apparatus used to flow air through the buffer solution containing DNA
nanotubes is shown in Fig. 4.1(a). Air was supplied via a motorized syringe pump equipped
with a 60 mL syringe. The air was delivered via polyethylene tubing, 0.58 mm ID (Inner
Diameter), to a humidifier consisting of a 15 mL centrifuge tube filled to 13.5 mL with
the buffer solution. Two stainless steel capillaries, passing through the cap and cemented
with silicon aquarium, sealant served as feedthroughs for air to and from the the airtight
humidifier chamber. To minimize sample evaporation, the air was bubbled through a 45 mL
9 cm column of buffer and delivered via the polyethylene tubing to the sample chamber.
The bubbles were generated at the end of a stainless steel capillary, 0.635 mm OD (Outer
Diameter) and 0.432 mm ID, connected to the end of the polyethylene tubing that was
pointed downward into the sample fluid, Fig. 4.1 (b). To minimize the amount synthetic
DNA used, the sample, typically consisting of 100 µL of fluid, was housed in a 2.0 mL
microcentrifuge tube (Sorenson BioScience, Inc., West Salt Lake, Utah). The nose of the
tube has a 4 mm ID and a depth of 6 mm. The tapered region flares out to a 1 cm ID.
Two air flow rates, 1.8 mL/min and 18 mL/min, were employed in the experiments. The
ratio of the size of the bubbles produced at the faster flow rate to that of the slower flow
rate was measured to be 1.74 via photographs taken of bubbles produced at the end of the

Chapter 4

Integrated DNA Technologies, Inc.) at equimolar concentration of 3.50 µM in a buffer

in 1× TAE 12.5 mM Mg++

in filtered ocean water

7.32 ± 0.29

7.01 ± 0.41

0.10

0.05

0.10

Normalized Frequency

time
(mins)

2.63 ± 0.13
0.30
0.20
0.10

1.04 ± 0.07

3.02 ± 0.23
0.30
0.20
0.10
1.02 ± 0.10

0.60

0.40

0.20

0 2 4 6 8 10 12 14 16 18 20

10 µm

Fragment length, L [µm]

scale bar = 10 µm

0 2 4 6 8 10 12 14 16 18

Figure 4.2.: (Right) Representative TIRF microscopy images of DNA nanotubes withdrawn from a sample with an initial volume of 100 µL after 0, 60, and 360 mL of air
had passed through the sample at a flow rate of 18 mL/sec. (Left) The corresponding normalized fragment length L histograms constructed from measuring the tube
lengths from such images. The mean tube length L̄ for each distribution is given at
the top of each histogram in µm.

capillary when immersed in buffer in a flask with flat side walls. The height and width of
the bubbles were measured and the volumes were computed under the assumption that the
bubbles are oblate spheroids. By counting the number of bubbles produced from a known
air volume, the volume of the bubbles produced at the slower flow rate (1.8 mL/min) was
determined to be Vb = 5.32 mm3 . From the ratio of the bubble volumes, the bubble volume
at the faster flow rate (18 mL/min) is Vb = 9.26 mm3 .
Following a procedure previously reported for the microscopy assay [YHS+ 08, HY10], a
1 µL volume of fluid was withdrawn and immediately diluted by a factor of 40 in buffer. A
5 µL volume of this diluted sample was then deposited between a cleaned [BHKQ03] microscope slide and coverslip and then imaged with a Total Internal Reflection Fluorescence
(TIRF) microscope [YHS+ 08], and quantified as described in [HY10].

Fragment length, L [µm]

〈Lt 〉[µm]

200
100
7.0

5.0
3.0
1.0
1/4 µm
1/2 µm
1/1 µm
1/8 µm

500

300
200

1 / 16

100

10
Time, t [min]

Chapter 4

[pM/µm]

400

µm

Figure 4.3.: DNA-nanotube fragmentation data plotted as a function of time at a
flow rate of 18 mL/min. (top) Total tube length per microscope field of view. The
horizontal line represents a constant total tube length of 159 µm per image. (middle)
Plot of the population ratio Pg . (bottom) Plot of the number of tubes in the length
range 0 < L < ∆bin for ∆bin = 1, 1/2, 1/4, 1/8, and 1/16 µm.

4.3. Results and Discussions
To follow the fragmentation of the DNA nanotubes by bubbling, an experiment, consisting
of two runs, was performed in which air at a flow rate of 18 mL/min was bubbled through
a 100 µL sample. In the first run, 1 µL volumes were drawn at time points when 0, 16,
and 240 mL of air had passed through the sample Va . In the second run, the data was
acquired at Va = 0, 9, 18, 36, 72, 180, and 360 mL. Representative TIRF microscopy images
taken from the second run samples and the corresponding length histograms are shown in
Fig. 4.2. The data of both runs were treated as a homogenous set.
Under shearing, the sum of tube lengths Lt should remain conserved. This was tested
by measuring the total tube length per image for the samples extracted during the run

at different time points. Fig. 4.3(top) shows that Lt remains constant as a function of
the air volume that has passed through the sample Va . Since Lt = N L̄ where N is the
total number of nanotubes and L̄ is the mean tube length, the constancy of Lt allows one
to infer the population ratio Pg = N/N0 , where N0 is the initial number of nanotubes,
via Pg = L̄0 /L̄ where L̄0 is the initial mean tube length. Pg , inferred by this method, is
plotted as a function of Va in Fig. 4.3(middle). There is a sevenfold increase in the number
of nanotubes by the time an air volume of 360 mL has passed through the sample. The
smooth curve is a fit to the function Pg = 1 + Pi (1 − e−Va /Vg ) with the fitting parameters
given by Pi = 7.13 ± 0.29 and Vg = 182 ± 13 mL.
To determine the smallest tube fragments that were produced, the number of tubes Nbin
in the length range 0 < L < ∆bin for ∆bin = 1, 1/2, 1/4, 1/8, and 1/16 µm was tabulated at
different Va . As was done in [HY10], nanotube lengths were inferred from photon counts
that were calibrated to the longest nanotube in the image; this method allowed us to infer
lengths below the diffraction limit of optical microscopy, so long as the photon counts
were sufficiently above background. In Fig. 4.3(c), we plotted Nbin /Ntotal ∆bin which is the
normalized observed tubes at the smallest bin of size ∆bin where Ntotal is the total number
of tubes at Va . For ∆bin ≥ 1/8 µm this quantity grows while ∆bin = 1/16 µm data remains
relatively fixed, indicating that fragments as short as 1/8 µm are produced.
In previously reported experiments [HY10] we have shown that the suddenly applied
fluid elongational rate ˙ required for mid-point scission of an n-helix single-stranded tile
DNA nanotube of length 2L in half is given by
˙ =

T ln(L/R)
πµL2

(4.1)

where R is the tube radius, µ is the viscosity of the fluid, and the tension T required to
break the tube is given by T = nfc where n is the number of duplex DNA strands along
the circumference of the tube and fc = 65 pN is the critical force to overstretch a DNA
helix. Here n = 7 and R ≈ 4 nm. The observation of 1/8 µm tube fragments implies that
tubes as short as 0.25 µm are broken in two via the hydrodynamic flows generated within
the bubbles of the experiment of Fig. 4.2. Taking µ = 1.0 × 10−3 Pa·sec, Eq. (4.1) indicates
that elongation flow rates as large as ˙ = 3.2 × 107 sec−1 are generated during bubble
rupture.
An estimate for the Vf (L) parameter can be obtained from a model of film hole dynamics.

The fragmentation volume Vf (L) is defined as the fluid volume in which all tubes of length
L or greater are broken on the passage of one air bubble through the sample. For a
film of uniform thickness, considered by Strutt and Rayleigh [Str99, Str02] and later by
Culick [Cul60] and Taylor [Tay59] in which the rupture is modeled as a circular hole that
propagates outward with the film fluid accumulating in a toroid at the hole perimeter.
From momentum balance, the hole propagates outward with a speed given by v =

2σ/ρδ

where σ is the surface tension of the film, ρ is the fluid density, and δ is the film thickness.
The elongation rate of the circumference is given by ˙ = v/r where r is the hole radius.
The volume of fluid swept up by the hole before the elongation rate falls below a particular
value ˙ is then given by Vf = πδr2 = 2πσ/(ρ˙2 ). Using Eq. (4.1), one obtains Vf =
1.37 × 10−3 m−1 × L4 / ln2 (L/R) where we have used ρ = 1 g/cm3 and σ = 73 dyn/cm for

require taking into account the geometry of a bubble contacting a water surface [BSB93],
which differs from that of a planar film of uniform thickness.
We repeated the experiment at an order of magnitude slower flow rate at 1.8 mL/min
to assess the extent to which fluid flow associated with bubble inflation was responsible for
the tube fragmentation. The mean tube length when 60 mL of air had passed through the
sample was 2.32±0.13 µm (Fig. ??) which is close to the 2.63±0.13 µm value observed at
flow rate of 18 mL/min (Fig. 4.2) for the same volume of air. However, because the slower
flow rate results in smaller bubbles (5.32 mm3 vs 9.26 mm3 ), we expect that the experiment
at the slower flow rate would produce more bubbles; 60 mL of air at the slower flow rate
is expected to produce a comparable number of bubbles as 104 mL of air at the faster
flow rate. According to the theoretical analysis of the preceding paragraph, fragmentation
volumes should depend predominantly on the number of bubbles, since larger bubbles will
additionally contribute only weaker flows that are incapable of breaking shorter nanotubes.
Using the phenomenological fitting equation for Pg and L̄ = L̄0 /Pg , we estimate that at the
faster flow rate, 104 mL of air would result in nanotubes with mean length L̄ = 1.78 µm.
Thus, the fragmentation per bubble at the slower flow rate is slightly less than that for the
faster flow rate, but still consistent with the notion that bubble bursting is the predominant
driver of fragmentation.

Chapter 4

the density and surface tension of water. Within this model, energy conservation requires
that half of the surface tension potential energy released must be dissipated within the
toroid, which implies that the micro-scale fluid flows within the toroid must be taken into
account in order to accurately determine Vf . In addition, an accurate calculation would

Normalized Frequency

0.35

2.32±0.13

0.20
0.10

0 i8 4

Fragment length, L [µm]

Figure 4.4.: The normalized nanotube length L histogram of the fragment lengths
after bubble bursting experiment at 1.8 mL/min for 33.3 minutes, i.e. 60 mL of air.

That fluid flows associated with bubble bursting are primarily responsible for tube breakage was demonstrated by the suppression of tube fragmentation through the addition of
100 µL of heptane to the sample vial to form a fluid layer on top of the solution. Air
bubbles rising through this layer would leave the hydrophilic DNA in the aqueous phase.
The aqueous fluid flows associated with this process are also reduced because of viscous
coupling of the buffer with the heptane at the interface [RQ06, MBBW94]. The mean tube

Normalized Frequency

length when 60 mL of air was bubbled through the sample was 6.03 ± 0.50 µm which is
comparable to the initial mean tube length 7.32 ± 0.29 µm and large compared to the mean
tube length 2.63 ± 0.13 measured at Va = 60 mL for the experiment of Fig. 4.2.
6.03±0.50
0.15
0.10
0.05

0 i8 4

Fragment length, L [µm]

Figure 4.5.: The fragment length histogram after subjecting DNA nanotubes to air
bubbles at 18 mL/min for 3.3 minutes in DNA buffer covered with a layer of heptane.

Finally, we demonstrated that fluid flows associated with bubble bursting are primarily
responsible for tube breakage by reducing the suppression of tube fragmentation through
the addition of 2 mM of the surfactant Sodium Dodecyl Sulfate (SDS) to the buffer. The
surfactant reduces the surface tension, increases surface viscosity effects [BS95], and in-

creases the bubble lifetime. These effects reduce nanotube breakage by reducing surfacetension driven flow velocities and by reducing the film fluid volume through film drainage.
The foam produced during this experiment necessitated using a 300 µL sample volume.
Even then it was necessary to periodically stop the air flow to allow the foam to subside.
Because of the 3× greater volume, the mean tube length L̄ = 6.23±0.5 µm at Va = 180 mL
for this experiment should be compared with the L̄ = 2.63 ± 0.13 µm at Va = 60 mL for the
experiment of Fig. 4.2. One sees that reducing the surface tension suppresses the breakage
of the nanotubes. In accord with the experience of other laboratories [DCS07,GCL+ 10], we
verified that DNA nanotubes are stable in SDS buffer by constructing a length histogram
of a sample that was incubated in SDS buffer for 30 min without air flow. The final mean
tube length 7.45 ± 0.54 µm was found to be essentially the same as the initial mean tube
length 7.65 ± 0.58 µm, indicating the stability of DNA nanotubes in SDS containing buffer.

Chapter 4

7.65±0.58
0.10
t = 0 min
(control)

0.05

Normalized Frequency

7.45±0.54
0.10

t = 0 mins
+ 30 mins in SDS buffer
(control)

0.05
6.23±0.45

0.15
0.10

t = 3.3 mins

0.05

0 i

12
16
Fragment length, L [µm]

Figure 4.6.: The normalized nanotube length L histogram of the fragment lengths
after bubble bursting experiment in SDS buffer at 18 mL/min for 0 and 3.3 minutes.

4.4. Conclusion
Our experiments show that DNA nanotube fragmentation can serve as a probe of elongational flows generated at small scales, and in complex fluid flows where imaging tracer
particles would be impractical.

4.5. Acknowledgments
The authors gratefully acknowledge Erik Winfree, Damien Woods, Rebecca Schulman,
John O. Dabiri, and Sandra Troian for helpful discussions. This work was supported
by NSF through the grants EMT-0622254, NIRT-0608889, CCF-0832824 (The Molecular
Programming Project), and CCF-0855212.

Could ocean hydrodynamic flows
have driven self-replication of the
protobiont?

An Inevitable Miracle (Ann Erpino)
www.annerpino.com

Abstract
That mechanical forces produced by ocean fluid flow could have been instrumental in
the origin of life by driving a primitive form of self-replication through fragmentation was
first suggested by [Opa52]. However, little work has been done to characterize the strength
of the ocean fluid flow. Using DNA nanotubes as a novel fluid flow sensor, we investigated
the effectiveness with which bursting bubbles can induce tension within particle aggregates
on the ocean water surface. This measurement is essential in assessing the effectiveness
with which ocean fluid motion could have driven self-replication of organic aggregates.

5.1. Introduction
Reproduction is a key feature of biological organisms that is carried out by elaborate
molecular machinery [YO10, Alb03] that consumes chemical energy, even for single-celled
organisms undergoing vegetative reproduction through cell division.The earliest ancestors
of biological organisms would have had simpler reproductive machinery that would nevertheless have required energy consumption, whether the self-replication process involved
the fissioning of a loose aggregate of molecules or the separation of the template from the
product for a template replicating molecule. Although prions are infectious agents operating in the complex biochemical environment of highly-evolved biological organisms, they
are suggestive of what the first replicators may have been like. Two key components of
prion replication [SCK+ 00, CDVW04] are (1) the linear growth of protein fibrils through
catalytic misfolding followed by the addition of protein molecules to the fibril ends and (2)
the fragmentation of these fibrils. This linear growth of both fibril ends and fragmentation
gives rise to exponential growth. Although, in vivo, enzymes [SL06] are instrumental in
the fragmentation of prion fibrils; in vitro, prions can be propagated through fluid flow
induced mechanical shearing [SCK+ 00, CDVW04]. Growth of an organic complex through
the aggregation of molecules followed by fragmentation, where the energy needed for frag-

The version presented in this chapter is not a final manuscript. This work is in preparation for submission
as:
Rizal F. Hariadi and Bernard Yurke
Could ocean hydrodynamic flows have driven self-replication of the protobiont?
in preparation
Author contributions
BY conceived and designed the experiments. RFH and BY built the microscope. RFH and BY
performed the experiments, analyzed the data, and revised the manuscript. RFH measured
the DNA nanotube fragment length.

mentation is supplied by mechanical rather than chemical means, provides an appealing
model for the first replicators may have been like. To this end,the prions can exhibit a
non-nucleic acid based form of inheritance in which the same protein can give birth to several distinct prion strains due to its capacity to mis-fold and arranged in several distinct
fibril forming configurations [CC07, AKN+ 10]. Natural selection pressure can act on these
distinct strains to favor one strain over the others.
The notion that self-replication through fragmentation via mechanical forces could have
played in an important role in the origin of life by providing a primitive mechanism for selfreplication was proposed by A. I. Oparin in his theory of abiogenesis [Opa52]. An important
step in his theory was the formation of coacervates (organic aggregates in aqueous solution)
in the primordial ocean. Fragmentation by fluid agitation was envisioned as a primitive
form of replication allowing natural selection to act on the coacervates. Among the origin
of life theories, mechanical fragmentation has also featured as a replication mechanism
for inorganic crystals in proposals by Cairns-Smith [CS66, CS08] and as a mechanism for
vesicle fissioning in proposals by Szostak [SBL01, ZS09, BS10]. Inspired by Cairns-Smith’s
proposal, Schulman and Winfree [SW05, Sch07] has devised a DNA-based tile system that

of these ribbons to evolve ever more complex tile patterns [SW11].
Although sources of mechanical energy to drive replication have been featured in an
number of proposals on abiogenesis, there seems to have been little work done to characterize the strength, availability, and suitability of the these sources. The shearing of small
particles by fluid flow requires large gradients in flow velocity in the vicinity of the particle. Although mechanical energy in the form of gravity driven or wind driven fluid flow is
ubiquitous much of this flow does not result in the large velocity gradients needed for small
particle fragmentation. It is also important to consider the nature of the environment in
which these forces act. In particular, the environment should allow for long residence time
and for the processing of the replicator through multiple rounds of replication. Erosional
environments such as sea shores and rivers are unattractive, in this regard, in that primitive replicators incapable of their own motility would have a tendency to be swept away. It
should be noted, however, that small replicators resistant to desiccation could, in principle,

Chapter 5

grows long ribbons in which tiles are added to the ends in a zig-zag growth pattern. The
composition of tile types in a given row of the growth front is a copy of the the composition
of tile types in the previous row. This endows the system with the capability of propagating
inheritance information to daughters produced by ribbon fragmentation in a manner similar
to that of in vitro prion replication. It has been shown that in principle, this system is
capable of open ended evolution in which suitable selection forces could drive a population

be wind dispersed against the prevailing direction of water flow and may provide a means
of survival of nonmotile replicators in an erosional environment. Similarly, depositional
environments such as the ocean or lake floors are unattractive in that replicators incapable
of their own motility would become buried.
The ocean surface has a number of features that make it worth considering as the place
of origin of the first replicator. This surface could provide an accumulation site for organic
molecules more buoyant the water, especially amphiphilic and hydrophobic molecules that
would tend to form buoyant aggregates. The concentration of organics at the ocean surface
would depend on the rate of their production in the prebiotic environment and on the rate
of their destruction, for example, by UV light, and on their rate of removal by sedimentation
through binding to silt or mineral precipitates to form aggregates less buoyant than water.
This last process would be most active in near shore environments where fresh sediment is
being suppled by river transport or beach erosion. The presence of stable prebiotic ocean
environments in which organic aggregates could concentrate and in which self-replicators
could have had long residence time is suggested by the existence of stable Gyres in modern
oceans in which plastic debris accumulates [LMFM+ 10]. Of particular significance for
mechanically driven self-replication, the ocean surface serves as an abundant source of
mechanical energy resulting from wind driven wave action. Wave motion can generate
regions of fluid flow with high velocity gradients. For the case of spilling breakers where
the crest spills over to form a toe on the slopes of the wave, high velocity gradients can
be expected to occur at the edge of the toe [LR95]. For the case of plunging breakers
in which the wave crest topples over to form a sheet of plunging water, high velocity
gradients can be expected to be found where the sheet of water plunges into the ocean
surface below [SS76, KNYO90, Bow92, BJ93, BC98, Ogu98, SB99, HAD02, BBS02, CAH04].
This process results in the copious generation of bubbles which rise within the wave to
form whitecaps. The bubbles themselves can be expected to produce flow fields with
high velocity gradients when they burst upon rising to the ocean surface. These velocity
gradients would reside within the bubble films and would come about as a result of the high
velocities that can be produced by surface tension at the edge of the hole of a bursting
bubble due to the bubble film’s low mass and water’s low viscosity. Elongational flows
within the bursting bubble will exert tensile stresses within a particle suspended in the
film. Fragmentation results if these stresses exceed the tensile strength of the particle.
Here we report on experiments using DNA nanotubes to measure the elongational rates
produced in bursting bubble films in a natural sea water sample obtained from a beach
near Ventura California.

5.2. Results
In this chapter, 7-helix DNA nanotubes were employed as scientific tools for measuring
the elongational flow rates in bursing bubbles of Pacific ocean buffer. The experimental
methods employed in these experiments are the same as those of reference [HY] and Chapter 4 except that sea water is used instead of TAE-based DNA buffer. Hence, only a brief
summary of the experimental procedure is given here.
A stock solution of DNA nanotubes was prepared as before [HY] by mixing 7 DNA
in 1x TAE/Mg++ buffer consisting. Then, the nanotube stock solution was diluted by a
factor of 20 in filtered sea water for the experiments. The sea water was collected from a
rock breakwater in San Buenaventura State Beach in Ventura, California. For use in the
experiments a 1 mL sample of sea water was filtered through a MILLEX GP Filter Unit,
0.22 µm (MILLIPORE) using a syringe. A detailed description of the bubble bursting
apparatus is given in [HY] and Chapter 4..
For the experiment, two samples were prepared. (1) A control sample was left undisturbed and served as a check on the stability of the DNA nanotubes in salt water [Fig.
5.1(a-b)]. (2) Air was bubbled through the second and samples were withdrawn when 0,
ning of the run, the mean fragment length of the control sample was determined to be
7.01 ± 0.41 µL. After one hour of incubation, the mean fragment length in the undisturbed
sample was measured to be 6.88 ± 0.41 µL, which is not significantly different from the
initial value. Therefore, DNA nanotubes are stable in sea water. In contrast, after only
20 min when 360 mL of air had been bubbled through the second sample, the mean fragment length was measured to be 1.02 ± 0.10 µL. This indicated that a substantial amount
of tube fragmentation had occurred.
To show that fragmentation in sea water is similar to fragmentation in 1x TAE/Mg++
buffer, we compare the population ratio Pg as a function of time for both experiments.
As before (Chapter 4), Pg is defined as Pg = N/N0 where N0 is the initial number of
nanotubes, and N is the number of nanotubes at time t. Pg can be calculated, as before
(Chapter 4), from the average lengths of nanotubes, and the data can be plotted and fit
with the phenomological fitting function Pg = 1 + Pi (1 − e−Va /Vg ), where Pi = 7.1 ± 1.3 and
Vg = 203±73 mL. For comparison, the corresponding results in 1× TAE/Mg++ buffer [HY]
is plotted as open circles and a dashed curve (Fig. 5.2). Bubble-bursting-induced DNA
fragmentation of the DNA nanotubes is very similar for sea water and 1× TAE/Mg++

Chapter 5

60, 120, and 360 mL of air had passed through the sample [Fig. 5.1(c-e)]. In the begin-

7.01±0.41
0.10

t = 0 min
(control)

0.05
6.88±0.42
0.10

t = 0 min
+ 60 mins in sea water
(control)

0.05

Normalized Frequency

0.30

3.02±0.23

0.20

t = 3.3 mins

0.10
1.53±0.14
0.40

t = 6.7 mins

0.20
1.02±0.10
0.60

0.40

t = 20 mins

0.20

i 4

Fragment length, L [µm]

Figure 5.1.: Fragment length histogram of DNA nanotubes in sea water at indicated
time points during bubbling. The mean±standard error of each distribution is presented on the horizontal axis of the plot. (a,b) One hour incubation in sea water does
not significantly change the length distribution. (c-d) Systematic exposure to bubbles
decreases the nanotube length.

7.0

5.0
3.0
in 1× TAE 12.5 Mg++
in Pacific ocean water

1.0

10
Time, t [min]

Figure 5.2.: DNA nanotube population ratio Pg plotted as a function of the air volume
Va passed through the sample. The red circles are the sea water data. The red curve
is a fit to the sea water data. For comparison, previous results in 1× TAE/Mg++
buffer instead of sea water are indicated by the blue circles and the blue line.
buffer.
To obtain information on how the tube length distribution evolves with time tube length
histograms were created with 1 µm bin size. The histograms are shown in Fig. 5.3 and
compared with results we had previously obtained [HY] for 1× TAE/Mg++ buffer. The

5.3. Concluding remarks and outlook
5.3.1. What have we learned?
Our experiments show that bursting bubbles in ocean water can produce sufficient elongational flow to break DNA nanotubes, which is a model system for organic aggregates. We
also discovered that DNA nanotubes are as stable in filtered Pacific ocean water as in the
standard DNA buffer in 1× TAE/Mg++ buffer.

5.3.2. Trip to Malibu beach
As I write this chapter, Bernard Yurke and I are preparing the second half of the manuscript.
Bernard Yurke, Erik Winfree, Damien Woods and I had been curious for sometime about
the abundance of significant elongational flow in the open ocean. The calculation relies
on the measured characteristic fragmentation volume Vf of air bubbles on the ocean water surface. The analysis also requires measurement of size distribution and the number

Chapter 5

two sets of histograms indicates that bubble-bursting driven DNA nanotube fragmentation
proceeds in a similar manner in the two fluids.

in filtered ocean water

in 1× TAE 12.5 mM Mg++
7.32 ± 0.29

7.01 ± 0.41

0.10

0.05

Normalized Frequency

time
(mins)

0.10

2.63 ± 0.13
0.30

0.30

3.02 ± 0.23

0.20

0.10

1.04 ± 0.07

1.02 ± 0.10

0.60

0.40

0.20

0 2 4 6 8 10 12 14 16 18 20
Fragment length, L [µm]

Figure 5.3.: Normalized DNA nanotube fragment length distributions in
1× TAE/Mg++ (left column) and sea water (right column) after 0 mL, 60
mL, and 360 mL of air had bubbled through the sample. The mean fragment
length of each histogram is indicated as solid circle on top the horizontal axis of the
histogram. Note that the range of the normalized frequency (y-axis) increases as the
bubbling experiments progress.

of bubbles produced by breaking waves to estimate for the frequency with which hydrodynamic flows of a given elongation rate are encountered in the ocean. Initially, in his
backyard in Boise, Bernard Yurke did a clever experiment to measure the bubble size distribution and the rate of air entrainment in plunging water jets. However, to arrive to a
valid conclusion, we realize that this essential measurement had to be done correctly. To
provide the proper data for the analysis, Bernard Yurke, Damien Woods, and I went to
Malibu beach to measure the bubble size distribution and bubble production rate within
the surf zone of the beach. The results of these experiments are being used to assess the
effectiveness with which ocean fluid motion could have driven self-replication of organic
aggregates. Our preliminary analysis indicates that that in order to undergo replication
cycles on a sub-annual time the organic aggregate must have a propensity for sticking to
the ocean surface or must be sufficiently buoyant to remain in the active layer of the ocean.1
Organic aggregates on the order of 10 µm in size could achieve the requisite buoyancy.

5.4. Acknowledgments
The authors gratefully acknowledge Erik Winfree, Damien Woods, Rebecca Schulman,
John O. Dabiri and Sandra Troian for helpful discussions. This work was supported by
gramming Project), and CCF-0855212.

The result and analysis of the experiment is still in preliminary stage and is not included in this thesis.

Chapter 5

NSF through the grants EMT-0622254, NIRT-0608889, CCF-0832824 (The Molecular Pro-

Single molecule analysis of DNA
nanotube polymerization

Joining / Scission (Ann Erpino)
www.annerpino.com

Abstract
DNA nanotubes are amenable materials for molecular self-assembly and can serve as
model systems for one-dimensional biomolecular assemblies. While a variety of DNA nanotubes have been synthesized and employed as models for natural biopolymer, an extensive
investigation of DNA nanotube kinetics and thermodynamic has been lacking. Using total internal reflection microscopy, DNA nanotube polymerization was monitored in real
time at the single molecule level over a wide range of free monomer concentrations and
temperatures. The measured polymerization rates were subjected to a global nonlinear fit
based on the polymerization theory in order to simultaneously extract kinetic and thermodynamic parameters. For the DNA nanotubes used in this study, the association rate
constant is (5.99 ± 0.15)×105 /M/sec, the enthalpy is 87.8 ± 2.0 kcal/mol, and the entropy is 0.251 ± 0.006 kcal/mol/K. The qualitative and quantitative similarities between
the kinetics of DNA nanotubes and microtubules polymerization highlight the prospect
of building building complex dynamic systems from DNA molecules inspired by biological
architecture.

6.1. Introduction
The design and construction of collective dynamics out of rigorously-characterized molecular components that rival complex cellular systems is a technical challenge at the interface
of biology, chemistry, physics, and computer science. The proof of principle demonstrations
of self-organization of matter with chemistry is ubiquitous in molecular biology [CW10].
As an example, the cytoskeleton is a system of intracellular biopolymers that evaluates
its environments to assemble and disassemble at the right time and the right place within
cells. Interactions between the cytoskeleton, molecular motors, and signaling proteins give
rise to self-organized intracellular structure [LG08] and motility [ML08], direct the growth
of tissues [LC04], and guide the movement of organisms [SW03, SS02].

The version presented in this chapter is not a final manuscript. This work is in preparation for submission
as:
Rizal F. Hariadi, Bernard Yurke, and Erik Winfree,
Single molecule analysis of DNA nanotube polymerization,
in preparation
Author contributions
RFH, BY, and EW conceived and designed the experiments. RFH and BY built the microscope. RFH performed the experiments and run stochastic simulations. RFH, BY, and EW
analyzed the data. RFH and EW prepared the manuscript.

DNA nanotubes have been proposed as a promising candidate material for constructing
an artificial cytoskeleton [RENP+ 04, ENAF04]. A successful demonstration of an artificial
cytoskeleton will recapitulate structural, dynamic, force generation, and assembly control
aspects of the biological cytoskeleton. Toward that goal, we must understand the design
principles of dynamic tubular architectures and develop an accurate physical model of how
monomers can assemble and disassemble tubular structures as they respond to information
in the environment.
In structural DNA nanotechnology, synthetic oligonucleotides can be engineered to form
a small DNA complex, called a DNA tile, that can polymerize to form larger structures
using the specificity of Watson-Crick hybridization [See82, WLWS98, Rot06, RENP+ 04,
YHS+ 08, SW07, LZWS10, ZBC+ 09]. DNA nanotubes provide a simple example of how a
long one-dimensional crystalline structure can arise from the interaction between DNA
tiles. Fig. 6.1 shows a DNA tile that possesses 4 short single-stranded regions, known as
sticky ends, that serve as binding domains. The sticky end arrangement, in addition to
the constraint provided by the biophysical properties of the DNA double helix, directs the
interaction of DNA tiles to form tubular DNA structures with a range of circumferences
whose distribution is determined by the thermodynamics and the kinetics of the DNA
nanotube assembly process.

axis of a DNA nanotube gives rise to a long persistence length, ξptube ∼ 20 µm [RENP+ 04,
ORKF06], which is comparable to the measured persistence length of actin filaments, ξpactin
= 17.7 µm [GMNH93]. Second, formation of cooperative polymers at reaction conditions
where spontaneous nucleation is rare, gives rise to long polymers. The mean length of the
DNA nanotubes used in this study is on the order of 5 µm for standard assembly conditions.
Each DNA tile added to the tip of a growing nanotube interacts with two neighbors, whereas
most of the collisions between DNA tiles in solution result in contact with only one neighbor.
As a result, there is a high kinetic barrier associated with nucleation whereas elongation
proceeds without significant barrier. Therefore, a relatively small number of nuclei grow
to form long nanotubes.
Engineering a dynamic DNA nanotube analog of the cytoskeleton requires an accurate

Chapter 6

The first challenge toward de novo engineering of an artificial cytoskeleton is constructing
a long and rigid polymer out of artificial non-covalently-bound subunits. DNA nanotubes
satisfy the length and rigidity criteria. Structurally, the DNA nanotubes used in this work
are cooperative polymers that are multiple monomers wide. The cooperativity has two
important consequences. First, the tubular organization of DNA tiles along the longitudinal

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Figure 6.1.: Identical DNA tiles (top) self-assemble into DNA nanotubes (bottom).
The four DNA strands form two DNA helices that are joined by two cross-over points,
depicted as orange connectors in the cartoon (bottom). The tiles are rigid because of
the crossover points. Each tile has four single stranded DNA sticky ends (A, A0 , B,
and B0 ). The four sticky ends are designed such that A is complementary to A0 (red
sticky end pairs) and B is complementary to B0 (black sticky end pairs). In the dimer
picture, the left monomer appears thinner due to 36 ◦ rotation along the horizontal
axis to match the minor and major groove between the ends of two monomers at the
sticky end region. For fluorescence imaging, we labeled one of the DNA strands with
Cy3 or Cy5 fluorophore (green circles).

polymerization model for DNA nanotubes. In the literature, there are two classes of models
that are relevant to the polymerization of DNA nanotubes, namely the kinetic Tile Assembly Model (kTAM) developed for DNA tile assembly and the polymerization theory developed for biopolymers. In the DNA self-assembly literature, the kTAM considers growth by
tile self-assembly to be a second order chemical reaction between crystals and monomers,
which will be described in more detail in section 6.4.1. The kTAM has been used to guide
the design and provide a deeper understanding of algorithmic self-assemblies of DNA tile
sets with various levels of complexity [FM09,RPW04,SW07,FHP+ 08,BSRW09,CSGW07].
In the biophysics literature, there is a different class of polymerization models for active
one-dimensional polymers that couple their polymerization with fuel consumption reactions
in the form of nucleotide hydrolysis [FHL94,FHL96]. Since DNA nanotubes are essentially
passive one-dimensional polymers that comprise a single monomer type, these two classes
of models are identical when applied to existing DNA nanotubes if one ignores the active
aspects of the biophysics model.
Despite the success of the kTAM for guiding the design of complex DNA self-assembly
systems, the theoretical framework and its assumptions have not been tested experimentally in detail. The rigorous testing of DNA nanotube polymerization theory requires assays
that can determine not only the concentration of free DNA tile monomers, but also the
number of nanotubes at any given time, and the direction of growth, without experimentally confounding effects, such as excessive spontaneous nucleation or the presence of tube
bundles. Early studies of DNA ribbons [SW07] used bulk UV absorbance data, in combination with static atomic force microscopy (AFM) assays, to measure the concentration

face [EHW12]. Despite their rigorous analysis, the interaction between DNA tiles and mica
surfaces complicated their measurements and limited their ability to determine quantitative
measurements of the rate constants and free monomer concentrations.
In this work, we adopted the standard assay in biopolymer research, namely time lapse
light microscopy [TW78, TW80, HH86]. The power of single-molecule cinematography has
enabled the continuous observation of non-equilibrium polymers. To minimize background

Chapter 6

of DNA tiles free in solution, and thereby to infer the kinetics of incorporation into ribbon
assemblies. Interpreting bulk data is complicated, because polymer growth kinetics depend
not only on free monomer concentration, but also on the size distribution of supramolecular
assemblies and on the number of such assemblies. This information cannot be accurately
measured in bulk UV absorbance assays and must be inferred indirectly, thus, introducing large uncertainties into the analysis. Recently, Evans et al. used a single-molecule
AFM movie to validate some of the kTAM assumptions for polymerization on mica sur-

fluorescence from the sea of unlabeled monomers in solution, fluorescent polymers must
be excited either with an evanescent wave by total internal reflection fluorescence (TIRF)
microscopy [AP01, KP05, FTT+ 02] or by confocal illumination [IGC02].
Here, we report the application of TIRF microscopy to the study of the polymerization
of self-assembled DNA structures. From a set of polymerization movies at a wide range of
tile concentrations and reaction temperatures, we were able to measure both the kinetic
and thermodynamic parameters of DNA nanotube assembly. The experimental results are
consistent with the kinetic Tile Assembly Model for DNA nanotubes and are in agreement
with previous kinetic and thermodynamic measurements of DNA hybridization systems.

6.2. Materials and Methods
6.2.1. Total Internal Reflection Fluorescence microscope
Optics
The polymerization movies were acquired with a home-made prism-based total internal
reflection fluorescence (TIRF) upright microscope (Fig. 6.2). A solid-state green laser
(GCL-025, 25 mW, CrystaLaser) equipped with an adjustable power supply (CL2005, CrystaLaser) provides the 532 nm excitation light. The beam was filtered with a Z532/10×
laser filter (Chroma). The filtered excitation beam passed through a quarter-wave plate
(Thorlabs) to produce a circularly polarized beam, which effectively has uniform polarization to counter the orientation-dependent fluorescence of Cy3. Two mirrors (Thorlabs,
not pictured in the drawing) were used to guide the illumination beam to the field of view
below the objective. Another mirror (Thorlabs) and a 15 cm focusing lens (CVI Melles
Griot) steered the excitation beam onto a Suprasil 1 right-angle prism (CVI Melles Griot)
at approximately 0◦ from the horizon to produce a weakly focused illumination spot. We
calculated that the incident angle between the incoming laser and the normal vector of the
microscope slide is sufficiently larger than the critical angle for evanescent wave to occur
at the interface between glass and liquid, where the sample and focal plane of the objective
are located.
In our experiment, DNA tiles and DNA nanotubes resided inside a glass capillary tube
that was optically coupled with the prism by a thin layer of immersion oil. The emitted
photons were captured by a 60× 1.2 NA water immersion objective (Nikon) and focused to
the electron multiplier CCD camera (C9100-02, Hamamatsu) by a 20 cm tube lens (double
achromat, CVI Melles Griot). The combination of bright samples, low background, and

efficient light collection produces images with high signal to noise ratio. We kept the laser
power at below 10 mW to minimize photobleaching during imaging.
CCD

LT
EF
CT

OBJ

OBJ
Out[30]=

QWP
LF

Figure 6.2.: (Left) The schematic drawing of the prism based TIRF microscope.
L = 532 nm 25 mW laser; LF = laser filter; QWP = quarter wave plate; S = mechanical shutter; FL = 15 cm focusing lens; M = mirror; P = temperature controlled
right angle prism; OBJ = temperature controlled 1.2 NA water immersion objective;
EF = emission filter; LT = 20 cm tube lens; CCD = electron multiplier Charged
Coupled Device; TC = temperature control. (Right) Capillary flow chamber (CT)
for the polymerization assay. In our upright microscope setup, the flow chamber is
sandwiched between the prism and the objective. We use immersion oil to optically
couple and mount the bottom surface of the 1 mm thick microscope slide with the
glass prism. A thin layer of epoxy was used to optically couple the glass capillary
chamber to a microscope slide.

Chapter 6

Autofocus
The autofocus and temperature control features of our microscope were central in automating the data acquisition. A rotary motor (Z-drive, ASI) was mechanically coupled
to the translation stage of the objective turret to control the vertical position of the objective via computer. We used an autofocus module in the µManager software (available
at http://micro-manager.org/) to find and maintain the best-focus-position of the objective based on the image sharpness. A focused image has a higher sharpness than an
out-of-focus image. The DNA nanotube images were sufficient for finding the best-focus
position without the need for fiduciary beads. The autofocus method was robust for long
time-lapse imaging. The µManager plugin used the image sharpness function as feedback

to the autofocus routine. We set the µManager to run the autofocus step either every 30
or 60 seconds to minimize photobleaching.
Temperature control
In our setup, we used two separate electronic circuits to control the temperature of the prism
and the objective. Each setup was composed of a heating tape (Omega), a thermocouple
(CHAL-005, Omega), and a temperature controller (Omega). We relied on the heat transfer
from the heated objective and prism to achieve the desired temperature in the sample.
This method produced highly reproducible sample temperatures. Consequently, in most
experiments, we only measured the temperature of the prism and the objective. Two
calibrated thermocouples (CHAL-005, Omega) were placed close to the field of view to
calibrate the sample temperature as a function of both the prism and the objective. In
this paper, we report the sample temperature based on our calibration table.
Flow chamber
A pre-cleaned glass capillary tube (Vitrotubes 5010, VitroCom) with inner dimensions of
100 µm × 1 mm × 5 cm was mounted on a 75 mm × 50 µm × 1 µm RCA-cleaned [BHKQ03]
plain microscope slide (Corning, 2947-75X25) by applying a thin layer of 5-minute epoxy
(Devcon) in between the two glass surfaces. The epoxy was left to cure at least overnight
prior to imaging. The mounted capillary chambers were stored in ambient environmental
conditions inside a microscope slide storage box and were used within a week. We believe
that the small openings of the capillary chamber hinder contamination and consequently,
it was safe to use the chamber as is, without any pre-cleaning step.
We serendipitously discovered epoxy to be a convenient adhesive to mechanically and
optically couple capillary tubes and microscope glass. First, the cured epoxy is inert with
respect to immersion water; thus, the epoxy does not stain the water-immersion objective.
Second, and more importantly, the refractive index of cured epoxy closely matches the
refractive index of the microscope slide and the capillary tube. (Any refractive index
mismatch increases the background signal due to more reflection.) An adhesive with a
much higher refractive index than glass will shift the total internal reflection location to
the interface between the adhesive and capillary glass surface. Conversely, an adhesive with
a refractive index close to water will result in an evanescent wave at the boundary between
the microscope slide surface and the adhesive. In the absence of adhesive, immersion water
penetrates the cavity between the two glass surfaces, and the evanescent wave occurs at the

microscope slide-immersion water interface instead of at the inner surface of the capillary
tube where the fluorescent sample resides. Thus, cured epoxy between the capillary tube
and microscope slide solves this problem.

6.2.2. DNA tile design
The DNA tile used here conforms to the “DAO-O” motif (double-crossover, antiparallel,
odd-odd) [FS93], which means that it is a double-crossover molecule. At crossover points,
strands bend to become antiparallel to themselves. It has an odd number of DNA half-turns
between crossover points in the same tile, and also an odd number of half-turns between
neighboring tiles (middle). We used the sequence of the previously published DAO-E tile
(double-crossover, antiparallel, odd-even) We used the sequence of the previously published DAO-E tile {Fig. 1(d, top left) of Ref. [WLWS98]} as the starting sequence for our
DAO-O tile. In the new tile, we increased the distance between intermolecular crossover
points by approximately half a turn of DNA, from 21 base pairs to 26 base pairs, which
is equal to 5 half-turns. The new DNA tile has 2 pairs of 6-nucleotide sticky ends, instead of 5-nucleotide sticky ends, with the goal being to bring the nanotube formation
temperature near 37 ◦ C as required for the artificial cytoskeleton project in our lab. All
of the original core and arm sequences were left unmodified during the sequence optimization. We used our custom MATLAB code to design the sequence for the extension of the
arms and new pairs of sticky ends based on spurious binding minimization (available at

Name
NB-1
NB-2
NB-3
NB-3-Cy3
NB-3-Cy5
NB-4

Sequence
50 -CTCTGA-CTACCGCACCAGAATCTCGG-30
50 -AATTCC-CCGAGATTCTGGACGCCATAAGATAGCACCTCGACTCATTTGCCTGCGGTAG-30
50 -TCAGAG-GGTACAGTAGCCTGCTATCTTATGGCGTGGCAAATGAGTCGAGGACGGATCG-30
5 -Cy3-TT-TCAGAG-GGTACAGTAGCCTGCTATCTTATGGCGTGGCAAATGAGTCGAGGACGGATCG-30
50 -Cy5-TT-TCAGAG-GGTACAGTAGCCTGCTATCTTATGGCGTGGCAAATGAGTCGAGGACGGATCG-30
50 -GGAATT-CGATCCGTGGCTACTGTACC-30

Table 6.1.: DNA sequences for a single-monomer-type DNA nanotube. For the
fluorophore-labeled strands, we inserted two additional T’s between the fluorophore
and NB-3 sequence as a spacer to minimize any potential side effect of having the Cy3
or Cy5 fluorophore at the end of a sticky end.

Chapter 6

6.2.3. Polymerization mix
Our polymerization mix consists of pre-formed banded nuclei, supersaturated DNA tile
solution, crowding agent, and buffer, as explained below.
DNA stock solution
Each DNA strand (synthesized by IDT DNA Technologies, Inc.) was resuspended separately and stored in purified water at a 10 µM stock concentration. To expedite the
subsequent sample preparation step, we typically store our tile as an annealed DNA nanotube stock solution in a 4 ◦ C refrigerator, and use it within 1 week after annealing. The
stock of DNA nanotube was made by mixing the four DNA strands at a final equimolar
concentration of 1.5 µM each in a buffer consisting of 1×TAE [40 mM Tris-acetate and
1 mM EDTA (Ethylenediaminetetraacetic acid)] with 12.5 mM Mg-acetate and then annealing from 90 ◦ C to 20 ◦ C at 1 ◦ C/min. In retrospect, we consider this annealing step to
be unnecessary because of another annealing step in the preparation of the supersaturated
DNA tile solution.
Pre-formed DNA nuclei with fiduciary markers
The simultaneous polymerization measurement of both DNA nanotube ends requires fiduciary markers. To create fiduciary markers, we pre-formed DNA nanotubes with random
banding patterns to be used as nuclei. The banding pattern along the DNA nanotubes
established fiduciary coordinates that enabled separate kinetic measurement of both ends
of each DNA nanotube. The DNA nanotubes with fiduciary markers were prepared, as
discussed below, from Cy3- and {Cy3, Cy5}-labeled nanotubes, which were called bright
and dim bands, respectively. All of the tiles in the bright nanotubes were labeled with
Cy3. For the separately prepared dim nanotubes, only 33% of the tiles were labeled with
Cy3 and the remaining 67% were labeled with Cy5. Instead of using an unlabeled tile,
we chose Cy5-labeled tiles to decrease the brightness of the fluorescence tube in the Cy3
channel. We hope that the physical similarity between the Cy5-DNA and Cy3-DNA tiles
will result in similar perturbation to the DNA tile and DNA nanotubes, e.g., in terms of
melting temperatures, kinetics, etc.
The DNA nanotube nuclei were prepared as follows: First, we annealed bright and dim
DNA nanotubes separately at a tile concentration of 1.0 µM from 90 ◦ C down to 50 ◦ C at
1 ◦ C/min and from 50 ◦ C to 20 ◦ C at 0.1 ◦ C/min. This annealing protocol produces DNA
nanotubes with mean length on the order of 5 µm. On the same day, equal volumes of 1 µM

bright and dim DNA nanotubes were fragmented into shorter nanotubes by subjecting the
DNA nanotube mix to a high elongational fluid flow within a 20 µm×20 µm constriction
in a microfluidic chip [HY10] at a 150 µL/min volumetric flow rate. The elongational flow
near the constriction was sufficient to induce significant tension and induce DNA nanotube
scission. The fragments had a mean size on the order of 1 µm. Subsequently, the stochastic
end-to-end joining between fragmented bright and dim DNA nanotubes produced hybrid
DNA nanotubes with random banding patterns [RENP+ 04, ENAF04].
The bright and dim segments are visible in the microscopy images (the left panels of
Figs. 6.3 and 6.4) and are more obvious in the kymograph (the right top panel of Figs. 6.3
and 6.4). As expected, the position of bright and dim segments did not move relative to
each other during the course of data acquisition, which justified the choice of band positions
along the DNA nanotubes to act as bonafide fiduciary markers.
Supersaturated DNA tile solution
For the polymerization assay, the supersaturated DNA tile solution was synthesized by annealing 10 µL of DNA mix at 15⁄8×of the desired DNA tile concentration in 1×TAE/Mg++
from 90 ◦ C to 50 ◦ C. The slow annealing was halted at 50 ◦ C because for experimental
concentrations, DNA nanotube nucleation is not noticeable at temperatures above 40 ◦ C.
At 50 ◦ C, which is approximately 10 ◦ C above the formation temperature, 5 µL of 3×0.3% (w/v)
methylcellulose (previously kept at 50 ◦ C) was added to the 10 µL supersaturated DNA

Crowding agent confines the nanotubes
We included 0.3%(w/v) methyl cellulose (viscosity 4,000 cP at 2 % in H2 O at 20 ◦ C,
purchased from Sigma-Aldrich M0512) as a crowding agent to confine DNA nanotubes

Chapter 6

tiles. Note that the formation temperature is concentration and time dependent. By the
end of the experiment, we determined that the observed formation temperature range is
35.2−38.3 ◦ C, which corresponds to the temperature where spontaneous nucleation was
observed in 100 nM and 500 nM samples after ∼5 minutes of imaging time, respectively.
Thus, 50 ◦ C incubation is above the formation temperature in any free monomer concentration in this work. The sample temperature was then lowered to 45 ◦ C. 2 µL of pre-formed
banded nuclei were added at 45 ◦ C and immediately the mix was gently injected into
the capillary tube, which was already at the specified reaction temperature between the
temperature-controlled prism and the objective. Both ends of the capillary chamber were
immediately sealed with Vaseline.

near the bottom (as well as top and side) of the glass surface where the focal plane and
evanescence field were positioned. In a crowded environment, the entropy of the system
is maximized when all of the long structures are pushed close to another surface, such
as capillary tube walls. This entropic confinement did not hinder the mobility of confined
DNA nanotubes within their confinement space (middle columns of Figs. 6.3 and 6.4). This
behavior is in accord with previous observations of confined biopolymers in the presence of
crowding agents [GCK+ 10, WGA+ 10]. The side effect of this confinement strategy is that
the same entropic force also favors confining DNA nanotubes to other surfaces, including
the surfaces of other DNA nanotubes. Consequently, at high DNA nanotube densities,
DNA nanotubes were observed to exhibit side-to-side joining and lateral aggregation. The
increasing intensity of tubes in images corresponds to the lateral “bundling” of multiple
DNA nanotubes or side-to-side joining (observed directly in Movies C.1 and C.4).

6.2.4. Data acquisition
Since polymerization is temperature sensitive, we paid close attention to the temperature
of our sample and minimized exposure to the room temperature.
Before the injection of DNA monomers, the empty sample chamber was mounted onto
the heated prism and under the heated objective and immersion water to bring the sample
chamber to the desired steady state temperature. Skipping this step will result in a sample
chamber that is initially at room temperature, which would cause DNA nanotubes to
nucleate very rapidly. In addition, our autofocus did not work well when the temperature
of the sample, prism, and objective changed rapidly, such as in the initial heating step of
our method of temperature control. The chamber was left empty at the desired steady
state reaction temperature until the polymerization mix was ready.
In contrast to adding a liquid sample to a filled chamber, injecting a sample into an empty
capillary chamber results in a known initial sample concentration. Previously, studies
that used a similar sample chamber would flush the filled chamber with at least twice
the chamber volume to ensure that the reaction conditions held during measurements.
Because the fluid flow approaches zero near the channel walls, it is difficult to produce
samples with known concentration using that method. The second advantage of starting
with an empty chamber is fast injection time. Due to stronger capillary action, injecting
the sample into an empty chamber requires less time than infusing a filled chamber with
sample. The fast injection may also be important in minimizing thermal contact between
the heated liquid of DNA tiles, DNA nanotubes, and the ambient room temperature.

However, an empty chamber also possesses an intrinsic problem; the fast injection flow
of DNA nanotubes, especially at high temperatures, induces DNA nanotube scission. We
minimized the scission problem by adding the sample gently at the opening of the empty
chamber. The injection time was approximately 5 sec for . 6 µL sample. Quantifying how
much scission occurs with our injection protocol is not necessary since the polymerization
rate measurements should be independent of the initial amount of fragmentation.
We identified three instances in our protocol in which the polymerization mix was exposed to ambient environment. First, we pipetted 5 µL methylcellulose to a supersaturated
tile solution with a pipette tip that was at room temperature. Second, after we incubated
the solution of supersaturated tiles and methylcellulose at 50 ◦ C, we took the sample
out from the temperature cycler and mixed it for ≈ 5 sec at room temperature. Third,
we injected the supersaturated tiles, methylcellulose, and pre-formed DNA nuclei at the
opening of the heated glass capillary chamber with a pipette tip that was not heated.
To minimize the potential problem, such as the rapid nucleation of DNA nanotubes from
supersaturated DNA tiles before the sample was injected to the heated glass capillary
chamber, we performed these three steps as rapidly as we could. The typical execution
time for these steps was 5 sec and no longer than 10 sec. In almost all cases, the fast
sample handling seems to be sufficient to avoid spontaneous nucleation before imaging,
with the exception of a polymerization assay at 600 nM and 41.4 ◦ C. An extrapolation
of the polymerization model predicted a net negative polymerization rate at600 nM and
41.4 ◦ C (see the bottom right plot of Fig. 6.5). While the model may be true in an ideal

DNA nanotube imaging
Our prism-based TIRF microscope, equipped with temperature control and automated focusing, monitored the dynamics of the DNA nanotubes that were confined close to the
glass surface (Figs. 6.3 and 6.4) for more than 2 hours of imaging. The signal to noise ratio
was very high, even in the presence of a high concentration of Cy3-labeled free monomers
in solution. For all of the nanotubes that were analyzed, we did not encounter any pausing
of polymerization in any of our movies, which provides evidence that the untreated glass
surface is not too sticky. The majority of DNA tiles were in the free monomer state.
The typical total concentration of DNA tiles in pre-formed DNA nuclei was less than

Chapter 6

protocol, we consistently observed spontaneous nucleation in our 600 nM and 41.4 ◦ C movie.
We attribute the observed nuclei as a result of spontaneous nucleation that was triggered
by the brief exposure to room temperature during one or more of the steps discussed in
this section.

10 nM, which is 10× smaller than the most dilute free monomer concentration in our assay
(100 nM). Even after 2 hours of imaging, we typically observed a difference of less than a
factor of 2 in contour length for all DNA nanotubes, which corresponded to a small DNA
tile concentration change.
In the reaction conditions where spontaneous nucleation was hardly observable, the DNA
nanotube polymerization was followed for at least 1 hour and no longer than 2 hours. Much
to our surprise, our imaging protocol did not require an oxygen scavenger buffer to achieve
and maintain a high signal-to-noise ratio for more than 2 hours of time-lapse imaging. At
an acquisition rate of typically 4 frames/min, we usually acquired enough data points in
less than 30 minutes. If significant spontaneous nucleation was observed, we terminated
the data acquisition after ∼5 minutes because the newly formed nuclei rapidly obscured the
visibility of the pre-formed nuclei. Moreover, the new nuclei can also end-to-end join to a
growing DNA nanotube end, which made our polymerization rate measurements unreliable.
Thus, spontaneous nucleation limited the range of temperatures and concentrations for
which we could obtain accurate rate measurements.

6.2.5. Data analysis
The polymerization rate was measured using two methods: (1) kymographs [KP07] or (2)
length measurements taken at two frames with a sufficient time difference. The kymograph
allows separate measurement of both nanotube ends at the cost of time to construct a kymograph. Obtaining the polymerization rate from the nanotube length at two data points
is fast but can only measure the net polymerization rate of a nanotube end. Any asymmetry in the polymerization rate at the nanotube ends will be lost during the measurement,
even in the presence of fiduciary markers.
We applied an ImageJ (available at rsbweb.nih.gov/ij/) plugin developed by Kuhn
and Pollard [KP07] to construct kymographs from a series of DNA nanotube images. We
used their image analysis routine to convert a rough hand trace of each DNA nanotube
to a refined trace of the nanotube by snapping each pixel along the trace to the DNA
nanotube axis. The intensity along the refined traces was used to construct equivalent
straightened images of the curvilinear DNA nanotubes. The straightened images of the
same nanotube at different time points were aligned and stacked into a kymograph. We
wrote Mathematica (Wolfram Research) code that shifted the longitudinal offset between
straightened DNA nanotubes until the sum of the correlations between straightened images
in a kymograph was maximized, i.e., the banding patterns were vertically aligned. The

longitudinal position of both nanotube ends in a kymograph was detected by setting a
chosen threshold for both DNA nanotube ends, typically less than the half maximum value
of any given straightened images. For each nanotube end, we performed linear fitting to
the coordinates in each stacked image to measure the polymerization rates.
In the second technique, we simply calculated the net polymerization rate from the ratio
of the length change between two frames and the time interval between the frames. Because
the kymograph integrates over multiple frames, its standard error is likely to be smaller.

6.3. Results
6.3.1. Polymerization rate measurements

At the critical monomer concentration for a given temperature [tile]crit = kofonf , i.e., the
tile attachment rate kon [tile]crit and the tile detachment rate kof f are equal, so each DNA
nanotube’s length fluctuates around the initial monomer concentration value. At a constant tile concentration away from [tile]crit , DNA nanotubes either elongate or shrink at
a constant rate. The polymerization rate constants discussed here refer to the elongation
or shortening of DNA nanotubes (and thus are measured in layers/M/s) and layers/s as
opposed to the association and dissociation of a DNA tile to a binding site as illustrated
in Fig. 6.8. (The subtle distinction will be discussed in section 6.4.1). The resolution of

in Figs. 6.3 and 6.4 by (1) constructing kymographs and (2) measuring DNA nanotube
lengths at two time points. We address the results and merits of both approaches below.
DNA nanotubes depolymerize at a steady rate below the critical monomer
concentration
To measure the rate at which monomers dissociated from DNA nanotubes, kof f , we diluted
1 µM of DNA tiles (as pre-formed DNA nanotubes) at room temperature by a dilution
factor of 143 in imaging buffer [1×TAE/Mg++ 0.3% (w/v) methylcellulose]. At 25 ◦ C,
the free tile concentration in the pre-formed DNA nanotube nuclei stock was estimated to

Chapter 6

the microscopy assay was diffraction limited at ∼250 nm or ∼18× the size of a DNA tile.
Our imaging optics produced movies that were sufficient to accurately track both ends
of individual DNA nanotubes. However, the optics were insufficient to discriminate the
precise tile arrangement at nanotube ends and could not detect individual tile attachment
and detachment events.
We measured the polymerization rate from time-lapse images such as those presented

be well under 25 nM, which is the measured critical monomer concentration of our DNA
nanotube at 33.6 ◦ C (see Table 6.3). The 143× dilution brought the free tile concentration
close to 0 nM and effectively eliminated the contribution of the forward reaction to the net
depolymerization rate.
Fig. 6.3 shows that DNA nanotubes depolymerize at 38.3 ◦ C with zero initial monomer
concentration. Since the critical monomer concentration is non-zero, we expected DNA
nanotubes to depolymerize at zero monomer concentration. Presumably, the monomer
concentration was not constant at 0 nM, but instead increased as more DNA tiles dissociated from the shrinking DNA nanotubes. The initial concentration of all monomers in
the pre-formed DNA nanotube nuclei was 7 nM, which sets the upper bound of the free
monomer concentration in the experiment with 0 nM initial free tile concentration. In the
worst case scenario, a complete depolymerization would increase the free tile concentration
by 7 nM, which is relatively small compared to the 100 nM concentration interval in our
data set. In practice, the concentration change is less significant than the theoretical upper
bound. We did not run the assay long enough for a significant fraction of DNA nanotubes
to become significantly shorter.

DNA nanotubes elongate at high free tile concentration
To measure the second-order forward rate constant kon at which DNA tiles associated to
DNA nanotube ends, we assayed the DNA nanotube polymerization at multiple DNA tile
concentrations with intervals of 100 nM and at multiple temperatures ranging from 28.9 to
41.3 ◦ C. As shown in Fig 6.4, DNA nanotubes elongated at a 400 nM tile concentration and
at 38.3 ◦ C. In these experiments, elongation due to association was offset by the previously
measured dissociation rate.
In the polymerization experiment here, in which the spontaneous nucleation was very
rare, the tile concentration was regarded as approximately constant. In contrast to the
concentration increase in the depolymerization assay, the elongation of DNA nanotubes
consumed free tiles from solution. The initial concentration of tiles incorporated tile in
DNA nuclei was 7 nM. Because of the slow DNA nanotube polymerization rate, we did
not assay the process sufficiently long enough to achieve doubling of the average DNA
nanotube length. Therefore, at the temperatures and free tile concentration parameters
where spontaneous nucleation was very rare, polymerization doubled, at most, the average
DNA nanotube lengths by consuming 7 nM of free monomer concentration from the buffer,
which was less than one tenth of the smallest non-zero concentration in our experiments.

L @monomerD

200

Time @minutesD

Frame Ò

100

200 0

100

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L @µmD

Chapter 6

Figure 6.3.: Real-time observation of nanotube depolymerization. (Left) Before and
after TIRF images of depolymerizing DNA nanotubes at 38.3 ◦ C and 0 initial tile concentration. Here, the original images were at higher resolution and were intentionally
blurred over a pixel radius of 4 to ensure image clarity. The higher resolution images
are conserved in Movie A.2. (Middle) The superposition of the 69 images shows that
the nanotubes were confined close to the glass surface, where the evanescent illumination is maximum and focal plane is positioned. More importantly, the nanotubes
were able to diffuse in the confinement space [WGA+ 10,GCK+ 10]. The diffusion was
mostly along the longitudinal axis of the nanotube and not sideways. In the middle of
the movie, the tube on the left switched between two paths. The bottom middle panel
is the superposition of DNA nanotube traces at different time points. The depolymerization is more noticeable when the nanotube curvilinear traces are straightened,
aligned, and presented as a kymograph (top right). Only the kymograph of the left
tube is shown in this figure. The linear fits of the DNA nanotube end positions show
that both ends depolymerized at constant depolymerization rates. The vertices of
the gray-shaded regions are the output of the edge detection algorithm. Most of the
outputs were included in the linear fitting process and are labeled as blue circles and
red triangles for left and right nanotube ends, respectively. The linear fits of both
straightened nanotube end positions are also presented as off-set white dashed lines
in the top right kymograph. From the linear fit, the polymerization rates for the left
and right nanotube ends were measured to be 0.11±0.01 and 0.14±0.01 layers/sec,
respectively.

L @monomerD
100 200 300

Frame Ò

120

160

4 0

L @µmD

Figure 6.4.: At concentrations above the critical monomer concentration for a given
temperature, DNA nanotubes grow at a constant polymerization rate. (Left) Before
and after images of DNA nanotubes after 42 minutes of polymerization at 38.3 ◦ C and
400 nM initial tile concentration in 1×TAE/Mg++ and 0.3% (w/v) methylcellulose.
The images were blurred over a pixel radius of 4 to reduce its sharpness for clearer
presentation. In the original image, DNA nanotubes appear thin and sharp, which
is hardly visible in small-sized images. All of the unmodified frames are compiled in
Movie C.2. (Middle) DNA nanotubes were mobile during the course of the experiment.
The correlated displacement of all DNA nanotubes in the field of view was likely due to
the mechanical drift of our sample stage. The drift was very slow (< 10 µm/40 min),
which was much slower than the exposure time and did not affect the data analysis.
(Right) The kymograph and linear fits of the right nanotube in the middle bottom
panel support our expectation that at high tile concentration, DNA nanotubes grow
at a constant polymerization rate. From the linear fit, the growth rate for the left and
right nanotube ends were determined to be 0.043±0.003 and 0.040±0.002 layers/sec,
respectively.

Time @minutesD

100 200 300 0
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Out[602]=

DNA nanotubes polymerize at steady rates
The linear fits of DNA nanotube end positions in Figs. 6.3 and 6.4 show that both polymerization and depolymerization of DNA nanotubes proceeded at steady rates. From the
kymographs, we discovered that asymmetric polymerization rates for the two ends of an
individual DNA nanotube were relatively common. A rigorous investigation of the physical source of this asymmetry would have required engineered pre-formed DNA nanotube
nuclei, which was beyond the scope of this study.

6.3.2. Local and global analysis of combined polymerization data
To test the polymerization model, we measured the polymerization rates of 347 DNA nanotubes within a 0−500 nM concentration range and a 28.9−41.3 ◦ C temperature range.
Having established confidence in the steady polymerization rate, the polymerization rates
were measured by comparing the nanotube lengths at two time points determined to be
sufficiently far apart. We excluded DNA nanotubes that had undergone spontaneous scission, end-to-end joining, or side-to-side joining from our data set (observed directly in
Movies C.1 and C.4). We used the ImageJ plugin by Kuhn and Pollard [KP05] to measure

The dependence of polymerization rates dn
dt [tile], T on free monomer concentrations

[tile] at different temperatures T (summarized in Fig. 6.5) was determined by non-linear
global fit using the equations
dn
([tile], T ) = kon [tile] − kof f ,
dt

(6.1)

where
kof f

= kon e−(∆H −T ∆S )/RT × u0

(6.2)

and n is the number of tile layers in a DNA nanotube, t is time, kon is the rate constant associated with polymer growth, kof f is the rate constant associated with polymer

Chapter 6

the DNA nanotube length from a refined trace of a curvilinear DNA nanotube image. In
contrast to the kymograph method, this technique does not differentiate DNA nanotube
ends and only measures the average polymerization rate of a DNA nanotube. This simple
measurement method is far quicker than constructing a kymograph for each DNA nanotube. Also, by bypassing the alignment process, we could measure the rates from DNA
nanotubes that did not have multiple bands.

shrinking at standard concentration u0 = 1 M, T is the temperature in Kelvin, ∆H ◦ is
the standard enthalpy of tile-DNA nanotube dissociation and ∆S ◦ is the standard entropic
cost of tile−DNA nanotube dissociation. In this model, we ignored the plausible (but
likely small) kinetic and thermodynamic parameter differences between DNA nanotubes of
different circumferences.
From the global fitting, the association rate constant kon , was inferred to be (5.99±0.15)
×105 /M/sec. The non-linear fit gave the thermodynamic parameters of the combined
polymerization data to be ∆H ◦ = 85.9±0.2 kcal/mol and ∆S ◦ = 0.251±0.006 kcal/mol/K.
As a comparison to the global fitting results, the local linear fit results of the plots in
Fig. 6.5 are summarized in Table 6.2. In these local fits, the polymerization rates dn
dt at a
given temperature T at different [tile] were subjected to linear fitting.
dn
dt

= kon [tile] − kof f ,

(6.3)

The inferred association rate constants, kon and dissociation constant Kd = kofonf from the
local linear fittings were plotted against the reaction temperature in Fig. 6.6. The inferred
values from local fits (solid circles) are in agreement with the theoretical model (solid line)
using the inferred values of kon , ∆H ◦ , and ∆S ◦ .
(◦ C)
33.6
35.2
36.7
38.3
39.8
41.4

(nanotubes)
16
35
39
48
68
62

[tile] range
(nM)
0−100
0−200
0−300
0−400
0−500
0−500

kon
(×105 /M/sec)
5.90±0.61
5.06±0.42
5.12±0.34
6.64±0.32
6.21±0.30
5.52±0.50

kof f
(min−1 )
0.87±0.24
1.01±0.31
2.87±0.36
7.59±0.46
15.96±0.57
29.83±0.93

Kd
(nM)
24.8±9.3
33.7±12.9
93.5±18.1
190±21
428±36
901±110

Table 6.2.: Summary of the inferred reaction rate constants from the local and global
fits
To obtain the thermodynamic facet of our analysis, we plotted the same rates in Fig. 6.5
against temperature at different free monomer concentrations in Fig. 6.7. We extended
the analysis by obtaining thermodynamic parameters from a local non-linear fitting with
Eqs. 6.1 and 6.2 . The inferred enthalpy and entropy parameters from the local fits are
summarized in Table 6.3. The kon , ∆H ◦ and ∆S ◦ from local fits in the range of were within

33.6 Î C

38.3 Î C

0.2
0.0

191

Polymerization rate
@layerêsecD

-0.2
-0.4
-0.6
100

200

300

400

100

200

300

400

Tile concentration @nM D

35.2 Î C

39.8 Î C

0.2

-0.2
-0.4

500

428

Polymerization rate
@layerêsecD

-0.4

500

-0.6

0.2
0.0

-0.2
-0.4

300

400

-0.6

100

200

300

400

200

36.7 Î C

41.4 Î C

-0.4
-0.6

0.2
0.0
-0.2
-0.4
-0.6

100

200

300

400

Tile concentration @nM D

500

200

300

400

500

100

Tile concentration @nM D

Figure 6.5.: Dependence of DNA nanotube polymerization rates on free tile concentration for several reaction temperatures. As expected, the polymerization rate was faster
at lower temperatures and higher free monomer concentrations. The polymerization
was assayed at 28.9−41.4 ◦ C and 0−500 nM in 1×TAE/Mg++ 0.3% (w/v) methylcellulose. At each temperature, assays were performed at 0, 100, 200, 300, 400, and
500 nM. The typical tile concentration of the nuclei was 7 nM. The gray-shaded region
represents the parameter space where we observed spontaneous nucleation and endto-end joining, which invalidates measurements due to side-to-side joining between
pre-formed nuclei and the newly nucleated nanotubes. Furthermore, the side-to-side
joining obscured the time evolution of individual DNA nanotubes. As a consequence,
the movies in the shaded parameter space were not analyzed. The fitting line is the
global linear fit (Eq. 6.1). The numbers on the top horizontal axis are the inferred
critical monomer concentrations, which were calculated by setting Eq. 6.1 to zero at
given temperature T . The data at a given temperature and at different monomer
concentrations was fitted separately (not shown), and the fitting results are presented
in Table 6.2. The critical tile concentration for each temperature is given at the top81
of each plot in nM.

Chapter 6

Polymerization rate
@layerêsecD

500

-0.2

100

Tile concentration @nM D

0.2

500

Tile concentration @nM D

Polymerization rate
@layerêsecD

-0.2

Tile concentration @nM D

0.0

-0.6

0.0

0.2

Association Constant
Kon [/M/sec]
Disassociation Constant
Kd [nM]

7 105
6 105
5 105

7 105
901

428
191
93
.4
41

.8
39

.3
38

.2
35

.6
33

.5
30

Temperature [˚C]

Figure 6.6.: (top) The inferred association rate constant kon is relatively constant at
different temperatures T . The solid line represents kon based on global fits. (bottom) The inferred dissociation constant, Kd , for DNA nanotube polymerization grew
exponentially (solid line) with the temperatures T . The dissociation constant was
calculated by taking the ratio of inferred kof f and kon parameters from the local fits.
The line was computed by employing the best fitted ∆H ◦ and ∆S ◦ parameters from
the global data fit and Eq. 6.2.

0.2

-0.2

-0.4

0.0

-0.2

-0.4

Temperature @Î CD

100 nM

400 nM

0.2

0.0

-0.6

-0.2

-0.4

-0.6

0.2

0.0

-0.2

-0.4
-0.6

Temperature @Î CD

200 nM

500 nM

0.2

0.0

-0.2

-0.4
-0.6

0.2

0.0

Chapter 6

Polymerization rate
@layerêsecD

0.2

Polymerization rate
@layerêsecD

-0.6

Polymerization rate
@layerêsecD

0.0

Polymerization rate
@layerêsecD

300 nM

Polymerization rate
@layerêsecD

0 nM

-0.2
-0.4
-0.6

Temperature @Î CD

Figure 6.7.: At a given free tile concentration, DNA nanotubes elongate faster at lower
temperatures, which reveals that DNA nanotube polymerization is at least partly
enthalpy-driven. The gray-shaded region indicates the concentrations where significant spontaneous nucleation was observed for a particular reaction temperature. The
solid line is the result of global fitting with Eq. 6.1 and 6.2

a factor of 10 from the global fit output. The local extractions of kon , ∆H ◦ and ∆S ◦ at
higher monomer concentrations were less reliable progressively because of the narrower
valid temperature range due to rapid nucleation at high free monomer concentrations.
Because of the inherent problem in extracting kinetics and thermodynamics parameters
from local fitting, we only use the global fitting values of kon , ∆H ◦ and ∆S ◦ in future
analysis and discussions.

[tile]
(nM)
100
200
300
400
500
global fit

(nanotubes)
162
55
47
39
26
30
347

T range
(◦ C)
30.5−41.4
33.6−41.4
35.2−41.4
36.7−41.4
38.3−41.4
39.8−41.4

kon
(10 /M/sec)
1.19±0.01
1.00±2.21
5.25±1.24
5.45±2.10
5.25±3.76
3.21±1.01
0.599±0.015

∆H ◦
(kcal/mol)
72.6±3.1
143±46
118±65
116±84
112±126
138±46
87.9±2.0

∆S ◦
(kcal/mol/K)
0.201±0.010
0.424±0.145
0.346±0.208
0.340±0.266
0.328±0.401
0.413±0.149
0.252±0.006

Table 6.3.: Summary of the best thermodynamic parameters from the local and global
fits.

6.4. Discussion
To summarize our measurements, we developed a TIRF microscopy assay to directly observe the polymerization dynamics of single DNA nanotubes for up to 2 hours of imaging
over a wide range of DNA tile monomer concentrations and temperatures. The long duration of time-lapse imaging requires stable temperature control and an autofocusing system.
The polymerization rates were measured by two methods, which were (1) constructing a
kymograph from straightened traces of DNA nanotubes and (2) measurement of the nanotube length difference at two time points. The first method was able to simultaneously
obtain the polymerization rates for both filaments and confirmed that each end depolymerizes (Fig. 6.3) or polymerizes (Fig. 6.4) at a steady rate. The second measurement
strategy was used to analyze a much larger number of DNA nanotube polymerizations
(N = 347 nanotubes) for extracting kinetic and thermodynamic parameters via global
fitting.

6.4.1. Interpretation of the measured kon and kof f rate constants
The polymerization of DNA nanotubes was modeled based on the kinetic Tile Assembly
Model (kTAM) developed for theoretical study and simulation of algorithmic DNA tile
self-assembly [Win98]. In the kTAM, the association between a tile and a binding site is
assumed to be a reaction with forward rate
site
rf = kon
[tile],

(6.4)

site is the second-order association rate constant for an individual tile to an individwhere kon

ual site. The reverse reaction rate depends on the stability of the binding and is modeled
to be

site
site −b∆Gse /RT +α
rr,b = kof
× u0 ,
f,b = kon e

(6.5)

where b is the number of sticky end bonds, ∆G◦se > 0 is the standard free energy for
breaking a single sticky end bond at standard concentration u0 = 1 M, and αRT is the
initiation energy for dsDNA formation with α ∼ ln(20) [Win98]. The standard free energy
◦ − T ∆S ◦ . In the kTAM, due to the weak
∆G◦se can be further expressed as ∆G◦se = ∆Hse
se

analysis, we ignored 1, 3, and 4 sticky end interactions and assigned the inferred ∆G◦ as
the free energy of an interaction with two sticky-ends ∆G◦ = 2∆G◦se − αRT , ∆G◦ > 0
(Fig. 6.8 right panel).

6.4.2. Asymmetric polymerization
One unresolved issue was the surprisingly prevalent observation of asymmetric polymerization of the two nanotube ends. Further, the range in measured polymerization rates
in a particular field of view was as large as a factor of 3. Local non-specific interaction
between the glass surface and the DNA nanotubes is not likely to explain the difference
because the local variation of glass surface is minimal and the measured DNA nanotubes
were consistently able to diffuse in the confined space close to the glass surface.

Chapter 6

bond strength of one sticky end interaction, a tile that binds with one sticky end will quickly
disassociate from the nanotube end, as illustrated by the large arrow in the left panel of Fig.
6.8. In DNA nanotube polymerization, configurations where an incoming tile can bind with
3 or 4 bonds can be neglected because a DNA nanotube end is highly unlikely to contain
any tile arrangement allowing for a tile to bind with 3 or 4 sticky ends. For the quantitative

Out[76]=

Out[385]=

kon

koﬀ,1

kon

koﬀ,2

Printed by Mathematica for Students

Out[76]=

Figure 6.8.: In the kinetic Tile Assembly Model [Win98], the rate of a free tile attachsite is independent of the number
ment to an available site in DNA nanotube end kon
of sticky ends in the potential binding site. To satisfy detailed balance, the reverse
rates depend on the number of available sticky ends. Hence, a DNA tile that only
binds with one sticky end (left panel) will dissociate from a DNA nanotube faster
than DNA tile with 2 bonds (right panel). The configuration of DNA nanotube ends
and the position of dark tiles are different between left and right panels. Here, the
highlighted attachment sites in the left and right panels provide 1 and 2 sticky ends,
respectively. The attachment sites are illustrated as darker colored tiles. The sticky
ends, illustrated as short green or orange tubes, are complementary when the colors
site than k site .
match. The faster rate is indicated by the larger arrow of kof
f,1
of f,2
Printed by Mathematica for Students

Printed by Mathematica for Students

Hypothesis 1: The location of fluorophores on one end of DNA nanotubes bias the
polymerization rate.
One intriguing hypothesis is that the asymmetry may arise from the physical difference
between DNA nanotube ends, such as the location of fluorophores with respect to the
attachment site. Since we put the fluorophore at one of the four corners of a DNA tile,
only the sticky ends on one end of the DNA nanotubes are decorated with fluorophore.
Hypothesis 2: The asymmetric circumference of the pre-formed DNA nanotube ends
gives rise to the observed asymmetric polymerization.
In our experiment, the formation of DNA nuclei involves stochastic end-to-end joining of
short DNA nanotube nuclei with either Cy3 or Cy5 fluorophores. These short nanotubes
has a range of nanotube circumferences. AFM measurements of opened DNA nanotubes on
mica have revealed the diameter distribution of our DNA nanotubes (Fig. 6.9). Stochastic end-to-end joining of the heterogenous DNA nanotubes would likely generate DNA
nanotubes with asymmetric ends.
mode = 7

Out[1309]=

0.3

0.2

0.1

5 6 7 8 9 1011

Circumference @DNA tilesD

Figure 6.9.: Our annealing protocol produces DNA nanotube nuclei that are 5−11 tiles
in circumference, with 7-tiles-wide DNA nanotubes as the most prevalent. Images
of individual opened DNA nanotubes for constructing this histogram are presented
in the (Fig. C.5). This measurement seems to be relevant to the variation in the
polymerization rates observed in this experiment. Heterogeneous diameters were also
observed in the in-vitro self-assembly of other tubular structures, such as protein
microtubule [WCJ90, WC93, CW91]. The error bars are the standard deviation for
each bin calculated using a bootstrapping method. (Insets) Representative images of
the opened DNA nanotubes with diameter of 5 (left) and 11 (right) DNA tiles.
From a theoretical standpoint, the total ensemble of possible tile configurations along
the circumference of DNA nanotubes gives rise to a dependence of the polymerization

Chapter 6

Normalized Frequency

0.4

rate on the nanotube diameter. Based on kinetic arguments, the only attachment site
configurations that contribute to the elongation of nanotubes are the ones that can provide
two sticky end bonds, b = 2. For multi-monomer-wide nanotubes, there are more binding
sites in wider nanotubes than in the thinner nanotubes. However, not all of the binding
sites can provide b = 2 available sticky ends. As examples, the top half of Fig. 6.8 show
a configuration of 8-monomer wide DNA nanotubes (m = 8). The configuration provides
m=8 = 7/8. The denominator of the calculated
7 sites with b = 2, which corresponds to fb=2

fbm is the nanotube circumference and accounts for the larger number of maximum b = 2
sites observed in wider nanotubes compared to thinner nanotubes.
The average fraction of sites that can provide b = 2 sticky ends per m-monomer wide
m i decreases with increasing nanotube circumference m. At the lower limit,
nanotubes hfb=2
m=1 i of a 1-monomer wide nanotube is 1. It is important to realize that a 1-monomer
hfb=2

wide nanotube is a chain that behaves differently from nanotubes with m ≥ 2. The
growth of a 1- monomer wide nanotube is isodesmic, which means that the strength of the
interactions between monomers in the middle of a 1-monomer wide nanotube is the same as
the interaction in the collision between free monomers in solution [dGM08]. It should also
be noted that in the analysis of this hypothesis, we are ignoring the diameter-dependent
strain energies that are undoubtably experienced by nanotubes [RENP+ 04,SS06] and which
in this case would probably be relieved by breaking stacking bonds at the nicks adjacent
to sticky ends.
For nanotube circumference m ≥ 2, our model assumed that for m monomer wide
nanotube, the arrangement at nanotube growth front is a one-dimensional random walk
with total number of steps equal to 2 × m (Fig. 6.10). The factor 2 is based on the number
of sticky end pairs (A and B) that serve as binding domains for m monomer wide DNA
nanotubes. To form a tubular structure, the numbers of A’s and B’s have be equal to m.
In Fig. 6.10, the A and B sticky end interactions are depicted as red (/) and blue (\) lines,
respectively. In the language of one-dimensional random walks, a series of A (red /) and
B (blue \) lines is equivalent to a sequence of left and right steps of a random walker.
Fig. 6.10 shows ensembles of possible tile configurations for the growing end of 1, 2,
and 3 monomer wide nanotubes. Each configuration is unique due to the rotational and
translational symmetry. The numbers of on-sites and off-sites were calculated by counting
the number of peaks and valleys, respectively. The valleys correspond to the attachment
sites (on-sites) with 2 available sticky ends. The peaks are the off-site locations where the
tile has to break 2 sticky ends to dissociate from the nanotube. Both valleys and peaks are

found when the random walk switch direction from A to B, and vice versa. Interestingly,
because both A and B have to be present in equal number in all configurations, the number
of valleys and peaks also have to be equal.
For finite diameters m, the number of red and blue steps must be equal, and therefore
there are global constraints on what configurations occur, from which we can see that
the probabilities cannot be simply those of an unbiased random walk with independent
steps. Nonetheless, we show that if nanotube growth occurs according to kTAM rates with
every step involving the addition or removal of a single tile that forms exactly 2 sticky
end bonds, then the steady-state distribution of random walk configurations (sequences of
an equal number of red and blue steps, m each, treating rotationally symmetric states as
distinct) must be uniform. Consider a continuous-time discrete-state Markov process on
these states, with transitions according to the kTAM. A configuration i that has n valleys
and n peaks, will have n neighbors, j, to which it can transition with rate rf , and from
which it can transition with rate rr,2 , as well as n neighbors, k, to which it can transition
with rate rr,2 and from which it can transition with rate rf . Letting pi be the steady-state
probability of configuration i, the dynamics gives
dpi X
(pj rr,2 − pi rf ) +
(pk rf − pi rr,2 ) .
dt

Substituting our ansatz that pi = 1/N where N is the size of the state space, we see that

+n
rf − rr,2 = 0,

which establishes that the uniform distribution is the unique steady state for this connected
Markov process.
The steady state behavior of nanotubes with m approaching ∞ is less sensitive to the
m=∞ i can be estimated from an unconconstraints on the random walk. Consequently, hfb=2

strained and unbiased one-dimensional random walk. At any position, the probability of
m→∞ i is 1 .
finding a valley (on site) or a peak (off site) is 21 . Therefore, the limit of hfb=2
m i is maximum for 1-monomer nanotubes, decreases with increasing
In summary, hfb=2

nanotube circumferences, and approaches 12 as the nanotube diameter approaches infinity.
m and k m ,
Finally, the kinetic rates of m-monomer wide DNA nanotube polymerization, kon
of f

can be effectively estimated from the kinetic rates of interaction for an incoming tile to

Chapter 6

dpi
=n
rr,2 − rf
dt

site and k site , by the simple
bind to an available site at the end of a DNA nanotube, kon
of f
m = hf m ik site and k m = hf m ik site .
expressions kon
b=2 on
of f
b=2 of f

We tested the width-dependent polymerization rate by running stochastic simulations for
DNA nanotubes with 1 to 16 monomer circumferences at different free monomer concentrations (Fig. 6.11). The rates at which a monomer arrived to an available site at nanotube
end, rf , and disassociated from a non-empty neighboring site, rr,b were computed based on
the kTAM. The simulations (Fig. 6.11) supported the theoretical dependence of the polym i for 1, 2, and
merization rate on the DNA nanotube circumference. Quantitatively, hfb=2

3 monomer nanotubes obtained from the simulations was 1, 0.67, and 0.61, respectively,
which is in agreement with the theoretical value based on the Markov chain analysis in
Fig. 6.10 (1, 2⁄3, and 3⁄5, respectively).

Because in the model considered here, we ignore any possible diameter-dependent strain
energy, the on-rates, off-rates, and critical monomer concentration do not depend on the
nanotube circumference. Thus, we see that there is the variability in overall growth rates
kon and kof f even when (or if) there is no thermodynamic variability for tile attachment and
site and k site both remain constant. That said, for the range of nanotube diameters seen in
kon
of f

our experiments (diameters 5 to 11, Fig. 6.9), our simulations show that the polymerization
rates should not depend strongly on diameter if there is no diameter-dependent strain
energy. In fact, simulated polymerization rates for diameters 5 to 11 were close to the
polymerization rate of 2-dimensional DNA lattices (bottom blue dashed line), which was
computed to be half the polymerization rate of 1-monomer nanotubes (top blue dashed
line).

Assuming that the experimentally observed asymmetric polymerization was due to the
heterogeneity in the distribution of the nanotube diameter, the dependence should have
arisen from the energetic dependence of m-monomer DNA nanotubes on the nanotube circumference rather than on the logical shape of tile attachment. It is important to note that
the kTAM assumes that both ∆H ◦ and ∆S ◦ are independent from nanotube circumference. Based on previous models of DNA nanotubes [RENP+ 04] and two-dimensional DNA
lattices (Appendix D), the contributions of electrostatic and twist penalty to the overall
energetics of DNA nanotubes are expected to depend on nanotube circumference.

3 on-sites ; 3 off-sites
degeneracy = 1

2 on-sites ; 2 off-sites
degeneracy = 3

2 on-sites ; 2 off-sites
degeneracy = 1

1 on-site ; 1 off-site
degeneracy = 3

1 on-site ; 1 off-site
degeneracy = 2

2 on-sites ; 2 off-sites
degeneracy = 3

1 on-site ; 1 off-site
degeneracy = 1

(3 × 1) + (2 × 3) + (2 × 3) + (1 × 3)
1+3+3+3

(2 × 1) + (1 × 2)
1+2

1× 1

f b=2

Figure 6.10.: The possible tile configurations along the nanotube end with circumference = 1, 2, and 3 monomers.
A tile is represented as a white diamond. Blue and red solid lines denote the sticky end types. Dashed lines
indicate connectivity between two longitudinal edges of the two-dimensional representation of a nanotube end.
m=2 are calculated
In all configurations, each tile is required to interact with ≥2 neighboring tiles. The value of fb=2
based on the circumference, numbers of on- and off-sites, and their degeneracies.

Nanotube
circumference
(monomer)

Chapter 6

site @tileD-k site
kon
off,2

HisodesmicL

@tileDcrit

nanotube
circumference
@monomerD

Polymerization rate @layerêminD

5-11 Hthis workL
¶ H2D crystalL

site @tileD-k site <
½µ8kon
off,2

site
-koff,2

-10

200

400

600

800

1000

Tile concentration @nMD

Figure 6.11.: Stochastic simulation reveals the dependence of polymerization rates on
DNA nanotube diameter. Nanotubes with larger circumference polymerize slower
than thinner nanotubes. In the plot above, the on rate and the standard free energy
site = 106 /M/sec and ∆G◦ = 8 RT for
of a single sticky end was chosen to be kon
se
site is defined as the disassociation rate of a
all nanotube diameters. In the plot, kof
f,2
site e−2∆G◦se +αRT . The polymerization rates
DNA tile with 2 bonds and is equal to kon
for 2-, 3-, and 4-monomer DNA nanotube are denoted as red, orange, and green
circles, respectively. Each data set was subjected to linear fit based on Eq. 6.3. The
simulation results from 5- to 11-monomer nanotubes, which is the circumference
range of the DNA nanotubes in our experiment, reside in the gray shaded region.
The upper bound (top blue dashed line) is the polymerization rate for 1-monomer
site [tile] − k site , while the lower bound (bottom blue dashed
DNA nanotubes = kon
of f,2
line) is the expected effective rate for the two-dimensional DNA lattice = 1/2 ×
site [tile] − k site }.
{kon
of f,2

6.4.3. Comparison with previously reported reaction rates of DNA
self-assembled structures
Inferred association rate constant
In section 6.3.2, we measured kon to be (5.99±0.15) ×105 /M/sec for the polymerization
model. In kTAM, the inferred association rate constant for a single DNA tile binding
site was expected to be ≈ 2 × k
to an available site at the end of a DNA nanotube kon
on =
site fell within the same order of magnitude as
2×(5.99±0.15)×105 /M/sec. The inferred kon

the previously reported forward rate measurements involving DNA hybridization [QW89,
GT81,WF91,MS93], and from numerical analysis of tile-based DNA self-assembly [ZW09].
Quartin and Wetmur [QW89] showed that the association reaction of a simple interaction
between two short DNA strands is diffusion limited and determined kon to be on the order
of 6×105 /M/sec. From a series of DNA toehold exchange experiments, Zhang and Winfree
obtained the range of forward rate to be (1−6)×106 /M/sec [ZW09].
The most comparable analysis of DNA self-assembly to the DNA nanotube polymerization reported here, is the kinetic Monte Carlo simulation of DNA ribbon growth done by
Chen et al [CSGW07]. However, their kinetic parameter measurement was indirect. To
obtain agreement between their AFM observation of assembly data and their simulations,
site to be 17 × 106 /M/sec, which is 14× faster than
Chen et al chose the forward rate kon

our measurement. Given the sensitivity of their simulation results to the two adjustable
site and the free energy of sticky-end interaction ∆G◦ , it is likely that
parameters, namely kon

the manuscript. In two separate works with different types of DNA ribbon, Schulman and
Winfree [SW07] as well as Fujibayashi and Murata [FM09] used 106 /M/sec as the typical
association rate constant in their analysis and found the number reasonable.

Thermodynamic parameters
To evaluate the inferred thermodynamic parameters of our measurement, we compared
the enthalpy and entropy values to theoretical predictions and to values from previously
reported studies of the free energy of DNA hybridization. Both inferred enthalpy and
entropy values are very close to the theoretical estimates used in the original presentation
of the kTAM paper [Win98]. In that framework, the expected enthalpy of disassembly
was calculated to be ∆H ◦ = R × sb×(4000 K), where s is the number of base pairs in a

Chapter 6

site value had significant uncertainty, which was not explicitly stated in
their inference of kon

sticky end and b is the number of sticky end bonds. For b=2, s=6, the simple expression
yielded the value of ∆H ◦ = 95 kcal/mol, which is within 10% of our measurement of
∆H ◦ = 87.9±2.0 kcal/mol. For the entropy, using the kTAM, α=ln(20) [Win98], the
theoretical value was predicted to be ∆S ◦ = R × (11sb + α) = 0.268 kcal/mol/K, which
is within 10% of the measured ∆S ◦ = 0.251±0.006 kcal/mol/K in our experiment. Finally,
our inferred values of ∆H ◦ ’s and ∆S ◦ ’s, we calculated the standard free energy of two
sticky end interactions at 37 ◦ C to be ∆G◦37◦ C = ∆H ◦ − T37◦ C ∆S ◦ = 12.2 kcal/mol and
9.5 kcal/mol for the values based on kTAM and our experiment, respectively. The ∆G◦37◦ C
from kTAM is within 30% difference from our measured ∆G◦37◦ C .
To the best of our knowledge, the only published values for thermodynamic parameters
of double crossover tile-based DNA structures in solution were obtained from bulk studies
of DNA ribbons of designed widths [SW07]. The ribbons of different widths were composed
of multiple tiles with 5 bp sticky ends, which is shorter than the 6 bp sticky ends in our
tiles. Schulman and Winfree extracted ∆H ◦ and ∆S ◦ from a series of UV absorbance data
by employing van’t Hoff analysis. They measured ∆H ◦ = 102.4 kcal/mol and ∆S ◦ = 0.300
kcal/mol/K. To account for their shorter sticky ends, we multiplied these values by 6/5,
which is the ratio of sticky end lengths of our DNA nanotube and Shulman and Winfree’s
ribbon, which gives ∆H ◦ = 122.9 kcal/mol and ∆S ◦ = 0.360 kcal/mol/K. Their adjusted
values of ∆H ◦ and ∆S ◦ are within 45% and 22% of our measurement, respectively. Using
these adjusted ∆H ◦ ’s and ∆S ◦ values, we calculated ∆G◦37◦ C = 11.3 kcal/mol, which is
within 18% of our measured ∆G◦37◦ C .
The thermodynamic parameters of DNA hybridization depend strongly on the DNA sequences and buffer condition, which could explain the difference of as much as 45% between
our measurements and the thermodynamic values obtained by Schulman and Winfree.
Moreover, the inter- and intra-monomer strain between DNA ribbons and DNA nanotubes
are likely to be different. Their published n-tile-wide ribbons assembled from 2(n-2) unique
single tile and two double tiles, each have different sticky end sequences compared to the
tile used in this work. In addition, their thermodynamic measurements were acquired in
the absence of crowding agent and in 12.5 mM concentration of Magnesium, compared to
10 mM in our polymerization buffer.
Furthermore, the measured thermodynamic values are also not incompatible with Nangreave et al.’s van’t Hoff analysis of their FRET measurement of quadruple-crossover (QX)
molecules [NYL09]. The QX molecule, in essence, is a flat sheet of 4 parallel DNA helices.
By attaching different 6 bp sticky ends to a QX pair, the thermodynamic properties of dif-

ferent configurations of sticky ends were extensively studied. The relevant subset of their
experiments is the measurement of the interaction between 2 pairs of sticky ends that are
located adjacent to each other. In the two variants that they constructed, the enthalpy was
measured to be 105.1±7.8 kcal/mol and 116.6±19 kcal/mol. For the entropy of the reaction,
they determined the values to be 0.301±0.025 kcal/mol/K and 0.334±0.057 kcal/mol/K.
These values are within a range that is less than 36% of our measurement.
Another relevant value to compute is the expected melting temperature Tm of DNA nanotubes in Kelvin. From simple thermodynamics, the melting temperature can be calculated
as
∆H ◦
(6.6)
Tm =
∆S ◦ − R ln[tile]
Using the theoretical values from kTAM [Win98], the melting temperature for a reaction
with 100 nM, 200 nM, 300 nM, 400 nM, and 500 nM free tile concentration is calculated to
be 43.5 ◦ C, 44.9 ◦ C, 45.7 ◦ C, 46.4 ◦ C, and 46.9 ◦ C , respectively. The calculated values are
less than 8 ◦ C higher than the measured equilibrium temperature in the polymerization
rate vs. temperature plots (Fig. 6.7), which is in close agreement with our measurement
and predictions based on a simple model. Similarly, the discrepancy in Tm is likely because
the kTAM number is derived from a simple model and ignores the sequence dependence of
∆H ◦ and ∆S ◦ . Nonetheless, this close agreement illustrates the usefulness of the simple
energetics model in the kTAM for estimating thermodynamic values in DNA self-assembly.

6.4.4. Comparison with the polymerization rates of actin and microtubules

as the kinetic model for actin polymerization [KP05]. The forward rates of DNA nanotube, actin filament, and microtubule assemblies are modeled as reactions that depend on
the free monomer concentration-dependent reaction. Actin filaments and microtubules are
asymmetric polymers. The polymer ends have different thermodynamic free energies and
kinetic rates. The association rate constant for an ATP bound actin monomer to attach
to an actin filament has been measured at the single molecule level to be 0.5×106 /M/sec
and 7.4×106 /M/sec for the pointed and the barbed end, respectively [KP05]. For microtubules, the association rate constant for α,β-tubulin bound GMP-CPP, an unhydrolyzable
analog of GTP, to dock to a microtubule at 37 ◦ C has been measured by bulk assay to
be 5.4×106 /M/sec [HSD+ 92]. The association rate constant kon values of actin and microtubules are comparable to the measured kon in our assay. The monomer dissociation

Chapter 6

The kinetic Tile Assembly Model posseseses the same kinetic and thermodynamic features

rate for actin and microtubule polymerization depends on the bond strength. The dissociation rate of fuel-bound monomers, such as ATP-actin and GTP-tubulin, is slower than
waste-bound monomers. The qualitative and quantitative similarities between the DNA
nanotube and actin provide additional support for the DNA nanotube as an attractive
engineering material for de novo creation of an artificial cytoskeleton.
Although both polymers have comparable kon values, typical polymerization of actin and
microtubules is on the order of 1 layer/sec or faster, compared to the 0.1 layer/sec mean
polymerization rate of DNA nanotubes reported here. Faster polymerization rate gives
actin and microtubules morphological flexibility. These biopolymers can assemble structures when cell needs them and stabilize them by capping proteins. The faster cytoskeleton
polymerization rate is a direct result of the higher free monomer concentration in cellular
milieu, which is on the order of 1 µM. In our study, the relatively high spontaneous nucleation rate in DNA nanotubes prevented us from performing polymerization assays at
comparable concentrations to those of the actin and microtubules. Hyman et al. [HSD+ 92]
have shown that the coupling between polymerization and stochastic GTP hydrolysis is
responsible for the slow spontaneous nucleation rate of protein microtubules. Docking of
an α,β-tubulin monomer that is bound to GTP on a growing microtubule, triggers the
stochastic GTP hydrolysis reaction, which weakens the tubulin−microtubule binding and
increases the dissociation rate significantly. Inspired by this elegant solution, it will be
interesting to examine how to incorporate energy consuming reactions into the interaction
between DNA tiles and between DNA tiles and DNA nanotubes in order to achieve a higher
nucleation barrier than the one observed in the existing passive DNA nanotube system,
such as the one used in this work.

6.5. Concluding remarks and outlook
From single-molecule movies, we were able to systematically test a mathematical model
of DNA self assembly while extracting both the kinetic and thermodynamic parameters
of DNA nanotube polymerization. The polymerization model depends on the tile concentrations and is sensitive to reaction temperature. To the best of our knowledge, this
experiment is the most accurate measurement of DNA tile-based self-assembly to date.
Our experiment justifies the use of polymerization theory developed for one-dimensional
cooperative polymers, such as microtubules and actin, to accurately model DNA nanotube
polymerization.
The most basic demonstration of non-equilibrium polymer dynamics is steady elonga-

tion or shortening at a constant monomer concentration that is far from the critical DNA
tile concentration. Toward this end, we have engineered a sustainable far-from-equilibrium
dynamic of DNA nanotubes. In the future, the coupling between DNA nanotube polymerization and an analog of nucleotide hydrolysis could potentially recapitulate the more complex non-equilibrium cytoskeleton-based dynamics [HH03], such as treadmilling [CLZ82]
and dynamic instability [MK84a], where polymerization and depolymerization co-exist at
steady state without ever reaching equilibrium. These novel dynamics can only be observed
at the single molecule level, as demonstrated with the TIRF assay reported here.

6.6. Acknowledgments
We would like to acknowledge Rebecca Schulman, Damien Woods, Matthew Cook, Tosan
Omabegho, Heun Jin Lee, Ethan Garner, Michael Diehl, Zahid Yaqoob, Nadine Dabby,
and Paul Rothemund for their helpful discussions. The authors especially thank Rebecca
Schulman and Ann McEvoy for pointing our attention to glass capillary chambers, and
Matthew Cook for analysis of 2D crystal growth front dynamics. The length measurements
were made possible because of Jeffry Kuhn’s generosity in sharing his filament snapping
and length measurement codes. This work was supported by NSF through the grants
EMT-0622254, NIRT-0608889, CCF-0832824 (The Molecular Programming Project), and
CCF-0855212.

Chapter 6

Toward de novo recapitulation of
cytoskeletal dynamics with
DNA nanotubes

Cytoskeletal Motor (Ann Erpino)
www.annerpino.com

“Ann envisioned a vine crawling across the desert by extending branches in one direction
and withering away in the other” as a macroscopic analog of a microtubule treadmilling in
a cellular environment." (adapted from Coagula Art Journal (85):22, April 2007)

Abstract
Cytoskeletal polymers, such as actin filaments and microtubules, harness energy from
nucleotide hydrolysis to exhibit asymmetric polymerization, such as treadmilling and dynamic instability. This study describes how a non-equilibrium polymer that can potentially
recapitulate cytoskeletal phenomena is created by rationally engineering existing equilibrium DNA nanotubes. We couple a DNA analog of a nucleotide hydrolysis reaction to
the polymerization of DNA nanotubes and embed a simple modification into the currently
passive DNA nanotube architecture. We inserted the EcoRI restriction sequence into one
sticky end pair on a DNA tile, so that docking the tile to a growing polymer will complete
the restriction site, shorten the sticky end length, and, thus, weaken the sticky end strength.
The recapitulation of non-equilibrium cytoskeletal phenomena with completely synthetic
structures may provide an ultimate test of our understanding of the design principles underlying cytoskeletal dynamics, in particular, the minimal architectural or mechanistic
requirements for treadmilling and dynamic instability.

7.1. Introduction
Living systems operate away from equilibrium. The cell, a unit of life, relies on active
cytoskeletal polymers, such as actin filaments and microtubules, to separate chromosomes
during mitosis [DM97], determine cell shape and polarity [LC04, LG08], probe the environment with filopodia [ML08], and direct cellular motility with lamellipodia [ML08].
These active polymers harness the energy from a reservoir of the fuel molecule nucleoside
triphosphate (NTP) by coupling their polymerization with an irreversible reaction, called
nucleotide hydrolysis. The energy derived from nucleotide hydrolysis powers active poly-

The version presented in this chapter is mostly for documentation purposes and is not a final manuscript.
This chapter will be revised and made more concise for submission as:
Rizal F. Hariadi and Erik Winfree,
Toward de novo recapitulation of cytoskeleton dynamics with DNA.
in preparation
The materials in the appendix D is taken from my class final project in APh 161: The physics of biological
structure and function. The class poster can be downloaded from the class web site
Author contributions
RFH and EW conceived and designed the experiments. RFH performed the experiments and
ran stochastic simulations. RFH and EW analyzed the data. RFH and EW revised the thesis
chapter.

100

mers, such as actin filaments and microtubules, with three properties not found in passive
polymers. First, nucleotide hydrolysis removes the constraint that the critical concentration
of free monomers near the two ends must be the same. Asymmetric critical concentration
permits the simultaneous elongation on one end of the polymer and shrinkage on the other
end that results in one class of cytoskeletal dynamics called treadmilling [HSD+ 92]. Second,
active polymers can stochastically switch between elongation and shrinking phases, thus
giving rise to cytoskeletal dynamics called dynamic instability [MK84b, MK84a]. Third,
nucleotide hydrolysis suppresses spontaneous nucleation [HSD+ 92]. As a result, polymerization occurs at concentrations far higher than the critical monomer concentration.
These non-equilibrium implications of nucleotide hydrolysis allow actin filaments and microtubules to respond quickly to signals and perform mechanical work to alter cell morphology during cell growth and motility without synthesizing new proteins or degrading
existing polymers.
To shed light on how these cytoskeletal polymers convert chemical energy into directional
motion, in this study we adopt an engineering approach in which a de novo artificial
cytoskeleton is constructed using DNA nanotubes. DNA nanotube polymerization and
an analog of nucleotide hydrolysis are coupled in order to investigate how the energy
consumption step can be converted to alter DNA nanotube polymerization. In particular,
we are interested in investigating minimal architectural and mechanistic features required
for treadmilling.
DNA nanotubes are promising candidate materials for the construction of an artificial
cytoskeleton [ENAF04, RENP+ 04] due to their programmability and their physical similarities to cytoskeletal polymers (Table 7.1). In structural DNA nanotechnology, short synthetic oligonucleotides can be designed to form a small DNA complex, called a DNA tile,
that can act as a monomer for the polymerization of larger crystalline structures using the
specificity of canonical Watson-Crick hybridization [See82, WLWS98, Rot06, RENP+ 04,
long one-dimensional crystalline structure can arise from the interactions between many
copies of a single DNA tile type. Fig. 6.1 shows a DNA tile that possesses four short
single-stranded regions, known as sticky ends, which serve as binding domains. The sticky
end arrangement, in addition to the constraint provided by the biophysical properties of
the single- and double-stranded-DNA, directs the interaction of DNA tiles to form tubular
DNA structures. Despite the advancement of structural DNA nanotechnology, embedding the suitable DNA implementation of cytoskeletal design principles, as described in

101

Chapter 7

YHS+ 08, SW07, LZWS10, ZBC+ 09]. DNA nanotubes present a simple example of how a

section 7.3, into DNA nanostructure has never been demonstrated.
The morphological, thermodynamic, and kinetic properties of DNA nanotubes have been
extensively studied. Single molecule assays of DNA nanotube dynamics have shown that
at 25−40 ◦ C, the forward reaction rate kon of both DNA nanotubes and microtubules are
comparable (see Chapter 6). The dissociation rate of DNA tiles from DNA nanotubes
can be fine-tuned to give desirable depolymerization rates by engineering the sticky end
length and sequence and by controlling external parameters, such as buffer conditions and
reaction temperatures.
In this study, we describe the strategy of incorporating a DNA analog of nucleotide
hydrolysis into DNA nanotube self-assembly. The scheme is characterized by gel assays,
visualized by single molecule movies, and theoretically probed by stochastic simulation.
The coupling of DNA nanotube polymerization with a DNA analog of nucleotide hydrolysis has the potential to recapitulate more complex cytoskeleton-based dynamics, such as
treadmilling and dynamic instability, where polymerization and depolymerization co-exist
at steady state without ever reaching equilibrium.

7.2. The biophysics of microtubules
We begin this section by introducing cytoskeleton composition, self-assembly, and their
roles in living cells. The physical similarities between α,β-tubulin and DNA tiles provide
the basis for our artificial cytoskeleton design. For clarity, we limit our discussion to
microtubules [H97]. A comparison of microtubule, DNA nanotube, and carbon nanotube
assembly is presented in Table 7.1.

7.2.1. The structure of microtubules
The study of microtubules structures and dynamics has a long history [H97]. Cellular
and developmental biologist purified microtubule-containing architectures in 1952 [MD52].
In 1960’s, scientists discovered the structural properties of the monomer [ST68]. The
structure contains two polypeptide chains (α- and β-tubulin) that act as the monomer
for microtubule. The α,β-tubulin dimer has a net ≈ 40 negative charges (at cellular
pH) and consists of ∼900 amino acid (∼100 kDa). Structurally, the α,β-tubulin dimer
is approximately an oblate spheroid 8 nm in one direction and 4 nm in the other two
dimensions.
In the study of microtubules dynamics, the first landmark study was the development
of a reliable protocol for the in vitro assembly of microtubules by Weisenberg [Wei72].

102

Microtubules
Structural properties
subunit
subunit size
subunit mass
net charges per subunit

α-β-tubulin
∼ 4 × 4 × 8 nm3
∼ 2 × 50 kDa
≈ 40 e−

DNA nanotubes
(described in chapter 6)

carbon nanotubes
[PF08]
carbon atom
0.263 nm3
12 Da

arc discharge,
laser ablation, CVPc
(harsh conditions)

persistence length

5.2×103 µm [GMNH93]

circumference

8-19 monomers
[CW91, WCJ90]

DNA tile
∼ 2 × 4 × 14 nm3
∼50 kDa
156 e−
∼20 µm
[RENP+ 04,
ORKF06]
5−14 DNA tiles
(Figs. 6.9 and C.5)

self-assembly under
physiological condition

self-assembly under
mild condition

0.50 µma −50 µmb
0.6−2.0 nm [ACP07]

Self-assembly
synthesis

association rate constant
driving force
subunit interaction
nucleating structures
fuel
energy consumption
Accessory molecules
molecular motor
accessory molecules
signaling

(Figs. 6.5 and 6.7)
5.4×106 M−1 sec−1 [HSD+ 92] (5.70±0.15)×105 M−1 sec−1
predominantly
entropy predominantly
enthalpy
drivene
drivend
non-covalent
non-covalent
γ-tubulin [ZWAM95]
DNA origamif
ssDNA
GTP
(partially demonstrated)
nicking reaction
GTP hydrolysis
(partially demonstrated)
kinesin, dynein
various MAPs
(Microtubule Accessory
Protein)s
protein network

enthalpy H driven
covalent
metal catalyst
N/A
N/A

DNA walkers
ssDNA activator
ssDNA deprotector
[ZHCW13]

N/A

DNA circuit
[ZHCW13]

N/A

has not been
demonstrated

N/A

Higher order system
self-organized architecture

self-organization of
microtubules
and motors [NSML97],
cellular architecture

Table 7.1.: A comparison of microtubules, DNA nanotubes, and carbon nanotubes.
The persistence length of acid etched carbon nanotubes [SKOS01].
The persistence length of acid pristine single walled nanotube [KDE+ 98].
Chemical Vapor Deposition
The microtubule polymerization is inhibited by low temperature T and high pressure p [Mar38]. Since the
Gibbs free energy is G = H − T S = E + pV − T S, the polymerization of microtubules is predominantly
driven by entropy S changes. This should not come as a surprise once the role of water molecules is
properly considered. In the presence of α,β-tubulin, water molecules are forced to order near hydrophobic
patches on the surface of monomers. Binding of two monomers hides these hydrophobic patches and
frees the water molecules into the solution.
Aside from spurious bindings at low temperature, the nucleation and elongation of DNA nanotubes are
inhibited by high temperature (Fig. C.6)
It is conceivable to adapt DNA origami structure to a nucleating structure for DNA nanotubes. Previous
studies have used DNA origami as a nucleating structures for algorithmic self-assembly of Sierpinski
triangle [FHP+ 08] and binary counter [BSRW09].

103

Chapter 7

The polymerization conditions was established at near-neutral pH, mild ionic strength,
and more importantly, mM concentration of GTP. Microtubules in polymers are held together by non-covalent interactions [Wei72]. Microtubules, actin, and other filaments of
the cytoskeleton are cooperative polymers. Cooperativity has an important consequence:
monomers added to the end of a growing filament interact with at least two neighbors,
whereas most of the collisions between monomers in solution result in contact with only
one monomer. As a result, there is a significant energy barrier associated with the nucleation of a new nanotube that is absent in the elongation of growing nanotubes.
An α,β-tubulin monomer binds one GTP [ST68], an energy-rich molecule analogous to
the fuel molecule for the molecular machine. The GTP hydrolysis reduces the length of
the fuel molecule and yields a shorter guanosine phosphate chain (GDP), and an inorganic
phosphate molecule Pi . Kinetics measurements of microtubule polymerization showed that
GTP is consumed during polymerization [Jac75]. Each tubulin interfaces catalyzes GTP
hydrolysis and releases the inorganic phosphate Pi to the environment. The release of the
inorganic phosphate increases the net entropy of the system. This local interaction rule
of coupling an energy consumption step and polymerization, gives rise to non-equilibrium
global dynamics in microtubules, such as treadmilling and dynamic instability.

7.2.2. GTP hydrolysis in microtubule polymerization gives rise to treadmilling
and dynamic instability
Microtubule polymerization still proceeds in the absence of GTP, such as in a polymerization reaction with a non-hydrolyzable GTP analog [HSD+ 92] and high concentration of
GDP. In the absence of GTP hydrolysis, the critical concentration [tubulin]crit would be
expected to be identical for both ends of the polymer, as the molecular interactions on both
ends are identical [Weg76]. Under steady state monomer concentrations, GTP hydrolysis
gives rise to asymmetic critical subunit concentrations between the two ends. In this state,
one end elongates while the other depolymerizes (treadmilling) [MW78, CB81, CLZ82].
The discovery of treadmilling was followed by the observation of another class of nonequilibrium microtubule phenomena, namely dynamic instability. In steady state, Mitchison and Kirschner [MK84b, MK84a] demonstrated that microtubules dynamics can exist
in two states, one elongates and one shrinks, with infrequent transition between these
states. Transitions from the polymerization state to the depolymerization state are named
catastrophes, and the opposite transitions are called rescues [WOP+ 88].

104

7.3. DNA nanotube implementation of the engineering principles
of cytoskeletal assembly
The simplified model of how microtubules work (adapted from Howard and Hyman [HH03])
is presented in Fig. 7.1(left). Other active cytoskeletal polymers, such as actin, ParM,
and FtsZ, employ the same principles for their non-equilibrium dynamics. Our proposed
artificial microtubule [Fig. 7.1(right)] is in essence, a DNA nanotechnology implementation
of the design principles in this model. This section presents the molecular features and
components of the proposed system and their justifications in the form of key experimental
observations in microtubules and DNA nanotubes. The component names of the biological
and the proposed artificial microtubules are summarized in Table 7.2.

Microtubules

DNA nanotube Analog of
Microtubules (NAoMi)

α,β-tubulin

incomplete-tile

GTP-tubulin

complete-tile

GDP-tubulin

cleaved-tile

GTP
GDP

fuel
waste

microtubules

DNA nanotube

Table 7.2.: Microtubules and DNA nanotube Analog of Microtubule (NAoMi) components.

Chapter 7

105

de novo engineering of artificial microtubules
with DNA nanotubes

microtubules

Howard & Hyman, Nature, 2003

short ssDNA
shorter ssDNA

(e)
incomplete DNA tile

(d)

(a)

DNA nanotube
complete
DNA tile

(c)

(b)

cleaved
DNA tile

Figure 7.1.: (Right) Inspired by the current understanding of non-equilibrium polymerization of cytoskeleton, we aim to engineer DNA nanotubes as an artificial microtubule. The coupling between DNA nanotube polymerization and an analog of nucleotide hydrolysis could potentially recapitulate the more complex non-equilibrium
cytoskeleton-based dynamics, such as treadmilling and dynamic instability. (Left)
Model of how microtubules work [HH03]. The red and brown α, β-tubulin denote GTP-tubulin and GDP-tubulin, respectively. (a) Docking of the α, β-tubulin
to the microtubule end. (b) Residues from the incoming α, β-tubulin complete the
reactive site for triggering the hydrolysis of the GTP bound to the lattice-attached
α, β-tubulin (Section. 7.3). (c) In microtubules, GTP-tubulin is more stable than
GDP-tubulin; consequently, GDP-tubulin dissociates faster than GTP-tubulin. (d)
In the free monomer state, GTP or GDP dissociates slowly from the tubulin. (e)
Because the concentration of GTP in living cells is much higher than the concentration of GDP, the newly displaced GTP or GDP will be effectively replaced by GTP
(Section 7.3).

106

Engineering principle 1:
Cytoskeletal polymers are long, rigid polymers formed from noncovalently-bound
monomers
In the cystoskeleton, noncovalently bound monomers give rise to long, rigid polymers.
DNA nanotubes satisfy this criteria. Structurally, DNA nanotubes in this work are cooperative polymers that are more than one monomer wide. This cooperativity has important
consequences. First, the tubular organization of DNA tiles along the longitudinal axis of a
DNA nanotube results in a long persistence length, ξptube ∼ 20 µm [RENP+ 04, ORKF06],
which is comparable to the persistence length of actin, ξpactin = 17.7 µm [GMNH93]. Second, in our lab DNA nanotubes can be prepared to have a relatively mean length on the
order of 5 µm. Spontaneous DNA nanotube polymerization is hampered by the unfavorable
nucleation of DNA tile oligomers.
Engineering principle 2:
The addition of fuel molecules to free monomers enables polymerization.

tubulin −→

(no microtubules)

polymerization

GTP + tubulin −→ GTP-tubulin −−−−−−−−−→

microtubules

The DNA tile as a monomer for DNA nanotubes
DNA strands can be designed to form a DNA complex, called a DNA tile, that acts as
a monomer for different classes of DNA nanotubes [See82, WLWS98, Rot06, RENP+ 04,
otube designs, we first needed to choose which DNA nanotube construct to use. The
subunit of microtubule polymerization comprises two components, namely (1) the fuel
molecule, GTP, and (2) the monomer, α,β-tubulin. Therefore, to directly implement the
design principles of dynamic microtubule assembly, the monomer must consist of at least
two molecules.
In our scheme, we chose the double-crossover tile construct [RENP+ 04, WLWS98], because it is the simplest and most characterized DNA tile system that is composed of more

107

Chapter 7

YHS+ 08, SW07, LZWS10, ZBC+ 09]. Being presented with many constructs of DNA nan-

than one DNA strand. Typical double-crossover molecules have four to five strands. One
of the strands will be designated as the fuel strand, analogous to GTP, and the rest of the
strands collectively act as an incomplete tile, analogous to α,β-tubulin. In our construct,
a DNA tile that carries fuel is called a complete tile (Table 7.2).
ssDNA as a fuel molecule
In microtubule polymerization, α,β-tubulins only polymerize in the presence of GTP. Similarly, we have shown that DNA tiles with either covered or missing sticky ends do not form
DNA nanotubes [ZHCW13]. These two observations suggest that the sticky end sequence
should be part of the fuel molecule.
Engineering principle 3:
Following polymerization, nucleotide hydrolysis destablizes the polymers.

polymerization

nonhydrolyzable +tubulin → nonhydrolyzable −−−−−−−−−→
GTP-analog
GTP-analog
tubulin

GDP

+tubulin →

GDP-tubulin

polymerization

−−−−−−−−−→

stable microtubule

unstable microtubule

DNA analog of nucleotide hydrolysis decreases the sticky end strength
A second crucial observation is that GDP-tubulin can only nucleate and elongate into
stable microtubules at very high α,β-tubulin monomer concentrations. On the contrary,
when GTP is substituted with nonhydrolyzable GTP, a low concentration of α,β-tubulin
is sufficient for stable microtubule polymerization [HSD+ 92]. The GTP microtubule depolymerizes at a negligible rate, an order of magnitude slower than the rate of GDP microtubule depolymerization. The difference in binding strength between GDP-tubulin and
GTP-tubulin indicates that the free energy of association for GDP-tubulin is weaker than
that of GTP-tubulin. In DNA thermodynamics, weaker binding is obtained with shorter
sticky ends or, to some extent, lower guanine/cytosine (G/C) content. Therefore, the
waste molecule, which is the DNA analog of GDP, is identical to the fuel molecule, but

108

with shorter sequence length and, consequently, weaker binding. In our design, a DNA
monomer that binds to waste molecule is called a cleaved tile.
To convert a complete tile to a cleaved tile, we employ the EcoRI restriction enzyme
to shorten the sticky end by n base pairs. In this chapter, n was chosen to be 2. We
developed a restriction site situation that tricks EcoRI into nicking the sticky end of a
DNA tile (Fig. 7.2) only after it has been incorporated into a DNA nanotube. One of the
two cutting positions of an EcoRI recognition site is a pre-existing nick between different
strands of neighboring DNA tiles. EcoRI will only cut the opposing cutting position of the
pre-existing nick. The product is a nick in the sticky end area, instead of two nicks that
occur in the conventional EcoRI-DNA reaction.
On the surface, our choice of using a restriction enzyme to create a nick on the sticky end
strand may appear problematic. Why not use a simpler nicking enzyme? Although nicking
enzyme might be simpler to design, nicking enzymes also have many intrinsic disadvantages: (1) they are expensive and (2) there is no published atomic structure, nor are there
extensive kinetic measurements. For EcoRI, many theoretical studies and experimental
work [WJM99,KEW+ 04,HO10,MFZ+ 97,KGL+ 90] have modeled and characterized EcoRI
activity, which later proved to be invaluable in our work. The crystal structure of EcoRI
has also been solved [KGL+ 90]. The atomic structure of EcoRI and the putative DNA tile
and DNA nanotube structures guided the placement of the EcoRI restriction sequences
along the DNA nanotubes.

Chapter 7

109

Free monomer does not have complete restriction site ! no nicking reaction

incomplete restriction site

The docking of a monomer onto a filament completes the restriction site and triggers stochastic nicking reaction

Figure 7.2.: A reaction between EcoRI and a DNA nanotube with strategically positioned restriction sites decreases the sticky end strength by two nearest-neighbor
terms and one nicked stacking interaction. (Top) A monomer by itself only contains a
partial recognition site for EcoRI. (Bottom) Binding of two identical DNA tiles, either
as part of a multimer or a DNA nanotube, completes the restriction site and triggers
the nicking reaction. In this construct, EcoRI can only make a nick, because the other
cutting site was designed as a pre-existing nick. The 2 nt fragment will dissociate from
the complex because of its weak binding and the configurational entropy gain from
being unbound from the complex. Since the calculated half-life of a DNA tile dimer
is shorter than the half-life of a DNA tile inside a DNA nanotube, within the physical
parameter range where DNA dimers are unstable, the nicking reaction is expected to
affect only the sticky ends inside the DNA nanotubes.

110

Engineering principle 4:
Nucleotide hydrolysis only proceeds in the polymer

no GTP hydrolysis

in free monomer:

GTP-tubulin

−−−−−−−−−−−→

in polymer:

GTP-tubulin

−−−−−−−−−→

GTP hydrolysis

GTP-tubulin

GDP-tubulin

Implementation of engineering principle 4: The recognition site is located at the
sticky end region.

111

Chapter 7

The third crucial observation is that in microtubule polymerization, GTP hydrolysis is
coupled with polymerization. Hydrolysis does not proceed in a free monomer, because
the residues that are responsible for the hydrolysis are split between opposite ends of
α,β-tubulin. Although the β-subunit pocket can bind to GTP, it lacks crucial residues
required for hydrolysis. These residues are donated by the α-subunit of its α,β-tubulin
neighbor, and in this way hydrolysis is triggered. Inspired by the tubulin structure, the
coupling of the EcoRI reaction with DNA nanotube polymerization can be achieved in
a carefully designed DNA monomer that has the restriction site at one of its sticky end
pairs as shown in Fig. 7.2. Analogous to the separation of the hydrolysis residues in the α
and β subunits of microtubules, each DNA tile has two halves of the restriction site at the
opposite ends of the tile, e.g., at the northeast and southwest positions. The restriction site
is only complete when one half of the restriction site meets with another half donated by a
different DNA tile, either in the context of a DNA tile oligomer or within a DNA nanotube.
In microtubules, the nucleotide hydrolysis destabilizes GDP-tubulin within a microtubule. Since the stability of each DNA tile monomer is dictated by the sum of sticky
end strength, one way to destabilize a DNA tile is by altering its sticky end. Therefore,
positioning the restriction site at the sticky end is justified.

Engineering principle 5:
Nucleotide exchange, or fuel recycling, maintains high concentrations of
fuel-monomers, well above the critical concentration for the polymers

GTP
GDP release

recycling

GDP-tubulin −−−−
−−−→ tubulin −−−−−→

GTP-tubulin

GDP
The destabilization of α,β-tubulin monomers in microtubules plays an important role in microtubule function, such as mechanical force generation during the shrinking phase. However, nucleotide hydrolysis also poses a problem for microtubules, because without waste
management, the fast polymerization rate can quickly deplete the pool of GTP-tubulin
monomers. The problem is solved by an elegant recycling trick. In the monomer state,
GTP and GDP can dissociate from α,β-tubulin. Since the physiological concentration
of GTP is much higher than GDP, when a GDP molecule dissociates from α,β-tubulin,
it is almost certain that the GDP molecule will be replaced by a GTP molecule. An
implementation of this recycling feature is shown in the right panel of Fig. 7.1. Analogous
to the recycling trick employed by microtubules, the fuel concentration in our test tube is
always significantly higher than the concentration of waste molecules. A recycling process
will effectively recharge any free cleaved-tile complex into a free complete-tile complex.
One last crucial piece of information about microtubule structure is that the recycling
only affects the free monomer. In microtubule polymers, the position of the GTP or GDP
molecule is buried, which in addition to the interaction between α,β-tubulin and GTP
or GDP, limits the disassociation of GTP or or GDP, limits the dissociation of GTP or
GDP. It is very difficult to bury any molecule in a DNA nanotube because of the relatively
simple molecular structure of the DNA double helix. However, in DNA nanotubes, the
waste or fuel strand is being held by an additional 4−6 bp sticky end domain. On the
contrary, the sticky end of a free DNA tile is, by default, free. This additional 4−6 bp
domain results in decreased dissociation by a factor of 16,000−2.1×106 relative to a free
DNA tile. Because the fuel or waste molecule remains bound to two monomers inside
DNA nanotubes, the nucleotide hydrolysis-induced modification to DNA nanotubes will

112

persist over a significantly long period of time.
Initially, we bypassed this recycling pathway by running the polymerization assay at a
very slow tile consumption rate with a small number of nuclei in a sea of free monomers. The
spontaneous nucleation of DNA nanotubes was suppressed by operating at a temperature
and a monomer concentration where nanotube nucleation is very rare. Typically, we started
the polymerization assay by introducing less than 10 pM of DNA nanotube nuclei. In
our measurement of the passive DNA nanotube polymerization, the fastest forward rate
(kon [tile] − kof f ) is no faster than 10 layers/min on each nanotube end. The highest initial
tile concentration in the polymerization assay experiments was 600 nM. Based on these
numbers, we expect the free monomer concentration to drop by 10 nM after no more
than 125 minutes. Hence, for the parameter range in the single molecule polymerization
assay, the recycling pathway is not necessary to keep the monomer concentration roughly
constant over the course of 60 minutes, which is the typical duration of our polymerization
assay in chapter 6. In this case, the consumed monomers are either incorporated into
DNA nanotubes or cleaved as tiles.

7.4. Results
7.4.1. The enzymatic activity of EcoRI on dsDNA with nicks
To evaluate the enzymatic activity of EcoRI on our unconventional recognition site structure, we first constructed three different dsDNA targets with different nick positions as
shown in Fig. 7.3. The first dsDNA target, named dsDNA-1, was a negative control and
did not have nicks near the recognition site. In the second construct (middle), one of the
cutting sites started with a nick. The position of the pre-existing nick in our sample was
similar to the pre-existing nick in the proposed molecule (Fig. 7.2). In the last construct,
EcoRI made two cuts with one of the cuts being 2 nt away from the pre-existing nick.
We ran the restriction enzyme experiment at room temperature and under our lab’s
EDTA (Ethylenediaminetetraacetic acid)] with 12.5 mM Mg-acetate. The test tube contained 10% v/v EcoRI, purchased from Roche (Cat. No. 703 737), which is equivalent to
1 U/µL. The reaction progress was monitored by a denaturing PAGE gel assay at 65 ◦ C gel
running temperature and driven by 100 V and ∼20 mA current. Surprisingly, increasing
the reaction temperature to 37 ◦ C did not accelerate the reaction. Previously, Muir et
al. has shown that the activity of wild type EcoRI is robust to temperature change in

113

Chapter 7

standard DNA self-assembly buffer consisting 1× TAE [40 mM Tris-acetate and 1 mM

reactant

product
product
product
dsDNA-1

reactant
product
product

dsDNA-2

reactant

product
product

dsDNA-3

Figure 7.3.: A pre-existing nick does not reduce the activity of EcoRI. We tested the
reaction for 2 µM dsDNA constructs with 0 nicks (top, dsDNA-1), 1 nick (middle,
dsDNA-2), and 1 nick that is located 2 base pairs from the cutting site (bottom,
dsDNA-3). The concentration of EcoRI was 10% v/v and the reaction was performed
in standard DNA self-assembly buffer consisting of 1×TAE (40 mM Tris-acetate and
1 mM EDTA [Ethylenediaminetetraacetic acid), pH 8.3] with 12.5 mM Mg-acetate at
37 ◦ C. The quantitative analysis of the gels are presented in Fig. 7.5 (top).
114

target
dsDNA-1
dsDNA-2
dsDNA-3

k [minutes−1 ]
0.085 ± 0.004
0.184 ± 0.014
0.490 ± 0.037

Table 7.3.: The inferred nicking reaction rates between 1 U/µL of EcoRI and 2 µM of
dsDNA-1, -2, and -3.
the range 34-42 ◦ C [MFZ+ 97]. Similarly, running the experiment in the manufacturer’s
enzyme buffer for EcoRI did not yield a significant rate difference.
Even more surprising, we discovered that the reactions with cleaved substrates (dsDNA2 and dsDNA-3) proceeded faster than the control substrate (dsDNA-1). A quantitative
analysis of the bands in Fig. 7.3 is shown in the top panel of Fig. 7.5 and summarized in
Table 7.3. The normalized intensity χP (t) was subjected to an exponential fit
χP (t) = χP∞ (1 − e−kt ),

(7.1)

where χP∞ and k are fitting parameters that represent the final fraction of completion
and first order reaction constant, respectively. The fitting parameter χP∞ will account for
any inaccuracy in the intensity measurement and any incompletion due to errors in DNA
synthesis or other unknown factors.
The faster kinetics of reactions with cleaved substrates should not be unexpected if one
properly considers the atomic coordinates of DNA when it interacts with EcoRI before the
hydrolysis of phosphodiester bonds. Kim et al. [KGL+ 90] have shown that in the crystal

7.4.2. Nicking reaction of DNA nanotubes
With the successfull demonstration of EcoRI activity near a nick, we tested the nicking
scheme on three different variants of DNA nanotubes (Fig. 7.4). The nicking rate within

115

Chapter 7

structures of the EcoRI recognition site complex, the enzyme bends dsDNA to catalyze the
hydrolysis of both dsDNA backbones. DNA bending results in the unstacking of the bases,
widening of the minor groove, and compression of the major groove. This results in the
phosphodiester linkage being broken closer to the active site of the enzyme, where it can be
cleaved. Local deformation of a cleaved dsDNA is expected to incur a lower energy penalty
than bending a pristine dsDNA. Lower energy cost implies smaller activation energy and
faster reaction rate. The argument presented here exemplifies the power of the atomic
structure of EcoRI in understanding our design.

sideways

NAoMi-A

outside

NAoMi-B

inside

NAoMi-C

Figure 7.4.: Nicking reaction of DNA nanotubes is sensitive to the orientation of EcoRI
at the restriction site. Based on the 3D models of DNA nanotube and EcoRI-dsDNA
complex [KGL+ 90], we varied the orientation of EcoRI at the restriction site along the
DNA nanotube such that the EcoRI is located between DNA tiles (top, NAoMi-A),
outside the DNA nanotube (middle, NAoMi-B), and inside the DNA nanotube cavity
(bottom, NAoMi-C). The quantitative analysis of the gels are presented in Fig. 7.5.
As expected, the fastest nicking reaction is measured for DNA nanotubes with outside
orientation. For scale, the diameter of the DNA helix (colored circles) is 2 nm.
116

DNA nanotubes was expected to be slower than with dsDNA for two main reasons, namely
(1) low accessibility of the restriction site, and (2) obstruction of one-dimensional diffusion [HO10] of EcoRI in the form of periodic crossover points along DNA nanotube surface.
First, a DNA nanotube is a collection of parallel dsDNA with periodic double-crossover
points at relatively close proximity (1.5 and 2.5 full DNA turns in the DNA tile used
in this experiment). In Appendix D, the DNA lattice was modeled as a collection of
isotropic, negatively charged beams that can be deformed with an elastic energy penalty
proportional to the persistence length of DNA, ξp . The energy minimization of the interplay between the repulsive coulombic interaction between negative charges and the elastic
energy penalty of deforming DNA helices gives rise to spacing between DNA tiles. The
spacing has been consistently observed in atomic force microscopy (AFM) [HW04, Rot06],
electron microscopy [DDL+ 09, DDS09], and cryo-electron microscopy [ADN+ 09].
In our design, we exploited the spacing to provide an access for fuel strand nicking by
EcoRI. The recognition site was placed on the flexible arm of each DNA tile, at the most
accessible region in the DNA nanotube. To further ameliorate potential accessibility and
steric hindrance problems, we resorted to a new DNA tile motif that has longer flexible
arms (Fig. 7.2) than any previously published DNA tile design. The flexible arm length of
our DNA nanotube was 26 bp ∼9 nm. For comparison, Rothemund et al. designed their
DNA nanotube to have 21 bp ∼7 nm flexible arm length.
Second, how does EcoRI find its target? The current model says that the searching process involves two diffusion steps [HO10, RS10]. Step one is the random three-dimensional
diffusion of EcoRI until it finds and weakly binds to a DNA target, regardless of sequence.
Step two is either one-dimensional diffusion or hopping along the DNA to locate the restriction sequence. This model has been supported by experiments with target dsDNA of
different lengths. The kinetics of the reaction with a longer dsDNA target is faster than
shorter dsDNA [WJM99], possibly because long dsDNA speeds up the three-dimensional
dimensional diffusion to be periodically suppressed as EcoRI meets the (periodic) crossover
points. As a result, we expect a significant decrease in the reaction rate. It is conceivable
that the one-dimensional diffusion of EcoRI along DNA nanotubes will involve frequent
hopping. In this case, the long DNA nanotube can potentially act as an antenna to capture EcoRI, which is analogous to long dsDNA accelerating three-dimensional diffusion of
EcoRI and increase the effective reaction rate.
Aided by the putative structure of DNA nanotubes and atomic structures of EcoRI

117

Chapter 7

diffusion step of the reaction. In the DNA nanotube structure, we expect the facilitated one-

and the dsDNA complex, we designed three DNA nanotubes that interact differently with
EcoRI. We assumed that each tile design does not produce racemic DNA nanotubes, i.e.,
every DNA nanotube has the same inside and outside surfaces. Fig. 7.4 shows a schematic
of the expected interaction between EcoRI and three variants of DNA nanotubes. The
diagram represents a cross section of an 8-monomer wide DNA nanotube perpendicular to
the longitudinal axis. The pairs of circles are cross sections of dsDNA along the DNA nanotube, and identical color indicates that the DNA helix pair belongs to the same DNA tile.
In the three panels, the atomic structure of EcoRI [KGL+ 90, FGM+ 84] was docked to the
cross section of the DNA nanotube. The relative scale between EcoRI, dsDNA helix, and
tile spacing is based on the three-dimensional structures and the calculation presented in
Appendix D. The arrow on top of the tile schematics shows where the designed nicking
position is located, based on the EcoRI restriction sequence.
The orientations of EcoRI at the restriction site of the three DNA nanotube variants were
determined from the orientation of the major and minor grooves along the DNA nanotubes.
The EcoRI orientation can be tuned by sliding the position of the restriction site along the
flexible arm of the tile. For NAoMi-A, EcoRI binds the recognition site at a sideways orientation. Due to the steric hindrance and limited space between DNA helices, the sideways
orientation is not optimal for nicking reactions. This sub-optimal design was a result of an
unintentional mistake when looking at EcoRI crystal structure. In the end, this mistake
turned into a valuable data point. The middle and bottom panels are the schematics and
gel data of two different DNA nanotubes that have an opposite orientation of the major
and minor grooves of the recognition site. Since we have not extensively characterized the
inside and outside surfaces of the DNA nanotubes, we designated a DNA nanotube with
faster kinetics (middle, NAoMi-B) and slower kinetics (bottom, NAoMi-C) as the one that
EcoRI attacks from outside and inside, respectively. In the inside orientation, EcoRI is
more likely to diffuse inside DNA nanotubes or between DNA helices before attacking the
recognition site with inside orientation.
Similar to the nicking assay of Fig. 1.3, the reaction progress was monitored with a timelapse denaturing 8% PAGE gel assay (Fig. 7.4). For a nicking gel assay of a tile composed
of different strands of unique lengths, such as NAoMi-A, a complete nicking reaction is
demonstrated by the total disappearance of the band corresponding to the yellow fuel
strand of length n and the emergence of another band of length n − 2 with the final total
intensity (n − 2)/n× the initial band intensity of the fuel strand. The intensity ratio is not
unity, because the gel intensity depends on the strand length, and the product is shorter
than the starting molecule by 2 nuclei.

118

Contrary to NAoMi-A, the nanotubes in the middle (NAoMi-B) and bottom (NAoMi-C)
panels, are symmetric and consist of two pairs of strands with equal lengths. The blue
and gray strands have the same length; the yellow strand was initially as long as the green
strand. For a nicking gel assay of a symmetric tile, a complete reaction is shown by the
decrease of band intensity by a factor of 2, since the other strand of equal length is not cut
by the enzyme. The product will appear as a new band at (n − 2)/2n× the initial band
intensity of the fuel strand. In Fig. 7.5(middle), the nicking reaction of NAoMi-B nanotubes
proceeded to completion. For unknown reasons, the reaction between NAoMi-C and EcoRI
did not go to completion. One plausible explanation is that the incompletion was caused
by nanotube aggregations and/or high concentrations of unpolymerized DNA tiles that
are created by poor DNA nanotube synthesis. If these aggregations are stable, accessing
the tube and scanning the DNA helices for the restriction site will be difficult and slow.
Assuming that our designation of inside orientation of EcoRI is correct, the incompletion
could also be caused by the small orifice size of a fraction of the DNA nanotubes in the test
tube. Based on the AFM images, we observed diameter distribution of NAoMi-B nanotubes
in the range of 5−11 tile widths (Fig. 6.9), which corresponds to DNA nanotube orifice
size distribution of 6−16 nm. If we modeled EcoRI as a sphere with a 5 nm diameter, the
opening of thin DNA nanotubes could be too small for an effective nicking reaction from
inside the nanotubes.
For all gels, the intensities of the highlighted bands were quantified and plotted in
Fig. 7.5. The normalized intensity ratio at different time points were subjected to the
nonlinear fitting in Eq. 7.1. The inferred rate constant for nicking reactions is summarized
in Table 7.4. NAoMi-B was found to be the DNA nanotube variant that reacted fastest
with EcoRI. The reaction kinetics of NAoMi-B and EcoRI were nicely described by the
fitting function of Eq. 7.1 in Fig. 7.5. The reaction between NAoMi-A and EcoRI has a
more complex kinetics and does not follow the first-order kinetics of Eq. 7.1. The reaction

These gels show that the DNA nanotube nicking depends on how EcoRI approaches
the nicking site and the orientation of EcoRI at the restriction site. Further investigation
is needed to provide convincing evidence of the correct designation of inside and outside
nanotube variants. Regardless of how correct our orientation assignment is, we now have
a DNA nanotube construct that works well for further experiments in the artificial microtubule project.

119

Chapter 7

between NAoMi-C and EcoRI did not reach 60% completion. Nonetheless, we fitted the
first 30 minutes of data of NAoMi-C to illustrate its poor performance.

Fraction of Product, cp

ÊÊÊ

0.8

0.6 Ê
0.4

Ê dsDNA-1
Ê dsDNA-2
Ê dsDNA-3

0.2 Ê
0.

120

Fraction of Product, cp

Time, t @minD

0.8

0.6

0.4 Ê
ÊÊ
ÊÊ
0.2 Ê

ÊÊ Ê
ÊÊÊ

Ê NAAoMi-A
Ê NAAoMi-B
Ê NAAoMi-C

120

Time, t @minD

Figure 7.5.: Nicking reaction between EcoRI and 200 nmDNA nanotube with outside
orientation (bottom, NAoMi-B, blue line) is relatively as fast as the nicking reaction
of 2 µM dsDNA without the nick (top, dsDNA-1, blue line). The top plot is the quantitative analysis of the interaction between EcoRI and the three different constructs
of double-stranded DNA shown in Fig. 7.3. The bottom plot shows the kinetics of
the nicking reaction in the context of DNA nanotubes with the three different EcoRI
orientations, as shown in Fig. 7.4.

DNA nanotube
NAoMi-A
NAoMi-B
NAoMi-C

k [minutes−1 ]
N/A
0.104 ± 0.006
0.095 ± 0.012

Table 7.4.: Nicking reaction rates of 1 U/µL of EcoRI and 0.2 µM of NAoMi-A, -B,
and -C.

120

7.4.3. Single molecule movie of DNA nanotube polymerization with nicking
reaction
Finally, we are in a position to experimentally evaluate the implications of the nicking
reaction on the stability of DNA nanotubes in real time. The effect of the nicking reaction
on DNA nanotube dynamics was assayed by using single molecule TIRF microscopy. Time
lapse microscopy enables measurement of nanotube lengths in solution at high data rates.
Because of these features, light microscopy has been widely used to study the dynamics of
biopolymers, such as microtubules and actin filaments.
Fig. 7.6 shows kymographs of DNA nanotube polymerization at zero tile concentration
with and without 5% v/v EcoRI. The imaging buffer contained 0.3% (w/v) methylcellulose
(Sigma, 4,000 cP, M0512−100G), which was added to the buffer to confine the nanotubes in
the two-dimensional space as described in the polymerization assay section. In this crowded
environment, the entropy of the system is maximized when long tubular structures are
near a two-dimensional surface, such as the microscope slide surface where the evanescence
excitation wave is concentrated, and the focal plane of the imaging optics is positioned. It is
important to note that crowding agent-induced confinement is a standard imaging trick in
microtubule [BLS+ 07], actin [KP05], ParM [GCM04], and other cytoskeleton studies. The
use of crowding agents for confining polymers close to the coverslip surface is yet another
example of the lessons that we learn from the more evolved single molecule imaging of
cytoskeletal dynamics.
The polymerization assay with EcoRI work is in the early stages; we have only constructed 1 kymograph [Fig. 7.6 (top right)] of the longest initial DNA nanotube length
in the data set. Kymographs of long DNA nanotubes tend to be more reliable because of
their large number of fiduciary data points for bona fide alignment between the straightened
DNA nanotube images. At 35.2 ◦ C, the depolymerization rates with the nicking reaction
were measured to be 9.8 ± 0.7 layer/min and 10.8 ± 0.4 layer/min for right and left nan-

As a control experiment, a kymograph produced from a polymerization assay without
EcoRI is presented in the left column of Fig. 7.6. The control kymograph is identical to the
data shown in Fig. 6.3. Linear fittings to the position of left and right ends determined the
polymerization rates to be 8.1 ± 0.8 layer/min and 6.7 ±0.4 layer/min, respectively. The
control experiment was not ideal because it was performed at 38.3 ◦ C, which was higher
than the 35.2 ◦ C for the EcoRI experiment. Based on the kinetic tile assembly model,

121

Chapter 7

otube ends, respectively. Within our measurement uncertainty, the depolymerization of
left and right nanotube ends appeared to be symmetric.

the depolymerization rate at lower temperature is calculated to be slower. Even with the
“penalized” control shown in Fig. 7.6, the depolymerization rate of EcoRI was still faster
than the depolymerization rate in the presented reaction without the nicking reaction. The
increased depolymerization in the presence of EcoRI is a clear indication that our scheme
works as designed.
A proper control of the EcoRI kymograph is the inferred depolymerization rate kof f at
35.2 ◦ C (see Table 6.2). In the previous chapter, the linear fitting of measured polymerization rates of 35 nanotubes at 0−300 nm tile concentration gives kof f at 35.2 ◦ C to be
1.01±0.31 layer/min and the global association constant kon = 6 ×105 /M/sec. The free
energy for dissociation of a tile bound by two full-length sticky end bonds at standard
concentration uo = 1 M was calculated by the equation
∆G◦f ull = −RT ln

koff × u0
kon

= 17.4 RT.

(7.2)

To calculate the expected off rate for tiles with cleaved sticky ends, recall that in the kTAM
i si ∆Gse ) − αRT, where si give the strengths of
the bonds attaching the tile to the nanotube. In this case, i si = 2, so ∆G◦se = 10.2 RT is
the strength of a single full bond. A cleaved bond is 23 that of a full bond, ignoring stacking

the free energy for tile dissociation is (

at the nicks and dangle energies, so we predict that for tiles attaching by one full bond and
one cleaved bond, ∆G◦cleaved = ( 23 + 1)∆G◦se − αRT = 14.0 RT and kof f = 29.9 layers/min.
From experiment, the depolymerization rates were measured to be 9.8 ± 0.7 and 10.8 ± 0.4
layer/min depolymerization rates for the left and right ends of the DNA nanotube in Fig. 7.6
(right). The calculated EcoRI enhanced shrinking rate at zero tile concentration and at
35.2 ◦ C is within a factor of 3 from the measured depolymerization rates. The faster slower
depolymerization rate can easily be explained by the uncertainties in the dangle energies
at the nicks in our calculation.

7.5. Discussion
The nicking reaction destabilizes interaction between monomer subunits in cleaved DNA nanotubes. Due to the weakened binding, the depolymerization rate kof f of the cleaved
DNA nanotube is faster than the control DNA nanotubes. The thermodynamics and
kinetics of the “instability” is straightforward. In the absence of enzyme, the nanotubes
are at zero free tile concentration, which is close to be the critical concentration of control

122

Reaction
Condition

no EcoRI HcontrolL

with EcoRI

0 nM tile , 38.3 ºC
1µ TAEêMg⁺⁺ 0.3% wêv methyl-cellulose

0 nM tile , 35.2 ºC
1µ TAEêMg⁺⁺ 0.3% wêv methyl-cellulose
0.5 UêµL H5% vêvL EcoRI

Kymograph

Frame Ò

Time @minutesD

Frame Ò

L @µmD

100 200 300 0

100 200 300
Ú Ú
Ú ÚÚ Ú
Ú ÚÚÚ
ÚÚ Ú Ú ÚÚ
ÚÚÚÚÚ ÚÚ Ú Ú Ú
Ú ÚÚ ÚÚ ÚÚ
Ú Ú
Ú ÚÚÚÚÚÚÚ ÚÚÚÚÚ Ú
ÚÚ Ú Ú
Ú Ú Ú
Ú Ú

Ê ÊÊ Ê
Ê Ê ÊÊ ÊÊÊÊ
Ê ÊÊÊÊÊ

100 200 300

Ê ÊÊÊ
Ê Ê Ê ÊÊÊÊÊÊ ÊÊÊÊ Ê
ÊÊÊ ÊÊ ÊÊÊ
Ê Ê ÊÊÊ
Ê Ê ÊÊ Ê Ê
Ê Ê
ÊÊ Ê

100 200 300 0

ÚÚ Ú Ú Ú Ú
ÚÚ ÚÚÚÚÚÚ ÚÚÚÚ
Ú Ú Ú
ÚÚÚÚÚÚÚÚÚÚ ÚÚ
Ú ÚÚ ÚÚÚ ÚÚ Ú Ú Ú
Ú ÚÚÚ Ú ÚÚÚÚÚÚÚ

Rate
Measurement

ÊÊ ÊÊ
Ê Ê Ê Ê Ê Ê ÊÊ
ÊÊÊ ÊÊÊÊÊÊÊÊÊ ÊÊÊ Ê ÊÊ Ê Ê Ê Ê
ÊÊ
Ê ÊÊÊ Ê ÊÊÊÊÊ ÊÊÊ Ê ÊÊÊ ÊÊ
ÊÊ ÊÊ Ê Ê Ê

L @monomerD

Time @minutesD

L @monomerD

L @µmD

123

Chapter 7

Figure 7.6.: Single molecule assay shows that nicking reaction by EcoRI destabilizes
DNA nanotubes, as indicated by the faster dissociation rate kof f in the reaction EcoRI
(right column) compared to the control experiment (left column). In a kymograph
of a DNA nanotube at zero tile concentration, the slopes of the nanotube end coordinates over time are a measure of depolymerization rate. The linear fitting (dashed
line) of the nanotube end in the experiment with EcoRI (bottom right) determines the
dissociation rates for the right and left ends to be 9.8 ± 0.7 layer/min and 10.8 ± 0.4
layer/min. The dissociation rates of the control experiment (bottom left) were measured to be 8.1 ± 0.8 layer/min and 6.7 ± 0.4 layer/min. Note that the control data
was obtained at a higher temperature.

DNA nanotube [tile]control
. After the addition of enzyme, the nicking reaction shortens one
crit
of the sticky ends, and the chemical energy is used to destabilize the nanotube, analogous
to how GTP hydrolysis destabilizes microtubules [CRS94]. The nicking reaction brings
the critical concentration up to [tile]cleaved
. In the EcoRI experiment in Fig. 7.6 and the
crit
control (Table 6.3), the calculated [tile]control
and [tile]cleaved
are 15 nM and 306 nM, recrit
crit
spectively. In the beginning of the reaction, although undetected, the DNA nanotubes are
stabilized by a “full tile” cap and depolymerized at a very slow rate. Eventually, the “full
tile” cap is lost and the DNA nanotube shrinks to bring the free monomer concentration
up to [tile]cleaved
. Since the total tile concentration in the nanotubes was less than 7 nM
crit
and much more dilute than [tile]cleaved
, the depolymerization will persist until all of the
crit

Polymerization rate
@layerêminD

nanotubes are completely depolymerized.
20

-20

-40

-60

-80
10

1000

Tile concentration, @tileD
@nMD

Figure 7.7.: Simulation of DNA nanotube polymerization with nicking rate at different
tile concentrations. The lines are colored by the type of nanotube ends in Fig. 7.1
(red − right end, blue − left end). Surprisingly, in our simulation, DNA nanotubes
exhibit asymmetric polymerization when the polymerization speed, in the absence of
the nicking reaction, is near the rate of the nicking reaction.
While the kinetics of polymerization with nicking at zero tile concentration is straight
forward, the kinetics of the reaction at non-zero free tile concentration is not trivial. To
provide an insight as to how the nicking reaction might alter DNA polymerization at
different tile concentrations, we modified our MATLAB simulation (chapter 6) for the
DNA nanotube polymerization assay by adding the nicking reaction at rate knicking . In

general, the bond strength of a DNA tile is computed as

si ∆Gse

124

− αRT , where

∆Gse is the free energy of one full sticky end and si is the strength of sticky end i.
For the following discussions, we chose ∆Gse to be 7.75 RT and we chose α = 0 for
convenience. Therefore, the bond strength of a DNA tile with two full sticky end bindings
∆Gf ull is 2×∆Gse = 15.5 RT. (Experimentally-inferred values for ∆Gf ull and ∆Gcleaved
can be found at the end of section 7.4. The energies in this simulation are lower than
the calculated energies based on experiments in chapter 6 and Fig. 7.6.) The docking of
an incoming monomer to 7-tile-diameter DNA nanotube triggers the nicking reaction with
site
reaction rate knicking . For the purpose of this analysis, we assumed the knicking
=1 min−1 .

(This is higher than the experimental value in Table 7.4, which requires higher enzyme
concentration). In the simulation, the nicking reaction reduced the length of one of the
sticky ends, from 6 bp to 4 bp, which is equivalent to a sticky end strength reduction from
1 to 2/3. Ignoring the energy cost of losing one stacking interaction, the free energy of a
DNA tile that is being held by one full sticky end and one cleaved sticky end is estimated to
be ∆Gcleaved = (1 + 2/3) × 7.75 RT = 12.9 RT. We chose the association rate for DNA tile site to be 106 M −1 sec−1 to match the typical polymerization rate observed
DNA nanotube kon

in the single molecule polymerization assay. Since we did not embed the recycling pathway
in all of our experiments, the recycling was disabled and the recycling rate krecycle was kept
at zero. All of the free tiles in the simulation have full sticky ends.

The simulated polymerization rate for a 7-tile-diameter DNA nanotube at 0−1000 nM
tile concentration is presented in Fig. 7.7. The blue and red lines are the polymerization
rates of the left and the right nanotube ends (Fig. 7.8), respectively. The upper dashed
line is the theoretical polymerization model of DNA tile in the absence of nicking reacfitting parameter that accounts for polymerization rate reduction in n monomer diameter
DNA nanotubes due to the different possible edge configurations. The bottom dashed line
is the polymerization rate of DNA nanotubes that are composed of DNA tile with one full
sticky end pair and one cleaved sticky end pair. Based on our model, we constructed the
site [tile]−k site e−∆Gcleaved /RT ×u ).
lower dashed line by the numerical evaluation of 0.55×(kon
on

The nanotube polymerization with nicking reaction at different tile concentrations can be
categorized into 4 regimes, which are:

125

Chapter 7

site [tile]−k site e−∆Gf ull /RT × u ). The factor 0.55 is a
tion, which is computed as 0.55×(kon
on

(1) Fast and symmetric depolymerization at [tile]= 0 nm
The extrapolation of both blue and red curves suggests that at zero tile concentration,
site e−∆Gcleaved /RT × u ). Equally important,
both ends depolymerize at the rate of 0.55 × (kon

the two ends depolymerize symmetrically. Both observations are in agreement with the
EcoRI experiment of DNA nanotubes at zero tile concentration presented in Fig. 7.6.
(2) Symmetric elongation at polymerization rate
nicking rate
On the other extreme, at high tile concentrations, the nicking reaction lags behind polymerization. Hence, the nicking reaction does not affect DNA nanotube polymerization, and
site [tile]−k site e−∆Gf ull /RT ×
both nanotube ends elongate symmetrically at the rate of 0.55×(kon
on

u0 )
(3) Asymmetric depolymerization
Interestingly, the simple modification of the local rule gives rise to a profound implication
for the case when the polymerization rate is near the nicking rate. Under depolymerization
ull
conditions where [tile] < [tile]fcrit
, the nicking reaction increases the depolymerization rate

asymmetrically. In the data points highlighted as squares in Fig. 7.7, the asymmetric depolymerization is expected at [tile] = 100 nM and 200 nM. Treadmilling, a subclass of the
asymmetric polymerization, will be discussed in the section below.
(4) Treadmilling
Remarkably, the simulation predicts that our proposed modification to the DNA nanotubes
ull
and polymerization rate near knicking . If we
could exhibit treadmilling at [tile] > [tile]fcrit

run the experiment at i×100 nM concentration, where i is a positive integer, the simulation
predicts that DNA nanotubes will exhibit treadmilling behavior at 300 nM and 400 nM
tile concentrations.
How does the asymmetry arise in a seemingly symmetric DNA nanotube construct? The
non-existence of asymmetry in the no-free-tile case indicates that the asymmetry should
involve an interaction between DNA nanotubes and incoming monomers. Fig. 7.8 shows a
particular series of events that produces asymmetric behavior between the nanotube ends.
For both nanotube ends, (1) docking of a new monomer triggers the stochastic nicking
rate. Initially, the new monomer attaches to the nanotube end with bond strength = 2. If

126

the polymerization is either slower or near the nicking rate, then the nicking reaction (2)
is completed before attachment of another monomer. In this scenario, the monomer at the
end of the DNA nanotube binds to the second layer with only 1+2/3 sticky end, and, as a
result, (3) the monomer will quickly dissociate from the nanotube ends. Up to this point,
this series of events has not broken the symmetry between the nanotube ends. Because
the nicking reaction only cuts one strand of a double-stranded sticky end bond, one of the
nanotube ends, which has been designated as the left end, is unaffected by this scenario
and always presents a ring of full sticky ends. Meanwhile, one half of the sticky ends in
the right end are shortened by the nicking reaction. As a result, with this regime, the left
end is predicted to polymerize faster than the right end.

left end

right end

(1)

(2)

(3)

127

Chapter 7

Figure 7.8.: An asymmetry between the left and right nanotube ends can arise after
(1) the docking of a free monomer to a DNA nanotube, which is followed by (2) the
fast nicking reaction and (3) the dissociation of the newly attached DNA tile from
the nanotube. As a result, the nanotube on the left presents two full sticky ends,
while the sticky ends exposed at the right end are composed of one cleaved and one
full sticky end. Due to the asymmetry in the sticky end strength (highlighted in the
dashed boxes), we expect the left end to polymerize faster than the right end.

7.6. Concluding remarks
In this study, we presented a simple modification to an existing DNA nanotube construct to
implement a de novo artificial cytoskeleton. We used a restriction enzyme to achieve a DNA
analog of GTP hydrolysis. The energy source is provided by a polymerization-triggered
nicking reaction. A preliminary bulk gel assay, single molecule polymerization movies, and
supporting simulation demonstrate the promise of our approach. The demonstration of a
treadmilling DNA nanotube is on the horizon and will be pursued upon the completion of
this study.
Despite the continuous emphasis of the similar physical properties of DNA nanotubes
and microtubules in this current study, the most profound insight may emerge from the
structural differences between the structures of the DNA nanotubes and microtubules. Dyche Mullins noticed one missing common microtubule feature in our construct, namely a
large conformational change that occurs after a DNA tile attaches to a growing DNA nanotube. The monomer-docking-induced conformational change has been observed on the
growing actin filaments [CLS96, LPH93] and microtubules [MMM91, CFK95, MH95], and
is thought to be responsible for the different kon ’s between the fast and slow polymer ends.
In microtubules, the end with faster kon and slower kof f polymerizes faster than the end
whose kon is slower and kof f is faster. Due to the absence of the conformational change in
our construct, the kon for both nanotube ends is expected to be identical. It is remarkable
that our simulation predicts a polymerization regime in which the nicking reaction gives
rise to the polymerization rate asymmetry. This predicted asymmetric behavior shows the
promise of DNA nanotube treadmilling.
Richard Feynman once said that “Experiment is the sole judge of scientific truth”. A
polymerization assay with nicking reactions over a wide range of tile concentrations will
be the ultimate test to evaluate the success of our scheme. A successful demonstration
of treadmilling would counter what one might think to be a reasonable assumption about
cytoskeletal dynamics, namely that conformational change is required for treadmilling polymers.
The construction of an artificial cytoskeleton can also potentially demonstrate an elegant
solution that nature has devised to solve challenges at molecular scale. As an example,
eukaryotic cells use the rapid depolymerization of microtubules and microtubule accessory
proteins to pull centrosomes apart during mitosis. Nicking-reaction-induced depolymerization, like the one shown in this study, can potentially pull apart another structure that
is mechanically coupled to the DNA nanotubes. In the future, incorporation of more biological design principles into DNA nanotube assembly, along with the creation of new

128

DNA nanotechnology analogs of cytoskeletal accessory proteins, will enable a more complex DNA-based dynamic system that can rival the complexity of cellular behavior.

Chapter 7

129

Supplementary materials for
Chapter 2: Programming DNA
Tube Circumferences

A.1. DNA sequence design
DNA sequences for the chain systems, 3-,4-,5-, and 6-helix ribbon systems, and 4-,5-, and
6-helix tube systems were designed and optimized using the SEQUIN software [See90] and
TileSoft software [YGB+ 04] to minimize sequence symmetry. The other systems were designed using an unpublishedthe design component of the NUPACK server (www.nupack.org)
to maximize affinity and specificity for the target structures. Sometimes, manual optimization was further performed on selected regions.

A.2. Sample preparation
DNA strands were synthesized by Integrated DNA Technology, Inc. (www.idtdna.com) and
purified by denaturing gel electrophoresis or HPLC. The concentrations of the DNA strands
were determined by the measurement of ultraviolet absorption at 260 nm. To assemble the
structures, DNA strands were mixed stoichiometrically to a final concentration of ∼1µM
for 20-helix ribbons and 20-helix tubes and ∼3 µM for other structures in 1×TAE/Mg++
buffer (20 mM Tris, pH 7.6, 2 mM EDTA, 12.5 mM MgCl2 ) and annealed in a water bath
in a styrofoam box by cooling from 90 ◦ C to 23 ◦ C over a period of 24 to 48 hours. For the
samples containing biotinylated strands, streptavidin was added to the aqueous solution

of the assembled structures for 1 hour at room temperature. The final concentration of
streptavidin matches the total concentration of the biotinylated strands. The samples were
further incubated overnight at 4 ◦ C before AFM imaging.

A.3. AFM imaging.
AFM images were obtained using an SPM Multimode with Digital Instruments Nanoscope
IIIa controller (Veeco) equipped with an Analog Q-control to optimize the sensitivity of
the tapping mode (Nano Analytics). A 40 µL drop of 1×TAE/Mg++ followed by a 5 µL
drop of annealed sample was applied onto the surface of a freshly cleaved mica and left for
approximately 2 minutes. Sometimes, additional dilution of the sample was performed to
achieve the desired sample density. On a few occasions, supplemental 1×TAE/8mM Ni++
was added to increase the strength of DNA-mica binding [HL96]. Before placing the fluid
cell on top of the mica puck, an additional 20 µL of 1×TAE/Mg++ buffer was added to the
cavity between the fluid cell and the AFM cantilever chip to avoid bubbles. The AFM tips
used were either the short and thin cantilever in the NP-S oxide sharpened silicon nitride
cantilever chip (Vecco Probes) or the short cantilever in the BS SiNi tip (Budget Sensor).

A.4. Fluorescence imaging and length measurements.
For fluorescence microscopy imaging, the 50 -ends of U1 and U5 strands were labeled with
Cy3 fluorophores. To measure the lengths of the nanotubes, fluorescence light microscopy
is preferred over AFM for two reasons: (1) the fast exposure time of the light microscopy,
which is on the order of 1 second per frame, as opposed to 200 seconds per frame for AFM;
and (2) the larger view field. A 4 µL drop of 10 nM SST sample was deposited onto an
untreated coverslip (Gold Seal, 3334). The presence of Mg++ and other multi-valent counterions in the buffer creates a net positively charged coverslip surface that immobilizes the
nanotubes. The light microscope is a home-built prism-based TIRF. A green wavelength
excitation from a solid-state 532-nm laser (CrystaLaser, Reno, NV) was used to excite the
immobilized DNA nanotubes through coupling between the prism and the glass coverslip.
The Cy3 emission was detected by a 60× water immersion objective (Nikon, NA = 1.2), a
DualView 2-channel filter cube (Roper Biosciences), and an electron multiplier CCD camera (Hamamatsu, C9100-02). The image was analyzed using the imageJ image processing
software (NIH) and MATLAB. A threshold was applied to each image to differentiate the

132

A.5. Thermal transition profiles.
Thermal transition experiments were performed using an AVIV 14DS spectrophotometer
(AVIV Biomedical, Lakewood, NJ) equipped with a water bath temperature controller.
UV absorbance at 260 nm was measured with a 1 nm bandwidth. The temperature step
was set at 0.1 ◦ C, deadband at 0.1 ◦ C with a equilibration time of 0.25 minute. Each data
point was smoothed with 10 neighbors to reduce instrument noise.

A.6. Curvature analysis
Adapting previously reported curvature analysis for DNA tubes [RENP+ 04, SS06], we describe below how to analyze the putative, approximate curvature of unstrained SST lattices
(e.g. not closed into tubes).
We use a B-DNA model where 21 bases finish exactly two full helical turns. Now consider
the three parallel helices depicted in Fig. A.2A. To study the curvature defined by the three
axes O1 , O2 , and O3 , we depict the cross-section view in Fig. A.2B. In the cross section
view, depict the projected positions of all the bases Bi in helix 2, where i = 0, . . . , 20, on
a circle. Note that Bi has exactly the same projected position as base Bi+21×k . Further
depict the position of base B0∗ . Denote the counter clockwise angle from B0∗ to Bk as θk .
As 21 bases finish two full helical turns, the counterclockwise angle about the helix center
between any two consecutive bases Bi and Bi+1 is α = 360 × 2/21 = 34.3◦ . The counter
clockwise angle from base B0 to its complementary base B0∗ is β = 150◦ [RENP+ 04]. Thus
the counter clockwise angle from base B0∗ to base Bk is:
θk = k × α − β = 34.3◦ × k − 150◦ .
In Fig. A.2B, the angle θ11 = 227.3◦ is depicted.
In unstrained SST lattices, we assume that the two contacting helices Hi and Hi+1 are
approximately tangent to each other. Thus, in the cross-section view, the center Oi of helix
Hi , the center Oi+1 of helix Hi+1 , and the two contacting bases that define the inter-helix
linkage, all lie on the same line. In the case of Fig. A.2B, O1 , base Bi on Helix 1, base B0∗

133

Appendix A

nanotubes and the glass surface. Each nanotube was then thinned down to a skeleton of
1-pixel thickness with the “skeletonize" command in imageJ. The length was then measured
from the skeleton patterns of the nanotubes.

Multi-stranded tile lattice

Multi-stranded tile

c*
b*

e*
f*

Sticky end

Crossover,
double-stranded linkage

Core

B Single-stranded tile

Single-stranded tile lattice

Half-crossover,
single-stranded linkage

Figure A.1.: Comparison between the multi-stranded tiles and single-stranded tiles.
(A) Left, a multi-stranded DX tile [FS93, WLWS98] contains a rigid structural core
(red) and four flexible sticky ends (blue). Right, sticky end mediated self-assembly of
DX tiles. The lattice structure comprises parallel DNA helices connected by doublestranded crossover points. Bold line segments represent the backbone of DNA; short
vertical bars represent base pairing; arrow heads indicate 30 ends. Letters marked
with * are complementary to the corresponding unmarked letters. (B) Left, a singlestranded tile contains only sticky ends (i.e. domains). Right, sticky end mediated
self-assembly of SST. The lattice structure comprises parallel DNA helices connected
by half-crossover points (i.e. single-stranded linkage).

on Helix 2, and O2 lie on the same line; O2 , base B11 on Helix 2, base Bj on Helix 3, and
O3 lie on the same line. The angle defined by O1 , O2 , and O3 in Fig. A.2B is determined
by the length k of domain a in Fig. A.2A. We immediately have that the angle formed
between the three helices O1 , O2 , and O3 is θk . In the case of Fig. A.2, k = 11, and hence
the angle is θ11 = 227.3◦ . For ease of analysis, we further define a curvature angle
δk = θk − 180◦ .
Now consider the molecular program (Fig. A.2C) that defines the 3-helix ribbon lattice

134

Appendix A

Helix 3
O3

δ11
Bj

Helix 2

B2
O2

B0*

Helix 2

Helix 3

Helix 1

θ11

C L3

δk = 34.3° × k − 330°

Figure A.2.: Curvature analysis of unstrained SST lattices.

135

in Fig. A.2A. As the length of domain a in strand U2 in Fig. A.2A equals its complementary
domain a∗ in strand U1, which in turn equals the value k associated with the green port
of U1 in Fig. A.2C, we immediately have the following formula for the curvature angle:
δk = 34.3◦ × k − 330◦ .
In Fig. A.2B, the angle δ11 = 47.3◦ is depicted.
Applying the above analysis, we immediately have that for the ribbons in Fig. 2 and
the unclosed 4-, 5-, 6-, 7-, 8-, and 10-helix tubes in Fig. 4, which have alternating 10-nt
and 11-nt green ports, the curvature angles alternate between δ10 = 13◦ and δ11 = 47.3◦ ,
averaging at (δ10 + δ11 )/2 = 30.2◦ per helix; and that for the 20-helix ribbon in Fig. 2
and the unclosed 20-helix tube in Fig. 4, which have only 10-nt green ports, the average
curvature per helix is δ10 = 13◦ .
Note that the above analysis is based on the assumption that in unstrained SST lattices,
two adjacent helices lie approximately tangent to each other to minimize the putative
molecular strain at the linkage points. This assumption, though theoretically plausible,
has not been experimentally verified. Also note that the above analysis is intended for
unstrained SST lattices and should not be applied to analyze the curvature of closed tubes.

136

Appendix A

B Molecular implementation

Nodal abstraction
Program
L3

DNA monomer strands

U1 a1*

a2*

L1 11

Self-assembled lattice structure

L3
a3* b3*

a3*

b3*

a3*

b3*

a3*

b3*

b3
a2*

a3
b2*

b3
a2*

a3
b2*

b3
a2*

a3
b2*

b3
a2*

b2 a2
a1* b1*

b2
a1*

a2
b1*

b2
a1*

a2
b1*

b2
a1*

a2
b1*

Annealing

Execution result
L3

b1*

b2*

Annealing

b3*

L3 a3*

a3
b2*

3-helix ribbon

a4*

b4*

a4*

b4 a4
a3* b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

b2 a2
a1* b1*

b2
a1*

a2
b1*

4-helix ribbon

b4*

a3
b2*

b5
a4*

a5
b4*

b5
a4*

b4 a4
a3* b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

b2 a2
a1* b1*

b2
a1*

a2
b1*

a5
b4*

a3
b2*

5-helix ribbon

b5
a4*

a5
b4*

b5
a4*

b4 a4
a3* b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

b2 a2
a1* b1*

b2
a1*

a2
b1*

6-helix ribbon

a5
b4*

a3
b2*

V16
V15
V14
V13
V12
V11
V10
V9
V8
V7
V6
V5
V4
V3
V2
V1
L1

20-helix ribbon

137

10 nm

Figure A.3.: Molecular program and secondary structure schematic for the 3-helix ribbon. (A) Top, the molecular program. The number associated with a port indicates
the number of nucleotides in the corresponding domain in the SST motif. Grey line
segment connects two complementary ports. Bottom, the lattice structure as the
output of the program depicted in the top panel. (B) The molecular implementation of the program depicted in A. The domain dimensions correspond to the port
dimensions
port)
(i.e.B5
|a1 | = 10 nt; |b1 | C
B2depicted in A: L1,
B310 (green port)-11
B4(pink
b6*
b6* a6*
a6*
L20
L6
= 11 nt ); U1, 10-11-11-10; U2, 11-10-10-11; L3,
10-11. See Appendix
A.7 for DNA
V19
V18
a6 b6
a6
b6
U5
V17
sequences.
a5* b5*
a5*
b5*
a5* b5*
a5*
b5*
L5

Program

Lattice structure

Program
L5

10
10

11
11

U1
L1

a4*

b4*

a4*

10
10

b4 a4
a3* b3*

b4
a3*

a4
b3*

10
10

11
11

b3
a2*

a3
b2*

b3
a2*

b2 a2
a1* b1*

b2
a1*

a2
b1*

b4*

a3
b2*

U4 11

10
10

U2
U1
L1

Lattice structure
a5* b5*

a5*

b5*

11
11

b5
a4*

a5
b4*

b5
a4*

11
11

10
10

b4 a4
a3* b3*

b4
a3*

a4
b3*

10
10

11
11

b3
a2*

a3
b2*

b3
a2*

b2 a2
a1* b1*

b2
a1*

a2
b1*

4-helix ribbon

a5
b4*

a3
b2*

5-helix ribbon

Program
L6

Lattice structure
b6*

a6*

b6*

U5 a5* b5*

a6
a5*

b6
b5*

b5
a4*

a5
b4*

b5
a4*

11
11

b4 a4
a3* b3*

b4
a3*

a4
b3*

11
11

10
10

b3
a2*

a3
b2*

b3
a2*

10
10

11
11

U1 a1* b1*

b2
a1*

a2
b1*

10
10

11
11

U4 11

10
10

U2
U1

a6*

a5
b4*

a3
b2*

6-helix ribbon
Figure A.4.: Molecular programs and secondary structure schematics for 4-, 5-, and 6helix ribbons. Left, molecular program. The number associated with a port indicates
the number of nucleotides in the corresponding domain in the SST motif. Grey line
segment connects two complementary ports. Right, secondary structure schematic.
The domain dimensions correspond to the port dimensions depicted in the left panel:
L1, 10-11; U1, U3, U5, 10-11-11-10; U2, U4, 11-10-10-11; L5, 10-11; L4, L6, 11-10.
See Appendix A.7 for DNA sequences.

138

a20*

b20*

a20* b20*

V19 b20 a20
a19* b19*

b20
a19*

a20
b19*

b19
a18*

a19
b18*

b19 a19
a18* b18*

V17 b18 a18
a17* b17*

b18
a17*

a18
b17*

V16

b17
a16*

a17
b16*

b17 a17
a16* b16*

V15

b16 a16
a15* b15*

b16
a15*

a16
b15*

V14

b15
a14*

a15
b14*

b15 a15
a14* b14*

V13 b14 a14
a13* b13*

b14
a13*

a14
b13*

L20

V18

Program
L20

11
V19
10

10
11

11
10

10
11

V12

b13
a12*

a13
b12*

b13 a13
a12* b12*

11
10

10
11

V11 b12 a12
a11* b11*

b12
a11*

a12
b11*

11
10

10
11

V10

b11
a10*

a11
b10*

b11 a11
a10* b10*

V9 b10 a10
a9* b9*

b10
a9*

a10
b9*

b9
a8*

a9
b8*

b9
a8*

a8
b7*

b8
a7*

a8
b7*

b7
a6*

a7
b6*

b7
a6*

V5 b6
a5*

a6
b5*

b6
a5*

a6
b5*

b5
a4*

a5
b4*

b5
a4*

V3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

V1
L1

b8
a7*

b2
a1*

a9
b8*

a7
b6*

a5
b4*

a3
b2*

Figure A.4.: Continued. Molecular program and secondary structure schematic for the
139
20-helix ribbon. The domain dimensions correspond to the port dimensions depicted
in the left panel: L1, 10-11; Vk , 10-11-10-11; L20, 10-11. See Section A.7 for DNA
sequences.

Appendix A

Lattice structure

1 μm

Figure A.5.: AFM images of (A) 3-helix ribbons, (B) 4-helix ribbons, (C) 5-helix ribbons, (D) 6-helix ribbons, and (E) 20-helix ribbons. Some ribbons appear to “branch"
in the AFM images. However, zoomed-in images reveal that such “branching" is primarily due to two ribbon segments lying (1) either on top of or (2) tangent to each
other. It is likely that the first case results from two separate ribbon segments landing
on the mica in a crossing configuration, and that the latter case occurs through electrostatic interactions between the ribbon segments during adsorption onto the mica
surface. Though we cannot completely rule out the possibility that such two ribbon
segments may share some edge strands, we suggest that such possibility is unlikely for
the following reasons. First, in dilute samples, the crossing/tangent co-localization
of the ribbons appears to be rare. Second, due to the flexibility of the single-strand
motif, an inter-ribbon linkage formed by one or two shared edge strands is likely
to be unstable and may be dissolved respectively through three- or four-way branch
migration.

140

9.6 nm

10.0 nm

9.4 nm

8.2 nm

9.2 nm

9.4 nm

8.2 nm

9.8 nm

10.0 nm

12.1 nm

12.9 nm

12.3 nm

13.3 nm

11.9 nm

11.8 nm

12.2 nm

13.1 nm

12.6 nm

12.9 nm

15.6 nm

15.4nm

15.4 nm

15.6 nm

13.9 nm

15.2 nm

14.3 nm

13.9 nm

14.6 nm

18.6 nm

19.0 nm

17.2 nm

18.0 nm

18.3 nm

19.2 nm

18.6 nm

16.9 nm

17.5 nm

17.1 nm

57.9 nm

58.5 nm

59.8 nm

59.0 nm

59.1 nm

59.6 nm

61.6 nm

57.7 nm

58.5 nm

Measured width, w (nm)

8.8 nm

60
50
40

w = 2.9 × k + 0.5

30
20
10
10
15
Designed helix number, k

easured width, w (nm)

Figure A.6.: SST ribbon width measurement. (A-E) 3-, 4-, 5-, 6-, and 20-helix ribbons. The section file screen shots are presented along with the measured widths
of the ribbons. Image size: 100 nm × 100 nm. (F) Width plot. Linear fit reveals
w = 2.9 × k + 0.5, where w is the measured width and k is designed helix number
for the ribbon. This linear relationship is approximated by w ≈ 3 × k. Note that
unlike in Fig. A.13 where 10 random DNA tube structure samples are measured to
establish that no 2 × k helix tubes are present, the measurements here are from 10
random points along one to three random ribbon samples for each k-helix ribbon.
The measured narrow width distribution thus reflects the uniform width distribution
along the ribbons and the narrow distribution of instrument measurement noise. This
measured ∼3 nm per helix width for SST lattice is used later in Fig. A.13 to establish
the circumference monodispersity for k-helix tubes.

141

Appendix A

Gaps

10 nm

Figure A.7.: High resolution AFM image for the 5-helix ribbon in Fig. 2C. (A)
Schematic. (B) High resolution AFM image. (C) AFM image annotated with red
dots indicating inter-helix gaps. The ∼3 nm per helix width measurement for k-helix
ribbon structures is greater than the 1.8 nm width of a single DNA helix. The reason
for this increased width is revealed in a high resolution image in Fig. A.7, which
also presents further unambiguous evidence for the correct formation of the ribbon
structures. (A) is a depiction of the expected DNA structure with bended helices and
gaps between the helices. The possible mechanism that causes this structure is as
follows. The electrostatic force between neighboring negatively charged DNA helices
pushes the helices away from each other, resulting in the bending of these helices,
which are inter-connected by half-crossovers. The interplay between the electrostatic
repulsion force and the bending deformation force is expected to result in a minimum energy lattice structure with alternating holes (indicated by red dots) and an
increased width (see Appendix D and [HW04]). The AFM image of the 5-helix ribbon
(B) agrees well with the above hypothesis, demonstrating an alternating pattern of
four layers of inter-helix gaps (C).

142

Lattice structure

Program
T5

b1
a4*

a1
b4*

b1
a4*

U3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

b2
a1*

a1
b4*

a3
b2*

4-helix tube
Program

U5
U4

Lattice structure

b1
a6*

a1
b6*

b1
a6*

U5 b6
a5*

a6
b5*

b6
a5*

a6
b5*

b5
a4*

a5
b4*

b5
a4*

U3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

b2
a1*

6-helix tube

Lattice structure
a1
b5*

b1
a5*

a1
b5*

b5
a4*

a5
b4*

b5
a4*

U3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

b1
a5*

b2
a1*

a5
b4*

a3
b2*

5-helix tube
Program
T7

Appendix A

Program

a1
a6*

a5
b4*

a3
b2*

Lattice structure
a1
b7*

b1
a7*

a1
b7*

b7
a6*

a7
b6*

b7
a6*

U5 b6
a5*

a6
b5*

b6
a5*

a6
b5*

b5
a4*

a5
b4*

b5
a4*

U3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

b1
a7*

b2
a1*

a7
b6*

a5
b4*

a3
b2*

7-helix tube

Figure A.8.: The molecular programs and the secondary structures for 4-, 5-, 6-, 7-,
8-, and 10-helix tubes. Left, molecular program. The number associated with a port
indicates the number of nucleotides in the corresponding domain in the SST motif.
Grey line segment connects two complementary ports. Right, secondary structure
schematic. The domain dimensions correspond to the port dimensions depicted in
the left panel: U1, U3, U5, U7, and U9 have domain dimensions of 10-11-11-10; U2,
U4, T4, U6, T6, U8, T8, and U10 have domain dimensions of 11-10-10-11; T5 and
T7 have domain dimensions of 10-11-10-11. See Appendix A.7 for DNA sequences.

143

Program

Lattice structure

Program
T10
U9

U5
U4

b1
a8*

a1
b8*

b1
a8*

a8
b7*

b8
a7*

a8
b7*

b7
a6*

a7
b6*

b7
a6*

U5 b6
a5*

a6
b5*

b6
a5*

a6
b5*

b5
a4*

a5
b4*

b5
a4*

U3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

b8
a7*

b2
a1*

a1
b8*

a7
b6*

a5
b4*

a3
b2*

8-helix tube

b1
a10*

a1
b10*

b1
a1
a10* b10*

U9 b10 a10
a9* b9*

b10
a9*

a10
b9*

b9
a8*

a9
b8*

b9
a8*

a8
b7*

b8
a7*

a8
b7*

b7
a6*

a7
b6*

b7
a6*

U5 b6
a5*

a6
b5*

b6
a5*

a6
b5*

b5
a4*

a5
b4*

b5
a4*

U3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

T10

b8
a7*

b2
a1*

10-helix tube
Figure A.8.: Continued.

144

Lattice structure

a9
b8*

a7
b6*

a5
b4*

a3
b2*

b1
a20*

a1
b20*

b1
a1
a20* b20*

V19 b20 a20
a19* b19*

b20
a19*

a20
b19*

b19
a18*

a19
b18*

b19 a19
a18* b18*

V17 b18 a18
a17* b17*

b18
a17*

a18
b17*

V16

b17
a16*

a17
b16*

b17 a17
a16* b16*

V15

b16 a16
a15* b15*

b16
a15*

a16
b15*

V14

b15
a14*

a15
b14*

b15 a15
a14* b14*

V13 b14 a14
a13* b13*

b14
a13*

a14
b13*

b13
a12*

a13
b12*

b13 a13
a12* b12*

V11 b12 a12
a11* b11*

b12
a11*

a12
b11*

b11
a10*

a11
b10*

b11 a11
a10* b10*

V9 b10 a10
a9* b9*

b10
a9*

a10
b9*

b9
a8*

a9
b8*

b9
a8*

a8
b7*

b8
a7*

a8
b7*

b7
a6*

a7
b6*

b7
a6*

V5 b6
a5*

a6
b5*

b6
a5*

a6
b5*

b5
a4*

a5
b4*

b5
a4*

V3 b4
a3*

a4
b3*

b4
a3*

a4
b3*

b3
a2*

a3
b2*

b3
a2*

a2
b1*

b2
a1*

a2
b1*

T20

V18

Program
T20

V19

V12

V10

b8
a7*

b2
a1*

a9
b8*

a7
b6*

a5
b4*

a3
b2*

20-helix tube
Figure A.8.: Continued. Molecular program and the secondary structure for the 20helix tube. The domain dimensions correspond to the port dimensions depicted in
the left panel: Vk , T20, 10-11-10-11. See Appendix A.7 for DNA sequences.
145

Appendix A

Lattice structure

Tubes

SST U1 U2 U3 U4 U5 U6 U7 U8 U9 T4 T5 T6 T7 T8 T10

4-helix tube x

5-helix tube x

6-helix tube x

7-helix tube x

8-helix tube x

10-helix tube x

Figure A.9.: The component strand table for 4-, 5-, 6-, 7-, 8-, and 10-helix tubes. The
strands labeled with the same name are identical in Fig. A.8. Consequently, by selecting appropriate subsets from a common pool of 15 distinct 42-nt SST species (U1-9,
T4-8, T10), we can construct monodisperse tubes with 6 distinct circumferences.

146

Appendix A

Figure A.10.: 3D illustration of 4-, 5-, 6-, 7-, 8-, 10-, and 20-helix tubes. The figure
shows both cross-section views and side views. The left column and the right column
describe the tubes that are closed along opposite directions. In other words, a tube
on the left is flipped inside out compared to the tube to its right. Based on this
geometrical modeling, the configurations on the left appear to be less strained and
are likely to dominate the configurations on the left thermodynamically. It is also
conceivable the left configurations may dominate the right configurations kinetically,
e.g. through faster cyclization. However, we have not performed experiments to
characterize the closure directions of the SST tubes. It is also interesting to note
the 10-base translational shift along the helix axial direction in the 5-helix tube and
the 7-helix tube and the consequent putative mechanical strain that these tubes
may have successfully absorbed.
147

Figure A.10.: Continued.

148

1 μm

1 μm
Figure A.11.: Panels A-G are respectively AFM images of 4-, 5-, 6-, 7-, 8-, 10-, and
20-helix SST tubes. Note that the persistent lengths of the tubes appear to increase (as expected) with the number of the circumferential helices. Also note that
the 4-helix tubes and 5-helix tubes sometimes assume spiral configurations when deposited on mica. The presence of these spiral configurations may reflect the expected
relatively shorter persistent lengths of the 4-helix and 5-helix tubes and/or the pos149
sibly relatively higher mechanical strain present in these tubes. Tube aggregations
are commonly observed in 20-helix tubes and occasionally in other tube systems.
Further, the 20-helix tubes typically appear significantly shorter than other tubes.

Appendix A

Closed tube
segment

Opened tube
segment

100 nm

Figure A.12.: AFM images for the opening of a 6-helix tube. The panels A-F present
sequential screenshots demonstrating the process of the opening of a 6-helix tubes by
the repeated scanning of an AFM tip. The tube is opened by the mechanical force
exerted by the AFM tip. The intact segments of the tube have higher height than
the opened segments, and thus appear brighter. This process reveals the tubular
nature of the 6-helix SST tubes.

150

12.2 nm

12.5 nm

14.8 nm

14.3 nm

12.5 nm

12.3 nm

12.1 nm

13.4 nm

12.0 nm

15.4 nm

13.9 nm

13.6 nm

14.1 nm

14.2 nm

13.9 nm

16.1 nm

13.0 nm

13.61 nm 13.8 nm

16.2 nm

15.9nm

17.8 nm

18.3 nm

17.8 nm

17.7 nm

14.9 nm

22.0 nm

20.3 nm

20.1 nm

19.8 nm

21.2 nm

20.4 nm

19.6 nm

21.4 nm

22.1 nm

24.9 nm

19.4 nm

17.8 nm

18.5 nm

25.4 nm

26.2 nm

23.4 nm

20.4 nm

23.8 nm

24.3 nm

22.5 nm

23.0 nm

22.3 nm

22.2 nm

27.0 nm

30.0 nm

27.0 nm

30.1 nm

29.2 nm

25.8 nm

28.0 nm

27.5 nm

31.0 nm

24.9 nm

55.1 nm

58.0 nm

43.8 nm

53.6 nm

60.3nm

44.7 nm

51.9 nm

48.2 nm

53.9 nm

44.8 nm

Width,w (nm)

w=6×k

13.2 nm

w = 4.5 × k
w=3×k

10
15
Designed helix number, k

Figure A.13.: SST tube circumference measurements. (A-G) 4-, 5-, 6-, 7-, 8-, 10-,
and 20-helix tubes. The AFM section file screen shots are presented along with
the measured widths of the opened tubes. Image size: 100 nm × 100 nm. (H)
Width plot of opened tubes. A k-helix opened tube is expected to have a width
w ≈ 3 × k nm, as determined by the width measurement of the k-helix ribbons
(Fig. A.6). A 2 × k-helix opened tube, by contrast, is expected have w ≈ 6 × k
nm. Lines corresponding to w = 3 × k, w = 4.5 × k, and w = 6 × k are plotted to
151
facilitate tube circumference monodispersity determination. For each k-helix tube,
10 random, opened tubes are measured. Tube aggregations are commonly observed
in 20-helix tubes and occasionally in other tube systems. Such aggregations are
excluded from width measurements.

Appendix A

N = 137

15
10
20 μm

20 μm

50
40
30
20
10

10
15
Length (μm)

N = 430

10
15
Length (μm)

N = 565

40
20
20 μm

20 μm

50
40
30
20
10

10
15
Length (μm)

N = 392

10
15
Length (μm)

Figure A.14.: Panels (A-D) are respectively fluorescence microscopy images (left) and
length profile (right) of 5-, 6-, 7-, and 10-helix tubes decorated with Cy3 fluorophores. N denotes sample size. The average lengths for 5-, 6-, 7-, and 10-helix
tubes are respectively ∼5.9 µm, ∼5.9 µm, ∼5.8 µm, and ∼6.8 µm.

152

A260

0.13

100 C

−3
8 x 10
−1
10
20

100 C

−3
8 x 10
dA260/dT 4
−1
10
20

100 C

−3
8 x 10
dA260/dT 3
−1
10
20

0.15
0.14

dA260/dT

0.12
0.11

0.10

0.09
0.08

A260

0.16
0.15
0.14
0.13
0.12
0.11

0.10

0.09
0.08

A260

0.14
0.13
0.12
0.11
0.10
0.09
0.08
10

0.20

0.18

A260

100 C

x 10 −3

0.16

dA260/dT 5

0.14

0.12
0.10
10

Appendix A

0.16

100 C

−5

Figure A.15.: Melting (red) and annealing (blue) curves for (A) 3-helix ribbons, (B) 4helix ribbons, (C) 4-helix tubes, and (D) 6-helix tubes. The transition temperatures
for melting/annealing (measured as the peaks of the derivates) are (A) 57◦ C and
45◦ C, (B) 58◦ C and 47◦ C, (C) 60◦ C and 48◦ C, and (D) 61◦ C and 48◦ C. Each
constituent DNA strand at 100 nM. Cooling/heating rate at 0.15◦ C per minute
for A-C and 0.115◦ C per minute for D. When repeating the experiment in D at a
slower cooling/heating rate of 0.023◦ C per minute, the transition temperatures for
melting/annealing become 60◦ C and 49◦ C (data not shown).
153

Assembly chemical potential
(not to scale)

Nucleation

Growth

Figure A.16.: Energetics of a conjectured assembly sequence for 4-helix SST tubes.
To speculate about possible kinetic assembly pathways, we adapt a nucleationelongation model in [SW07]. The figure describes the hypothetical pathway for
assembling 4-helix SST tubes under slightly super saturated conditions, where the
attachment of one SST to the lattice with two sticky ends (i.e. domains) is favorable but with one sticky end is unfavorable. The rate-limiting nucleation step
(left) that involves unfavorable events leads to the formation of a presumed critical
nucleus, followed by growth (right) composed of only favorable events. Note that
the downhill growth steps involve the formation of twice as many base pairs as the
uphill nucleation steps. Large black arrows, forward-biased reaction steps. Small
green arrows, unfavorable steps. The schematic is adapted from the depiction of the
“standard sequence model” in [SW07] .

A.7. DNA sequences
The DNA sequences for the systems described in the paper are presented both as secondary
structure schematics and as text sequences annotated with domain names. The domain
names are consistent with those in the secondary structure schematics figures.

154

Sequence
5’-GGCGATTAGG-ACGCTAAGCCA-CCTTTAGATCC-TGTATCTGGT-3’
5’-/5Cy3/TT-GGCGATTAGG-ACGCTAAGCCA-CCTTTAGATCC-TGTATCTGGT-3’
5’-GGATCTAAAGG-ACCAGATACA-CCACTCTTCC-TGACATCTTGT-3’
5’-GGAAGAGTGG-ACAAGATGTCA-CCGTGAGAACC-TGCAATGCGT-3’
5’-GGTTCTCACGG-ACGCATTGCA-CCGCACGACC-TGTTCGACAGT-3’
5’-GGTCGTGCGG-ACTGTCGAACA-CCAACGATGCC-TGATAGAAGT-3’
5’-CCTAATCGCC-TGGCTTAGCGT-3’
5’-GGAAGAGTGG-ACAAGATGTCA-3’
5’-GGTTCTCACGG-ACGCATTGCA-3’
5’-GGTCGTGCGG-ACTGTCGAACA-3’
5’-GGCATCGTTGG-ACTTCTATCA-3’

Table A.1.: DNA sequences: 3-, 4-, 5-, 6-helix ribbons

Name
U1: a1*-b1*-a2-b2
V1: a1*-b1*-a2-b2
V2: a2*-b2*-a3-b3
V3: a3*-b3*-a4-b4
V4: a4*-b4*-a5-b5
V5: a5*-b5*-a6-b6
V6: a6*-b6*-a7-b7
V7: a7*-b7*-a8-b8
V8: a8*-b8*-a9-b9
V9: a9*-b9*-a10-b10
V10: a10*-b10*-a11-b11
V11: a11*-b11*-a12-b12
V12: a12*-b12*-a13-b13
V13: a13*-b13*-a14-b14
V14: a14*-b14*-a15-b15
V15: a15*-b15*-a16-b16
V16: a16*-b16*-a17-b17
V17: a17*-b17*-a18-b18
V18: a18*-b18*-a19-b19
V19: a19*-b19*-a20-b20
L20: a20*-b20*

Sequence
5’-GGCGATTAGG-ACGCTAAGCCA-CCTTTAGATCC-TGTATCTGGT-3’
5’-GGCGATTAGG-ACGCTAAGCCA-CCTTTAGATC-CTGTATCTGGT-3’
5’-GATCTAAAGG-ACCAGATACAG-CCACTCTTCC-TGACATCTTGT-3’
5’-GGAAGAGTGG-ACAAGATGTCA-CCGTGAGAAC-CTGCAATGCGT-3’
5’-GTTCTCACGG-ACGCATTGCAG-CCGCACGACC-TGTTCGACAGT-3’
5’-GGTCGTGCGG-ACTGTCGAACA-CCAACGATGC-CTGATAGAAGT-3’
5’-GCATCGTTGG-ACTTCTATCAG-ATGCACCTCC-AGCTTTGAATG-3’
5’-GGAGGTGCAT-CATTCAAAGCT-AACGGTAACT-ATGACTTGGGA-3’
5’-AGTTACCGTT-TCCCAAGTCAT-AACACTAGAC-ACATGCTCCTA-3’
5’-GTCTAGTGTT-TAGGAGCATGT-CGAGACTACA-CCCTTGCCACC-3’
5’-TGTAGTCTCG-GGTGGCAAGGG-TACTACCGCT-CCATTAAGAAT-3’
5’-AGCGGTAGTA-ATTCTTAATGG-ATCCGTCTAT-CTACACTATCA-3’
5’-ATAGACGGAT-TGATAGTGTAG-AGACGAAATC-AGCAGAACTAA-3’
5’-GATTTCGTCT-TTAGTTCTGCT-CTGCGAAGTA-ATCAGCCGAGC-3’
5’-TACTTCGCAG-GCTCGGCTGAT-GAACTCGCTC-CAGAATCGACG-3’
5’-GAGCGAGTTC-CGTCGATTCTG-AACTTTCAAT-ATCATATCGTA-3’
5’-ATTGAAAGTT-TACGATATGAT-CCGTAGCAGT-ATAAGCGATCT-3’
5’-ACTGCTACGG-AGATCGCTTAT-CGCTAGCCAC-CAAGATCAAGC-3’
5’-GTGGCTAGCG-GCTTGATCTTG-CAATCGGACC-TGCCTTATCCT-3’
5’-GGTCCGATTG-AGGATAAGGCA-GACACGGCAC-CACTTACTCAT-3’
5’-GTGCCGTGTC-ATGAGTAAGTG-3’

Table A.2.: DNA sequences: 20-helix ribbons. Note that strands V1 and U1 have
identical sequences, but different domain partitions. The same is true for V3 and U3,
and V5 and U5. L1 is the same as in Table A.1.

155

Appendix A

Name
U1: a1*-b1*-a2-b2
U1-Cy3:
U2: a2*-b2*-a3-b3
U3: a3*-b3*-a4-b4
U4: a4*-b4*-a5-b5
U5: a5*-b5*-a6-b6
L1: a1-b1
L3: a3*-b3*
L4: a4*-b4*
L5: a5*-b5*
L6: a6*-b6*

Name
U6: a6*-b6*-a7-b7
U7: a7*-b7*-a8-b8
U8: a8*-b8*-a9-b9
U9: a9*-b9*-a10-b10
T4: a4*-b4*-a1-b1
T5: a5*-b5*-a1-b1
T6: a6*-b6*-a1-b1
T7: a7*-b7*-a1-b1
T8: a8*-b8*-a1-b1
T10: a10*-b10*-a1-b1

Sequence
5’-GGCATCGTTGG-ACTTCTATCA-ATGCACCTCC-AGCTTTGAATG-3’
5’-GGAGGTGCAT-CATTCAAAGCT-AACGGTAACTA-TGACTTGGGA-3’
5’-TAGTTACCGTT-TCCCAAGTCA-AACACTAGAC-ACATGCTCCTA-3’
5’-GTCTAGTGTT-TAGGAGCATGT-CGAGACTACAC-CCTTGCCACC-3’
5’-GGTTCTCACGG-ACGCATTGCA-CCTAATCGCC-TGGCTTAGCGT-3’
5’-GGTCGTGCGG-ACTGTCGAACA-CCTAATCGCC-TGGCTTAGCGT-3’
5’-GGCATCGTTGG-ACTTCTATCA-CCTAATCGCC-TGGCTTAGCGT-3’
5’-GGAGGTGCAT-CATTCAAAGCT-CCTAATCGCC-TGGCTTAGCGT-3’
5’-TAGTTACCGTT-TCCCAAGTCA-CCTAATCGCC-TGGCTTAGCGT-3’
5’-GTGTAGTCTCG-GGTGGCAAGG-CCTAATCGCC-TGGCTTAGCGT-3’

Table A.3.: DNA sequences: 4-, 5-, 6-, 7-, 8-, 10-helix tubes. Note that strand U7
and V7 have identical sequences, but different domain partitions. The same is true
for U9 and V9, and U11 and V11.

Name
T20: a20*-b20*-a1-b1

Sequence
5’-GTGCCGTGTC-ATGAGTAAGTG-CCTAATCGCC-TGGCTTAGCGT-3’

Table A.4.: DNA sequences: 20-helix tubes: The sequences for strands V1 to V19 are
listed in Table A.2.

156

Supplementary materials for
Chapter 3:
Elongational-flow-induced
scission of DNA nanotubes

B.1. Underlying scission theory
Here we present the hydrodynamic model used for comparison with our experiment. First,
we derive an expression for the tension produced at the midpoint of a long cylinder. Then,
an expression for the maximum elongation rate ˙ for the microfluidic device is obtained.
In the approach taken to determine the tension produced at the midpoint of a long
cylinder, the exact solution for fluid flow in the presence of a cylinder of infinite length is
approximately matched with an exact solution for axially symmetric elongational flow in
the absence of the rod.
For the case of low Reynolds number flow in an incompressible fluid, the continuity
equation and Navier-Stokes equations are reduced to
∇·u = 0
∇P

= µ∇2 u,

(B.1)
(B.2)

where u is the velocity field, P is the pressure, and µ is the viscosity. From these two

equations, it follows that ∇2 P = 0. One can verify by direct substitution that

ur =
rln
2µ

r R2
− +
2r

(B.3)

and
z,
uz = − ln

(B.4)

is an exact solution of Eqs. (B.1) and (B.2) where C and R are integration constants. The
solution represents a fluid flow around a cylinder of radius R of infinite extent for no-slip
boundary conditions that is evident from the fact that the fluid velocity vanishes at r = R.

ur
uz

-½L

½L

Figure B.1.: (Color) A rigid rod in an axially symmetric elongational flow

The fluid velocity field without the rod representing axially symmetric fluid flow with
an elongational rate of ˙ along the z-axis is given by
˙
ur = − r

(B.5)

uz = z,

(B.6)

as can be verified by direct substitution into Eqs. (B.1) and (B.2). Since the first term of
Eq. (B.3) dominates when r is large, a good approximate match between the solution given
by Eqs. (B.3) and (B.4) and that of Eqs. (B.5) and (B.6) at the characteristic crossover

158

distance r = L/2 is obtained by setting
C=−

(B.7)

where R and L are the radius and the length of n-helix DNA nanotube, respectively.
Equation (B.4) then becomes
uz = ˙

ln(r/R)
z.
ln(L/2R)

(B.8)

The flow induced stress in the z direction on the cylinder’s surface is given by
σrz ≡ µ

µz
∂uz
∂r r=R Rln(L/2R)

(B.9)

The line tension at the center of the cylinder is thus given by
Z L/2

σrz dz =

T = 4πR

πµL
˙ 2
4ln(L/2R)

(B.10)

This expression is similar to the recently published expression of the elongational-flowinduced drag force in reference [VCS06]. In our work (Eq. B.10), we provide a derivation
of the O(1) geometric constant for our device.
The scission occurs when the midpoint tension T is larger than the critical tension
required to break all DNA helices simultaneously across the nanotubes. This critical tension
is expected to be given by
Tcrit = n × fc ,

(B.11)

where n is the nanotube circumference and fc is the tension required to break a single
DNA helix. In the DNA nanotubes, the DNA helices are aligned along the axis of the
tube. Tension is thus exerted along the length of the binding domains of the participating
DNA strands. One expects these binding domains to fail when the tension along the
binding domains is greater than required to overstretch a DNA helix [SCB96]; that is, one
expects fc to be close to 65 pN.
In our device geometry, the flow into the narrow channel is approximately radial. We

159

Appendix B

µ˙
ln(L/2R)

take the mean flow velocity (averaged over height) ū to be given by
ū(ρ) = −

uw w
πρ

(B.12)

where ρ is the radial distance to the channel entrance and uw is the mean flow velocity
across the orifice.
The elongational flow (averaged over height) ˙ is defined as
˙ ≡

uw w
∂ ū
∂ρ
πρ2

(B.13)

The elongational flow ˙ is maximum near the orifice where πρ = w
˙max ≡

πuw
∂ ū
π V̇
= 2 ,
∂ρ ρ= w
w h

(B.14)

where V̇ is the volumetric flow rate of our syringe pump and is equal to uw multiplied by
the orifice cross-sectional area.
In Fig. 3.4, the theoretical prediction of Lcrit for scission experiment of n-helix nanotube
over a range of V̇ is obtained by setting L = Lcrit , T = Tcrit , ˙ = ˙max and substituting
Eqs. (B.11) and (B.14) to Eq. (B.10) that yields the equation below:
Tcrit =

πµ˙max L2crit
4ln(Lcrit /2R)

(B.15)

where Tcrit is given by Eq. (B.11) and ˙max is elongational flow at the center of the channel
and at a distance of ρ = w/π from the orifice where the maximum elongation flow is
expected to occur.
Note that the radial flow approximation in Eq. (B.12) is only valid for a point far away
from the constriction. Our scission model calculates the location of all scission events in
all of our experiments to be at a distance ρ > w/π from the orifice in order to produce
the observed mean fragment length from the initial DNA nanotube distribution. This
calculation is consistent with the expected position of ˙max in Eq. (B.14) and the calculated
˙ profiles in similar constriction devices reported in [KCdlT96,NK90]. Therefore, the radial
flow approximation in Eq. (B.12) is justified.

160

B.2. Bayesian inference and stochastic scission simulation
In our data analysis, we utilized a Bayesian inference method to extract Lcrit out of the fragP r(H |Lcrit ) × P r(Lcrit )/P r(H ), where the a priori P r(Lcrit ) is taken to be uniform
over 0 ≤ Lcrit ≤ 10 µm and zero otherwise. The upper bound is approximately twice
the average nanotube length in the control experiment. P r(H ) is treated as a normalization constant and is set by constraining

P r(Lcrit |H ) = 1. P r(H |Lcrit ) was calcu-

lated by assuming the measured fragment length histograms {Wi (H )}N
i=1 , where N is the
number of bins and Wi is the number of nanotubes in bin i, were generated by independent, indentically-distributed fragment samples from length distribution predicted by the
model {Wi (Lcriti )}N
i=1 . Then, P r(H |Lcrit ) can be conveniently calculated as likelihood:
lnP r(H |Lcrit ) = D + Σi [Wi (H ).lnWi (Lcrit )], where D is a constant independent of Lcrit
and absorbed during normalization.
The fragment length distribution predicted by the scission model was computed from
stochastic scission simulation of a large number of nanotubes (> 40, 000) having the experimentally measured length distribution of the DNA nanotubes before passage through
the microfluidic device. These DNA nanotubes were subjected to the following stochastic
scission rules.
First, we note that the number of DNA nanotubes that crosses the orifice at position
(x, y) is proportional to the flow rate at the orifice uw (x, y). By solving the Navier-Stokes
equation for incompressible flow in a rectangular channel, one can obtain an expression for
the flow profile involving an infinite series:
("

uw (x, y) = E

x2 −

2 #

n=∞

8 (−1)n cosh(αn y)
cos(αn x) ,
n=o a αn cosh(αn h/2)

(B.16)

where αn = (2n + 1) w
and E is a constant obtained by setting uw (0, 0) to be the maximum

flow rate umax
w . In this coordinate system, (x = 0, y = 0) is chosen to be the center of
the channel where the maximum flow occurs and the range of width and height of the
flow channel are [−w/2, w/2] and [−h/2, h/2], respectively. In our simulation, we use
the normalized uw (xi , yi ) as the probability distribution for stochastically assigning (xi , yi )
to nanotube i. s Second, the fragment size produced by scission of nanotube i depends
on (xi , yi ). Using the same reasoning as employed in the position-dependent flux and

161

Appendix B

ment length histogram data H by calculating the a posteriori probability P r(Lcrit |H ) =

Eqs. (B.10) and (B.12), one obtains the following expression for the critical length at
(xi , yi ):

umax
w / ln[Lcriti (xi , yi )/(2R)]Lcriti (xi , yi ) =

uw (xi , yi )/ ln[Lcrit /(2R)]Lcrit .

In our model, an initial nanotube i of length Li will experience a total of mi mid-point
scission rounds, where mi is the largest non-negative integer that satisfies
Lcrit (xi , yi ) ⩾

Li
2mi

(B.17)

From the equation above, mi will be given by mi = bln[Li /Lcriti (xi , yi )]/ ln(2)c, where the
floor notation b.c denotes rounding down to the nearest integer. In our simulation, initial
tube i of length Li yields 2mi output fragments that have identical length of Li /(2mi ).
The simulation generated fragments were then tabulated to construct the fragment length
distribution predicted by the scission model {Wi (Lcriti )}N
i=1 for computing P r(Lcrit |H ).

B.3. Best Lcrit fit by Bayesian inference
Fragment length distributions for 6-, 8-, and 10-helix nanotubes for volumetric flow rates
√ n
with values given by 2 mL/hr where n is an integer in the range −2 ⩽ n ⩽ 4 are shown
in Fig. B.2. In each analysis, the fragment length measurement was stopped when the
fragment counts reached ≈ 250 fragments. Bayesian inference of 250 simulated fragments
with a chosen Lcrit shows robust results within ±12% from the chosen Lcrit , for Lcrit
smaller than the mean of initial nanotube distribution. The blue dot with blue error bars
represents the average fragment length for each run. The Bayesian analysis was performed
by comparing our measurement with simulation using one adjustable parameter, namely
critical length Lcrit , as described in the main text. The best simulated distribution by
Bayesian a posteriori probability (orange line) fits our data fairly well. The orange circle
denotes the most probable Lcrit in each experiment. The orange error bar spans the range
where P r(Lcrit |H ) is over 90% based on our model.

B.4. Best Lcrit fit by Bayesian inference with truncated
Gaussian noise
Best Lcrit fit for the scission model with the addition of truncated Gaussian noise, summarized in Fig. B.3, shows that adding noise to account for unmodeled physical source of
randomness does not significantly improve the Bayesian fit. With the addition of noise,

162

normalized frequency

8-helix nanotube

3.95

4.75

0.3

0.2

0.1

normalized frequency

0.707 mL/h

normalized frequency

1.00 mL/h

normalized frequency

1.41 mL/h

normalized frequency

0.2

0.1

0.2

0.1

0.3

0.2

0.1

0.3

0.2

0.1

0.3

0.2

0.1

1.45

0.3

0.2

0.1

fragment length [µm]

1.65

0.3

1.50

1.75

0.3

1.80

2.20

0.3

2.15

0.3

2.70

0.3

2.45

0.3

3.70

0.3

2.80

0.2

0.3

4.20

0.3

1.50

normalized frequency

0.3

1.80

normalized frequency

3.95

2.10

2.00 mL/h

0.3

2.70

2.83 mL/h

4.85

0.3

3.00

4.00 mL/h

10-helix nanotube

Appendix B

0.500 mL/h

6-helix nanotube

fragment length [µm]

163

Figure B.2.: (Color) Best Lcrit fit by Bayesian inference (see Appendix B.3 for details).

each scission event produces two not exactly equal fragment lengths. For nanotube i, the
standard deviation of the truncated Gaussian noise σi was chosen to be proportional to tube
length Li , reflecting the results of the induced drag force calculation for which the region
where the tension reaches plateau becomes narrower as the nanotube tube gets shorter.
We truncated the Gaussian noise at 0 and Li fragment sizes to eliminate unphysical fragment outputs in our simulation, namely fragments with negative lengths and fragmented
nanotubes longer than initial fragment length Li . The Bayesian fit was performed over a
wide range of model parameters (0.02Li < σi < 0.50Li , 0.05 < Lcrit < 10.00). The upper
bound of the σi corresponds to substantially large noise, such that for a nanotube length
Li , where Li > 2Lcrit , the probability of scission at any point along the fragment, including
no scission at all, is approximately equal. Note also that the distribution of the truncated
Gaussian with the upper bound of σi is close to uniform distribution between 0 and Li .
The orange and red circles with error bars represent the best Lcrit fit by Bayesian inference
for polymer scission without and with noise, respectively. Similarly, the orange and red
lines are the best distribution fit to our normalized fragment length histogram based on
simulation without and with noise, respectively.
The Bayesian histogram fits of the model with (red lines) and without noise (orange lines)
show similar shapes (Fig. B.3) and further support our simple scission model presented in
the main text. The extracted Lcrit from the Bayesian inference with noise are consistent
within 15% of the fit in the absence of noise. The agreement is within 5%, if we exclude
the slowest volumetric flow rate data where the inference have the widest 90% confidence
bands. The maximum value of the most probable σi overall fits is 0.20Li . This value of σi
still represents truncated Gaussian noise distribution whose width is substantially smaller
than the tube length Li .

164

6-helix nanotube

8-helix nanotube

normalized frequency

0.3

0.2

0.1

normalized frequency
normalized frequency

0.707 mL/h
1.00 mL/h

normalized frequency

1.41 mL/h

normalized frequency
normalized frequency

0.2

0.1

2.70

2.80

0.3

0.2

0.1

0.2

0.1

0.2

0.1

1.80

1.75

0.3

0.2

0.1

1.45

1.50

1.65

0.3

0.2

0.1

0.3

2.20

0.3

2.15

0.3

0.2

0.3

2.70

0.3

2.45

0.3

3.70

0.3

4.20

0.3

1.50

normalized frequency

3.95

1.80

2.00 mL/h

0.3

2.10

2.83 mL/h

4.85

0.3

3.00

4.00 mL/h

10-helix nanotube

4.75

fragment length [µm]

Appendix B

0.500 mL/h

3.95

fragment length [µm]

165

Figure B.3.: (Color) Best Lcrit fit by Bayesian inference with truncated Gaussian noise
(see Appendix B.4 for details). The red lines are the Bayesian fits with noise.

Supplementary materials for
Chapter 6: Single molecule
analysis of DNA nanotube
polymerization
In English, if you say "I see", it
means that you understand
something
(Sir John Pendry,
KNI Colloquium at Caltech,
05-14-2007)

C.1. Movie of anomalous diffusion and side-to-side joining

Figure C.1.: TIRF images of mobile DNA nanotubes close the glass surface at 36.7 ◦ C
and 0 nM initial monomer concentration in 1× TAE/Mg++ and 0.3% (w/v) methylcellulose. In the presence of the crowding agent, the entropy of the system is maximized when the nanotubes were confined close to a surface, such as the capillary
walls. The same entropic force also drives side-to-side joining or “bundling”, such as
between the short nanotubes and the long nanotubes at the center of this movie. After joining, the DNA nanotubes remained mobile relative to each other (length-wide
sliding occurred) while they depolymerized from both ends as a physical response
to low free monomer concentration. At the end of the movie, the short nanotubes
dissociate from the long one, possibly because the entropic gain of the side-to-side
joining of short nanotubes is less favorable compared to longer ones.

168

C.2. Movie of depolymerization experiment

Appendix C

Figure C.2.: DNA nanotubes shrink at 38.3 ◦ C with zero initial monomer concentration and 7 nM initial nuclei concentration, as shown in Fig. 6.3 of the main text.

169

C.3. Movie of DNA nanotube growth

Figure C.3.: DNA nanotubes elongated at 38.3 ◦ C with 400 nM initial monomer concentration and 7 nM initial nuclei concentration, as shown in Fig. 6.4 of the main
text.

170

C.4. Movie of complete depolymerization of DNA nanotubes
followed by annealing of newly released free DNA tiles
The annealing of free monomers at high concentration nucleates a significant number of
new nuclei which immediately elongated and underwent side-to-side joining with other
newly-formed nuclei. The total tile concentration was 500 nM and the reaction buffer contains 1× TAE/Mg++ and 7.5 mg/mL casein. We used casein to passivate the glass surface

ture (37.4 ◦ C). The sample was then melted by increasing the prism temperature to 70 ◦ C.
We did not measure the temperature profile of the sample during the spontaneous cooling. The annealing was achieved by simply turning off the prism heater and allowing the
sample to spontaneously cool down to 37.4 ◦ C, the elevated room temperature. During
this time, the average intensity of DNA nanotube nuclei increased over time, which is
the signature of side-to-side joining. Experimentally, the side-to-side joining obscures the
elongation of individual DNA nanotube and makes single molecule polymerization measurements unattainable.

171

Appendix C

and to confine long DNA nanotubes close to the surface. The movie was acquired while
the whole microscope room and the sample were initially at an elevated room tempera-

0 sec

45 sec

90 sec

135 sec

180 sec

225 sec

270 sec

315 sec

360 sec

405 sec

450 sec

495 sec

Figure C.4.: In the presence of crowding agent, complete melting of a high concentration of DNA tiles (500 nM) followed by fast annealing produces DNA nanotube
“bundles”. After the spontaneous nucleation of short nuclei, the newly formed nanotubes “side-to-side” join with each other to maximize the entropy of the crowded
environment. Scale bar is 20 µm.

172

C.5. AFM images of opened DNA nanotubes
AFM images were acquired with a tapping mode AFM on a Nanoscope IIIa controller
(Veeco Instruments) equipped with nanoAnalytics Q-control III (Asylum Research) under
1× TAE/Mg++ (40 mM trisacetate and 1 mM ethylenediaminetetraacetic acid (EDTA)
with 12.5 mM Mg-acetate.4H2 O, pH 8.3) buffer and 110 µm, 0.38 N/m spring constant
SNL silicon nitride cantilever (Veeco Instruments). The DNA nanotubes were annealed at
1.0 µM tile concentration. Following annealing, the samples were diluted to 100 nM with
on a freshly cleaved piece of mica surface (Ted Pella), approximately 1 cm × 1 cm in size,
affixed to a 15 mm diameter magnetic stainless steel puck (Ted Pella) using a hot glue
gun. DNA nanotubes spontaneously open on the mica surface, possibly due to the energy
gain from the formation of salt bridges between DNA and the mica surface [RENP+ 04].
Under the Mg++ buffer, DNA tiles are not completely immobilized and can still attach
to or detach from an immobilized opened DNA nanotube. The DNA tile−DNA nanotube
interaction effects the validity of circumference measurements of opened DNA nanotubes.
To avoid such effect, after 5 minutes, to completely quenched the reaction, 20 µL of 9 mM
Ni++ in 1×TAE/Mg++ was added to the mica puck. The nickel buffer facilitates stronger
binding between DNA and mica than the Mg++ buffer [HL96].
We imaged one sample of a pre-formed nuclei stock solution at 1 µm × 1 µm at multiple
random coordinates. We used custom-written MATLAB code to flatten the images by subtracting a fitted first order polynomial from each scan line and match intensity histograms
between scan lines. The circumference was measured by counting the number of DNA
tiles at 5 random points along the longitudinal-axis of each DNA nanotube. The average
value was then used as the circumference of that particular DNA nanotube. Hence, the
tabulated DNA nanotube circumference is not restricted to positive integer numbers. A
histogram (Fig. 6.9) was then constructed by binning the data from 1 µm to 15 µm within
bin width = 1 µm.

173

Appendix C

1×TAE/Mg++ . 10 µL of the diluted sample and 20 µL of 1×TAE/Mg++ were deposited

Figure C.5.: AFM images of 53 randomly chosen opened DNA nanotubes reveal the
circumference heterogeneity of the nuclei. The strong interaction between negativelycharged mica surface, multivalent Ni++ ions, and DNA nanotubes leads to the spontaneous DNA nanotube opening. The circumference histogram of DNA nanotube
diameter is shown in Fig. 6.9

174

C.6. UV absorbance of DNA nanotube
We chose the reaction temperature range based on the annealing curve for 200 nM Cy3labeled DNA tiles. The UV absorbance measurement were performed using an AVIV
14DS spectrophotometer (AVIV Biomedical, Lakewood, NJ) equipped with a computer-

.4
41
.2

0.34

0.30
Out[226]=

0.26

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Tm,100 %

Tm,50 %

0.22

Temperature @Î CD

Figure C.6.: The annealing and melting curves of Cy3-labeled DNA nanotubes at
200 nM tile concentration guided the reaction temperature range of this work. The
shaded region denotes the temperature range where the collected valid measurements
of DNA nanotube polymerization at a 200 nM concentration of free tiles. At that
tile concentration, DNA nanotube nucleation becomes noticeable at ≈35 ◦ C. In the
bottom left plot of Fig. 6.7, we were able to acquire valid polymerization rate measurements at this tile concentration down to 35.2 ◦ C (the lower bound of the gray-shaded
region).
The maximum temperature of our assay was set by the safe operation temperature of
our objective heater, and not by any insight from the melt experiment or other assay. It is

175

Appendix C

controlled sample temperature. We informally defined the formation temperature as the
temperature at which the slope of the annealing curve suddenly changed due to the formation of DNA nanotube nuclei and elongation of the stable nuclei. Because nucleation is a
kinetic phenomena, the measured formation temperature depends on the speed of annealing. In Fig. C.6, the formation temperature was measured to be roughly 35 ◦ C. Indeed,
we did not observe DNA nanotube nucleation in all 200 nM polymerization experiments at
temperatures above 35 ◦ C resulting in valid rate measurements. In contrast, all polymerization data that were taken at 200 nM free monomer concentration at temperature below
35 ◦ C suffers from spontaneous nucleation, consistent with the bulk UV measurement.

wise to not heat the objective above 50 ◦ C. In this work, we had to heat the objective at
47 ◦ C to achieve a 41.4 ◦ C sample temperature. However, as the DNA nanotube melting
temperature is only slightly above 42 ◦ C, in this case, experiments at higher temperatures
would not have been interesting.

176

Supplementary materials for
Chapter 7: Toward de novo
recapitulation of cytoskeleton
dynamics with DNA nanotubes

D.1. The spacing between neighboring DNA tiles in DNA lattice.
In this model, ionic strength effect is incorporated into the two-dimensional DNA crystal
model. Each charge on the phosphate backbone is effectively reduced by the condensed
counterions, lowering the contribution of the Coulombic interaction to the lattice energy.
The current model is in fair agreement with the experimental measurement of the spacing
between neighboring subunits. The spacing of the DNA lattice is also predicted in various
salt concentrations and using different DNA molecule designs, which is easily tested by
trivial AFM imaging.
DNA double-helix
We begin by modeling the DNA double-helix as a rigid, charged cylindrical beam with
radius r0 ≈ 1 nm and persistence length ξp ≈ 50 nm. In this coarse model, the negative
charges along DNA backbones is replaced by a continuous linear charge in the center of
the cylindrical beam and its density with charge density λ ≈ 2eo /3.38 Å. The line charge
density corresponds to one negative charge per phosphate group. The Manning parameter
or dimensionless linear polyanion charge is ξ ≈ λlB /eo = 4.1, where lB is the Bjerrum

length defined as the distance where the electrostatic energy is equal to the thermal energy
lB := eo 2 /4πkB T . For water and dilute solution at room temperature lB = 7.14 Å.

Double-crossover (DX) molecule and two-dimensional DNA lattice
To provide a quantitative model of the lattice, we constructed a simple parameterized
double-crossover (DX) molecule, with only one free parameter, namely bending radius
Rbend . Later in this calculation, we will minimize the lattice energy with respect to the
bending radius Rbend . The structural approximation of a DX molecule consists of six cylindrical segments, and each has the same mechanical and electrostatic property of DNA
double strands. The middle two segments (A and B) are joined due to the presence of
the two crossover points, where the four strands cross-linked. The outer four segments
(C-F) are bendable with identical curvatures, and each is assumed to be an arc of a circle. Furthermore, the bending of each bendable segment is constrained such that it keeps
the overall structure as a two-dimensional geometrical object. Note that the model construction reduces the dimensionality of the system from three-dimensional geometry to a
two-dimensional system, which reduces the complexity of the calculation while still capturing the important physics of the system.

Free energy calculation of the two-dimensional lattice
A mathematical description of the energetics of lattice packing must reflect the two competing factors, namely the electrostatic and bending energy, plus other terms that do not
depend on the bending radius. The basic idea of our approach is to minimize the total
energy with respect to bending radius. As a consequence, we do not need to calculate
energy terms that are assumed to be independent with the lattice structure in order to find
the Rbend where the energy is minimum.

Electrostatic free energy
The interaction energy between segment i and j is calculated as double integrations

Gint =

178

dsi

→ −
kB T lB −κ|−
dsj (1 − Zθ)2 λ2 →
e si − sj | ,
| {z }
| si − sj |
{z
= r2
= VDH

(D.1)

Rbend = 4 nm

Rbend = 16 nm

Rbend = 64 nm

Appendix D

Rbend

Figure D.1.: The model of a DNA double-crossover tile employed in this calculation.
The part of the tile between the two crossover points is modeled as fixed beams (segments A and B). The segments C - F are bendable with persistence length ξp = 50 nm.
In our calculation, the elastic and electrostatic energy of the DNA crystal are functions of one free parameter, namely the bending radius Rbend of the arm segments
(C - F). Larger bending radius corresponds to larger crystal spacing, larger elastic
penalty, and smaller Coulombic repulsion. The three models of DNA tile in this figure were constructed with the bending radius Rbend = 4 nm (left), 16 nm (middle),
and 64 nm (right). For scale, the diameter of each helix is 2 nm.

179

where si parameterizes the center of the cylindrical segment i and VDH is the Debye-Hückel
potential. The (1 − Zθ) factor is the renormalization (r) to the counterion condensation
per unit charge (θ) and valence (Z). The magnitude of r is solved by using the Manning
parameter, and the result is given by
Zθ ≃ 1 −

Zξ

(D.2)

The κ−1 is the Debye screening length defined via
κ2 = 4πlB

Zi 2 ci ,

(D.3)

where Zi and ci are the valence and concentration of the salt species i, respectively.

Bending energy
In the generic language of beam theory, the energy cost to bend four identical bendable
segments in a DX molecule scales with the bending radius Rbend and is given by
Gbend = kB T

2Γξp
R2 bend

(D.4)

where Γ is the length of the bendable segments and ξp is the persistence length that depends
on the temperature and Debye screening length of the form.
ξp = ξint + ξel = ξint +

4κ2 lB

(D.5)

Spacing between neighboring DNA tiles
Spacing is defined as the distance between two neighboring DX molecules as shown by the
cartoon in Fig D.1. In order to compare the result of our energy minimization calculation
with the experimental data, we convert the bending radius into spacing s.

s = ro + Rbend 1 − cos

180

Rbend

(D.6)

Note that the conversion above gives the a priori range of spacing to be within 4 nm
to 14 nm, which corresponds to the close packed structure and fully stretched lattice,
respectively, as shown in Fig. D.1.
The equilibrium lattice spacing in the AFM images
Fig. D.2 shows the result of the bending calculation and the numerical integration of the
electrostatic interaction energy at our standard buffer condition for AFM imaging, with

181

Appendix D

Debye screening length κ−1 =0.84 nm. Both energy terms contain the product kB T as a
factor, which makes it convenient to regard kB T as our unit energy. The contributions from
the electrostatics and mechanical bending of the lattice are minimal at ∼5 nm calculated
spacing and are in fair agreement with the 6.6 nm spacing measured from AFM images,
considering our rough representation of the DNA helix. This agreement demonstrates the
promise of the beam theory to explain the two-dimensional DNA crystal structure.

Figure D.2.: Our calculation (right) is in qualitative agreement with the observed spacing between DNA tiles in the AFM image (left). Here, the lattice spacing is defined as
the distance between two neighboring tiles at perpendicular orientation with respect
to the DNA axis. DNA lattice with zero empty space between the neighboring tiles
has a 4 nm spacing. The simple energy argument predicts ∼5 nm lattice spacing,
instead of 4 nm. This predicted spacing provides an access for EcoRI to perform the
nicking reaction on the bendable arms of the DNA tile inside a lattice.

182

Bibliography
[ACP07]

Phaedon Avouris, Zhihong Chen, and Vasili Perebeinos. Carbon-based electronics. Nature Nanotechnology, 2(10):605–615, 2007.

[ADN+ 09]

Ebbe S. Andersen, Mingdong Dong, Morten M. Nielsen, Kasper Jahn,
Ramesh Subramani, Wael Mamdouh, Monika M. Golas, Bjoern Sander, Holger Stark, Cristiano L. P. Oliveira, Jan Skov Pedersen, Victoria Birkedal,
Flemming Besenbacher, Kurt V Gothelf, and Jorgen Kjems. Self-assembly of
a nanoscale DNA box with a controllable lid. Nature, 459(7243):73–76, 2009.

[AKN+ 10]

Rachel C. Angers, Hae-Eun Kang, Dana Napier, Shawn Browning, Tanya
Seward, Candace Mathiason, Aru Balachandran, Debbie McKenzie, Joaquín
Castilla, Claudio Soto, Jean Jewell, Catherine Graham, Edward A. Hoover,
and Glenn C. Telling. Prion strain mutation determined by prion protein conformational compatibility and primary structure. Science, 328(5982):1154–
1158, 2010.

[Alb03]

Bruce Alberts. DNA replication and recombination. Nature, 421(6921):431–
435, 2003.

[AP01]

Kurt Amann and Thomas Pollard. Direct real-time observation of actin filament branching mediated by Arp2/3 complex using total internal reflection
fluorescence microscopy. Proceedings of the National Academy of Sciences of
the United States of America, 98(26):15009–15013, 2001.

[APS08]

Faisal A. Aldaye, Alison L. Palmer, and Hanadi F. Sleiman. Assembling
materials with DNA as the guide. Science, 321(5897):1795–1799, 2008.

[BBS02]

Tamer Bagatur, Ahmet Baylar, and Nusret Sekerdag. The effect of nozzle
type on air entrainment by plunging water jets. Water Quality Research
Journal of Canada, 37(3):599–612, 2002.

183

[BC98]

T. Brattberg and H. Chanson.

Air entrapment and air bubble disper-

sion at two-dimensional plunging water jets. Chemical Engineering Science,
53(24):4113 – 4127, 1998.
[BCTH00]

Victor A. Bloomfield, Donald M. Crothers, Ignacio Tinoco, and John E.
Hearst. Nucleic acids: structures, properties, and functions. University Science Books, 2000.

[BD72]

Ray D. Bowman and Norman Davidson. Hydrodynamic shear breakage of
DNA. Biopolymers, 11(12):2601–2624, 1972.

[BdRCS10]

James C. Bird, Rielle de Rüiter, Laurent Courbin, and Howard A. Stone.
Daughter bubble cascades produced by folding of ruptured thin films. Nature,
465(7299):759–762, 2010.

[BHKQ03]

Ido Braslavsky, Benedict Hebert, Emil Kartalov, and Stephen R. Quake.
Sequence information can be obtained from single DNA molecules. Proceedings of the National Academy of Sciences of the United States of America,
100(7):3960–3964, 2003.

[BJ93]

F. Bonetto and R. T. Lahey Jr. An experimental study on air carry under
due to a plunging liquid jet. International Journal of Multiphase Flow, 19(2):
281 – 294, 1993.

[BLS+ 07]

Peter Bieling, Liedewij Laan, Henry Schek, E. Laura Munteanu, Linda
Sandblad, Marileen Dogterom, Damian Brunner, and Thomas Surrey. Reconstitution of a microtubule plus-end tracking system in vitro. Nature,
450(7172):1100–1105, 2007.

[Bow92]

P. A. Bowyer. The rise of bubbles in a glass tube and the spectrum of bubbles
produced by a splash. Journal of Marine Research, 50(4):521–543, 1992.

[BPB77]

Edward Baylor, Virginia Peters, and Martha Baylor. Water-to-air transfer
of virus. Science, 197(4305):763–764, 1977.

[BR09]

Yuriy Brun and Dustin Reishus. Path finding in the tile assembly model.
Theoretical Computer Science, 410(15):1461–1472, 2009.

184

[BRW05]

Robert D. Barish, Paul W. K. Rothemund, and Erik Winfree. Two computational primitives for algorithmic self-assembly: Copying and counting. Nano
Letters, 5(12):2586–2592, 2005.

[BS70]

Duncan Blanchard and Lawrence Syzdek. Mechanism for the water-to-air
transfer and concentration of bacteria. Science, 170(3958):626–628, 1970.

[BS95]

Jeremy Boulton-Stone. The effect of surfactant on bursting gas bubbles.
Journal of Fluid Mechanics, 302 IS -:231–257, 1995.

[BS10]

Itay Budin and Jack W. Szostak. Expanding roles for diverse physical phenomena during the origin of life. Annual Review of Biophysics, 39(1):245–263,
2010.

[BSB93]

J. M. Boulton-Stone and J. R. Blake. Gas bubbles bursting at a free surface.
Journal of Fluid Mechanics, 254:437–466, 1993.

[BSLS00]

Carlos Bustamante, Steven B. Smith, Jan Liphardt, and Doug Smith. Singlemolecule studies of DNA mechanics. Current Opinion in Structural Biology,
10(3):279–285, 2000.

[BSRW09]

Robert D. Barish, Rebecca Schulman, Paul W. K. Rothemund, and Erik Winfree. An information-bearing seed for nucleating algorithmic self-assembly.
Proceedings of the National Academy of Sciences of the United States of
America, 106(15):6054–6059, 2009.

[BT07]

Jonathan Bath and Andrew J. Turberfield. DNA nanomachines. Nature
Nanotechnology, 2(5):275–284, 2007.

[BZK+ 04]

Brett A. Buchholz, Jacob M. Zahn, Martin Kenward, Gary W. Slater, and
Annelise E. Barron. Flow-induced chain scission as a physical route to narrowly distributed, high molar mass polymers. Polymer, 45(4):1223–1234,
2004.

[CAH04]

H. Chanson, S. Aoki, and A. Hoque. Physical modelling and similitude of air
bubble entrainment at vertical circular plunging jets. Chemical Engineering
Science, 59(4):747–758, 2004.

185

[CB81]

Richard H. Cote and Gary G. Borisy. Head-to-tail polymerization of microtubules in vitro. Journal of Molecular Biology, 150(4):577–599, 1981.

[CC07]

John Collinge and Anthony R. Clarke. A general model of prion strains and
their pathogenicity. Science, 318(5852):930–936, 2007.

[CDVW04]

Sean R. Collins, Adam Douglass, Ronald D. Vale, and Jonathan S. Weissman. Mechanism of prion propagation: amyloid growth occurs by monomer
addition. PLoS Biology, 2(10):e321, 2004.

[CFK95]

Denis Chrétien, Stephen David Fuller, and Eric Karsenti. Structure of growing microtubule ends: two-dimensional sheets close into tubes at variable
rates. Journal of Cell Biology, 129(5):1311, 1995.

[CH92]

Robert Cherry and Carl Hulle. Cell death in the thin films of bursting bubbles. Biotechnology Progress, 8(1):11–18, 1992.

[CLS96]

John K. Chika, Uno Lindberg, and Clarence E. Schutt. The structure of
an open state of β-actin at 265 Å resolution. Journal of Molecular Biology,
263:607–623, 1996.

[CLZ82]

Michael Caplow, George M. Langford, and Barry Zeeberg. Concerning the
efficiency of the treadmilling phenomenon with microtubules. Journal of
Biological Chemistry, 257(24):15012–15021, 1982.

[CRS94]

M. Caplow, R. L. Ruhlen, and J. Shanks. The free energy for hydrolysis
of a microtubule-bound nucleotide triphosphate is near zero: all of the free
energy for hydrolysis is stored in the microtubule lattice. The Journal of Cell
Biology, 127(3):779–788, 1994.

[CS66]

A. G. Cairns-Smith. The origin of life and the nature of the primitive gene.
Journal of Theoretical Biology, 10(1):53–88, 1966.

[CS08]

A. Graham Cairns-Smith. Chemistry and the missing era of evolution. Chemistry – A European Journal, 14(13):3830–3839, 2008.

[CSGW07]

Ho-Lin Chen, Rebecca Schulman, Ashish Goel, and Erik Winfree. Reducing
facet nucleation during algorithmic self-assembly. Nano Letters, 7(9):
2913–2919, 2007.

186

[Cul60]

F. E. C. Culick. Comments on a ruptured soap film. Journal of Applied
Physics, 3:1128–1129, 1960.

[CW91]

Denis Chrétien and Richard H. Wade. New data on the microtubue surface
lattice. Biol Cell, 71(1-2):161–174, 1991.

[CW10]

Kenneth Campellone and Matthew Welch. A nucleator arms race: cellular
control of actin assembly. Nature Reviews Molecular Cell Biology, 11(4):237–
251, 2010.

[Dan78]

Barry M. Dancis. Shear breakage of DNA. Biophysical Journal, 24(2):489–
503, 1978.

[DCS07]

Shawn M. Douglas, James J. Chou, and William M. Shih. DNA-nanotubeinduced alignment of membrane proteins for NMR structure determination.
Proceedings of the National Academy of Sciences of the United States of
America, 104(16):6644–6648, 2007.

[DdGBW98] G. Debrégeas, P.-G de Gennes, and F. Brochard-Wyart. The life and death
of “bare” viscous bubbles. Science, 279(5357):1704–1707, 1998.
[DDL+ 09]

Shawn M. Douglas, Hendrik Dietz, Tim Liedl, Bjorn Hogberg, Franziska
Graf, and William M. Shih. Self-assembly of DNA into nanoscale threedimensional shapes. Nature, 459(7245):414–418, 2009.

[DDS09]

Hendrik Dietz, Shawn M. Douglas, and William M. Shih. Folding DNA into
twisted and curved nanoscale shapes. Science, 325(5941):725, 2009.

[dGM08]

Tom F. A. de Greef and E. W. Meijer. Materials science: Supramolecular
polymers. Nature, 453(7192):171–173, 2008.

[DKRLJ05] Marileen Dogterom, Jacob W. J. Kerssemakers, Guillaume Romet-Lemonne,
and Marcel E Janson. Force generation by dynamic microtubules. Current
Opinion in Cell Biology, 17(1):67–74, 2005.
[DM97]

Arshad Desai and Timothy J. Mitchison. Microtubule polymerization dynamics. Annual Review of Cell and Developmental Biology, 13:83–117, 1997.

187

[DMBW95] G. Debrégeas, P. Martin, and F. Brochard-Wyart. Viscous bursting of suspended films. Physical Review Letters, 75(21):3886, 1995.
[DMSW98]

David C. Duffy, J. Cooper McDonald, Olivier J. A. Schueller, and
George M. Whitesides.

Rapid prototyping of microfluidic systems in

poly(dimethylsiloxane). Analytical Chemistry, 70(23):4974–4984, 1998.
[EHW12]

Constantine G. Evans, Rizal F. Hariadi, and Erik Winfree. Direct Atomic
Force Microscopy Observation of DNA Tile Crystal Growth at the SingleMolecule Level. Journal of the American Chemical Society, 134(25):10485–
10492, 2012.

[ENAF04]

Axel Ekani-Nkodo, Kumar Ashish, and Deborah Kuchnir Fygenson. Joining
and scission in the self-assembly of nanotubes from DNA tiles. Physical
Review Letters, 93(26):268301, 2004.

[ESF97]

L. J. Evers, S. Yu. Shulepov, and G. Frens. Bursting dynamics of thin free liquid films from newtonian and viscoelastic solutions. Physical Review Letters,
79(24):4850–4853, 1997.

[ESK+ 10]

Masayuki Endo, Tsutomu Sugita, Yousuke Katsuda, Kumi Hidaka, and Hiroshi Sugiyama. Programmed-assembly system using DNA jigsaw pieces.
Chemistry – A European Journal, 9999(9999):NA, 2010.

[FBK+ 06]

Marcin Fialkowski, Kyle J. M. Bishop, Rafal Klajn, Stoyan K. Smoukov,
Christopher J. Campbell, and Bartosz A. Grzybowski. Principles and implementations of dissipative (dynamic) self-assembly. Journal of Physical
Chemistry B, 110(6):2482–2496, 2006.

[FGM+ 84]

Christin Frederick, John Grable, Michele Melia, Cleopas Samudzi, Linda JenJacobson, Bi-Cheng Wang, Patricia Greene, Herbert Boyer, and John Rosenberg. Kinked DNA in crystalline complex with EcoRI endonuclease. Nature,
309(5966):327–331, 1984.

[FHL94]

Henrik Flyvbjerg, Timothy E. Holy, and Stanisla Leibler. Stochastic dynamics of microtubules: a model for caps and catastrophes. Physical Review
Letters, 73(17):2372–2375, 1994.

188

[FHL96]

Henrik Flyvbjerg, Timothy E. Holy, and Stanislas Leibler. Microtubule dynamics: Caps, catastrophes, and coupled hydrolysis. Physical Review E,
54(5):5538–5560, 1996.

[FHP+ 08]

Kenichi Fujibayashi, Rizal F. Hariadi, Sung Ha Park, Erik Winfree, and
Satoshi Murata. Toward reliable algorithmic self-assembly of DNA tiles: A
fixed-width cellular automaton pattern. Nano Letters, 8(7):1791–1797, 2008.

[FM09]

Kenichi Fujibayashi and Satoshi Murata. Precise simulation model for DNA
tile self-assembly. IEEE Transactions on Nanotechnology, 8(3):361–368, 2009.

[FN06]

Udo Feldkamp and Christof Niemeyer. Rational design of DNA nanoarchitectures. Angewandte Chemie International Edition, 45(12):1856–1876, 2006.

[FS93]

Tsu Fu and Nadrian Seeman. DNA double-crossover molecules. Biochemistry,
32(13):3211–3220, 1993.

[FTT+ 02]

Ikuko Fujiwara, Shin Takahashi, Hisashi Tadakuma, Takashi Funatsu, and
Shin’ichi Ishiwata. Microscopic analysis of polymerization dynamics with
individual actin filaments. Nature Cell Biology, 4(9):666–673, 2002.

[GBT08]

S. J. Green, J. Bath, and A. J. Turberfield. Coordinated chemomechanical
cycles: A mechanism for autonomous molecular motion. Physical Review
Letters, 101(23):238101–4, 2008.

[GCK+ 10]

J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchgeßner,
B. Hoffmann, R. Merkel, and M. Giesen. Tube width fluctuations in F-actin
solutions. Physical Review Letters, 105(3):037801, 2010.

[GCL+ 10]

Elton Graugnard, Amber Cox, Jeunghoon Lee, Cheryl Jorcyk, Bernard
Yurke, and William L. Hughes. Kinetics of DNA and RNA hybridization
in serum and serum-SDS. IEEE Transactions on Nanotechnology, 9(5):603–
609, 2010.

[GCM04]

Ethan C. Garner, Christopher S. Campbell, and R. Dyche Mullins. Dynamic instability in a DNA-segregating prokaryotic actin homolog. Science,
306(5698):1021–1025, 2004.

189

[GCWM07] Ethan C. Garner, Christopher S. Campbell, Douglas B. Weibel, and R. Dyche Mullins. Reconstitution of DNA segregation driven by assembly of a
prokaryotic actin homolog. Science, 315(5816):1270–1274, 2007.
[GHD+ 08]

Russell P. Goodman, Mike Heilemann, Soren Doose, Christoph M. Erben,
Achillefs N. Kapanidis, and Andrew J. Turberfield. Reconfigurable, braced,
three-dimensional DNA nanostructures. Nature Nanotechnology, 3:93–96,
2008.

[GMNH93]

Frederick Gittes, Brian Mickey, Jilda Nettleton, and Jonathon Howard. Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape. The Journal of Cell Biology, 120(4):923, 1993.

[GSW00]

Bartosz A. Grzybowski, Howard A. Stone, and George M. Whitesides. Dynamic self-assembly of magnetized, millimetre-sized objects rotating at a
liquid–air interface. Nature, 405(6790):1033–1036, 2000.

[GT81]

Cal Green and Clark Tibbetts. Reassociation rate limited displacement of
DNA strands by branch migration. Nucleic Acids Research, 9(8):1905–1918,
1981.

[HAD02]

M. El Hammoumi, J. L. Achard, and L. Davoust. Measurements of air entrainment by vertical plunging liquid jets. Experiments in Fluids, 32(6):624–
638, 2002.

[HH86]

Tetsuya Horio and Hirokazu Hotani. Visualization of the dynamic instability
of individual microtubules by dark-field microscopy. Nature, 321:605–607,
1986.

[HH03]

Joe Howard and Anthony A. Hyman. Dynamics and mechanics of the microtubule plus end. Nature, 422:753–758, 2003.

[HL96]

H. G. Hansma and D. E. Laney. DNA binding to mica correlates with cationic
radius: assay by atomic force microscopy. Biophysical Journal, 70(4):1933–
1939, 1996.

[HL10]

Yu He and David R. Liu. Autonomous multistep organic synthesis in a single
isothermal solution mediated by a DNA walker. Nature Nanotechnology,
5:778–782, 2010.

190

[HM84]

A. F. Horn and E. W. Merrill. Midpoint scission of macromolecules in dilute
solution in turbulent flow. Nature, 312(5990):140–141, 1984.

[HO10]

Mark Hedglin and Patrick J O’Brien. Hopping enables a DNA repair glycosylase to search both strands and bypass a bound protein. ACS Chemical
Biology, 5(4):427–436, 2010.

[HSD+ 92]

Anthony A. Hyman, S. Salser, D. N. Drechsel, N. Unwin, and Timothy J.
Mitchison. Role of GTP hydrolysis in microtubule dynamics: information
from a slowly hydrolyzable analogue, GMPCPP. Molecular Biology of the
Cell, 3(10):1155, 1992.

[HW04]

Rizal F. Hariadi and Erik Winfree. Atomic force microscopy movies and
measurements of DNA crystals. Foundations of Nanoscience (Poster), 1,
2004.

[HY]

Rizal F. Hariadi and Bernard Yurke. Elongational rates in bursting bubbles
measured using DNA nanotubes, in preparation.

[H97]

Timothy E. Holy. Physical aspects of the assembly and function of microtubules, 1997.

[HY10]

Rizal F. Hariadi and Bernard Yurke. Elongational-flow-induced scission of
DNA nanotubes in laminar flow. Physical Review E, 82(4):046307, 2010.

[IGC02]

Ilia Ichetovkin, Wayne Grant, and John Condeelis. Cofilin produces newly
polymerized actin filaments that are preferred for dendritic nucleation by the
Arp2/3 complex. Current Biology, 12(1):79–84, 2002.

[Jac75]

M Jacobs. Part IX. nucleotide-tubulin interactions: Tubulin nucleotide reactions and their role in microtubule assembly and dissociation. Annals of the
New York Academy of Sciences, 253:562–572, 1975.

[KCdlT96]

K. D. Knudsen, J. G. Hernández Cifre, and J. García de la Torre. Conformation and fracture of polystyrene chains in extensional flow studied by
numerical simulation. Macromolecules, 29(10):3603–3610, 1996.

191

[KDE+ 98]

A. Krishnan, E. Dujardin, T. W. Ebbesen, P. N. Yianilos, and M. M. J.
Treacy. Young’s modulus of single-walled nanotubes. Physical Review B,
58(20):14013–14019, 1998.

[KEW+ 04]

Michael Kurpiewski, Lisa Engler, Lucyna Wozniak, Anna Kobylanska, Maria
Koziolkiewicz, Wojciech Stec, and Linda Jen-Jacobson. Mechanisms of coupling between DNA recognition specificity and catalysis in EcoRI endonuclease. Structure, 12(10):1775–1788, 2004.

[KGL+ 90]

Young Chang Kim, John C. Grable, Robert Love, Patricia J. Greene, and
John M. Rosenberg. Refinement of EcoRI endonuclease crystal structure: a
revised protein chain tracing. Science, 249(4974):1307–1309, 1990.

[KLZY06]

Yonggang Ke, Yan Liu, Junping Zhang, and Hao Yan. A study of DNA
tube formation mechanisms using 4-, 8-, and 12-helix DNA nanostructures.
Journal of the American Chemical Society, 128(13):4414–4421, 2006.

[KNT+ 08]

Stoyan Karakashev, Phong Nguyen, Roumen Tsekov, Marc Hampton, and
Anh Nguyen. Anomalous ion effects on rupture and lifetime of aqueous foam
films formed from monovalent salt solutions up to saturation concentration.
Langmuir, 24(20):11587–11591, 2008.

[KNYO90]

Daisuke Kusabiraki, Hidefumi Niki, Kazuaki Yamagiwa, and Akira Ohkawa.
Gas entrainment rate and flow pattern of vertical plunging liquid jets. The
Canadian Journal of Chemical Engineering, 68(6):893–903, 1990.

[KP05]

Jeffrey R. Kuhn and Thomas D. Pollard. Real-time measurements of actin
filament polymerization by total internal reflection fluorescence microscopy.
Biophysical Journal, 88(2):1387–1402, 2005.

[KP07]

Jeffrey R. Kuhn and Thomas D Pollard. Single molecule kinetic analysis
of actin filament capping: Polyphosphoinositides do not dissociate capping
proteins. Journal of Biological Chemistry, 282(38):28014–28024, 2007.

[KWSS07]

Kinori Kuzuya, Risheng Wang, Ruojie Sha, and Nadrian C. Seeman. Six-helix
and eight-helix DNA nanotubes assembled from half-tubes. Nano Letters,
7(6):1757–1763, 2007.

192

[LC04]

Clive Lloyd and Jordi Chan. Microtubules and the shape of plants to come.
Nature Reviews Molecular Cell Biology, 5(1):13–23, 2004.

[LCC96]

N. Y. Liang, C. K. Chan, and H. J. Choi. Dynamics of the formation of an
aureole in the bursting of soap films. Physical Review E, 54(4):R3117–R3120,
1996.

[LCH+ 06]

Haipeng Liu, Yi Chen, Yu He, Alexander E. Ribbe, and Chengde Mao. Approaching the limit: Can one DNA oligonucleotide assemble into large nanostructures?
2006.

[LF09]

Angewandte Chemie International Edition, 45(12):1942–1945,

Allen Liu and Daniel Fletcher. Biology under construction: in vitro reconstitution of cellular function. Nature Reviews Molecular Cell Biology, 10(9):644–
650, 2009.

[LG08]

Rong Li and Gregg G. Gundersen. Beyond polymer polarity: how the cytoskeleton builds a polarized cell. Nature Reviews Molecular Cell Biology,
9(11):860–873, 2008.

[LLRY06]

Chenxiang Lin, Yan Liu, Sherri Rinker, and Hao Yan. DNA tile based self
assembly: Building complex nanoarchitectures. ChemPhysChem, 7(8):1641–
1647, 2006.

[LMD+ 10]

Kyle Lund, Anthony Manzo, Nadine Dabby, Nicole Michelotti, Alexander
Johnson-Buck, Jeanette Nangreave, Steven Taylor, Renjun Pei, Milan Stojanovic, Nils Walter, Erik Winfree, and Hao Yan. Molecular robots guided
by prescriptive landscapes. Nature, 465(7295):206–210, 2010.

[LMFM+ 10] Kara Lavender Law, S. Moret-Ferguson, Nikolai A. Maximenko, Giora
Proskurowski, Emily E. Peacock, Jan Hafner, and Christopher M. Reddy.
Plastic accumulation in the north atlantic subtropical gyre. Science,
329(5996):1185–1188, 2010.
[LPH93]

Michael Lorenz, David Popp, and Kenneth C. Holmes. Refinement of the
F-actin model against X-ray fiber diffraction data by the use of a directed
mutation algorithm. Journal of Molecular Biology, 234(3):826–836, 1993.

193

[LPRL04]

Dage Liu, Sung Ha Park, John H. Reif, and Thomas H. LaBean. DNA nanotubes self-assembled from triple-crossover tiles as templates for conductive
nanowires. Proceedings of the National Academy of Sciences of the United
States of America, 101(3):717–722, 2004.

[LPSC97]

R. G. Larson, T. T. Perkins, D. E. Smith, and S. Chu. Hydrodynamics of a
DNA molecule in a flow field. Physical Review E, 55(2):1794–1797, 1997.

[LR95]

J. C. Lin and D. Rockwell. Evolution of a quasi-steady breaking wave. Journal
of Fluid Mechanics, 302:29–44, 1995.

[LS04]

Shiping Liao and Nadrian C. Seeman. Translation of DNA signals into polymer assembly instructions. Science, 306(5704):2072–2074, 2004.

[LYL05]

D. C. Lin, Bernard Yurke, and N. A. Langrana. Inducing reversible stiffness
changes in DNA-crosslinked gels. Journal of Materials Research, 20(6):1456–
1464, 2005.

[LYZ+ 06]

Jonathan W. Larson, Gregory R. Yantz, Qun Zhong, Rebecca Charnas,
Christina M. DAntoni, Michael V. Gallo, Kimberly A. Gillis, Lori A. Neely,
Kevin M. Phillips, Gordon G. Wong, Steven R. Gullans, and Rudolf Gilmanshin. Single DNA molecule stretching in sudden mixed shear and elongational
microflows. Lab on a Chip, 6:1187–1199, 2006.

[LZWS10]

Wenyan Liu, Hong Zhong, Risheng Wang, and Nadrian Seeman. Crystalline
two-dimensional DNA-origami arrays.

Angewandte Chemie International

Edition, 50(1):264–267, 2010.
[Man08]

Stephen Mann. Life as a nanoscale phenomenon. Angewandte Chemie International Edition, 47:5306–5320, 2008.

[Mar38]

Douglas A. Marsland. The effects of high hydrostatic pressure upon cell
division in Arbacia eggs. Journal of Cellular and Comparative Physiology,
12(1):57–70, 1938.

[MBBW94]

P. Martin, A. Buguin, and F. Brochard-Wyart. Bursting of a liquid film on
a liquid substrate. Europhysics Letters, 28(6):421–426, 1994.

194

[MD52]

Daniel Mazia and Katsuma Dan. The isolation and biochemical characterization of the mitotic apparatus of dividing cells. Proceedings of the National
Academy of Sciences of the United States of America, 38(9):826–838, 1952.

[MFZ+ 97]

R. Scott Muir, Humberto Flores, Norton D. Zinder, Peter Model, Xavier
Soberon, and Joseph Heitman. Temperature-sensitive mutants of the EcoRI
endonuclease. Journal of Molecular Biology, 274(5):722–737, 1997.

[MH95]

B. Mickey and J. Howard. Rigidity of microtubules is increased by stabilizing
agents. The Journal of Cell Biology, 130(4):909–917, 1995.

[MHM+ 04]

James C. Mitchell, J. Robin Harris, Jonathan Malo, Jonathan Bath, and
Andrew J. Turberfield. Self-assembly of chiral DNA nanotubes. Journal of
the American Chemical Society, 126(50):16342–16343, 2004.

[MK84a]

Timothy J. Mitchison and Marc Kirschner. Dynamic instability of microtubule growth. Nature, 312:237–242, 1984.

[MK84b]

Timothy J. Mitchison and Marc Kirschner. Microtubule assembly nucleated
by isolated centrosomes. Nature, 312:232–237, 1984.

[MKB+ 07]

Julia Morfill, Ferdinand Kuhner, Kerstin Blank, Robert A. Lugmaier, Julia
Sedlmair, and Hermann E Gaub. B-S transition in short oligonucleotides.
Biophysical Journal, 93(7):2400–2409, 2007.

[ML08]

Pieta K. Mattila and Pekka Lappalainen. Filopodia: molecular architecture
and cellular functions. Nature Reviews Molecular Cell Biology, 9(6):446–454,
2008.

[MLK+ 05]

Frederick Mathieu, Shiping Liao, Jens Kopatsch, Tong Wang, Chengde Mao,
and Nadrian C. Seeman. Six-helix bundles designed from DNA. Nano Letters,
5(4):661–665, 2005.

[MlKS07]

Frank Müller, ller, Ulrike Kornek, and Ralf Stannarius. Experimental study
of the bursting of inviscid bubbles. Physical Review E, 75(6):065302, 2007.

[MMM91]

Eva-Maria Mandelkow, Eckhard Mandelkow, and RonaldA. Milligan. Microtubule dynamics and microtubule caps: a time-resolved cryo-electron microscopy study. The Journal of Cell Biology, 114(5):977–991, 1991.

195

[MS93]

Larry E. Morrison and Lucy M. Stols. Sensitive fluorescence-based thermodynamic and kinetic measurements of DNA hybridization in solution. Biochemistry, 32(12):3095–3104, 1993.

[MW78]

Robert L. Margolis and Leslie Wilson. Opposite end assembly and disassembly of microtubules at steady state in vitro. Cell, 13(1):1–8, 1978.

[NK90]

Tuan Q. Nguyen and Henning H. Kausch. Effects of solvent viscosity on
polystyrene degradation in transient elongational flow.

Macromolecules,

23(24):5137–5145, 1990.
[NK92]

Tuan Q. Nguyen and Henning H. Kausch. Chain extension and degradation
in convergent flow. Polymer, 33(12):2611–2621, 1992.

[NN09]

Phong Nguyen and Anh Nguyen. Drainage, rupture, and lifetime of deionized
water films: Effect of dissolved gases? Langmuir, 26(5):3356–3363, 2009.

[NSML97]

F. J. Ndlec, T. Surrey, A. C. Maggs, and Stanislas Leibler. Self-organization
of microtubules and motors. Nature, 389(6648):305–308, 1997.

[NYL09]

Jeanette Nangreave, Hao Yan, and Yan Liu. Studies of thermal stability
of multivalent DNA hybridization in a nanostructured system. Biophysical
Journal, 97(2):563–571, 2009.

[Ogu98]

Hasan N. Oguz. The role of surface disturbances in the entrainment of bubbles
by a liquid jet. Journal of Fluid Mechanics, 372:189–212, 1998.

[OHSC+ 96] P. J. Oefner, S. P. Hunicke-Smith, L. Chiang, F. Dietrich, J. Mulligan, and
R. W. Davis. Efficient random subcloning of DNA sheared in a recirculating
point- sink flow system. Nucleic Acid Research, 24(20):3879–3886, 1996.
[OK62]

F. Oosawa and M. Kasai. A theory of linear and helical aggregations of
macromolecules. Journal of Molecular Biology, 4:10–21, 1962.

[OK86]

J. A. Odell and A. Keller. Flow-induced chain fracture of isolated linear
macromolecules in solution. Journal of Polymer Science Part B: Polymer
Physics, 24(9):1889–1916, 1986.

[Opa52]

196

A. I. Oparin. The origin of life. Dover, 1952.

[ORKF06]

Patrick O’Neill, Paul W. K. Rothemund, Ashish Kumar, and D. K. Fygenson.
Sturdier DNA nanotubes via ligation. Nano Letters, 6(7):1379–1383, 2006.

[OT94]

J. A. Odell and M. A. Taylor. Dynamics and thermomechanical stability of
DNA in solution. Biopolymers, 34(11):1483–1493, 1994.

[PBL+ 05]

Sung Ha Park, Robert D. Barish, Hanying Li, John H. Reif, Gleb Finkelstein, Hao Yan, and Thomas H. LaBean. Three-helix bundle DNA tiles selfassemble into 2D lattice or 1D templates for silver nanowires. Nano Letters,
5(4):693–696, 2005.

[PF08]

Francesco Pampaloni and Ernst-Ludwig Florin. Microtubule architecture:
inspiration for novel carbon nanotube-based biomimetic materials. Trends in
Biotechnology, 26(6):302–310, 2008.

[PH94]

I. G. Panyutin and P. Hsieh. The kinetics of spontaneous DNA branch migration. Proceedings of the National Academy of Sciences of the United States
of America, 91(6):2021–2025, 1994.

[PKTG09]

Rob Phillips, Jane Kondev, Julie Theriot, and Hernan Garcia. Physical biology of the cell. Garland Science, 2009.

[PTS+ 06]

Renjun Pei, Steven K. Taylor, Darko Stefanovic, Sergei Rudchenko,
Tiffany E. Mitchell, and Milan N. Stojanovic. Behavior of polycatalytic assemblies in a substrate-displaying matrix. Journal of the American Chemical
Society, 128(39):12693–12699, 2006.

[Qua03]

M. Quail. Encyclopedia of the Human Genome. Nature Publishing, London,
2003.

[QW89]

Robin Quartin and James Wetmur. Effect of ionic strength on the hybridization of oligodeoxynucleotides with reduced charge due to methylphosphonate
linkages to unmodified oligodeoxynucleotides containing the complementary
sequence. Biochemistry, 28(3):1040–1047, 1989.

[RBHW77]

C. M. Radding, K. L. Beattie, W. K. Holloman, and R. C. Wiegand. Uptake
of homologous single-stranded fragments by superhelical DNA IV: Branch
migration. Journal of Molecular Biology, 116(4):825–839, 1977.

197

[RENP+ 04] Paul W. K. Rothemund, Axel Ekani-Nkodo, Nick Papadakis, Ashish Kumar,
Deborah Kuchnir Fygenson, and Erik Winfree. Design and characterization of
programmable DNA nanotubes. Journal of the American Chemical Society,
126(50):16344–16352, 2004.
[RHF+ 10]

Lynn M. Russell, Lelia N. Hawkins, Amanda A. Frossard, Patricia K. Quinn,
and Tim S. Bates. Carbohydrate-like composition of submicron atmospheric
particles and their production from ocean bubble bursting. Proceedings of the
National Academy of Sciences of the United States of America, 107(15):6652–
6657, 2010.

[Rot06]

Paul W. K. Rothemund. Folding DNA to create nanoscale shapes and patterns. Nature, 440(7082):297–302, 2006.

[RPW04]

Paul W. K. Rothemund, Nick Papadakis, and Erik Winfree. Algorithmic
self-assembly of DNA Sierpinski triangles. PLoS Biology, 2(12), 2004.

[RQ06]

É. Reyssat and D. Quéré. Bursting of a fluid film in a viscous environment.
Europhysics Letters, 76(2):236, 2006.

[RS10]

Donald Rau and Nina Sidorova. Diffusion of the restriction nuclease EcoRI
along DNA. Journal of Molecular Biology, 395(2):408–416, 2010.

[RSB+ 05]

Dustin Reishus, Bilal Shaw, Yuriy Brun, Nickolas Chelyapov, and Leonard
Adleman. Self-assembly of DNA double-double crossover complexes into highdensity, doubly connected, planar structures. Journal of the American Chemical Society, 127(50):17590–17591, 2005.

[SB99]

G. J. Storr and M. Behnia. Experiments with large diameter gravity driven
impacting liquid jets. Experiments in Fluids, 27(1):60–69, 1999.

[SBL01]

Jack W. Szostak, David P. Bartel, and P. Luigi Luisi. Synthesizing life.
Nature, 409(6818):387–390, 2001.

[SCB96]

Steven B. Smith, Yujia Cui, and Carlos Bustamante. Overstretching B-DNA:
The elastic response of individual double-stranded and single-stranded DNA
molecules. Science, 271(5250):795–799, 1996.

198

[Sch07]

Rebecca Schulman. The Self-Replication and Evolution of DNA Crystals.
PhD thesis, California Institute of Technology, May 2007.

[SCK+ 00]

Tricia R. Serio, Anil G. Cashikar, Anthony S. Kowal, George J. Sawicki, Jahan J. Moslehi, Louise Serpell, Morton F. Arnsdorf, and Susan L. Lindquist.
Nucleated conformational conversion and the replication of conformational
information by a prion determinant. Science, 289(5483):1317–1321, 2000.

[SCM00]

Rava Silveira, Sahraoui Chaïeb, and L. Mahadevan. Rippling instability of a
collapsing bubble. Science, 287(5457):1468–1471, 2000.

[SCW08]

David Soloveichik, Matthew Cook, and Erik Winfree. Combining self-healing
and proofreading in self-assembly. Natural Computing, 7(2):203–218, 2008.

[See82]

Nadrian C. Seeman. Nucleic acid junctions and lattices. Journal of Theoretical Biology, 99(2):237 – 247, 1982.

[See90]

Nadrian C. Seeman. De novo design of sequences for nucleic acid structural
engineering. Journal of Biomolecular Structure & Dynamics, 8(3):573–581,
1990.

[See03]

Nadrian C. Seeman. DNA in a material world. Nature, 421(6921):427–431,
2003.

[See07]

Nadrian C. Seeman. An overview of structural DNA nanotechnology. Molecular biotechnology, 37(3):246–257, 2007.

[SKOS01]

Masahito Sano, Ayumi Kamino, Junko Okamura, and Seiji Shinkai. Ring
closure of carbon nanotubes. Science, 293(5533):1299–1301, 2001.

[SL06]

James Shorter and Susan Lindquist. Destruction or potentiation of different
prions catalyzed by similar hsp104 remodeling activities. Molecular Cell,
23(3):425–438, 2006.

[SP04]

Jong-Shik Shin and Niles A. Pierce. A synthetic DNA walker for molecular transport. Journal of American Chemical Society, 126(35):10834–10835,
2004.

199

[SS76]

E. Van De Sande and John M. Smith. Jet break-up and air entrainment by
low velocity turbulent water jets. Chemical Engineering Science, 31(3):219 –
224, 1976.

[SS02]

Andrew P. Somlyo and Avril V. Somlyo. Signal transduction and regulation
in smooth muscle. Nature, 372:231–236, 2002.

[SS04]

William B. Sherman and Nadrian C. Seeman. A precisely controlled DNA
biped walking device. Nano Letters, 4(7):1203–1207, 2004.

[SS06]

William B Sherman and Nadrian C Seeman. Design of Minimally Strained
Nucleic Acid Nanotubes. Biophysical Journal, 90(12):4546–4557, 2006.

[SSW10]

David Soloveichik, Georg Seelig, and Erik Winfree. DNA as a universal substrate for chemical kinetics. Proceedings of the National Academy of Sciences
of the United States of America, 107(12):5393, 2010.

[SSZW06]

Georg Seelig, David Soloveichik, David Yu Zhang, and Erik Winfree. Enzymefree nucleic acid logic circuits. Science, 314(5805):1585–1588, 2006.

[ST68]

Michael L. Shelanski and Edwin W. Taylor. Properties of the protein subunit
of central-pair and outer-doublet microtubules of sea urchin flagella. The
Journal of Cell Biology, 38(2):304–315, 1968.

[Str99]

John William Strutt. Scientific Papers, volume 1. Cambridge University
Press, Cambridge, 1899.

[Str02]

John William Strutt. Scientific Papers, volume 3. Cambridge University
Press, Cambridge, 1902.

[SW03]

Manfred Schliwa and Günther Woehlke.

Molecular motors.

Nature,

422(6933):759–765, 2003.
[SW05]

Rebecca Schulman and Erik Winfree. Self-replication and evolution of DNA
crystals. Advances in Artificial Life, pages 734–743, 2005.

[SW07]

Rebecca Schulman and Erik Winfree.

Synthesis of crystals with a pro-

grammable kinetic barrier to nucleation. Proceedings of the National Academy
of Sciences of the United States of America, 104(39):15236–15241, 2007.

200

[SW11]

Rebecca Schulman and Erik Winfree. Simple evolution of complex crystal
species. Lecture Notes in Computer Science, 6518:147–161, 2011.

[SWY+ 98]

Nadrian C. Seeman, Hui Wang, Xiaoping Yang, Furong Liu, Chengde Mao,
Weiqiong Sun, Lisa A. Wenzler, Zhiyong Shen, Ruojie Sha, Hao Yan, Man Hoi
Wong, Phiset Sa-Ardyen, Bing Liu, Hangxia Qiu, Xiaojun Li, Jing Qi,
Shou Ming Du, Yuwen Zhang, John E. Mueller, Tsu-Ju Fu, Yinli Wang,
and Junghuei Chen. New motifs in DNA nanotechnology. Nanotechnology,
9(3):257–273, 1998.

[SY10]

Rebecca Schulman and Bernard Yurke. A molecular algorithm for path selfassembly in 3 dimensions. In Proceedings of Robotics: Science and Systems,
2010.

[Tay59]

Geoffrey Taylor. The dynamics of thin sheets of fluid. III. disintegration of
fluid sheets. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 253(1274):313–321, 1959.

[The00]

Julie A. Theriot. The polymerization motor. Traffic, 1:19–28, 2000.

[THSOD98] Yvonne Thorstenson, Scott Hunicke-Smith, Peter Oefner, and Ronald Davis.
An automated hydrodynamic process for controlled, unbiased DNA shearing.
Genome Research, 8(8):848–855, 1998.
[TPSW97]

Bernard Tinland, Alain Pluen, Jean Sturm, and Gilbert Weill. Persistence
length of single-stranded DNA. Macromolecules, 30(19):5763–5765, 1997.

[TW78]

D. L. Taylor and Y. L. Wang. Molecular cytochemistry: incorporation of fluorescently labeled actin into living cells. Proceedings of the National Academy
of Sciences of the United States of America, 75(2):857, 1978.

[TW80]

D. L. Taylor and Y. L. Wang. Fluorescently labelled molecules as probes of
the structure and function of living cells. Nature, 284(5755):405, 1980.

[UCT+ 00]

Marc A. Unger, Hou-Pu Chou, Todd Thorsen, Axel Scherer, and Stephen R.
Quake. Monolithic microfabricated valves and pumps by multilayer soft
lithography. Science, 288(5463):113–116, 2000.

201

[VCS06]

Siva A. Vanapalli, Steven L. Ceccio, and Michael J. Solomon. Universal
scaling for polymer chain scission in turbulence. Proceedings of the National
Academy of Sciences of the United States of America, 103(45):16660–16665,
2006.

[VDR+ 07]

Suvir Venkataraman, Robert M. Dirks, Paul W. K. Rothemund, Erik Winfree, and Niles A. Pierce. An autonomous polymerization motor powered by
DNA hybridization. Nature Nanotechnology, 2(8):490–494, 2007.

[WC53]

James D. Watson and Francis H. C. Crick. A structure for deoxyribose nucleic
acid. Nature, 171:737–738, 1953.

[WC93]

Richard H. Wade and Denis Chrétien. Cryoelectron microscopy of microtubules. Journal of Structural Biology, 110(1):1–27, 1993.

[WCJ90]

Richard H. Wade, Denis Chrétien, and D. Job. Characterization of microtubule protofilament numbers. How does the surface lattice accommodate?
Journal of Molecular Biology, 212(4):775–786, 1990.

[Weg76]

Albrecht Wegner. Head to tail polymerization of actin. Journal of Molecular
Biology, 108(1):139–50, 1976.

[Wei72]

Richard C. Weisenberg. Microtubule formation in vitro in solutions containing low calcium concentrations. Science, 177(54):1104, 1972.

[WF91]

James Wetmur and Jacques Fresco. DNA probes: Applications of the principles of nucleic acid hybridization. Critical Reviews in Biochemistry and
Molecular Biology, 26(3-4):227–259, 1991.

[WG02]

George M. Whitesides and Bartosz Grzybowski. Self-assembly at all scales.
Science, 295(5564):2418–2421, 2002.

[WGA+ 10]

Bo Wang, Juan Guan, Stephen Anthony, Sung Bae, Kenneth Schweizer, and
Steve Granick. Confining potential when a biopolymer filament reptates.
Physical Review Letters, 104(11):118301, 2010.

[Win98]

Erik Winfree. Simulations of computing by self-assembly. Caltech CS Tech
Report, 22, 1998.

202

[Win06]

Erik Winfree. Self-healing tile sets. Nanotechnology: science and computation, pages 55–78, 2006.

[WJM99]

David Wright, William Jack, and Paul Modrich. The kinetic mechanism of
EcoRI endonuclease. Journal of Biological Chemistry, 274(45):31896–31902,
1999.

[WLWS98]

Erik Winfree, Furong Liu, Lisa A. Wenzler, and Nadrian C Seeman. Design
and self-assembly of two-dimensional DNA crystals. Nature, 394(6693):539–
544, 1998.

[WM05]

Bryant Wei and Yongli Mi. A new triple crossover triangle (TXT) motif for
DNA self-assembly. Biomacromolecules, 6(5):2528–2532, 2005.

[WOP+ 88]

R. A. Walker, E. T. O’brien, N. K. Pryer, M. F. Soboeiro, W. A. Voter, H. P.
Erickson, and E. D. Salmon. Dynamic instability of individual microtubules
analyzed by video light microscopy: rate constants and transition frequencies.
The Journal of Cell Biology, 107(4):1437, 1988.

[Wu81]

Jin Wu. Evidence of sea spray produced by bursting bubbles. Science,
212(4492):324–326, 1981.

[WWAS+ 06] Stefan Westermann, Hong-Wei Wang, Agustin Avila-Sakar, David G. Drubin, Eva Nogales, and Georjana Barnes. The Dam1 kinetochore ring
complex moves processively on depolymerizing microtubule ends. Nature,
440(7083):565–569, 2006.
[YCCP08]

Peng Yin, Harry M. T. Choi, Colby R. Calvert, and Niles A. Pierce. Programming biomolecular self-assembly pathways. Nature, 451(7176):318–322,
2008.

[YGB+ 04]

Peng Yin, Bu Guo, Christina Belmore, Will Palmeri, Erik Winfree,
Thomas H. LaBean, and John H. Reif. TileSoft: Sequence optimization software for designing DNA secondary structures, 2004. TR-CS-2004-09, Duke
2004.

[YHS+ 08]

Peng Yin, Rizal F. Hariadi, Sudheer Sahu, Harry M. T. Choi, Sung Ha Park,
Thomas H. LaBean, and John H Reif. Programming DNA tube circumferences. Science, 321(5890):824–826, 2008.

203

[YO10]

Nina Yao and Mike O’Donnell. Snapshot: The replisome. Cell, 141(6), 2010.

[YPF+ 03]

Hao Yan, Sung Ha Park, Gleb Finkelstein, John H. Reif, and Thomas H.
LaBean. DNA-templated self-assembly of protein arrays and highly conductive nanowires. Science, 301(5641):1882–1884, 2003.

[YTM+ 00]

Bernard Yurke, Andrew J. Turberfield, Allen P. Mills, Friedrich C. Simmel,
and Jennifer L Neumann. A DNA-fuelled molecular machine made of DNA.
Nature, 406(6796):605–608, 2000.

[ZBC+ 09]

Jianping Zheng, Jens J. Birktoft, Yi Chen, Tong Wang, Ruojie Sha,
Pamela E. Constantinou, Stephan L. Ginell, Chengde Mao, and Nadrian C.
Seeman. From molecular to macroscopic via the rational design of a selfassembled 3D DNA crystal. Nature, 461(7260):74–77, 2009.

[ZHCW13]

David Yu Zhang, Rizal F. Hariadi, Harry M. T. Choi, and Erik Winfree.
Integrating DNA strand-displacement circuitry with DNA tile self-assembly.
Nature Communications, 4:1965, 2013.

[ZS09]

Ting F. Zhu and Jack W. Szostak. Coupled growth and division of model protocell membranes. Journal of the American Chemical Society, 131(15):5705–
5713, 2009.

[ZS11]

David Yu Zhang and Georg Seelig. Dynamic DNA nanotechnology using
strand-displacement reactions. Nature Chemistry, 3(2):103–113, 2011.

[ZW09]

David Yu Zhang and Erik Winfree. Control of DNA strand displacement
kinetics using toehold exchange. Journal of the American Chemical Society,
131(47):17303–17314, 2009.

[ZWAM95]

Yixian Zheng, Mei Lie Wong, Bruce Alberts, and Timothy J. Mitchison.
Nucleation of microtubule assembly by a γ-tubulin-containing ring complex.
Nature, 378(6557):578, 1995.

204