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Microfluidic Technologies for Structural Biology
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Hansen, Carl Lars Genghis
(2004)
Microfluidic Technologies for Structural Biology.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/N9T3-7114.
Abstract
In the post-genomic era, X-ray crystallography has emerged as the workhorse of large-scale structural biology initiatives that seek to understand protein function and interaction at the atomic scale. Despite impressive technological advances in X-ray sources, phasing techniques, and computing power, the determination of protein structure has been severely hampered by the difficulties in obtaining high-quality protein crystals. Emergent technologies utilizing microfluidics now have the potential to solve these problems on several levels, both by allowing researchers to conduct efficient assays in nanoliter reaction volumes, and by exploiting the properties of mass-transport at the micron scale to improve the crystallization process. The technique of Multilayer Soft Lithography (MSL) has been used to developed a set of microfluidic tools suitable for all stages of protein crystallogenesis, including protein solubility phase-space mapping, crystallization screening, harvesting, and in silicone diffraction studies. These tools represent the state of the art in on-chip fluid handling functionality and have been demonstrated to dramatically improve protein crystallization.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
combinatorial mixing; crystallization; diffraction; fast mixing; free interface diffusion; high throughput; in silicone diffraction; microcrystallization; microfluidics; nanocrystallogenesis; precise metering; robust metering; structural biology
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Quake, Stephen R.
Thesis Committee:
Quake, Stephen R. (chair)
Rees, Douglas C.
Elowitz, Michael B.
Painter, Oskar J.
Bjorkman, Pamela J.
Phillips, Robert B.
Defense Date:
28 May 2004
Record Number:
CaltechETD:etd-06012004-144201
Persistent URL:
DOI:
10.7907/N9T3-7114
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No commercial reproduction, distribution, display or performance rights in this work are provided.
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2350
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CaltechTHESIS
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01 Jun 2004
Last Modified:
02 Jul 2025 21:02
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MICROFLUIDIC TECHNOLOGIES
FOR STRUCTURAL BIOLOGY

Thesis by
Carl L Hansen

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

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California
2004
(March 28, 2004)

ii

CARL L HANSEN

iii
ACKNOWLEDGEMENTS

I would first like to thank my advisor, Stephen Quake, for his unwavering direction and
steadfast resolve. Steve has been without exception a first rate mentor and role model.

From the inception of this work James Berger has been an instrumental part. I thank him
for his willingness to innovate and his continued faith in this project. I also would like to
thank Emmanuel Skordalakes and Jan Erzberger of the Berger lab for there excellent
collaboration.

Additionally, I have had the opportunity to work with a number of excellent academic and
industrial collaborators. In particular I would like to thank Pamela Bjorkman, Douglas
Rees, and Francis Arnold for generously donating samples and for their continuing interest
in this project. I would further like to thank Kyle Self and Gajus Worthington of Fluidigm
Corporation for their huge effort and commitment to this project.

Special thanks goes to Morten Sommer who worked with me on the Formulator project
while visiting Caltech as an undergraduate.

His relentless enthusiasm and “naïve”

optimism make working with him an absolute pleasure. I expect that he will have terrific
success in his career.

iv
Many thanks also go out to Todd Squires whose discussions over coffee have been both
enjoyable and insightful. In particular I thank him for his insight into the fluid mechanics
of the rotary mixer and water permeation in the harvesting device.

I extend my sincere gratitude to many colleagues whose exceptional ability and warm
camaraderie have made my time at Caltech so enjoyable. In particular I thank Sebastian
Maerkl, Vincent Studer, Joshua Marcus, Mark Adams, Frederick Balagadde, and Jian Liu,
with whom I have worked most closely. I would also like to extend my thanks to Emil
Kartalov, Heun Jin Lee, Jordan Gerton, Larry Wade, Michael Vandam, Michael Diehl, and
Ido Braslovski for their comradeship. I am further grateful to Marcus Enzelberg for his
patience and mentorship early in my graduate career.

Many of my fondest memories at Caltech are from cycling through the mountains around
Pasadena. I thank Michael Johnson, Tobias Kippenberg and Peter Meinhold for their
valued friendship and motivation. Tobias Kippenberg I also thank for teaching me patience
through his persistent tardiness, and for being a worthy adversary.

I would like to acknowledge my undergraduate research advisor and new colleague, Andre
Marziali, for introducing me to the fields of biophysics and biotechnology and for being my
advocate over the past 5 years.

I am very grateful to the Canadian government for their continued investment in Canadian
scholars, and for the financial support they provided me in the form of a Julie Payette
scholarship during the 2nd and 3rd years of my graduate career.

Finally, I thank those that are dearest to me and who have supported me through all my
endeavors. My parents, Don and JJ, I thank for their commitment to training, their
enthusiasm for science, and their philosophical guidance. I thank my sisters, Elsa and
Johanna, who through their own scientific careers are a continual source of encouragement
and support. I thank my sister in law, Tiffany, for many good laughs on the phone and on
vacations. I am hugely grateful to my twin brother Maxim for his example, his solidarity,
and his strength. Above all I would like to express my deepest appreciation to Tara for her
continued love, encouragement, and support over the past four years. I could not have
done this without her.

Carl L. Hansen
May 13, 2004

vi
ABSTRACT

In the post-genomic era, X-ray crystallography has emerged as the workhorse of large-scale
structural biology initiatives that seek to understand protein function and interaction at the
atomic scale.

Despite impressive technological advances in X-ray sources, phasing

techniques, and computing power, the determination of protein structure has been severely
hampered by the difficulties in obtaining high-quality protein crystals.

Emergent

technologies utilizing microfluidics now have the potential to solve these problems on
several levels, both by allowing researchers to conduct efficient assays in nanoliter reaction
volumes, and by exploiting the properties of mass-transport at the micron scale to improve
the crystallization process. The technique of Multilayer Soft Lithography (MSL) has been
used to developed a set of microfluidic tools suitable for all stages of protein
crystallogenesis, including protein solubility phase-space mapping, crystallization
screening, harvesting, and in silicone diffraction studies. These tools represent the state of
the art in on-chip fluid handling functionality and have been demonstrated to dramatically
improve protein crystallization.

vii
TABLE OF CONTENTS

Acknowledgements ...........................................................................................iii
Abstract.............................................................................................................. iv
Table of Contents............................................................................................... v
List of Figures.................................................................................................... vi
Nomenclature ...................................................................................................vii
Chapter I: Overview.......................................................................................... 1
Introduction.................................................................................................... 1
Context........................................................................................................... 3
Organization and Collaboration .................................................................... 5
Chapter II: Robust and Scaleable Microfluidic Metering ........................... 9
Introduction.................................................................................................... 9
Pressurized Outgas Priming ........................................................................ 13
Geometric Metering .................................................................................... 15
Positive Displacement Cross-Injection Metering....................................... 23
Chapter III: Microfluidic Free Interface Diffusion: Optimal Mixing ...... 28
Introduction.................................................................................................. 28
Characteristic Energies of Nucleation and Growth .................................... 32
Mixing at Low Grashof Number................................................................. 39
Chapter IV: Microfluidic Free Interface Diffusion: Screening Device ... 50
Parallel Implementation of µFID ................................................................ 50
Crystallization Results................................................................................. 55

viii
Chapter V: Systematic Solubility Studies: Formulator Device ................ 71
Introduction.................................................................................................. 71
Combinatorial Mixing on Chip ................................................................... 72
Robust and Precise Picoliter Metering........................................................ 76
Cross-Contamination Issues........................................................................ 79
I/O Interfacing ............................................................................................. 85
Chapter VI: Microfluidic Mixing: Scaling Laws and Optimization........ 90
Introduction.................................................................................................. 90
Dispersion in Low Aspect Ratio Channels ................................................. 95
Rotary Mixing: Scaling Laws and Simulation ........................................... 99
Valve Optimization ................................................................................... 104
Chapter VII: Systematic Solubility Characterization: Case Study ....... 107
Introduction................................................................................................ 107
Automation and Data Aquisition............................................................... 108
Precipitation Detection .............................................................................. 108
Solubility Fingerprinting ........................................................................... 110
Protein Phase-space Mapping ................................................................... 112
Solubility Hysteresis.................................................................................. 113
Optimal Crystallization Screening ............................................................ 115
Crystallization Variability ......................................................................... 117
Chapter VIII: Clear Path to Structure ....................................................... 120
Introduction................................................................................................ 120
Direct Harvesting from Screening Device................................................ 120

ix
Permeability Effects .................................................................................. 123
Transporting Conditions to Conventional Formats .................................. 128
Scaling Up µFID Reactions....................................................................... 130
Growth Device........................................................................................... 134
Harvesting from Growth Device............................................................... 140
Diffraction Device: Membrane-mediated Vapor Diffusion..................... 141
Crystallization Using “Osmotic Bath” Protocol....................................... 149
Crystallization Using “Permeation Barrier” Protocol .............................. 150
Diffraction Device: In Silicone Diffraction Studies ................................. 152
Chapter IX: Practical Considerations: Fabrication and Operation ....... 160
Introduction................................................................................................ 160
Multilayer Soft Lithography: Background ............................................... 161
Elastomer Shrinkage.................................................................................. 168
Layer-Layer Registration .......................................................................... 170
Substrate Adhesion.................................................................................... 171
Robust Multilayer Bonding....................................................................... 173
Bubble Formation...................................................................................... 174
Controlling Reagent Dehydration ............................................................. 175
Push-Up Valves ......................................................................................... 177
Variable Pressure Valves .......................................................................... 179
Multilevel Molds ....................................................................................... 180
Microfluidic Filters.................................................................................... 184
Microwell Fabrication ............................................................................... 186

Appendix A: Fabrication Protocols............................................................. 190
Appendix B: Matlab Script for Mixing Simulations ................................. 201
Appendix C: Phase-space Diagrams ........................................................... 204
Appendix D: Optimal Crystallization Screen for Xylanase ..................... 208
Bibliography ................................................................................................... 209

xi
LIST OF FIGURES

Figure 1: Pressurized Outgas Priming……………………………………... 15
Figure 2: Geometric Metering……………………………………………... 17
Figure 3: Parallel Geometric Metering…………………………………….. 19
Figure 4: Variable Geometric Metering…………………………………… 20
Figure 5: Nanopipette Array………………………………………………. 21
Figure 6: Variable Mixing using Nanopipette Array………………………. 23
Figure 7: Positive Displacement Cross-Injection Junction………………… 24
Figure 8: Parallel Array of PCI Junctions………………………………….. 26
Figure 9: Parallel PCI Metering……………………………………………27
Figure 10: Crystallization Hits……………………………………………... 30
Figure 11: Activation Barrier for Nucleation………………………………. 34
Figure 12: Nucleation Rate for Spherical Aggregate……………………….. 36
Figure 13: Regimes of Solution Saturation………………………………… 38
Figure 14: Vapor Diffusion and Microbatch Phase Space Evolution………. 41
Figure 15: Free Interface Diffusion………………………………………… 43
Figure 16: Phase Space Evolution of Free Interface Diffusion…………….. 45
Figure 17: Microfluidic Free Interface Diffusion Reactors………………… 48
Figure 18: Phase Space Evolution of

FID Reactions……………………... 49

Figure 19: Screening Device………………………………………………...51
Figure 20: Layout of Screening Device…………………………………….. 52
Figure 21: Carrier Device…………………………………………………... 53

xii
Figure 22: Screening Chip Loading…………………………………………54
Figure 23: Protein Crystals Grown in Chip: Gallery I……………………… 57
Figure 24: Histogram of Crystallization Hits………………………………. 58
Figure 25: Mixing Ratio Dependance……………………………………… 60
Figure 26: Protein Crystals Grown in Chip: Gallery II……………………... 64
Figure 27: Layout of Formulator Device…………………………………… 73
Figure 28: Combinatorial Mixing Using Formulator Device………………. 75
Figure 29: Precise and Robust Microfluidic Metering……………………....78
Figure 30: Comparison of Injector Designs…………………………………80
Figure 31: Contamination in Parallel Multiplexing Structure……………….82
Figure 32: Binary Tree Multiplexing Structure……………………………...85
Figure 33: Reagent Manifold for Formulator Device………………………. 87
Figure 34: Formulator Device with One-Touch Connectors………………...88
Figure 35: Channel Dispersion……………………………………………... 94
Figure 36: Channel Flow Profiles…………………………………………... 97
Figure 37: Transverse Parabolic Flow in Low Aspect Ratio Channels…….. 98
Figure 38: Scaling of Mixing Time in Rotary Mixer……………………….. 102
Figure 39: Simulation of Rotary Mixer..…………………………………….103
Figure 40: Valve Actuation………………………………………………… 105
Figure 41: Automatic Detection of Precipitation…………………………… 109
Figure 42: Solubility Fingerprints of Xylanase……………………………...111
Figure 43: Comparison of Phase-Space Mapping: Chip and Microbatch…...113
Figure 44: Solubility Hysteresis……………………………………………. 114

xiii
Figure 45: Enhanced Crystallizaiton by Optimal Screening………………... 116
Figure 46: Crystallization Variability………………………………………. 118
Figure 47: High Resolution X-ray from Nanovolume Crystallogenesis……. 121
Figure 48: Boundary Conditions Governing Chip Dehydration/Hydration… 124
Figure 49: Crystallization Correspondence………………………………… 129
Figure 50: Simulation of Microfluidic Free Interface Diffusion…………… 132
Figure 51: Layout of Growth Device………………………………………. 135
Figure 52: Scaling up Crystallization to Growth Device…………………… 138
Figure 53: Crystallization Dependence on Channel Geometry……………...139
Figure 54: Diffraction Device……………………………………… ………144
Figure 55: Layout of Diffraction Device…………………………………… 145
Figure 56: Cross Section of Elastomer Membrane…………………………. 146
Figure 57: Membrane Mediated Vapor Diffusion………………………….. 147
Figure 58: Influence of Osmotic Bath Solution on Crystallization………….148
Figure 59: Crystals of Rho Grown in Diffraction Device…………………... 152
Figure 60: Room Temperature In Silicone Diffraction Studies of MscL …...154
Figure 61: Cryogenic In Silicone Diffraction Studies of Lysozyme………... 158
Figure 62: MSL Bonding Process………………………………….. ………163
Figure 63: Process Flow Diagram of Multilayer Soft Lithography… ………164
Figure 64: MSL Valves……………………………………………………...165
Figure 65: Peristaltic Pump………………………………………………….166
Figure 66: Parallel-Channel Multiplexer…………………………… ………168
Figure 67: Push-Up Valves………………………………………… ………178

xiv
Figure 68: Variable Pressure Valves………………………………………...180
Figure 69: Negative Master of 25 µm High Control Features……… ……….181
Figure 70: Replica of Hybrid SU8-5740 Negative Master…………………. 182
Figure 71: Hybrid 5740-SU8 Negative Master……………………………...184
Figure 72: Removable Filter for Column Stacking………………………… 186
Figure 73: Hybrid 5740-SU8 Master with Microwells……………………... 187
Figure 74: Microwells Etched in Soda Lime Glass………………………… 189

Chapter 1

OVERVIEW
Introduction
The industrialization of DNA sequencing and completion of numerous genome projects has
set the stage for the next great endeavor, illuminating the cellular proteomes. Just as the
invention of the microscope helped to bring about an understanding of life at the cellular
scale (1), X-ray crystallography has allowed scientists to observe proteins at the atomic
level, causing a structural revolution in the biological and medical sciences.

conservative estimate is that through alternative splicing, the 30 000 genes that have been
identified in the human proteome will give rise to over 100 000 proteins whose structures
and functions are largely unknown. The diversity of proteomes across species, the need to
elucidate complex protein/protein interactions, and the visualization of ligand and drug
binding, imply an effectively limitless number of crystallization targets (2).

Technological advances in synchotron X-ray sources, phasing techniques, and computing
power have revolutionized data collection and model building techniques (3-5). These
innovations have not however been matched by the development of techniques to rapidly
obtain high-quality crystals.

Major bottlenecks in the expression, purification, and

crystallization of macromolecule targets continue to thwart high-throughput structural
biology initiatives (6). As structure determination efforts begin to focus less on the most
tractable crystallization targets (typically small soluble proteins), and instead on more
challenging macromolecules, including large protein complexes and membrane proteins,

the need to develop novel and enabling technologies has become urgent (7-9).

The

bottlenecks associated with generating diffraction quality crystals are further exacerbated
by the fact that many of the most interesting crystallization targets are difficult to express
and purify in large amounts.

Microfluidic technologies have the potential to provide unprecedented economies of scale
and massively parallel sample processing, making them ideal candidates for applications
where the screening and processing of precious reagents is required (10-12). The fluid
handling functionality necessary for realizing diverse and complex biological assays on a
chip requires the integration of active valves.

A recent breakthrough in fabrication

techniques, Multilayer Soft Lithography (MSL) (13), uses non-conventional soft materials
to fabricate true sealing valves. As a fundamental building block, these valves may be used
to build up higher level fluidic components such as pumps, mixers, and injectors (13, 14).

Beyond reduction in sample consumption, the reduced length scale of microfluidic
structures allows access to unique regimes of mixing and fluid flow that are not manifested
in macroscopic devices. Realizing the true potential of microfluidic technologies therefore
requires an understanding of the fluid physics that dominate at the micron scale. Exploiting
the physical behaviors that are characteristic to the micro-environment thereby allows for
the implementation of assays with increased sensitivity and higher efficiencies than are
achievable by conventional techniques.

The focus of this thesis is the application of Multilayer Soft Lithography to the
development of microfluidic tools that accelerate and improve protein crystallogenesis.
The emphasis of this work is on realizing the highest possible scientific impact by enabling
science that has hereto been intractable, and the marriage of engineering and science is a
central theme in this work. The utility of a technology depends not only on sound scientific
principals, but further on maximal robustness, reliability, and accessibility.

These

engineering principals must be present from the inception of design, and are inextricably
coupled to the underlying science.

Furthermore, effective technology development requires intimate familiarity with the
current methodologies and problems. Only once the inventor is immersed in the field and
able to consolidate this experience with his technical expertise do the most elegant and
simple solutions present themselves. Throughout this work a large effort has therefore
been directed towards validating the technology through application to outstanding
crystallization problems.

Context
This work builds upon the Multilayer Soft Lithography (MSL) technology developed by
previously in our lab by Unger et al. (13). At the time the author began his work on protein
crystallization in microfluidic devices, MSL was an emerging technology with enormous
potential and obvious advantages over existing methodologies. It was still however in a
nascent form, and technical issues severely limited the complexity of devices that could be

realized. The author has had a major role in resolving these issues and establishing MSL as
a robust and reliable technology platform.

This thesis describes the first application of microfluidics to protein crystallization. In this
work the development of a variety of microfluidic devices suitable for all aspects of protein
crystallogenesis is described. The most mature of these technologies is a device for ultrasmall volume screening of crystallization conditions by microfluidic free interface
diffusion. This screening device has advanced past the prototype stage and has been
extensively tested in the crystallization of diverse and challenging macromolecule targets.
The screening device has been developed into a commercial product by Fluidigm Corp.,
and is being successfully used in structure determination projects at major pharmaceutical
companies in the United States and Great Britain.

A microfluidic formulator device has been developed for the systematic characterization of
protein solubility over a broad range of chemical conditions. This device allows for the
first practical implementation of high-throughput solubility characterization in nanoliter
volume reactions. Additionally, this device has enabled the first implementation of true
combinatorial mixing on chip and represents the state of the art in microfluidic
functionality and precision. The formulator device is currently in the 10th prototype version
and is being refined for routine use an instrument for rational protein crystallization.

A diffraction device has been developed to allow for successful chip-based crystallization
conditions to be exported with high correspondence to larger volume formats.

Additionally, this device allows for the rapid harvesting and mounting of crystals, and for
in silicone diffraction studies both at cryogenic and at room temperatures.

The

diffraction device is in a early prototype stage and is currently being developed both at
Caltech and at Fluidigm Corp. for commercialization.

Organization and Collaborations
Chapter 2 discusses the extension of MLS technology to the development of robust and
scaleable methods for metering and dispensing reagents on chip, a fundamental
requirement for all liquid handling systems. The Chapter begins by introducing the method
of pressurized outgas priming. This technique is central in solving problems of device
priming, small-volume sample loading, suppressing bubble formation, and maintaining
sample hydration. Pressurized outgas priming allows for the simple implementation of
robust metering scheme called geometric metering, which is used in the protein
crystallization screening device.

A second metering technique, positive displacement

cross-injection (PCI) metering is also presented. This technique is used in the formulator
device to realize precise and robust programmable metering on chip.

Chapter 3 begins with an introduction to the characteristic energies of protein
crystallization and growth. Simple physical models are presented to provide a framework
for later discussions of mixing kinetics and crystal nucleation. In particular, the concept of
“crystallization phase-space” is presented.

The properties of mass transport that are

manifested in microfluidic devices allow for the efficient sampling of crystallization phasespace by a technique called microfluidic free interface diffusion.

Chapter 4 describes a protein crystallization screening device that uses geometric metering
to realize a parallel implementation of microfluidic free interface diffusion.

The

effectiveness of this device is evaluated in the context of both well-characterized
crystallization standards and challenging real-world crystallization targets. Protein samples
used in these trials were generously provided by a number of academic collaborators: most
notably the labs of J. Berger, P. Bjorkman, D. Rees, F. Arnold, and D. Eisenberg.

Chapter 5 describes a microfluidic formulator device designed for the systematic
exploration of protein phase-space behavior.

This device integrates valves, pumps,

multiplexers, and a mixer to achieve programmable combinatorial mixing on chip.
Characterization of chip reliability, metering precision and robustness are presented.
Additionally, issues of cross-contamination and i/o interfacing are discussed. This work
was done in equal collaboration with M. Sommer.

Chapter 6 discusses achieving fast mixing in the formulator device through mixer
optimization. The application of simple fluid mechanics is used to determine the scaling
laws that govern mixing times in a rotary mixer. This discussion follows work done by T.
Squires. The behavior of the mixer is further investigated through numerical simulations
done in equal collaboration with M. Sommer. Finally, the optimization of valve response
time for achieving high flow rates in the rotary mixer is discussed.

Chapter 7 describes the use of the formulator device in the systematic study of the
solubility behavior of Endo-1,4-β-xylanase (xylanase) from Trichoderma reesei. Solubility
fingerprinting and phase-space mapping are used to characterize xylanase in a variety of
precipitating agents. Information gained from these studies is used to design an optimal
crystallization screen that dramatically enhances the chance of crystallization when
compared to commercial sparse matrix screens (15).

This work was done in equal

collaboration with M. Sommer.

Chapter 8 describes a diffraction device that allows successful crystallization conditions
identified in the screening device to be transported with high correspondence to a larger
volume format. A technique for rapid harvesting and mounting of crystals for in silicone
diffraction studies at cryogenic and room temperatures is presented. By minimizing crystal
manipulations and providing a harvesting format amenable to automation this device
establishes a clear path from crystals to structure.

Chapter 9 begins with an overview of multilayer soft lithography (MSL) as developed by
Unger et al. The goal of the remainder of the Chapter is to highlight various technical
issues related to MSL technology, and to document some useful solutions that have been
realized throughout the course of this work. It is the author’s hope that this section will
provide a useful resource to students new to the field. Practical considerations and design
problems that previously limited the reliability and achievable complexity of devices are
discussed. Other issues related to fabrication and component design are presented. In

cases where the author had a major contribution only in the conception of solutions, with
the implementation carried out by other students, appropriate references are made.

Chapter 2

ROBUST AND SCALEABLE MICROFLUIDIC METERING
Introduction
In the same way that miniaturization has impacted the electronics industry, microfluidic
technologies promise to spark a revolution in the biological sciences by integrating ultra
small-volume sample processing within a chip format. The use of nanoliter reaction
volumes and highly scaleable parallel sample processing makes microfluidic technologies
ideally suited to protein crystallography, where the screening and processing of precious
reagents is required. Beyond reduction in sample consumption, the unique properties of
mixing and fluid flow at the micron scale also allow for the implementation of assays that
are highly efficient at detecting crystallization conditions (16).

Despite this enormous

potential, several technical problems have prevented the realization of the full potential of
microfluidic devices for protein crystallization.

Central to the realization chip-based protein crystallization and other lab-on-chip
technologies is achieving the fundamental fluid handling capability of precisely metering
and mixing fluids at the sub-nanoliter scale. In order to be scaleable and to have general
applicability, such a system must further be insensitive to both the surrounding fluidic
architecture and to the properties of the working fluids.

In the case of protein

crystallography, this latter requirement is particularly important since the solutions used in
crystal trials cover a large range of chemistries, viscosities, ionic strengths, and pH.

10
The early work in microfluidics was focused on the development of glass microchips that
exploited electrokinetic manipulation of fluids for applications such as enzymatic assays
and molecular separations. This work demonstrated that microfabricated fluidic structures
may be used to accurately meter and mix fluids on the picoliter scale (17-22). Although
these systems have proven useful in niche applications such as capillary electrophoresis,
they have not proven to be scaleable, and have fundamental limitations that prevent there
universal application. For example, the electrokinetic force used in these devices depends
strongly on both the properties of the working fluid and on its interaction with the channel
walls. Small changes in pH or salt concentration, that result from ion drift over time, can
lead to more than a tenfold variation in injected volume (23, 24). These systems are also
dependent on the viscosity and on the fluidic resistance due the surrounding channel
architecture. As a result, electrokinetic devices must be recalibrated for every fluid, and are
not suitable for high-throughput screening applications with a diverse ensemble of
unrelated reagents.

Moreover, since electrokinetic systems have no active valves, reagents diffuse through
junctions and channels over time. This leaking dilutes and contaminates samples over
time, restricting the maximally achievable incubation times and the density at which
assays may be integrated on chip. The problem of reagent storage is particularly acute
for crystallization applications where assays may be required to incubate for several days
or weeks.

11
All of these problems may be addressed by using MEMS (micro-electro-mechanical
systems) fabrication techniques to incorporate active mechanical valves on chip.
Traditional MEMS techniques, using “hard” materials such as glass or silicon, may be
used to fabricate true, leak-proof mechanical valves.

However, MEMS fabrication

techniques are expensive and require many processing steps, rendering the integration of
many valves on a chip a difficult and expensive process. Furthermore, since these valves
are fabricated from hard materials, a large actuator area is needed to achieve valve
closure at attainable actuation forces. The large actuators of each valve and the low yield
of the fabrication process impose practical constraints on the degree of integration that is
possible in microfluidic devices made from traditional MEMS techniques.

While there is a thriving MEMS community making silicon-based valves and
microfluidic devices, alternative fabrication techniques using non-traditional materials,
including hydrogels (25), plastics, and elastomers (26, 27), are gaining popularity and
have been developed for the quick and inexpensive fabrication of passive and active
microfluidic devices. In particular a technique developed by Unger et al., Multilayer Soft
Lithography (MSL), enables facile and inexpensive large-scale integration of valves on
chip (27). MSL uses consecutive soft lithography molding and bonding steps to generate
complex multilayer fluidic devices. In this way, planar channel structures separated by
only a thin flexible elastomeric membrane may be integrated into a monolithic polymer
chip. The orthogonal crossing of channel structures in two adjacent layers creates a
deflectable membrane valve. A hermetic seal of the channel structure may be easily
achieved at by application of modest hydraulic or pneumatic pressure to the control

12
structure. The low Young’s modulus of the elastomer ( ~1 MPa compared to ~100 GPa
for crystalline silicon) allows for the large deflection of membranes with small active
areas (typically 10000 µm2), thereby enabling the large-scale integration of valves on a
chip (27).

Moreover, the softness of the channel and valve structure ensures the

formation of a robust seal even in the presence of particulates or fabrication
imperfections.

This Chapter describes the extension of MSL technology to the development of two
metering techniques that are both scaleable and robust to the properties of the working
fluid. The first of these techniques, geometric metering, relies on the ability to easily prime
arbitrary connected fluidic structures via the pressurized outgas priming (POP) method.
Geometric metering is a static technique whereby the final aliquot volumes and mixing
ratios are defined by the fluidic structure. This robust technique is extremely powerful by
virtue of its simplicity of operation and scalability to massively parallel architectures, and is
central to the implementation of a protein crystallization screening device (Chapter 4). An
extension of this technique, in the form of variable volume nanopipettes, allows for a
degree of programmability to be achieved through the analogue or discrete tuning of cavity
volumes. A second technique, positive displacement cross-injection (PCI) metering, is a
dynamic technique that allows for the programmable serial dispensing of an arbitrary
number of reagents. This versatile method is used to realize the first demonstration of true
combinatorial mixing on chip (Chapter 5).

13

Pressurized Outgas Priming
The realization of highly integrated and complex fluidic devices requires that the problem
of priming, or initially filling the device with fluid, be addressed. For microfluidic devices
made from conventional hard materials such as silicon or glass, this requirement may
prevent the use of multiply crossing, highly complex fluidic architectures. Such devices
must be primed using a flow-through method, which requires an outlet through which
displaced gas may be vented. The introduction of the priming fluid through a complex
fluidic structure may trap air bubbles at junctions and other channel features. Surface
tension effects at the liquid-gas interfaces of these bubbles result in large pressure drops so
that bubbles can not be easily removed and adversely affect the performance of the device.
Furthermore, since a single priming fluid must pass through the entire device, it may
subsequently contaminate or dilute sample solutions. These difficulties can be surmounted
in silicone devices by exploiting the gas permeability of a soft silicone polymer (28, 29).
The permeability of silicone rubber to a variety of gases is listed in Table 1 (30).

Penetrant

Permeability (Barrer)

H2

890 ± 30

O2

800 ± 20

N2

400 ± 10

CO2

3800 ± 30

Table 1: Permeability of poly(dimethylsiloxane) to various gases. 1 Barrer = 10-10
cm3(STP)·cm/cm2·s·cm Hg.

14
Arbitrarily complex, connected fluidic structures may be filled in minutes by a technique
called Pressurized Outgas Priming (POP). Using the POP technique, a fluid is injected into
a closed channel structure, causing the gas ahead of it to be pressurized. Due to the
permeability of the elastomer, the pressurized gas quickly diffuses into the bulk material,
allowing the priming fluid to completely fill the flow structure. Figure 1 shows a time
sequence of a 7 nL well being dead-end filled at 8 psi loading pressure. Despite the low
surface energy of PDMS (22 mJ/m2), aqueous solutions may be easily introduced, at
moderate pressures (1-8 psi), into channels having a minimum dimension of 1 µm,
eliminating the need for surface modification protocols. Since no outlet is needed for the
venting of gas, dead-end reaction chambers and channels may be used, allowing significant
design flexibility. Furthermore, since the priming is selective and integrated valves may be
used to direct flow of the fluid, a device can be primed with many different fluids in
different channels or chambers. This latter property is the basis of the geometric metering
scheme described below. A more comprehensive introduction to MSL technology and
various relevant technical issues is provided in Chapter 9.

15

Figure 1: Opical micrographs showing the dead-end filling of a 7.5 nL reaction chamber
at 8 psi using the pressurized outgas priming (POP) method. Scale bar is 100 µm.

Geometric Metering
The ability to fill a device with many different fluids in different channels and chambers
using the POP technique allows for the implementation of a simple and robust geometric
method of metering solutions. The principle behind this scheme is to set up a geometry in
which interface valves are used to partition a continuous microfluidic reactor into sections
of well-defined volume. Each section may be separately filled with different solutions
through separate inlet channels. Once filling is complete, the inlet channels are sealed by
actuation of containment valves, thereby isolating the reactor from the rest of the device.
De-actuation of selected interface valves allows for adjacent sections of the reactor
containing different reagents to be combined.

16
A simple fluidic structure for the geometric metering of two reagents at three different
mixing ratios is shown in Figure 2A. With a central interface valve closed, the chambers
on either side of the interface are first dead-end filled with two different solutions using the
POP technique (Figure 2B).

Once both chambers have been completely filled, the

containment valves are actuated, thereby isolating the chambers from the rest of the chip
and defining the total volume of the reactor. The interface valve is then opened to create
fluidic connection between the chambers, allowing them to mix by diffusion. Figure 2C
shows the complete diffusive mixing of an organic dye with water, creating a set of three
distinct concentrations in separate reaction chambers.

17
Figure 2:

Geometric metering.

(A) Three pairs of coupled microwells.

Control

channels are filled with 20 mM Orange G (Aldrich Chemical Company). (B) Loading of
reagents using POP method. The interface valve (center) is actuated and reagents are
loaded into adjacent sides of compound wells. The bottom wells are being dead-end
loaded with water, and the top wells have been loaded with 13 mM bromophenol blue
sodium salt (Aldrich Chemical Company). (C) A gradient of dye concentration. The
containment valves (top and bottom) isolate compound wells, and the interface valve is
released to allow diffusive mixing. Image shows complete mixing after 2 hours. (D)
Histogram showing the insensitivity of BIM to fluid viscosity. BIM was used to combine
7 mM bromophenol blue sodium salt with water (η ≅ 1 cP) or 34% m/m sucrose (η ≅ 4
cP) tens times each at mixing ratios of (Dye:water/sucrose) 1:4, 1:1, and 4:1. Water
measurements are shown in blue, and sucrose is shown in red. The variations in the
concentration measurements (~ 10%) are comparable to those taken on solutions of
known concentrations.

In this way the chambers effectively act as microfluidic measuring cups, precisely
determining the mixing ratio by the relative chamber volumes. Since the metering depends
only on the volume of the chambers it is an inherently robust technique that is insensitive to
resident fluid properties. Figure 2D shows a histogram of mixing ratios achieved in 20 sets
of 3 reaction chambers using two fluids of varying viscosity. Similar experiments using
solutions of sodium chloride ranging from 0 M to 2 M have shown that metering is
independent of ionic concentration (data not shown).

18
In this simple configuration, mixing is dominated by diffusion of the reagents, which
takes on the order of an hour for small molecules in an aqueous solution. This purely
diffusive mixing is sometimes advantageous in that it removes the confounding effects of
convection, thereby allowing for slow equilibration of the various reagents. In cases for
which speed is an issue, it is straightforward to implement the BIM scheme in alternative
geometries, such as a ring, and then accelerate mixing by dispersion induced through
active pumping around the ring (see Chapter 6). This scheme has found applications in
single-cell gene expression analysis and large-scale multiplexed PCR reactions (31, 32).

A major advantage of this technique lies in its simplicity of control and scalability. The
volume of the reaction chambers is precisely defined during lithography and molding so
that there is no need to calibrate the system. Each of the steps in the metering and mixing
process (interface actuation, filling, containment, and diffusive equilibration) proceeds to
completion prior to the initiation of the next step, so that there is no requirement of
precise valve actuation timing. Hence, thousands of reactions can be implemented in
parallel using only two control lines irregardless of differences in the length of loading
channels or in the fluid properties. Figure 3 shows a section of a device designed to
implement 144 simultaneous metering and mixing experiments. The ability to implement
large-scale parallel metering and mixing of reagents without increasing control
complexity has been exploited in a variety of applications including protein
crystallography (29, 33), multiplexed PCR reactions (32), and cell-library screening (27).

19

Figure 3: Parallel implementation of geometric metering. Section of a device designed
for the simultaneous mixing and metering of a single sample (blue) with 48 unique
reagents (clear) using only two control lines (orange).

Geometric metering is primarily a static technique in which the final dispensed volumes are
“hard-wired” into the fluidic structure. Nevertheless a degree of programmability may be
achieved by the inclusion of redundant valves and/or channels. Figure 4 shows a channel
and valve geometry designed to allow for 10 alternate mixing ratios to be achieved by
selection of one of many possible interface valves (I1 – I10) located at different locations
along a reaction chamber defined by two containment valves (C). Additionally, a series of
channel inlets could be included between each of the 12 valves to allow for many different
numbers of reagents and mixing ratios to be implemented. Although this allows a large
number of alternative configurations, such geometries greatly increase the control
complexity of the device and may introduce severe routing problems that make them no
longer scaleable to parallel implementations.

20

Figure 4: Channel architecture for programmable geometric metering. Selection of
specific interface channel (I1 – I10) determines mixing ratio of fluids introduced at the
channel inlets.

Alternatively, the geometric metering scheme may be extended to structures in which the
total volume of the reaction chamber may be tuned in a continuous or discrete fashion by
deflection of a membrane. Figure 5 shows a column of a microfluidic chip with an array of
1 nanoliter fixed-volume nanopipettes. Each column of nanopipettes is addressed by a
separate input channel (clear). Each nanopipette has a containment valve at the inlet and a
deflectable membrane. The size of each membrane defines the metered volume and is
varied across the row.

The simple two-component metering of solutions at a variety of fixed mixing ratios is
implemented as follows. The first fluids to be mixed are introduced into separate columns
of the array via a multiplexing structure (not shown). The chip outlet is then closed and the
nanopipette containment valves are opened to allow for the dead-end filling of each
reaction chamber by the POP method. Once filled, the reaction chambers are sealed by
actuation of the containment lines, and the next fluids to be mixed are flushed down the
columns. Figure 5A shows 3 nanopipettes filled with an organic dye (20 mM bromophenol

21
blue sodium salt, TRIS·HCl pH 8.0). To execute the metering task the containment valves
are opened and the membranes are inflated, ejecting a well-defined volume from each
pipette (Figure 5B). The ejected volume is flushed from the column and replaced with the
second solution (Figure 5C). The membranes are then deflated, causing a well-defined
volume of the second reagent to enter the nanopipette (Figure 5D).

Figure 5: Parallel operation of fixed volume nanopipette. (A) Nanopipettes are filled
first reagent (blue), containment valves are actuated, and inlet channel is flushed. (B)
Membranes are inflated to expel a well-defined volume of first reagent. (C) Inlet

22
channel is flushed and loaded with second reagent. (D) Relaxation of membranes results
in aspiration of a well-defined volume of second reagent.

In this setup the mixing ratio is determined by the membrane geometry and is therefore
hard-wired into the device. Since a separate reagent is introduced to each column of the
array and each nanopipette is designed to achieve a specific mixing ratio, this strategy
allows for the parallel screening of different reagents at different mixing ratios. Figure 6
shows the mixing of two organic dyes (orange G and bromophenol blue sodium salt) at 0:1
(A), 1:3 (B), 1:1 (C), and 2:1 (D) ratios. In cases where parallel architectures are not
required the nanopipette may be used to meter fluids in an analogue fashion. Varying the
actuation pressure applied to deflect the membrane allows for continuous tuning of the
nanopipette volume.

23

Figure 6: Parallel mixing at variable mixing ratios using an array of 1 nL nanopipettes.
(A) 1 blue : 0 orange. (B) 3 blue : 1 orange. (C) 1 blue : 1 orange. (D) 1 blue : 2
orange.

Positive Displacement Cross-Injection Metering
Formulation applications require arbitrary combinations and concentrations of a large
number of distinct reagents to be mixed on chip. This “mix-on-command” requirement
necessitates a robust and programmable metering scheme that can accommodate a large
number of input solutions. Positive displacement cross-injection metering allows for the
sequential injection of precise sample aliquots from a single microfluidic channel into
reaction chambers through a positive-displacement cross-injection (PCI) junction (Figure
7).

The PCI junction is formed by the combination of a three-valve peristaltic pump (13) and a
four-port cross-injection junction with integrated valves on each port (Figure 7A). Two
sets of valves at the junction inlets are actuated to direct the flow either horizontally or
vertically. Prior to metering the flow is switched vertically through the junction, charging
the cross-injector with the sample fluid (Figure 7B). The flow is then directed horizontally
through the junction and the three valves forming the peristaltic pump are actuated in a five
state peristaltic sequence to advance the fluid in the horizontal direction (Figure 7C). Each
cycle of the peristaltic pump injects a well-defined volume of sample (approximately 80
pL) determined by the dead volume under the middle valve of the peristaltic pump. The

24
deflection of the valve membranes when not actuated is determined by the pressure
difference across the membrane. The volume injected during each cycle therefore may be
tuned continuously, allowing for variable positive displacement metering. By repeating the
injection sequence, the volume of injected solution may be increased in 80 pL increments,
allowing for the programmable quantized control of the final downstream sample
concentration.

After each injection sequence the junction is flushed and recharged

allowing for the sequential introduction of different reagents down the line (Figure 7D).

Figure 7: Positive displacement cross-injection (PCI) for robust and programmable
high-precision dispensing on chip. (A) Schematic of a four port PCI junction. The splitchannel architecture creates a larger volume injector region, thereby allowing for an
increased number of injections before recharging. (B) Charging of the injector region of
the pci junction. Junction valves are actuated to direct the flow vertically through the

25
junction, filling the injector region. (C) Precise positive displacement metering by
actuation of peristaltic pump valves in pumping sequence.

(D)

PCI junction is

sequentially charged with different solutions to create complex multi-component
mixtures.

Certain applications may require the parallel injection of reagents into an array of reaction
chambers containing different reagents/cells/bacteria. An array of five PCI junctions is
shown in Figure 8A.

The corresponding junction valves of all gated cross-injection

junctions are interconnected, allowing an entire injection array, potentially of hundreds of
junctions, to be controlled using only two control lines. The channel sections contained
between the rightmost horizontal gate valves, and the peristaltic pump, define 5 reaction
chambers, each having a volume of 2.6 nL. To execute the metering task the flow is first
directed vertically, charging the junctions (Figure 8B).

The flow is then directed

horizontally through the junctions, and the peristaltic pump advances the fluid in the
horizontal direction, injecting an even aliquot of sample into each reaction chamber. By
operating the peristaltic pump at low frequency so that the response is linear, the amount of
injected fluid is independent of the fluidic resistance of the channels. Figure 8C shows the
even injection of sample solution into 5 reaction chambers of unequal fluidic resistance,
and containing fluids of differing viscosity. For a similar pressure-driven injection, shown
in Figure 8D, the flow through middle chamber leads that of the adjacent chambers due to
the lower fluidic resistance and viscosity.

26

Figure 8: Parallel array of PCI junctions. (A) 5 PCI junctions controlled in parallel by
5 control lines. (B) Flow is directed vertically to charge PCI junctions with blue dye (10
mM bromophenol blue sodium salt). (C) Even injection of dye down 5 channels of
varying fluidic impendence using peristaltic pump. Length of channels to outlet is (top to
bottom) 2.5 mm, 1.5 mm, 1 mm, 1.5 mm, 2.5 mm. (D) Uneven pressure-driven injection
of dye down channels due to varying fluidic impedence. Scale bars are 2mm.

Repeating the injection sequence allows for the volume of injected solution may be
increased in discrete steps, so that programmable and quantized control of the final sample
concentration is realized. Once the correct volume has been dispensed, the fluids are
contained, and allowed to mix by diffusion. Absorption measurements for five adjacent
reaction chambers of varying fluidic resistance and viscosity are shown in Figure 9. All

27
five data sets show excellent linearity, having r2 values between .980 and .996. The
average slope was determined to be 103 pL / injection, with a standard deviation of 6%,
and a maximum deviation of 9%.

Figure 9: Absorption measurements of parallel metering using and array of 5 PCI
junctions. Volume of injected dye (10 mM bromophenol blue sodium salt, TRIS·HCl
pH8.0) is insensitive to changes in solution viscosity and fluidic impendence.

28
Chapter 3

MICROFLUIDIC FREE INTERFACE DIFFUSION: OPTIMAL MIXING
Introduction
The crystallization of a biological macromolecule is realized by the manipulation of one or
more chemical and thermodynamic variables such that the solubility of a target molecule in
a concentrated solution is reduced, thereby promoting a transition to the solid phase in the
form of a well-ordered crystal. In principal a stable protein solution may be brought to a
state of supersaturation through the manipulation of any physical parameter that appears in
the thermodynamic equation of state of the protein. This is typically accomplished through
the addition of precipitating agents that lower the solubility of the protein (often
accompanied by a slow concentration of the solution). Traditional precipitating agents
include salts, polymers, organic solvents, buffers, and various additives. When successful,
these reagents promote specific protein-protein interactions by modifying solution
properties such as pH, dielectric constant and ionic strength.

Natural macromolecule targets for crystallography are both large and extremely varied.
Proteins, for example, are complicated polymers of amino acids with polar, non-polar,
charged, and aromatic residues that interact with each other and with the external
environment. These complicated interactions result in a highly varied and complicated
phase-space diagram that cannot be deduced a priori. Consequently, macromolecular
crystallization requires a brute force approach in which as large a volume of chemical
phase-space as possible must be explored. The vastness of phase-space that must be

29
explored implies that a thorough investigation by conventional techniques is impractical.
The initial search is therefore typically directed towards a sparse matrix or incomplete
factorial sampling of likely crystallization agents (15, 34).

For macromolecules possessing a large volume of phase-space that is conducive to
crystallization, there is a good chance that one of the randomly screened conditions will
result in crystal formation. Since the first ‘hit’ is not likely to be optimal, initial successes
are usually of poor quality, and may consist of spherulites (Figure 10A), phase separation
(Figure 10B), micro-crystals (Figure 10B), needles, needle clusters, thin plates (Figure
10C), plate stacks (Figure 10D), or small single crystals (Figure 10E).

These starting

conditions can be used to initiate focused and refined screening, eventually producing
diffraction quality crystals (Figure 10F). If only a very narrow range of conditions is
conducive to crystallization, initial screens may be too coarse to uncover promising
conditions and further screening may be required. For macromolecules that require very
specific crystallization conditions, almost invariably the ones of greatest interest to the
investigator, many thousands of experiments may be required before a hit is detected, if at
all.

30

Figure 10:

Examples of initial crystallization hits from a single on-chip screening

experiment of a type II topoisomerase ATPase domain/ADP; 12 mg/mL. (A) Irregular
spherulite. (B) Phase separation and spherulites with nucleating microcrystals. (C) Thin
plate clusters. (D) Thick plate stacks. (E) Well-formed microcrystals. (F) Large single
crystals. All scale bars are 100 µm.

Moreover, many important crystallization targets are only available in very small
quantities. The large number of experiments required to uncover successful crystallization
conditions therefore is what represents the most formidable obstacle to determining the
structure of many important biological macromolecules. For example, membrane proteins
play a central role in cell signaling and are often excellent targets for small molecule
therapeutics. Unfortunately, the structures of only a very few (approximately 50) have

31
been determined to date, primarily because of the difficulties associated with expressing,
solubilizing and stabilizing these molecules in the large quantities required for
crystallization trials (> 1 mg) (35-37). Similarly, many proteins work in the cell as large
complexes.

Structural information of these targets provides invaluable information

regarding complex biochemical reactions and protein/protein interactions.

As with

membrane proteins these assemblies are exceedingly difficult to purify in large amounts,
and at times must even be purified by processing kilogram quantities of native sources (38,
39).

Traditional techniques for the crystallization of macromolecules include concentration
through slow dehydration (vapor diffusion), batch and dialysis methods, and both liquidliquid and liquid-gel diffusion experiments (For review see [40]). Practical limitations of
traditional fluid handling approaches require that the minimum volume per assay for these
techniques ranges from 0.2 µL to 1 µL for vapor diffusion and microbatch methods, and up
to 50 µL for micro-dialysis. Since protein samples may only be available in milligram
quantities, and target molecule concentrations are generally required in excess of 10
mg/mL, the ability to routinely perform nanoliter scale assays using microfluidics not only
helps to promote a more comprehensive screening strategy, but further allows for
experimentation with ultra-low-abundance macromolecules.

The probability of success in a crystallization screening experiment is proportional both to
the number of independent trials, and to the chance of success of each trial. An optimal
screening methodology must therefore maximize not only the number of independent trials

32
through small volume sample processing, but also the efficiency of each assay. Although
the appropriate chemical variables cannot be ascertained in advance, it is possible to use the
universal phase properties of the precipitant-protein interaction to systematically design
experiments with optimal mixing kinetics, and thereby enhance the chance of crystal
growth. In addition to the impressive economy of scale provided by microfluidic devices,
the physical properties of fluid flow at the micron scale allow for the implementation of
highly efficient crystallization assays.

Characteristic Energies of Nucleation and Growth
The successful crystallization of a macromolecule is determined both by thermodynamic
and kinetic considerations. A concentrated solution of the target molecule must first be
brought to a state in which the crystal phase is energetically favorable, and then kept in this
state to allow crystal nucleation and growth to occur. An essential feature of crystal
nucleation and growth is that it is necessarily a non-equilibrium process. A measure of
how far out of equilibrium a system is, and therefore of the tendency towards
crystallization, is the saturation defined as C/C0, where C is the concentration of protein
and C0 is the maximum concentration of protein in thermodynamic equilibrium. By
definition, saturation below unity describes a stable protein solution in which no phase
change will be observed. All supersaturated solutions (S > 1) are unstable and will
ultimately exhibit a phase transition to an amorphous or crystalline state. An emerging
crystalline phase will continue to grow at the expense of the soluble phase until the
concentration of soluble protein is reduced to C0 and the chemical potentials of both phases

33
are equal. In equilibrium, the probability of observing a solution with concentration C is
given by the Boltzman distribution as

⎛ ∆G ⎞
= Exp⎜ −
⎟,
C0
⎝ KT ⎠

(1)

where ∆G is the Gibbs free energy of the solution relative to that of the solution in
equilibrium with the crystalline phase. The chemical potential is identically the number
specific Gibbs free energy of an ensemble so that taking the log of this expression gives the
chemical potential of the crystalline phase relative to equilibrium as (41)

µ = − KT ln⎛⎜ C C ⎞⎟ .

(2)

Thus, if the protein concentration in solution is greater than C0,the crystal is energetically
favored and will continue to grow.

Favorable interactions with neighboring molecules compensate for the net loss of entropy
associated with incorporating a protein molecule into the growing lattice. On the surface of
a growing crystal these interactions are incomplete, giving rise to an unfavorable surface
term. The net free energy of a crystalline aggregate is therefore given by

G=−

KTV

ln⎛⎜ C ⎞⎟ + σS ,
⎝ C0 ⎠

(3)

34
where S is the surface area of the growing aggregate, σ is the surface energy crystal/solvent
interface, V is the volume of the aggregate, and υ is the volume occupied by a protein
molecule in the crystal. A hypothetical plot of the free energy of a growing nucleus as a
function of radius is shown in Figure 11. The competition between the surface and volume
terms gives rise to a finite activation barrier. Only after an aggregate achieves a critical
radius does it become stable.

Figure 11: Activation barrier to crystal nucleation. Competition between favorable
volume interactions and unfavorable surface interactions results in a minimum critical
nucleus radius R* that is stable.

35
If the critical radius is large compared to the size of each protein molecule, the growth of
the nucleus can be well approximated as a continuous process. In this limit the nucleation
process can be modeled as thermal activation of a quasiparticle over an energy barrier of
height G*, with a rate given by Kramer’s relation (42):

⎛ G* ⎞
⎟⎟ ,
J = Κ 0 Exp⎜⎜ −
KT

(4)

where J is the expected number of nucleation events per second per unit volume. The
prefactor Κ0 may be loosely interpreted as the escape attempt rate of a quasi-particle
oscillating in the potential well near the activation barrier, and is therefore determined by
the curvature potential in the vicinity of the soluble state minimum, the curvature near the
transition state (critical nucleus), and is proportional to the concentration of molecules in
solution.

An expression for the activation barrier, and hence the dependence of the nucleation rate on
the degree of solution saturation may be deduced if an assumption is made as to the shape
of the growing aggregate. For the case of a spherical aggregate the activation barrier may
be expressed as (43)

16πυ 2σ 3
⎟.
J = K 0 Exp⎜⎜ −
2 ⎟
⎝ 3KT (KT ln(C C 0 )) ⎠

(5)

The very strong dependence of the nucleation rate on saturation is illustrated in Figure 12.
By defining a characteristic reaction volume Vexp, and a relevant experimental timescale τ,

36
the rate of nucleation may be used to classify a supersaturated solution into one of two
regimes. An average time to nucleation 1/(J Vexp) that is much longer than τ defines the
metastable regime. In this regime the growth of large, high-quality crystals is supported
but nucleation events are rare, requiring impractically long incubation times. Experiments
that stay in this region will likely appear as clear drops and will be unremarkable. It is
worth noting that since the average time to nucleation scales with the volume of the
reaction, small volume crystallization formats must achieve higher levels of supersaturation
for crystals to be observed in reasonable times.

Figure 12: Nucleation rate of a spherical aggregate as a function of solution saturation.

Systems in which the average time to nucleation 1/(J ν) is much shorter than τ are said to be
in the labile regime. In this regime multiple nucleation events will be observed in time τ.
Polycrystalline aggregates and high levels of defect incorporation are characteristic of rapid
crystal growth in the labile regime (44). Furthermore, very high levels of supersaturation

37
often result in showers of microcrystals that may be too small to distinguish from
amorphous precipitate, a problem that can cause promising conditions to be overlooked.

In conventional macromolecular crystallization a stable protein sample is brought into a
state of supersaturation through the addition of a crystallizing agent. This process is
represented as a deformation of a free energy landscape defining a crystalline and a soluble
phase (Figure 13), where the aggregate radius has been replaced by a generalized reaction
coordinate that encompasses all degrees of freedom in the system. Initially the protein
sample is stable in the soluble form, having a free energy below that of the crystalline
phase (Figure 13A). Perturbation of the system through the addition of a precipitating
agent that lowers the solubility of the protein induces a state of supersaturation in which the
energy of the soluble phase rises above that of the crystalline phase. If the degree of
supersaturation is small this will result in a metastable state characterized by a large
activation barrier (Figure 13B). If a higher degree of supersaturation is achieved, say
through the addition of more precipitating agent, a labile state conducive to crystal
nucleation is achieved in which the activation barrier has been substantially reduced
(Figure 13C).

The three-dimensional aggregation of target molecules into a critical nucleus from which
crystal growth may proceed is a process that requires a higher activation energy, and hence
higher supersaturation, than the subsequent one- or two- dimensional nucleation needed for
crystal facet growth. For this reason, an optimal crystal growth scheme should allow for

38
initial nucleation by transiently high levels of supersaturation followed by passage into
lower supersaturation levels that support high-quality crystal growth (Figure 13D) (44, 45).

Figure 13: Hypothetical free energy diagrams characteristic of different regimes of
solution saturation. (A) Stable regime. The soluble phase “S” has lower free energy and
is stable. (B) Metastable regime. Growth of crystalline phase “C” is favored but
nucleation events are rare due to large activation barrier. (C) Labile regime. A small
activation barrier leads to rapid nucleation events and poor quality growth.

(D)

Metastable regime after nucleation. Activation barrier is reduced due to the presence of a
critical nuclei in solution. High-quality crystal growth is supported.

39

Mixing at Low Grashoff Number
In the thermodynamic limit of infinite equilibration time, and with other thermodynamic
variables held constant (i.e. pressure and temperature), the phase of the protein solution will
be uniquely determined by the concentration of protein and precipitating agent in solution.
This behavior may be represented by a hypothetical two-dimensional phase-space having
concentration of protein and concentration of precipitating agent as variables. This phasespace represents the interaction of a given protein with a specific precipitating solution, and
is therefore unique to that solution.

Complex phase-space behavior arising from

interactions such as specific protein/ligand interactions, protonation/deprotonation of amino
acids, detergent micelle formation, and protein denaturation, results in highly varied and
unpredictable phase behavior. The different phases that may exist within a single phase
diagram include monomeric soluble phase, aggregate soluble phase, condensed liquid
phase, amorphous aggregate, denatured protein, and various crystalline forms.

In the simplest non-trivial case there will exist at least two distinguishable phases: a soluble
phase and a solid phase. At low protein and low precipitant concentrations the soluble
phase is stable. This region is bounded by a solubility curve that determines the maximum
stable concentration C0(Cprec) of protein as a function of the precipitating agent
concentration, which by definition must be single valued. For precipitating agents that
have the potential to induce crystallization there exists a metastable region located just
above the solubility curve. In this region the protein solution is out of equilibrium, and
given sufficient time, will undergo a phase transition to a crystalline solid. Beyond the

40
metastable region, at higher protein and precipitant concentrations, lies the labile region
where the nucleation of crystalline or amorphous aggregates is a rapid process. The
boundary between these regions, which depends on the relevant timescale of the
experiment, is referred to as the precipitation curve.

The equilibration of a crystallization assay can thus be represented as a parametric plot
through phase-space, having time as the independent variable. It is instructive to examine
the phase-space evolution of the two most commonly used crystallization screening
formats, microbatch and vapor diffusion (Figure 14). In microbatch crystallization the
protein is mixed at a one to one ratio with a precipitating agent and then incubated under a
layer of immiscible oil. The immiscible oil prevents dehydration/concentration of the drop
so that a microbatch experiment samples only a point of phase-space.

41
Figure 14:

Schematic diagram of the evolution of hanging drop and microbatch

experiments

through

two-dimensional

phase-space

having

macromolecule

concentration and precipitating agent concentration as variables. The phase-space is
divided into Stable, Metastable, and Labile regions. In microbatch experiments incubated
under an immiscible oil (1:1 mixing ration) are represented as a single point (red) on the
bisection of a tie-line connecting the initial protein concentration (Po) and precipitant
concentration (Co). Hanging drop experiments allow post-mixing equilibration through
vapor diffusion with a large reservoir of precipitating agent, slowly concentrating the
reagents, and driving the sample into the super-saturation region (orange). Depletion of
protein due to precipitation or crystal growth is not included in the figure.

In vapor diffusion experiments the protein and precipitant solutions are initially mixed at a
one to one ratio, and are then suspended over a large reservoir of the concentrated
precipitant solution. The drop subsequently equilibrates with the reservoir through a
process of vapor diffusion until the vapor pressures of the drop and the reservoir are equal.
This results in a monatomic concentration of the drop over time.

This evolution is

represented by an upward arrow in phase-space (orange).

Microbatch and vapor diffusion methods exhibit phase trajectories that are stagnant or
monotonically increasing in supersaturation. The point sampling behavior of microbatch
experiments results in an inefficient sampling of phase-space when compared to vapor
diffusion which allows for a continuum of conditions to be explored through drop
evaporation.

However, the monatomic increase in both protein and precipitant

42
concentration does not provide the desired transiently high levels of supersaturation for
nucleation followed by regression to the metastable regime for high-quality crystal growth.
Furthermore, in microbatch or hanging-drop experiments, the sudden addition of the
precipitating agent to the protein sample induces rapid convective mixing resulting large
transient concentration gradients throughout the drop. The corresponding high levels of
supersaturation that occur at the fluid/fluid interface often result in the immediate and
irreversible precipitation of the protein.

As an alternative to microbatch and vapor diffusion formats, the technique of free interface
diffusion (FID) allows for both slow and controlled mixing and efficient phase-space
evolution. In conventional FID experiments a liquid/liquid interface is established between
the protein and precipitant solutions in a capillary tube (top of Figure 15).

As the reaction begins, a slow equilibration of the molecular species across the interface
occurs by diffusion. Each species present in the reaction equilibrates at a rate determined
by its diffusion constant. The diffusion constant of a particle may be approximated through
the Stokes-Einstein relation:

D =

KT
6 πη r

(6)

where η is the solution viscosity in kg/ms, and r is the hydrodynamic radius of the particle.
The inverse dependence of the diffusivity on radius implies that small molecule
precipitating agents will equilibrate much faster than larger protein molecules.

For

43
example, a salt ion with a radius of 1 Ǻ has a diffusion constant in water of approximately
1000 µ2/s. By comparison a typical protein molecule of radius 10 nm will have a diffusion
constant of 10 µ2/s. The counter-diffusion of analytes with different diffusion constants
along a capillary of constant cross section results in a complex spatial-temporal evolution
of the concentration profiles (Figure 15) (46, 47).

Figure 15: Conventional FID reaction. (top) Protein (blue) and salt (red) solutions are
brought into intimate contact at a fluid-fluid interface within a capillary of constant cross
section. (bottom) Evolution of protein (blue) and salt (red) concentration profiles due to
counter-diffusion of species across the interface. Diffusion constants of salt and protein
are taken to be 1000 µ2/s and 10 µ2/s respectively. Concentration profiles are shown at
even 1 day time intervals from t = 0 days (step function) to t = 10 days.

44
Let us consider two observation points, A and B, located some fixed distance on either side
of the interface (Figure 15). Shortly after the reaction commences the protein concentration
at point A changes very little, while that of the precipitating agent, which typically has a
much larger diffusion constant, increases towards the final concentration determined by
initial the mixing ratio. Subsequently, over a larger timescale, the protein concentration
equilibrates, decreasing towards the final protein concentration that is again determined by
the mixing ratio. The concentration profile at point A therefore travels a curved path
through phase-space, potentially sampling efficient crystal nucleation conditions in the
labile region prior to settling into a high-quality growth regime in the metastable region.
As the solutions homogenize, the evolution at point B follows a complementary trajectory
to A, ultimately converging to the same final state (Figure 16).

45
Figure 16: Phase-space evolution of FID reaction at two observation points (Figure 15)
equidistant from the fluid-fluid interface. Points represent even 1 hour time steps from t
= 0 hours to t = 240 hours.

Free interface diffusion has long been recognized as an efficient means of detecting
crystallization conditions that has distinct advantages over microbatch or vapor diffusion
techniques (45). Despite the favorable kinetics of conventional free interface diffusion, this
method has not been widely adopted in the protein crystallography community for a
number of reasons.

For example, conventional FID setups require that solutions be

carefully introduced into opposite ends of the capillary using a thin needle. This is a
delicate and labor-intensive technique making it illsuited to high-throughput screening.
Moreover, the diameter of the capillary must be of substantial size (typically 1mm),
necessitating the use of relatively large sample volumes (generally > 5 µL). Furthermore,
the introduction of the second fluid causes transient convection, resulting in a poorlydefined interface which may only be reduced by cumbersome procedures such as the
introduction of hydro-gels or the prior freezing of the first solution.

The intrinsic

drawbacks of large required volume, delicate dispensing, and poorly-defined interface have
thus prohibited the use of FID as either a routine or large-scale automated screening
technique.

Even when a well-defined fluidic interface can be created, buoyancy-driven convection,
due to density differences in the solutions causes complex mixing at the interface. To
avoid unwanted mixing, capillaries must be stored with the long axis parallel to gravity,

46
and with the more dense solution on the bottom. This configuration creates a stable fluidic
interface, but often causes nucleated crystals to fall away from the interface and out of the
optimal growth conditions. It has thus been proposed that free interface diffusion would
only realize its practical advantages in microgravity environments were gravity-induced
convection is eliminated (40, 48).

However, the unusual properties of fluid flow in

microfluidic devices make it both possible and practical to implement nearly ideal free
interface diffusion conditions in terrestrial devices. The relevant non-dimensional number
that governs the onset of convection in a closed fluidic system is the Grashof number
(which measures the ratio of buoyant to viscous forces):

Gr =

α∆ cgL3
ν2

(7)

where α is the solutal expansivity (cm3/mg), ∆c is the difference in solute concentration
(mg/cm3), g is the acceleration of gravity (cm/s2), L is the characteristic dimension of the
container (cm), and ν is the kinematic viscosity (cm2/s).

At low Grashof number the interface between two distinct solutions brought into intimate
fluidic contact is stable. Inspection of Equation 7 suggests that this condition may be
achieved at high solution viscosity (49), in microgravity environments (50) or at small
characteristic length scales. Space-born free interface diffusion experiments have been
conducted in microgravity environments. These investigations have shown that stable
fluidic interfaces are achievable and further suggest that crystals of increased perfection
may be grown in microgravity (50, 51). However, the enormous expense of conducting

47
space-born experiments prohibits its use as a screening technique, so that investigation has
been limited to well-characterized model proteins.

Artificially increasing the solutal viscosity through the addition of polymerizing hydrogels
has been investigated as a technique for achieving low Grashof number mixing in terrestrial
devices (49, 52). In particular, the gel-acupuncture method has been advanced as a method
of realizing purely diffusive mass transport in crystallization assays. This method has been
successful over a broad range of crystallization targets and has been used to produce highquality crystals of novel crystallization targets. Despite this success, several limitations
have prevented general use of this technique. In particular, this technique has not proved
amenable to small volume, large-scale crystallization screening.

Additionally, the

requirement of including a polymerizing gel into the crystallization reagents presents an
undesirable constraint on the chemistry. An optimal crystallization technique should allow
for independent control over both the chemical composition and mixing kinetics.

The third power dependence of the Grashof number on the characteristic length suggests
reducing the critical dimension of the reactor as a means to suppress convection and
achieve purely diffusive mass transport. Five microfluidic reactors designed to provides
exactly this property are shown in Figure 17. Microfluidic free-interface diffusion (µFID)
through a constricted channel connecting two microwells allows for the slow counterdiffusion of the precipitant and protein solutions.

48

Figure 17: Microfluidic free interface diffusion (µFID) reactors. 5 pairs of microwells
are designed to implement 5 simultaneous FID reactions at mixing ratios 4:1, 2:1, 1:1,
1:2, and 1:4. Total volume of each reactor is 10 nL.

In this configuration the final concentration of each reactor is determined by the relative
volume of the coupled microwells. Opening the interface valve that separates the protein
from the precipitating solution creates a well-defined fluidic interface that allows for
diffusive equilibration of the coupled microwells. Due to the different mixing ratios the
individual trajectories of each reactor fan out in phase-space, thereby providing efficient
coverage of potential crystallization zones (Figure 18).

49

Figure 18: The evolution of 3 µFID reactions having mixing ratios 3:1, 1:1 and 1:3.
Curves represent the average state of both the sample side (top) and precipitating agent
side (bottom) of each compound well. The curves are representative of a counterdiffusion between Lysosyme and sodium chloride and agree qualitatively with numerical
finite element simulations. A decrease in protein concentration due to precipitation or
crystal growth is not included in the figure.

A further advantage of the constricted channel between the two wells is that only a very
small fraction of the protein sample is exposed to large transient gradients that occur
shortly after the interface is established. More concentrated precipitating solutions may
therefore be used with negligible immediate precipitation so that higher levels of
supersaturation may ultimately be achieved.

50
Chapter 4

MICROFLUIDIC FREE INTERFACE DIFFUSION: SCREENING DEVICE
Parallel Implementation of µFID
The simple geometric metering architecture (Figure 17) allows for the facile
implementation of nanoliter µFID crystallization assays in which the endpoint, and hence
the trajectory through phase-space, may be accurately controlled. Furthermore, since this
technique is robust to the properties of the resident fluid and does not require precise valve
timing it is scaleable to massively parallel architectures. The robust and precise metering,
simplicity of control, and highly efficient mixing kinetics of this technique have been used
to implement a microfluidic screening device for protein crystallization in ultra-small
volume reactions (Figure 19) (29). The current version of this device implements 240
simultaneous metering and mixing reactions while consuming only 3.0 µL of protein
solution; this represents a reduction of approximately 100-fold in sample consumption
when compared to traditional crystallization techniques.

51

Figure 19: Microfluidic protein crystallization screening device.

A layout of the chip showing 48 reaction centers, each consisting of 5 µFID reactors with
mixing ratios of 1:4, 1:2, 1:1, 2:1 and 4:1 is shown in Figure 20. Each pair of chambers is
connected to the protein sample and one of 48 crystallization solution inlets. Parallel
control of 720 integrated valves is achieved through two control lines that separately
address 240 interface valves and 480 containment valves.

By virtue of this parallel

architecture the device may be used to simultaneously mix and meter 48 solutions of
varying viscosity, surface tension, pH, and ionic strength at five different mixing ratios
using only two hydraulic control lines.

52

Figure 20: Layout of crystallization screening device. Flow layer is molded from a
multilevel negative master having both 13 µm high flow channels fabricated from 5740
photoresist (blue), and 45-micron-high microwells and inlet channels fabricated from
SU8 2050 resist (black). The high SU8 inlet structures prevent channel collapse during
loading. Control structure (red) consists of two separately addressable networks for
actuation of interface and containment valves. Forty-eight 4 µL reagent wells allow for
direct loading of the crystallization reagents.

53

The chip is contained within a carrier device (Figure 21) that facilitates loading, storage,
and interfacing with the control lines. The chip is secured in the base of the carrier with the
interface line directly connected to one of two carrier interface pins that are externally
accessible. The containment line interface pin is connected to the chip through a pressure
accumulator. Once charged, this accumulator acts as an on-board pressure source to
maintain actuation of the containment valves for several weeks, thereby allowing the chip
to be stored and transported without the need for any external connections.

Figure 21: Crystallization chip inside carrier device. Pressure reservoir (right) allows
for free transport and storage of chip. Interface pins (front) allow for easy loading and
control of chip valves.

54
The top of the carrier has two cavities with a raised lip around their periphery and stainless
steel input ports for pressurization. The cavities mate with the 48 reagent wells, creating a
seal against the compliant elastomer chip when the plates are pressed together.

3 µL of

each of the 48 crystallizing agents is introduced into the reagent wells of the chip using gel
loading pipette tips (Figure 22). Since the crystallization reagents are loaded directly onto
the chip there is no need for connecting 48 separate tubing connectors, greatly simplifying
operation. Once the carrier is assembled the cavities are pressurized, simultaneously
injecting the 48 crystallizing agents into the chip. The protein sample is then loaded
through a single port located in the center of the chip. 4 µL of protein sample are aspirated
into a pipette tip, and the tip is inserted into the protein port. The tip is then pressurized
through an adapter, injecting the protein into the 240 reaction chambers. Since the sample
is introduced through a single port, there is very little lost at the interface, and a true
economy of scale is realized with more than two thirds of the sample being used in the
crystallization assays.

Figure 22: Loading of crystallization agents directly into reagent wells.

55
This device represents the first scaleable implementation of free interface diffusion in a
format suitable for high-throughput structural biology initiatives. The ability to efficiently
screen crystallization conditions in a small-volume format represents an enormous savings
in the costs associated with upstream expression and purification processing. The modest
requirements in peripheral fluidic hardware, small footprint, and simple operation make
this device practical for use in both high-throughput crystallization facilities and in
specialized academic labs.

Furthermore, the inexpensive fabrication of these devices

should be possible once adequate production technology is in place, making chip-based
crystallization economical when compared to commercial liquid handling robots. It is
hoped that this will democratize the field of structural biology, making small volume
crystallization accessible to small academic laboratories.

Crystallization Results
An initial validation study of on-chip protein crystallization by µFID was conducted on 8
model macromolecules including 7 commercially available crystallization standards,
(Lysosyme, Glucose Isomerase, Xylanase, Thaumatin, Protease K, Bovine Trypsin, and
Beef Liver Catalase), and 1 protein with unpublished structure (bacterial primase catalytic
core domain).

The bacterial primase catalytic core domain was chosen since it had

previously been extensively screened, and was known to be difficult to crystallize. Each
protein was tested against two or more commercially available standard sparse matrices of
precipitants. To compare crystallization in chip against standard crystallization methods,
crystallization experiments were repeated for 9 of the model macromolecules using the

56
conventional microbatch and hanging-drop techniques; this allowed the precipitant
chemistries to be kept constant while varying the kinetic scheme for crystal growth.

Crystal growth was observed in the chips for all model macromolecules tested, and showed
an excellent degree of correlation with successful conditions revealed by more standard
screening techniques. Crystals of 6 different protein models grown in chips are shown in
Figure 23. A histogram comparing the number of successful experiments obtained by each
method for 8 model proteins (Figure 24) shows enhanced crystallization success in the
chip-based experiments. Sparse matrix screens led to crystal growth more often in the chip
than by conventional techniques in all but two cases (protease K and bovine trypsin). The
large number of crystallization hits obtained for Protease K in microbatch experiments is
difficult to explain on the basis of mixing kinetics since microbatch should be the least
efficient assay format. Subsequent experimentation with a broad range of crystallization
targets has shown this result to be anomalous – chip based crystallization screening has
been found to generally produce more hits than conventional techniques.

57

Figure 23: Optical micrographs of macromolecule crystals grown in chip. (A) Chicken
Egg White Lysosyme (Sigma-Aldrich); 50 mg/mL in 0.2 M sodium acetate pH 4.7.
Mixing ratio of 4:1 with 0.2 M Magnesium Chloride hexahydrate, 30% w/v iso-propanol,
0.1 M Hepes-Na pH 7.5. (B) Bacterial Primase catalytic core domain; 15 mg/mL in
50mM sodium chloride, 20mM TRIS-HCl pH 8.0, 1mM DTT. Mixing ratio of 4:1 with
1.4 M potassium/Sodium Phosphate pH 6.8.

(C)

Type II Topoisomerase ATPase

58
Domain / ADP; 12 mg/mL in 100mM sodium chloride, 20 mM TRIS pH 7.0. Mixing
ration of 1:1 with 0.2 M ammonium fluoride, 20% w/v polyethylene glycol 3350, pH 6.2.
(D) Thaumatin (Sigma-Aldrich); 50 mg/mL in 0.1 M ADA (Sigma Aldrich) pH 6.5.
Mixing ration of 1:1 with 0.8 M potassium sodium tartrate tetrahydrate, 0.1 M HEPES
pH 7.5. (E) Xylanase (Hampton Research); 43% w/v glycerol, 180 mM Na/K phosphate
pH 7.0. Mixing ratio of 4:1 with 0.2 M calcium chloride dihydrate, 28% v/v polyethelene
glycol 400, 0.1 M HEPES pH 7.5. (F) Glucose Isomerase (Hampton Research) 31
mg/mL in 10 mM ammonium sulfate. Mixing ratio of 1:1 with 0.2 M calcium chloride
dihydrate, 28% polyethelene glycol 400, 0.1 M HEPES pH 7.5. Scale bars are 100 µm.
All scale bars are 100 µm.

Figure 24: Histogram of crystallization hits for sparse matrix screens of model proteins.
Number of screens tested on each protein are Lysosyme (Lys) = 2, Glucose Isomerase (GI)
= 2, Protease K (PK) = 1, Bovine Liver Catalase (BLC) = 1, Xylanase (Xy) = 2, Bacterial
Primase catalytic core domain (BPC) = 3, Bovine Pancreas Trypsin (BPT) = 1, Thaumatin
(Th) = 1, mycobacterial RNase (MBR) = 3.

59

In the case of the bacterial primase catalytic core domain the chip-based experiments
showed a dramatic improvement in success rate.

µFID experiments identified 11

conditions that produced needle crystals of dimensions greater than 100 µm while no hits
were observed in either macroscopic method.

An additional on-chip experiment

optimizing around the crystallization conditions identified from the initial screen produced
crystals whose largest dimension exceeded 400 µm (Figure 23B). These conditions were
subsequently transported to microbatch format. This example suggests that optimized onchip crystallization conditions may be successfully exported to macroscopic techniques.

Finally, crystal growth in µFID experiments was generally observed to be faster than in
microbatch or hanging-drop formats. For the type II topoisomerase ATPase domain crystal
growth in microbatch required 2 weeks while crystals grown on chip with the same
conditions appeared after only 4 hours of incubation. When crystals grew on chip in less
than 12 hours, they were always observed on the protein side of the compound well,
suggesting that the short crystallization times are due to the high degree of supersaturation
achieved in the initial phase of diffusive equilibration.

In conventional screening formats reagents are generally mixed in a one-to-one ratio so that
the influence of mixing ratio is rarely investigated. In chip based experiments different
mixing ratios are set in parallel with no increase in setup time or complexity. In many
cases protein/precipitant mixing ratio was found to be an important screening parameter,
influencing both the success and morphology of crystallization. Figure 25 shows the

60
dependence of mixing ratio on the crystallization of a type II topoisomerase ATPase
domain and of DNA B/C helicase complex.

Figure 25: Variability in crystallization behavior due to different protein/precipitant
mixing ratios. (A) Crystals of DNA B/C helicase; 14 mg/mL grown at 4:1 (left), 1:1
(center), and 1:4 (right) mixing ratios of protein sample with 2.0 M (NH4)2SO4,
phosphate-citrate pH 4.5. (B) Crystals of Type II Topoisomerase ATPase Domain /
ADP; 12 mg/mL in 100mM sodium chloride, 20 mM TRIS pH 7.0. Mixing ratio of 4:1

61
(left), 1:1 (center), and 1:4 (right) with 0.2 M ammonium fluoride, 20% w/v polyethylene
glycol 3350, pH 6.2. All scale bars are 100 µm.

Consistent with the localization of large initial concentration gradients to the relatively
small volume of the connecting channel, µFID-based chip experiments resulted in reduced
protein precipitation.

It was observed that the mixing ratios and concentration of

crystallization agents that lead to crystallization on chip often caused the protein to
immediately precipitate in hanging drop and microbatch experiments. In the case of a type
II topoisomerase ATPase domain, the final concentration of precipitating agent achievable
in chip was 4 times greater than that possible for microbatch.

Beyond experimentation with well-characterized crystallization standards the present
technique has proven useful in the crystallization of outstanding and challenging
macromolecule targets. During these trials, chip-based µFID reactions have been used to
crystallize membrane proteins, large macromolecule complexes, and targets that had failed
to produce crystals by conventional screening techniques.

The crystallization device has been used for the de novo crystallization of 3 targets (a type
II topoisomerase, a transferring receptor heterodimer complexed with HFE (hdTfR/HFE),
and 10 MDa vault protein assembly) that had not previously been successfully screened by
conventional methods.

A single device was used to screen the topoisomerase protein

against a commercially available sparse matrix screen (Hampton Crystal Screen I;
Hampton Research). After 24 hours of incubation this screen identified 18 conditions that

62
gave crystals exhibiting varied quality and morphologies including some large single
crystals (Figure 23C). Crystals obtained from 10 of these conditions were reproduced in
microbatch format and were ultimately used to collect data at a resolution of 2 Ǻ (53).

hdTfR/HFE is a complex of an engineering heterodimer of transferrin receptor mutants
(hdTfR) and HFE, a protein implicated in hereditary hemochromatosis (54).

The

hdTfR/HFE complex was screened against 4 commercially available sparse matrix screens
(Hampton Crystal Screen I, Hampton Crystal Screen II; Hampton Research, Wizard I,
Wizard II; Emerald Biostructures), resulting in the identification of 3 conditions that gave
rise to small (approximately 5 micron) plate clusters.

Two rounds of subsequent

optimization using systematic grid screens resulted in plate clusters and some single plates
having maximum dimensions of approximately 50 microns (Figure 26A).

It was

determined that hdTfR/HFE crystallized only in a very narrow range of conditions, and in a
specific protein/precipitant mixing ratio. Changing the concentration of precipitant (PEG
MME 750) by as little as 1% from the successful condition (17% v/v PEG MME 750, 100
mM TRIS·HCl pH 7.6, 250 mM NaCl) did not produce crystals. Efforts to export these
conditions to microbatch and hanging drop formats have thus far been unsuccessful despite
highly resolved screening of precipitant and salt concentrations.

63

64
Figure 26: Optical micrographs of macromolecule crystals grown in chip. (A) Needle
clusters of hdTfR/HFE complex. 13 mg/mL sample mixed at 1:1 ratio with precipitant
(17% v/v PEG MME 750, 250 mM sodium chloride, 100 mM TRIS·HCl pH 7.6). (B)
Rod cluster of P450 Alkane Hydroxylase MUT 139-3. 30 mg/mL sample mixed at 1:1
ratio with precipitant (30% w/v PEG 8000, 0.2 M sodium acetate, 50 mm sodium citrate
pH 5.5). (C) Rod crystals of DNA helicase B/C complex. 15 mg/mL sample mixed at
1:1 ratio with precipitant (1.26 M (NH4)2SO4, sodium cacodylate pH 6.5) (D) Crystals
of Vault. 3 mg/mL protein sample mixed 1:1 with precipitant (15% PEG 400, 0.2 M
sodium citrate, TRIS·HCl pH 8.5) (E) Crystals of E. coli aquaporin AqpZ. 20 mg/mL
sample mixed at 3:1 ratio with precipitant (28% v/v PEG MME 2000, 200 mM , 4%
isopropanol 100 mM magnesium chloride, 100 mM sodium cacodylate pH 6.5 ) (55) (F)
Crystal of Probable ribonuclease III (RNASE III) from mycobacterium tuberculosis
Rv2925. 7 mg/mL sample mixed at 1:3 ratio with precipitant (20% (w/v) PEG-8000,
Ca(OAc)2, MES pH 6.0) (G) Crystal of 70s ribosome. Approximately 5 mg/mL sample
mixed at 1:1 ratio with precipitant (18% w/v PEG 8000, 0.2 M calcium acetate, 100 mM
sodium cacodylate pH 6.5) (H) Crystals of mechanosensitive ion channel of large
conductance (MscL) from E. coli. 20 mg/mL sample mixed at 1:4 ratio with precipitant
(35 % PEG 600, 100 mM ammonium sulfate, 100 mM sodium cacodylate pH 6.5). (I)
Crystals of DNA condensin complex cndD/G/H. 20 mg/mL sample mixed at 4:1 with
precipitant (10 % w/v PEG 8000, 8% v/v ethelyne glycol, 0.1 M HEPES pH 7.5)

65

Vault is an extremely large (13-MDa) ribonucleoprotein assembly, composed of three
proteins (TEP1, 240 kDa; VPARP, 193 kDa; and MVP, 100 kDa) that are highly
conserved in eukaryotes and an untranslated RNA (vRNA). This complex is of interest
to nanotechnology as a potential vehicle for drug delivery and has also been implicated in
the multidrug resistance in cancer cells (56). Although two-dimensional crystals were
reported during cryo-electron microscopy studies, severe limitations in sample
availability had prevented conventional crystal screening, making it an ideal target for
chip-based experimentation.

Vault was screened in the µFID format against (3)

commercial sparse matrix screens (Crystal Screen; Hampton Research, Wizard I and
Wizard II; Emerald Biostructures). Large single plate crystals having largest dimensions
of approximately 100 microns were detected in three conditions (Figure 26D). These
conditions were successfully exported directly to hanging drop format. Preliminary
diffraction data at low resolution has been collected from these crystals (D. Eisenberg,
personal communication).

Different crystal forms of a macromolecule can exhibit large variations in robustness,
size, shape, and perfection. Since not all crystal forms will be suitable for high-quality
diffraction studies, it is often of interest to detect new crystallization conditions. The
greater efficiency of µFID crystallization screening allows for novel conditions to be
identified which were missed by traditional screening. A previously unidentified crystal
form of the bacterial 70S ribosome was obtained (Figure 26G) in three conditions of a

66
sparse matrix of precipitants (Hampton Crystal Screen I), demonstrating that large
protein/nucleic acid complexes may be crystallized in chip (C. Hansen, A. Vila-Sanjurjo,
and J. Cate, personal communication).

P450 139-3 is refers to the heme domain of a mutant of P450 BM-3 from Bacillus
megaterium (P450 BM-3). P450 139-3 is a highly efficient catalyst for the conversion of
alkanes to alcohols (57). P450 139-3 had failed to produce crystals from initial screens in
vapor diffusion format.

Subsequent broad-based screening gave rise to very thin

(minimum dimension less than 1 micron) needle crystals. A single round of chip-based
screening using standard sparse matrix screens resulted in the identification of novel
conditions giving rise to single three-dimensional rod-shaped crystals (Figure 26B).
Crystals were scaled up and harvested using larger-volume µFID format (see Chapter 8),
and subjected to diffraction studies.

Initial diffraction produced reflections out to

approximately 10 Ǻ resolution. The low resolution diffraction was likely in part due to
poorly optimized cryo-protection and mechanical damage during harvesting; crystals
showed visible cracking and melting during harvesting process.

Subsequent protein

preparations gave rise to markedly different behavior, failing to produce crystals. This
study was ultimately abandoned due to difficulties in obtaining protein samples of
consistent quality from our collaborators.

Chip-based µFID has further proved applicable to the crystallization of integral membrane
proteins. In one study (performed at Fluidigm Corporation in collaboration with B. Stroud)
a successful condition for the crystallization of an ion channel (aquaporin AqpZ from E.

67
coli) identified in hanging drop, and transported directly to chip resulted in large single
crystals; demonstrating that membrane proteins can be crystallized in nanoliter volume
silicone µFID reactors (Figure 26E).

In a second study a previously crystallized mechanosensitive ion channel (MscL) was
screened against 5 sparse matrix screens (Hampton Crystal Screen I, Hampton Crystal
Screen II, Hampton Peg Ion Screen, Emerald Biostructures Wizard I, Emerald
Biostructures Wizard II) at 20 °C and 4 °C. MscL refers here to the mechanosensitive ion
channel of large conductance from E. coli. MscL is a member of a large family of
mechanosensitive channels implicated in the regulation of osmotic pressure in prokaryotes
(58). 10 successful conditions were identified in the experiments performed at 4 °C; room
temperature screening produced only phase separation. The chip-based crystallization
conditions showed excellent agreement with those identified in hanging drop experiments,
and included an additional crystallization condition. This novel condition was optimized
and transported to larger volume µFID format (see Chapter 8) to grow large crystals that
diffracted to low resolution (approximately 9 Ǻ). Attempts to improve resolution by
screening cryo-protectants were unsuccessful. The low resolution diffraction is consistent
with data collected from crystals optimized from hanging drop formats and suggests low
intrinsic crystal order. One possible source of crystal disorder that has been suggested is
the incomplete cleavage of HIS tags from the protein subunits, resulting in a heterogeneous
protein sample (S. Steinbacher, personal communication).

68
For target macromolecules that exhibit a very narrow crystallization slot, the growth of
high-quality crystals is dependent on achieving optimal mixing kinetics. In some cases,
such as the hdTfR/HFE complex, crystallization may require very specific mixing kinetics
and conditions which are difficult to acheive in microbatch or vapor diffusion formats. In
other cases, the highly efficient mixing kinetics realized in µFID reactions may be used to
change the habit and improve the quality of crystals grown using conventional techniques.
One such example is the crystallization of a 450 KDa DNA B/C helicase loader complex.
DNA B is the bacterial hexameric replicative helicase and DNA C is the accessory protein
that mediates DnaB loading at replication initiation sites. In this study hanging drop
conditions based on sulfate salts were found that produced very small (maximum
dimensions of 5 µm, minimum dimensions < 1 µm) poorly formed needles.

No

improvement in the size or morphology of these crystals was achieved despite attempts at
optimization through extensive grid and additive screening. Independent screening of this
complex against standard sparse matrix screens identified similar crystallization conditions
based on ammonium and lithium sulfate salts. Chip-based crystals were however of much
higher quality, exhibiting three-dimensional hexagonal rod morphology with maximum
dimensions of 200 microns, and minimum dimension of 25 microns (Figure 26C).
Although harvesting of these chip-grown crystals has been problematic, initial diffraction
studies from a single crystal that was grown in hanging drop (and could not be reproduced)
showed reflections to 3 Ǻ resolution. Indexing data from chip-grown crystals confirmed
that the space group and lattice constants (space group P3; unit cell dimensions a=b=174.5
Ǻ, c=87.98 Ǻ, α=β=90° γ=120°) were the same, suggesting that the crystals are
intrinsically well ordered.

69

Perhaps the most striking result of these studies has been the rapid identification of
crystallization conditions for novel targets that had been exhaustively screened without
success. In one instance, crystals of a mycobacterial RNase were obtained from a single
experimental condition on chip (Figure 26F), whereas no crystals had been observed for
this sample despite extensive prior trials using traditional methods. Subsequent broadbased screening efforts around this condition using hanging-drop vapor diffusion setups
proved successful, but only after the protein concentration was increased from 7 mg/mL to
> 40 mg/ml. Crystals grown by vapor diffusion diffracted to 2 Ǻ resolution and were used
to solve the structure of this protein (D. Aiky, personal communication).

In another striking example a 750 KDa ternary complex (DNA D/G/H) (59), that had been
in crystallization trials for over two years without success, was screened against 4 sparse
matrix screens in chip. DNA D/G/H refers here to a subassembly of the S. cerevisiae
condensin complex comprised of the CndD, CndG, and CndH subunits. It lacks the two
ATP-binding subunits of condensin, Smc2 and Smc4. After 2 days of incubation at 20 °C
single three-dimensional crystals with rounded edges (maximum dimension 20 microns)
were observed at a mixing ratio of 3:1 (precipitant : protein) in two related chemical
conditions based on PEG 3350 and sodium acetate. This condition was reproduced in a
subsequent chip-based experiment performed at 4 °C, resulting in three-dimensional
polyhedron-shaped crystals (maximum dimension 20 microns) with well-defined edges. A
systematic grid screening strategy varying precipitant concentration, salt concentration, and
pH was used to successfully transfer this condition to hanging drop. Initial diffraction

70
studies of these crystals gave very poor diffraction (highest-order reflections at
approximately 20 Ǻ). Subsequent protein preparations failed to produce crystals despite
repeated trials over a period of approximately 4 months. Crystals were finally recovered in
chip-based trials by conducting a partial proteolytic digest of c-terminal residues (Figure
26I).

Initial diffraction studies of chip-grown crystals displayed reflections to

approximately 5.5 Ǻ resolution. The crystals were in space group P3 with unit cell
dimensions a = 223.11 Å, b = 223.11 Å, c = 265.56 Å, α = β = 90.0°, γ = 120° (S. Gradia,
personal communication).

Attempts to transfer this condition to hanging drop vapor

diffusion format by systematic screening based on the chip condition were unsuccessful
until a detergent additive was used. The condition that ultimately gave crystals in hanging
drop format included a detergent additive, had higher salt concentration, and lower peg
concentration when compared with the successful chip condition. These crystals showed
diffraction to 5.5 Ǻ. Unfortunately, subsequent protein preparations have again failed to
crystallize despite meticulous reproduction of the initial expression, purification, and
crystallization protocols.

Continued crystallization trials attempting to reproduce this

success are currently underway. Additionally, orthologues of this complex derived from a
variety of organisms are being investigated as potentially more tractable crystallization
targets (J. Berger, personal communication).

71
Chapter 5

SYSTEMATIC SOLUBILITY STUDIES: FORMULATOR DEVICE
Introduction
Understanding the phase behavior of proteins is an essential part of the crystallization
process.

The growth of crystals from a protein solution requires the existence of a

nontrivial phase diagram which allows the protein state to be manipulated between at least
two thermodynamic phases: soluble and precipitated. The processes of crystal nucleation
and growth arise on the boundary between these two phases, and are governed by subtle
effects in physical chemistry. There are a variety of schemes that manipulate the kinetics
of the crystallization process, and all take advantage of generic features of these phase
diagrams (44). However, in practice the phase behavior of very few proteins has been
studied in detail (60-68), and solubility information for a specific protein is rarely available
for crystallization and optimization experiments (69, 70).

Furthermore, it is often an arduous process to find the right combination of chemicals that
yields appropriate phase behavior for a given protein. Every protein is different, and even a
modest subset of stock precipitating solutions comprise a vast chemical phase-space that
must be explored. The large amounts of sample required make systematic exploration by
conventional techniques infeasible, and screening is typically directed towards random
sampling using an incomplete factorial or sparse-matrix approach, which is a brute-force
process requiring large numbers of experiments (15, 34). There have been numerous
attempts to rationalize this procedure, for example by using computational approaches to

72
predict phase behavior (71, 72) or by trying to correlate measurements of osmotic 2nd virial
coefficients (73, 74) with crystallization conditions. Practical limitations have thus far
prevented these techniques from being generally applicable.

Although the small-scale characterization of protein solubility by a pre-crystallization
solubility assay has been reported (15, 75, 76), this technique has not been widely adopted
since the large required sample volumes make it unsuitable for targets that cannot be
expressed and purified in large quantities. Microfluidic technologies enable ultra-small
volume processing and hence are ideally suited to address these problems. Previously
microfabricated dispensers have been used to reduce sample consumption in cases where
the sequential addition of reagents to a levitated drop of microliter volume is sufficient to
explore a restricted chemical space (76). This Chapter describes the development of a
microfluidic device that allows for the practical and systematic exploration of protein
phase-space behavior.

Combinatorial Mixing on Chip
Thorough characterization of protein solubility behavior requires accessing a vast chemical
space through the combinatorial mixing of a limited number of stock reagents. The layout
of a microfluidic formulator device that combines precise and robust PCI metering with
microfluidic mixing (14) and multiplexing elements (27) is shown in Figure 27. This
design allows for unprecedented fluid handling capability and represents the first
implementation of true combinatorial mixing on chip.

73

Figure 27: Microfluidic formulator device. Device allows programmable combinatorial
mixing of 32 stock solutions (top), 8 buffer solutions (left) and a sample solution (center).
27 pneumatic and hydraulic control lines are interfaced to external solenoid actuators
through an array of control ports (bottom). The control layer mold is patterned from a
single mask shown in blue. A multilevel flow layer is patterned from three separate
lithography steps; 50 µm SU8 2075 for low impedance inlets and outlets (pink), 13 µm
5740 for rounded channel structures compatible with integrated valves (green), and 10
µm SU8 2015 for observation windows of rectangular cross section (yellow).

The active region of an earlier version of the microfluidic formulation chip that allows for
the arbitrary combinatorial mixing of 16 stock reagents into one of 16 buffer solutions is

74
shown in Figure 28A. Two 16-solution multiplexer arrays, actuated by 8 control lines,
allow for the selection of buffers (left) and reagents (bottom). A PCI junction, formed by a
3-valve peristaltic injection pump (red) and cross-injection valves (center green) dispenses
directly into a 5 nL ring reactor. Once the reactor has been flushed, a reagent line is
selected and the cross-injection sequence is executed. The extended split channel region
increases the volume of the cross-injection junction, thereby allowing for up to 15
injections. The maximum number of consecutive injections that may be executed before
the junction needs to be recharged depends on the Taylor dispersion (77) of the injected
fluid as it is pumped down the channel, and is therefore a function of the analyte diffusivity
and the flow rate. Figure 28B shows the injection of 4 slugs, each having a volume of 80
pL, into the ring reactor. Arbitrary combinations of 16 reagents may be produced in the
reactor by sequential flushing and injection steps. Figure 28C shows a color gradient
formed from the sequential injections of water, blue dye, green dye, yellow dye, and red
dye. In screening applications that require the interrogation of a precious sample against
many pre-mixed reagent formulations, the cross-injection flushing step is wasteful and is
circumvented by the injection of sample through a separate sample injection site (Figure
28D). After the ring is filled with the desired reagents, they are mixed by active pumping
around the ring (14).

75

Figure 28: Combinatorial mixing using a microfluidic formulator. (A) Integration of
multiplexer (dark blue), peristaltic pumps (red), rotary mixer (yellow), and PCI junction
(center green) components for on-chip combinatorial formulation.

The parallel

multiplexer shown has been replaced with a binary tree multiplexer in more recent
designs. (B) Injection of approximately 250 pL (4 injection cycles) of blue dye into
rotary mixer. (C) Color gradient formed by consecutive injections into mixing ring (8
injections blue, 8 injections green, 8 injections yellow, 8 injections red). (D) Pumping
around ring for 3 seconds results in complete mixing of dye. Blue dye is added to
mixture through sample injection inlet (bottom right).

76
Robust and Precise Picoliter Metering
The reagents used in crystallization exhibit a large variation in physical properties such as
viscosity, surface tension, ionic strength, and pH. This variation presents a formidable
challenge for fluid handling systems that must allow for arbitrary fluid combinations and
proportioning. The positive displacement cross-injection metering method overcomes this
obstacle, allowing for variable dispensing to be dynamically programmed by the user in 80
picoliter increments with less than 5% variation over a broad range of fluid properties.

The precision of metering was evaluated by injecting variable amounts of dye
(bromophenol blue sodium salt; Sigma) into a reactor, mixing, and performing absorption
measurements. Measurements were taken to determine the concentration of bromophenol
blue sodium salt (absorption peak at 590 nm). A 9 µm high segment of the mixing ring
(approximately 300 µm by 80 µm) having rectangular cross section was illuminated with a
590-nm diode (AND180HYP; Newark Electronics) and imaged through a stereoscope
(SMZ 1500; Nikon) onto a charge coupled device camera. Pixel intensities were averaged
and compared to an identical adjacent reference channel containing the undiluted dye (2
mM bromophenol blue sodium salt, 100 mM TRIS-HCl pH 8.0). In some experiments
glycerol was added to the injected dye to vary the viscosity. Dye concentrations were
calculated using the Beer-Lambart relation as
⎛ I − I back ⎞
ln⎜⎜ 0
I data − I back ⎟⎠
C data
C max
⎛ I − I back ⎞
ln⎜ 0
⎜I −I
back ⎠
⎝ ref

(8)

77
where I0 is the intensity measured prior to injections, Iback is the background ccd intensity,
Iref is the intensity measured in the reference channel, and Idata is the intensity measured in
the ring. The injected volume was then calculated from the measured concentration
assuming a nominal ring volume of 5 nL determined by the measured height and geometry
of the master mold.

A set of 900 sequential titration experiments (Figure 29A) shows the metering to be both
precise and reproducible, with a slope of 83.4 pL per injection cycle and a coefficient of
correlation of 0.996. The standard deviation of the injected slug volume was determined to
be approximately 0.6 pL. Although the positive displacement metering ensures that the
injected volume is robust to changes in the fluid viscosity, the viscosity of the working
fluid does however reduce the bandwidth of the injector. It was found that for a solution
having viscosity of 400 cP the frequency response of the injector began to roll off at 10 Hz.
When operating at an injection frequency of 5 Hz all solutions having viscosities below
400 cP produced even injection volumes. Since the metering mechanism is completely
mechanical, there is no dependence on the pH or ionic strength of the injected fluid.
Additionally, since the fluid is not dispensed from the chip, there is no phase interface, and
therefore little dependence on surface tension, so that the metering technique is truly robust
to the physical properties of the injected fluid. Titration experiments with fluids of varying
glycerol concentration show the injection volume to vary by less than 5% over a viscosity
range of 1 cP to 400 cP without any modification to the injection sequence (Figure 29B).

78

Figure 29: Precise and robust microfluidic metering. (A) Absorption measurements
showing high precision and reproducibility of PCI injections. Each of the 9 clusters
represents 100 identical injection sequences. (B) Absorption measurements of 4 sets of
20 injection and mixing sequences showing metering to be robust to the viscosity of the
injected fluid. Fluids contain varying amounts of glycerol and have viscosity ranging
from 1 cP to 400 cP (black = cP, blue = 40, red = 100 cP, green = 400 cP).

79

Cross-Contamination Issues
The cross-contamination of reagents is a concern in formulation experiments that are
sensitive to residual amounts of various chemicals that are present in the stock solutions.
Within the formulator device cross-contamination may occur by three mechanisms: carryover within the PCI junction, adsorption to the elastomer walls, and unwanted mixing
within the multiplexer structure.

Carry-over within the PCI junction may be minimized by proper fluidic design and
sufficient flushing protocols. To ensure the complete exchange of reagents within the PCI
junction during a flushing cycle it is necessary to minimize the dead volume of the
junction.

This is accomplished by ensuring that the inlet of the junction is, within

fabrication tolerances, directly adjacent to the mixing ring inlet. A comparison between a
poorly designed injector and a low dead volume injector is shown in Figure 30. In the
poorly designed injector (Figure 30A) a significant volume of fluid is caught in a stagnation
region adjacent to the ring inlet and therefore is not efficiently exchanged by convection.
In this case the complete exchange of fluids within the injector is limited by the
characteristic time for diffusion of species out of the stagnation region. In the low dead
volume injector (Figure 30B) there is no appreciable stagnation region near the inlet so that
convection can rapidly exchange the fluids. In this case the flushing speed is only limited
by the diffusion of species across the gradient of the flow profile (width of the channel) and
is therefore much faster. It should be noted that incomplete flushing at the stagnation area
near the outlet of the injector does not contribute to contamination.

Absorption

80
measurements were used to quantify the injector carry-over during a flush cycle of 1.5
seconds. Using a low viscosity solution and standard operating pressure the carry-over
(residual concentration of dye) was determined to be less than 5 parts in 10,000 (the limit
of detection).

Figure 30: Comparison of injector designs. (A) Poorly designed injector having
substantial dead volume. (B) Low dead volume injector.

Possible contamination due to nonspecific adsorption of molecules to the walls of the
container has not been thoroughly investigated. The highly hydrophobic surface of the
PDMS makes the adsorption of soluble small molecules unlikely. However, due to their
amphiphilic properties, the adsorption protein molecules to the elastomer surface is a
concern. For applications in which modest protein concentrations are employed this effect
can be significant due to the large surface to volume ratio that is characteristic of
microfluidic structures. In the case of protein crystallization, this effect can safely be
ignored due to the very high protein concentrations. Considering a section of low aspect
ratio channel of width 100 µm and height 10 µm, the surface area per unit length is 220

81
µm2. The adsorption of a densely packed monolayer of protein having a characteristic
dimension of 5 nm to this surface would require 8.8 x 106 molecules per unit length.
Assuming a molecular mass of 40,000 Da, the total mass of protein adsorbed from a 1 km
section of channel (1 mL) is approximately 0.5 mg. Since protein concentrations used in
crystallization are typically 10 mg/mL or more this represents only 5% of the total protein
in solution.

The parallel multiplexing structure (27) reported by Thorsen et al. consists of an array of
parallel channels which are connected to a single cross-channel and addressed via an array
of valves. The large dead volume at the downstream end of each channel within this
parallel multiplexing structure makes a certain degree of reagent cross-contamination
unavoidable (Figure 31). Although this contamination can be reduced to acceptable levels
at the PCI junction by sufficient flushing it causes serious problems in the vicinity of the
multiplexer due to unwanted reactions between reagents.

In the case of protein

crystallization the stock solutions include various salts, polymers, buffers, and organic
solvents. The inadvertent mixing of certain combinations of these reagents can lead to
phase separation, aggregation, or the formation of insoluble salts. For instance, the mixture
of phosphate salts with salts containing magnesium or calcium anions results in the
instantaneous formation of insoluble magnesium/calcium phosphate salts. Once insoluble
salts are formed they quickly clog the microchannels and ultimately lead to device failure.
This reagent incompatibility imposes very stringent demands on the fluidic design and
flushing protocols.

82

Figure 31: Contamination in parallel multiplexing structure. (A) Selection of reagent
causes contamination in dead volumes at the inlets of remaining channels and at
multiplexer outlet. (B) Sequential selection of reagents causes unwanted mixing within
multiplexer.

Initial attempts to eliminate this problem used an additional flush channel through which
the front of the multiplexer could be flushed after every injection step. A protocol of
successive flushing and peristaltic pumping was used to prevent the unwanted mixing of
reagents within the multiplexer. Initially the multiplexer is filled with dionized water
through the flush channel. A reagent is selected and used to charge the PCI junction. Once
the reagent flush step is complete the multiplexer valves are closed and the front of the

83
multiplexer is flushed through the flush channel. The valves of the multiplexer are then
actuated in a peristaltic sequence to expel any contaminated reagent from the multiplexer.
The front of the multiplexer is then flushed again and the multiplexer valves are pumped in
the reverse peristaltic sequence to refill the multiplexer with dionized water. In this way a
“buffer” of water is used to maintain separation between the reagents and prevent unwanted
mixing. This protocol was successful in eliminating the formation of insoluble salts over a
two week period of operation; in the absence of this protocol insoluble salt formation was
observed within a minute of device operation.

Although the protocol of successive flushing and pumping steps is effective at eliminating
unwanted reagent mixing it adds considerable control complexity and has two undesirable
drawbacks. Firstly, the additional flushing and pumping steps are very time consuming and
account for nearly half of the experiment time. Secondly, it was found that in order to
avoid unwanted mixing it was necessary to have more reverse pumping steps than forward
pumping steps, leading to the growth of the dionized water “buffer” region over time.
Charging of the PCI junction with a selected reagent requires that this buffer region be
completely expelled and therefore requires that the flush time be increased. Since the size
of the “buffer” is determined by the history of the flushing sequence it is difficult to
ascertain the appropriate length of each flush cycle. Additionally, if a reagent is not used
for extended periods of time the “buffer” becomes impractically large extending off the
chip and into the connecting tubing.

84
In order to eliminate reagent cross-contamination and avoid cumbersome flushing
protocols a low dead volume multiplexing structure was designed. A binary tree flow
channel structure that allows for low dead volume multiplexing of reagents is shown in
Figure 32 (personal communication S. Maerkl). N consecutive bifurcations originating at a
single channel allow for the 2N inlet channels to be connected through equivalent fluidic
paths. Each level of the binary tree has pairs of valves at the bifurcations which allow for
flow to be directed either to the left or right. At the final level of the binary tree every
second channel is a flush channel connected in parallel to a common flush inlet containing
dionized water (Figure 27). Operation of the device is as follows. The reagent with which
the PCI junction will be charged is selected and flushed through a path of the binary tree.
Once the injection sequence is complete the least significant valves on the binary tree are
reversed, causing water to be flushed through the tree by the same path that the previous
reagent followed. The binary tree is thereby restored to its original state and is ready for
the next injection sequence. Provided that the flushing step is complete this protocol
completely eliminates the possibility of unwanted mixing within the multiplexer.

85

Figure 32:

Binary tree multiplexing structure.

Low dead-volume junctions and

interleaved flush lines (blue) allow for zero reagent cross-contamination. (A) Selected
reagent (green) is flushed through unique path of binary tree. (B) Reversing logic of
least significant valves (top) restores the multiplexer to its original state.

I/O Interfacing
The utility of a technology depends ultimately on the ease with which it can be used.
Invariably, time spent optimizing the robustness of a device, and engineering practical
interfaces, results in increased productivity. The large number of solution and control

86
inlets used in the formulator device presents a significant challenge for chip i/o interfacing.
Individually connecting the 78 required fluidic connections that must be made is very time
consuming and introduces the risk of incorrect connections being made. Additionally,
since the formulator uses extensive flushing protocols, and can operate for weeks at a time
it is necessary that there be a sufficient reservoir of flushing, buffer, and stock reagents.

In the case of the screening device the problem of introducing 49 separate solutions into the
chip was solved by introducing each reagent into a separate inlet well using a pipette and
then applying pressure to all reagents simultaneously via a seal with the top of the device.
In the case of the formulator device, the footprint of the wells required to supply a
sufficient volume of stock solutions (approximately 100 µL) is impractical. To address this
issue a manifold was designed that allows for 1 mL reservoirs of reagents to be interfaced
to the device. The base of the manifold consists of a Delrin® block into which an array
circular holes has been machined to accommodate 1 mL Nalgene® centrifuge tubes (Figure
33A). The holes are designed such that, when inserted, the tops of the tubes are just below
the surface of the block. The block has a cover plate with an array of tapped 10-32 through
holes that are aligned with the tubes (Figure 33B). Fittings with 20 gauge stainless steal
pins are screwed into each hole of the plate (Figure 33C). O-ring seals at each fitting make
an air-tight seal with the plate. An O-ring seal between the plate and the block creates a
closed chamber that may be pressurized through a single inlet located on the side of the
block. When assembled (Figure 33D) the end of each pin is immersed a separate reagent
tube so that pressurizing the chamber causes the reagent to flow through the tube. A thin
layer of paraffin oil is added to the top of each tube to ensure minimal evaporation during

87
the course of an experiment. The large volume of reagent in each tube (1 mL) is sufficient
for continuous operation of the formulator over several weeks.

Figure 33:

Reagent manifold for formulator device.

(A)

Delrin block with

pressurization port (bottom left). One reagent tube in inserted in hole array. (B) Top
plate of manifold. (C) Fitting with o-ring and pin. (D) Assembled manifold shown with
8 of 16 wells connected to tubing. Remaining ports are occupied by plugs.

In order to quickly and correctly establish the large number of connections required for the
formulator operation, a standard one-touch connector was designed.

The connector

consists of an aluminum piece with two rows of 16 through-holes bored at a 0.1˝ pitch.

88
The rows are separated by a distance of 0.1˝ and offset by 0.05˝. Each hole accommodates
a 1˝ long 20 gauge stainless steal pin that extends ¼ ˝ from the surface of the connector that
mates with the chip (bottom). The pins on the top of the connector are bent 90° and
interface with microbore Taigon® tubing that is connected to the reagent manifold. This
32 pin connector is easily inserted and removed from the device to make quick
connections. The connection of a formulator device to 32 reagent lines and 32 control
inputs via two one-touch connectors is shown in Figure 34.

Figure 34: Microfluidic formulator device with one-touch 32 pin fluidic connectors.
Stock reagents are introduced from manifold through a 32 pin one-touch connector (top).

89
Pneumatic and hydraulic control lines are interfaced through a separate 32 pin connector
that interfaces with solenoid manifolds.

90
Chapter 6

MICROFLUIDIC MIXING: SCALING LAWS AND OPTIMIZATION
Introduction
Rapid microfluidic mixing is necessary for conducting the large number of experiments
required for systematic phase-space mapping in a pratical time. This Chapter discusses
how the basic physics of microfluidic fluid flow and mass transport affect the design and
optimization of the rotary mixer used in the formulator device.

Achieving efficient mixing in the microfluidic environment is problematic due to the
characteristic laminar flow that is manifested in these devices. At the small length scales
that are characteristic of microfluidic devices viscosity becomes dominant over inertial
effects in mass transport phenomena. Put simply, this implies that the fluid has no memory
and that the flow field is instantaneously determined by the imposed boundary conditions.
In particular the advection of momentum, which leads to turbulent mixing in macroscopic
systems, is suppressed so that the flow is laminar. The relative importance of viscous and
inertial forces, and hence the onset of turbulence, is determined by the Reynolds number:

Re =

ρUL

(9)

where ρ is the fluid density (g/cm3), U is the characteristic velocity (cm/s), L is the
characteristic channel dimension (cm) and µ is the viscosity of the fluid (g/cm·s). For most
flows in small channels the Reynolds number is small so that the flow is laminar and the

91
familiar turbulent mixing of macroscopic devices vanishes. The transition from laminar to
turbulent flow occurs at Reynolds numbers of approximately 2000. By comparison, the
flow of water at 1 cm/s down a 10 µm high channel has a Reynolds number of 10-1, and is
therefore completely laminar.

All mixing is ultimately accomplished by diffusion. Accelerated mixing may therefore be
accomplished by generating convective flows to increase interface areas, decrease
characteristic diffusion lengths, and enhance concentration gradients.

In the case of

macroscopic fluidic devices (like a coffee cup) this may be readily achieved through
turbulent mixing. Turbulent mixing gives rise to exponential reduction in characteristic
separations, thereby causing rapid and efficient mixing. For example, pulling a spoon
through a coffee cup causes complete mixing within seconds.

Turbulent mixing cannot be accessed in microfluidic devices that operate in the regime of
low Reynolds number. It is nevertheless possible to achieve exponential mixing by the
process of chaotic advection.

The implementation of chaotic advection for efficient

microfluidic mixing has been reported using three-dimensional flows created by spiral
mixers (78), herringbone mixers (79), and reverse-micelle mixers (80).

All of these

strategies achieve chaotic advection by means of a three-dimensional flow field.

Generally, steady two-dimensional flows are integrable and cannot access exponential
mixing by means of chaotic advection. However, geometric mixing can be accomplished
by the repeated “folding” or “kneading” of a fluid onto itself. A rotary mixer based on this

92
principal was proposed by Chou et al. (14). In this mixer two or more fluids occupying
different sections of a ring-shaped channel structure are homogenized by active pumping
around the ring. Unlike the herringbone and spiral flow-through mixers which accelerate
mixing between laminate streams of fluids flowing in juxtaposition along a channel, the
rotary mixer is a batch mixer that homogenizes fluids that are serially introduced into the
ring. Fluids pumped around the ring are subject to a transverse gradient in the flow
velocity due to the non-slip boundary conditions at the channel walls, resulting in the axial
dispersion of analytes. Mixing in this structure is accelerated through the combination of
this axial dispersion and the periodic boundary conditions imposed by the ring structure.

During mixing, molecules are subject to the combined effects of convection and diffusion.
As molecules diffuse transversely across the channel they sample different flow rates. The
net dispersion, and hence the time required to homogenize different reagents, therefore
depends on the relative contributions of convection and diffusion. A comparison of the
importance of these two effects is given by the non-dimensional Peclet number:

Pe =

UL

(10)

where U is the fluid flow velocity, L is the characteristic spatial dimension (say the width
of the channel), and D is the diffusion constant of the analyte.

The dispersion of an analyte due to pressure-driven flow down a channel of circular cross
section was first described by G.I. Taylor in 1953 (77). A thin slug of tracer particles

93
flowing down a channel is stretched by the non-uniform velocity profile. The non-slip
boundary condition imposed at the channel wall implies that a line of tracer particles is
stretched to a thickness Umaxt in time t. Therefore, in the absence of diffusion, the
dispersion of the plug is generally linear in time.

Diffusion of the molecules within the flow stream acts to significantly reduce dispersion.
As the plug is stretched by the flow a transverse concentration gradient is established,
thereby causing molecules to diffuse across streamlines from regions of high velocity to
regions of low velocity and vice versa. The characteristic time for a molecule to diffuse the
width of the channel is τ = h2/D. At the end of this time interval the molecule will be
located somewhere within the slug that has stretched to a length of Umaxτ. Therefore, at
time t the net progress of the molecule down the channel can be approximated as a random
walk of t/τ steps having an average step size of Umaxh2/D. The dispersion of the molecules
is therefore diffusive in nature with an effective diffusivity proportional to Umax2h2/D. At
long times a collection of molecules initially defined within a thin slug will evolve into a
Gaussian distribution centered at Uavgt having mean squared displacement proportional to
Umax2 h2/(Dt). Figure 35 shows a finite difference time domain simulation of the dispersion
of a line of tracer molecules in a two-dimensional parabolic flow profile. Concentration
profiles are shown after 10 seconds of dispersion for a maximum flow velocity of 100
µm/s, and an analyte diffusivity of 100 µm2/s. The Peclet number is varied by changing the
channel width in each simulation to illustrate the qualitatively different behavior. The
Taylor dispersion description is only valid at long times when the molecules have sampled

94
the entire flow profile and large transverse gradients are relaxed. In the simulation this
condition is achieved in the case of Pe = 10.

Figure 35: Finite difference time domain simulation of dispersion of tracer particles in
parabolic flow profile at varying Peclet number. Diffusion constant is 100 µm2/s and
maximum velocity is 100 µm/s so that Peclet number is equal to the channel width in
microns.

95
Dispersion in Low Aspect Ratio Channels
The distribution of analyte along the stretched plug is determined by the gradient of the
flow profile and hence depends on the exact geometry of the channel. The viscous flow of
an incompressible Newtonian fluid through a static structure satisfies the Navier-Stokes
equation subject to non-slip boundary conditions. For steady-state flow within a channel of
constant cross section, and in the absence of body forces, this reduces to the onedimensional Poisson equation subject to Dirichlet boundary conditions,

∇P

= ∇ 2U z = Const

∂U z ∂z = 0

(11)

U z ∂Ω = 0
The form of solutions to this equation is completely determined by channel geometry and is
proportional to the ratio of the pressure gradient to the viscosity, which by similarity
arguments must be constant along the channel. In the previous discussion the Peclet
number determining the Taylor diffusivity was based on the width of the channel. As
discussed below, this is appropriate for channels of semi-ellipsoidal (rounded) cross section
but not for channels of rectangular cross section.

Flow through low aspect ratio channels of rectangular cross section is described by HeleShaw flow. In general, viscous drag effects in low aspect ratio structures with constant
height are dominated by the constricted dimension (height), so that lateral features
(obstacles) only have significant effect on length scales comparable to the height. In

96

situations where Re << h/w << 1, flow lines reproduce those of two-dimensional potential
flow (flow at infinite Reynolds number) with a thin boundary layer.

In the case of low Reynolds number flow through a shallow rectangular channel viscous
drag is dominated by the height dimension so that only within a distance comparable to the
height of the channel is there a significant effect of the wall.

This results in a velocity

profile that is essentially constant across the width of the channel (Figure 36A). In the
vertical direction the flow profile is parabolic, resulting in large velocity gradients. Since
the channel height is much smaller than the channel width, gradients due to the wall no-slip
condition do not significantly contribute to Taylor dispersion. The relevant Peclet number
for determining the Taylor dispersion in a shallow channel of rectangular cross section is
therefore based on the channel height. The nearly constant velocity profile across the
largest dimension of the channel results in a dramatic reduction in Taylor dispersion when
compared to flow through a channel of equal circular cross section. The effective “Taylor
diffusivity” in a rectangular 1:10 aspect ratio channel is U2A/(2100D) compared to
U2A/(48πD) for a circular channel of equal cross sectional area A.

97

Figure 36: False color plots of normalized flow velocity profiles down a 10 µm high,

100 µm wide rectangular channel (top A) and a 13 µm high, 100 µm wide semiellipsoidal channel (top B).

Average velocity profiles across channels obtained by

integrating out height dependence (bottom A and B). Curve fit to average flow profile in
B is y = 1 – x2.

Annealing flow molds to generate a rounded channel cross section has a dramatic effect on
the flow profile and the magnitude of Taylor dispersion. A common standard MSL flowchannel geometry is a width of 100 µm and a 13 µm high semi-ellipsoidal cross section.
The tapering of the height of channel away from the centerline results in a greatly enhanced
fluid drag at the edges. This drag generates large transverse velocity gradients and hence
enhances dispersion. Figure 36B shows a finite difference simulation of the flow profile
through a 1:10 aspect ratio channel with semi-ellipsoidal cross section. Integrating out the
height dependence yields a flow profile that is nearly perfectly parabolic. This profile is
observed in experiments (Figure 37). The flow profile in the vertical direction is also
essentially parabolic due to the small curvature of the channel.

However, since the

characteristic diffusion time across the width of the channel is much greater than that across
the height (by a factor of 100 for 1:10 aspect ratio), the dispersion arising from the velocity
gradient across the width dominates. The appropriate Peclet number for channels of semiellipsoidal cross section is therefore based on the width.

98

Figure 37: Parabolic flow profile observed across width of semi-ellipsoidal channels.

It is interesting that the thermal reflow of flow channels necessary for complete valve
sealing results in the nearly perfect parabolic flow profile that is the two-dimensional
analogue of Poiseuille flow through circular capillaries (the geometry treated in Taylor’s
original paper). The dispersion in the channel case is however greater than that of the
capillary case. In the capillary geometry the velocity is a function of the radius so that the
occupancy of molecules is biased towards low velocities. The parabolic flow profile
combined with opposing linear occupancy results in a constant average concentration along
the dispersing slug in the limit of very high Peclet number. In the semi-ellipsoidal channel
geometry the occupancy is biased towards high velocities due to the varying channel
height, creating a more dispersive flow.

99
Rotary Mixing: Scaling Laws and Simulation

In the rotary mixer the dispersion of analytes due to the combination of diffusion and
convective dispersion is exploited to accelerate mixing. As the Peclet number at which the
rotary mixer is operated increases, the dominant mechanism of mixing changes. The
scaling laws that determine the mixing time as a function of Peclet number may be
determined for three separate regimes of mixer operation.

Very low Peclet number defines a regime of mixing that is dominated by diffusion. In this
regime a molecule has ample time to diffuse the full width of the channel before convection
can impart any significant downstream displacement. The molecules thus sample the entire
flow velocity profile and therefore do not undergo appreciable flow-induced dispersion.
The dispersion of a line of tracer particles will therefore be dominated by diffusion and will
spread out into a Gaussian distribution centered at Uavgt:

c( z, t ) ≈

⎛ (z − tU avg )2 ⎞
⎟,
exp⎜ −
Dt
2πDT

(12)

where strict equality holds in the limit of Pe Æ 0, and Uavg is the average flow velocity over
the channel cross section. The mixing time at low Peclet number is therefore approximated
by the time for a molecule to diffuse the circumference of the ring:

τ mix ≈

(2πR )2 ,

(13)

100

where R is the radius of the mixing ring. Assuming a ring radius of 1 mm, the time require
for a salt solution ( D ≈ 1000 µm2/s) to be completely mixed is approximately 10 hours.

At intermediate Peclet numbers the dispersion of a slug of tracer molecules is determined
by the interplay of diffusion and convection in mass transport as described by Taylor
dispersion. The required mixing time at intermediate Peclet number therefore has the
dependence

τ mix ∝

(2πR) 2

U max h 2 Dt

∝ Pe − 2 .

(14)

A flow of salt solution ( D ≈ 1000 µm2/s) at 100 µm/s down a channel having a width of
100 µm corresponds to a Peclet number of 10 which is an intermediate value. Once again
assuming a ring radius of 1 mm, the time required for complete mixing of this solution is
on the order of several minutes.

As mentioned previously, the Taylor dispersion analysis is only valid once the molecules
have had sufficient time to sample the entire flow profile so that significant transverse
gradients have been eliminated. The periodic boundary conditions imposed in the rotary
mixer structure imply that at high Peclet number this condition will not be achieved the
ring and mixing is accomplished by a mechanism of “convective stirring.” At flow rates
where h2/D >> πR/U tracers will be stretched around the ring before they have a chance to
diffuse across the channel. Each circuit of the ring wraps the line of tracer particles back

101

onto itself in thin interlaced streams. The characteristic distance between these streams
decreases linearly with the number of cycles and is given by d*=h/2N, where N is the
number of cycles. The mixing time can therefore be approximated as the required time to
ensure that the separation distance between streams becomes comparable to the diffusion
length. Equating d*=(Dt)1/2 and substituting N = Ut/2πR gives (T. Squires and S.R. Quake;
Review of Modern Physics, in press)

⎛ h 2π 2 R 2 ⎞ 3
−2
⎟ ∝ Pe 3
τ mix ≈ ⎜⎜
2 ⎟
⎝ DU ⎠

(15)

A flow of salt solution ( D ≈ 1000 µm2/s) at 5000 µm/s down a channel having a width of
100 µm corresponds to a Peclet number of 1000. Assuming a ring radius of 1 mm, a line of
salt tracer molecules will make approximately 10 circuits of the loop in the time required to
diffuse the full width of the channel. The time for mixing in this situation will therefore be
on the order of a second.

The scaling of mixing time with Peclet number is shown in Figure 38. Mixing time may be
monotonically decreased by raising the Peclet number within the system.

Since the

diffusivity is a material property of the particular reagents being mixed, achieving rapid
mixing requires either modifying the channel geometry or increasing the flow velocity.
The size of the channel directly influences the Peclet number by scaling the appropriate
length dimension. Generally, larger channels have higher effective dispersivity. However,
at high Peclet number the mixing time has an explicit dependence on the channel critical

102

dimension. This reflects the fact that the dispersion of molecules is only enhanced in the
axial direction.

Figure 38: Scaling of mixing time as a function of Peclet number.

Figure 39 shows finite time difference simulations of the evolution of tracer molecules
originally occupying half the volume of a rotary mixer. Simulations were performed in
MatLab® using a first-order finite time difference algorithm. The script used for these
calculations is included in Appendix B. The simulations are carried out for flow velocities
(10 ≤ Pe ≥ 10 000) chosen to illustrate the transition from the Taylor diffusion regime (Pe =
10) to the “convective stirring” regime (Pe = 10 000). The simulations show the dramatic
enhancement in mixing efficiency as the flow velocity is increased. Also of interest is the
delayed mixing within the center of the channel at high Peclet numbers. This effect is due
to the direct dependence of mixing time on width and is accentuated by the small velocity
gradients present near the channel center.

103

Figure 39: Finite difference time domain simulations of rotary mixer. Evolution of

concentration profiles are shown at various times T (seconds).

Periodic boundary

conditions are imposed at ends of 1000 µm channel to simulate dispersion in ring.

104

Channel width is 100 µm and diffusion constant is 100 µm2/s so that the Peclet number is
equal to maximum flow velocity (A: Pe=10, B: Pe=100, C: Pe=1000, D: Pe=10000).

Fast Valve for Fast Mixing

Regardless of the specific channel geometry, optimal mixing requires that the flow rate be
maximized. When operated in the linear regime, the speed of flow driven by a peristaltic
pump is proportional to the pump cycle rate so that achieving rapid mixing requires that the
valve response be optimized. Actuation of a pneumatic or hydraulic valve requires that a
volume of fluid be displaced down the control line to deflect the valve membrane (Figure
40). The valve response is therefore dependent on the speed at which fluid can be pushed
in and out to displace the membrane. For low aspect ratio control channels of rectangular
cross section the flow rate determining the time constant of actuation can be approximated
as (81),

Q=

wh 3
∆P ,
12 µL

(16)

where Q is the volume flow rate, h is the channel height, w is the channel width, L is the
channel length, ∆P is the driving pressure, and µ is the fluid viscosity.

105

Figure 40: Valve actuation. Opening (top) and closing (bottom) of valve requires

transport of finite volume ∆V through control structure.

In order to optimize pumping speed, the control channel height was changed from 10 µm to
25 µm, and ∆P was raised by increasing both the actuation pressure and the fluid pressure
by 5 psi. As an added benefit, raising the back-pressure of the fluid was found to suppress
the nucleation of air bubbles. This enabled the control line fluid to be changed from water
(viscosity 1cP) to air (viscosity 0.01 cP).

Although the use of a compressible fluid (air) in the control lines adds capacitance to the
control structure, the greater reduction in fluidic resistance results in a net improvement in
response time. The response of the control structure to a pressure input can be modeled as
an exponential rise having an RC time constant, with the channel resistance defined by
Equation 18 and the channel capacitance defined as the ratio of control volume input to
change in pressure. As a first approximation the capacitance of the control structure can be
written as the sum of the intrinsic capacitance of the channel structure due to the

106

compliance of the elastomer (82), the fluid capacitance due to the compressibility of the
fluid, and the capacitance due to the expansion of the membrane.

It was determined using absorption measurements that the height of the channel increases
by approximately 40% when pressurized to 15 psi. The capacitance of the channel is
therefore approximately 0.4 times the channel volume per atmosphere pressure. The
capacitance of the membrane is approximately 100 pL per atmosphere and is negligible in
comparison. Pressurizing air to 15 psi results in approximately a 50% volume reduction so
that the fluid capacitance is approximately the channel volume per atmosphere pressure.
The relative increase in capacitance associated with using a compressible fluid instead of
water is therefore of order 1 (approximately 3 fold). Therefore, since the viscosity of air is
100 times smaller, the net reduction in the actuation time constant should be on the order of
30 fold. This argument does not include corrections for air permeation into the elastomer
which would further slow the response.

The combined effects of changing the fluid control height, changing the actuation fluid, and
increasing the back pressure allowed for the pump frequency to be increased from 10 Hz to
100 Hz. At this frequency the valve actuation speed is limited by the maximum frequency
of off-chip solenoid actuation. 100 Hz pumping frequency resulted in a maximum flow
velocity of approximately 2 cm/s; this represents a 10 fold improvement over previously
reported work using similar channel geometries (13, 14). At these flow rates complete
mixing of non-viscous reagents is achieved in less then 3 seconds, and solutions with
viscosities of approximately 100 cP may be mixed less than 9 seconds.

107
Chapter 7

SYSTEMATIC SOLUBILITY CHARACTERIZATION: CASE STUDY

The flexibility, precision, fast mixing, and small volume requirements of the formulator
device make feasible the systematic mapping of crystallization phase-space. In order to
demonstrate the utility of ab initio solubility characterization prior to crystallization trials
we exhaustively explored the solubility behavior of a commercially available crystallization
standard, Endo-1,4-β-xylanase (xylanase) from Trichoderma reesei (83, 84). Xylanase is a
21 KDa member of the gluconase enzyme family of industrial interest in the processing of
pulp and paper due to its ability to break down xylans. Xylanase was chosen for solubility
studies since it is stable for long periods of time at room temperature, and is known to be
more challenging to crystallize than other crystallization standards.

Endo-1,4-β-xylanase (xylanase) from Trichoderma reesei (Hampton Research) was
prepared in deionized water from stock (36 mg/mL protein, 43% wt/vol glycerol, 0.18 M
sodium/potassium phosphate pH 7.0) by repeated buffer exchange at 4 C using a
centrifugal filter with a molecular weight cutoff of 10,000 Da (Micon Bioseparations).
Protein concentration was measured by absorption at 280 nm and adjusted to 120 mg/mL.
10 µL aliquots were flash frozen in liquid nitrogen and stored at –80 °C. To avoid samplesample variations, a single sample preparation was used for all solubility screening, phasespace mapping and corresponding crystallization experiments.

108
Automation and Data Aquisition

Automation of metering, mixing and data acquisition allows for thousands of solubility
experiments to be executed without the need for user intervention. In each solubility
experiment a unique mixture of the 32 reagents and the protein sample is produced. All
device control and data acquisition was implemented using a custom software driver
developed in LabView (National Instruments). Mixing recipes were generated using a
spread-sheet program and translated into valve actuation sequences by the software driver.
Off-chip solonoid valves (Lee Products Ltd.), controlled using a digital input output card
(DIO-32HS; National Instruments), were used to generate square-wave pressure signals at
the device control ports. A frame-grabber card (Imagenation PXC200A; CyberOptics) was
used to automate image acquisition from a charge coupled device camera.

Precipitation Detection

Precipitation of the protein was automatically detected by imaging a portion of the mixing
ring, calculating the standard deviation of the pixel intensities and comparing this value to
the background (no protein added). To ensure even illumination, images were taken at 112
times magnification at a 9 µm high section of the mixing ring having rectangular cross
section. As a metric of precipitation, the standard deviation of imaged pixels not only
allows for distinction between precipitated and soluble conditions, but further allows for a
rough quantitative measure of the degree of precipitation. Beyond the precipitation limit,
the pixel standard deviation increases linearly with the protein concentration, and therefore
is proportional to the concentration of precipitated protein present in the solution (Figure

109

41). A video of on-chip protein titration and precipitation is included as supporting
information.

Figure 41: Precipitation measurements at varying concentration of xylanase in 0.6 M

potassium phosphate with 0.1 M TRIS/HCl pH 6.5.

Standard deviation of pixels

provides a quantitative metric of protein precipitation. Below the precipitation limit
standard deviation shows constant background level with low variation.

Above 12

mg/mL solution is in the precipitation regime where the pixel standard deviation exhibits
an approximately linear dependence on protein concentration. All points represent the
mean of 5 identical experiments with error bars indicating standard deviation of
measurements.

110
Solubility Fingerprinting

A two-step protocol was used to map out the solubility space. An initial coarse search was
used to identify reagents that have a strong precipitating effect on the target
macromolecule. In this step concentrated protein sample is combined with a wide range of
potential precipitating agents (chemical conditions) at high concentrations. This generates
a solubility fingerprint of the crystallization target.

Each precipitation peak in this

fingerprint represents a chemical condition that exerts a pronounced effect on solubility.
Chemical conditions that do not result in protein aggregation even at high concentrations
are dismissed as unlikely crystallizing agents and are not explored further.

The solubility fingerprint of xylanase generated by 4 independent runs, each consisting of
approximately 4000 titration experiments, is shown in Figure 42. This fingerprint is highly
reproducible and is characteristic of the protein studied. The chemical conditions tested in
Figure 42 were grouped by the identity of the major precipitating agent so that each peak
represents the effect of this reagent over a range of pH values and concentrations. The
large width of these peaks indicates a high level of experimental redundancy, suggesting
that a more efficient search could be conducted using less related chemical conditions.

111

Figure 42:

Solubility fingerprints of xylanase over approximately 4200 chemical

conditions. Each data series represents a separate fingerprinting experiment using the
same basis of chemical conditions. The top solubility fingerprint (blue), generated using
a sample having elevated protein concentration (90 mg/mL), exhibits both higher signal
to noise and additional peaks not present in the other data series (70 mg/mL). The two
center solubility fingerprints were generated sequentially on a single device (first orange,
then green) with the same loaded sample, demonstrating the stability of the protein over
the time of the experiment (approximately 20 hours). The bottom solubility fingerprint
(red) was generated using the same sample as orange on a separate device, showing
reproducibility across devices.

The solubility fingerprint of xylanase revealed 5 salts (sodium citrate, di-potassium
phosphate, ammonium sulfate, and sodium/potassium tartrate) as likely crystallizing
agents. A high molecular weight polymer (polyethelyne glycol 8,000) in combination with

112

various salt additives was also identified to be a strong precipitating agent at high pH
values. The high isoelectric point of xylanase suggests that the reduced effectiveness of
this precipitant at low pH values is due two-body electrostatic repulsion. A smaller
molecular weight polymer (polyethelyne glycol 3,350) was found to be a much weaker
precipitating agent and was not investigated further in phase-space mapping experiments.

Protein Phase-space Mapping

The identified xylanase precipitating conditions were expanded in 24 systematic grid
searches over all accessible protein and precipitant concentrations. Each grid consists of 72
separate mixing experiments, creating a two-dimensional phase-space with protein
concentration and precipitant concentration as variables.

All 24 phase-spaces were

generated sequentially on a single device using less than 3 uL of protein sample
(approximately 100 nL per phase-space) and are included in Appendix C. A comparison of
precipitation phase-spaces measured for xylanase in chip (5 nL reactions) and in
microbatch format under paraffin oil (5 µL reactions) shows good agreement in detecting
the precipitation boundary (Figure 43). Since measurements of precipitation are made
immediately after mixing (within 3 seconds), the locus of points that separate the
precipitated and soluble regions of the graph generate a precipitation curve that is distinct
from the thermodynamic solubility curve.

Conditions that reside just below the

precipitated region may be in a metastable state conducive to crystallization.

113

Figure 43: Comparison of phase mapping done on chip (small yellow circles) and in

microbatch (large red circles) experiments. Microbatch experiments were set at a final
volume of 2 µL and actively mixed under oil by repeated aspiration with a pipette.

Solubility Hysteresis

The formulator has been used to make a direct observation of the supersaturation region of
chicken egg white lysozyme. The concentrations of salt and lysosyme were manipulated
while keeping the buffer concentration constant in order to evolve the chemical state of the
mixing ring radially out from the origin and then back again.

Measurements of

precipitation were taken at approximately 1 minute intervals. The addition of a family of
such radial titrations was used to generate two phase-space diagrams for chicken egg white
lysosyme; one for the outward titrations and one for the return titrations (Figure 44). The
first observation of protein precipitation appears at higher salt and protein concentration
during the outward trajectory than on the return path, thereby exhibiting solubility

114

hysteresis. The intersection of the soluble region of the outward phase-space with the
precipitated region of the return path phase-space provides a direct observation of a
metastable regime in which the aggregate phase is thermodynamically stable but not
observed at short times. The observation of the reversible formation of a protein aggregate
may be used to distinguish between denatured and well-folded protein aggregates.
Additionally, identified metastable regions in phase-space provide likely candidates for
crystal seeding and growth experiments.

Figure 44: Overlay of two phase-space diagrams generated by outward and return

titrations. Observed hysteresis in precipitation threshold identifies metastable region of
phase-space.

115
Optimal Crystallization Screening

A detailed knowledge of protein solubility behavior provides an empirical basis for the
design of maximum likelihood crystallization trials. The 24 phase-spaces generated for
xylanase were used to design an optimal crystallization screen consisting of 48 reagents. A
single batch crystallization trial using the optimal screen was set by combining relative
amounts of protein and precipitant stock so that the final condition was located on the
boundary of the precipitation region. The efficiency of this screen was evaluated by
comparison with standard commercially available sparse matrix screens (Crystal Screen I,
Crystal Screen II; Hampton Research, Wizard I, Wizard II; Emerald Biostructures). 2
batch crystallization trials of 48 unique conditions were prepared for each of the 4 sparse
matrix screens for a total of 384 individual assays. For each commercial screen final
protein concentrations of 12.5 mg/mL and 25 mg/mL were used; the recommended
concentration range for the crystallization of xylanase is 10 mg/mL to 40 mg/mL. All
batch crystallization trials were actively mixed by repeated aspiration and incubated under
paraffin oil.

Crystallization trials were inspected daily for a period of two weeks.

Observed crystals were confirmed to be protein crystals by staining (IZIT dye; Hampton
Research) and were recorded as crystallization hits. The optimal screen formulations and
crystallization results are listed in Appendix D.

Twenty-seven crystallization conditions were observed in the optimal screen compared to a
total of 3 crystallization conditions in the 8 standard sparse matrix screens. The use of ab
initio solubility information therefore resulted in a 72-fold enrichment in crystallization
success (Figure 45). A surprising result was that xylanase crystals were observed in the

116

optimal screen for all the precipitants identified in coarse screening. These results suggest
that achieving optimal levels of supersaturation is more important in the crystallization of
xylanase than is the broad sampling of chemical space.

Additionally, crystallization

conditions were identified in the optimal screen that gave large single three-dimensional
crystals (Figure 45B); flat plate clusters were observed in the standard screens.

Figure 45: Comparison of microbatch crystallization experiments using commercially

available sparse matrix screens to an optimal crystallization screen based on solubility
phase-spaces. (A) Histogram showing number of successful crystallization conditions
identified with sparse matrix screens (each at protein concentrations of 12 mg/mL and 23
mg/mL) and optimal screen. (B) Polarized micrograph of large single crystals grown
directly from optimal screen (16% polyethelyne glycol 8000, 65 mM sodium chloride, 65
mM TRIS-HCl pH 8.2, 42 mg/mL xylanase). Scale bar is 100 µm.

117
Crystallization Variability

Subsequent crystallization experiments based on the optimal screen were repeated using
different protein sample obtained from the same vendor and prepared in the same way as
the original sample. 14 of 17 polyethelyne glycol conditions that gave crystals in the
original experiment were reproduced using the second sample, compared to 1 of 10 for the
salt based conditions. To determine if this discrepancy was due to variations in phasespace behavior a complete phase-space of one condition (sodium/potassium tartrate,
TRIS·HCl pH 8.5) was measured in microbatch format for both samples (Figure 46). It
was discovered that although both samples exhibited comparable phase-space behavior
they produced vastly different crystallization results. The reason for this difference in
behavior is unclear but may be due to slight sample-sample variations or trace amounts of
chemical contaminants introduced during purification or concentration steps.

It is

interesting that some crystallization conditions (those based on PEG 8000) may be more
robust to batch-dependent perturbations.

118
Figure 46: Crystallization variability. Two phase-space mapping and crystallization

experiments with different batches of Xylanase. All experiments were set in microbatch
format under paraffin oil with a final volume of 2 µL. Active mixing by repeated
aspiration through a pipette was used.

Location of soluble (green circles) and

precipitation (black circles) conditions correspond well between batches. Crystallization
conditions (blue diamonds) were observed after one week of incubation.

Another application of protein solubility phase-space mapping is in transporting successful
crystallization conditions from one experimental format to another.

The successful

crystallization of a protein is determined both by the established thermodynamic variables
and the kinetic trajectory of an experiment. For this reason experiments conducted with
different crystallization kinetics (e.g., Hanging drop vapor diffusion, microbatch, freeinterface diffusion) using the same precipitating agents will not necessarily produce similar
results. For example, the hydroxylase domain of a cytochrome p450 alkane hydroxylase
(Mutant 139-3 of BM-3) did not produce crystals in initial hanging drop trials, but was
found to crystallize readily by microfluidic free interface diffusion (29) (1 part protein 20
mg/mL, 1 part 30% m/v polyethelyne glycol 8000, 0.2 M sodium acetate, 0.1 M TRIS-HCl
pH 7.0). This condition was unsuccessful when set in hanging drop vapor diffusion format,
resulting only in amorphous precipitate. The microfluidic formulator was used to generate
a phase-space at constant buffer and salt concentration (100 mM TRIS-HCl pH 7.3; 200
mM sodium acetate) with polyethelene glycol concentration and protein concentration as
variables. Two hanging drop experiments were designed to equilibrate near the solubility
limit determined from the phase-space map. One condition (8 µL of 35 mg/mL protein

119

sample mixed with 6.7 µL of 10% polyethelene glycol, 100 mM sodium acetate, 50 mM
TRIS-HCl pH 7.3, and equilibrated at 20 °C against 1 mM of 20% polyethelene glycol,
200 mm sodium acetate, 100 mM TRIS-HCl pH 7.3) produced crystals within 3 days. This
success demonstrates the usefulness of solubility mapping in transporting conditions across
crystallization formats.

120
Chapter 8

CLEAR PATH TO STRUCTURE

Introduction

Nanoliter-scale protein crystallization screening in µFID reactors has proven a powerful
technique for identifying protein crystallization conditions over a broad range of
challenging crystallization targets. In particular, the ability to screen very small sample
volumes and the number of successful crystallization studies with targets that have proven
intractable by conventional screening techniques highlights the potential of this technology
to have a large impact on structural biology. The realization of this potential however
depends crucially on establishing a clear path from chip-based crystallization to structure.
This Chapter discusses the ongoing development of general methods for growing highquality crystals of sufficient size for diffraction studies, and harvesting these crystals
without damaging them.

Direct Harvesting from Screening Devices

Once crystallization conditions giving rise to high-quality crystals are determined in chipbased screening experiments a method must exist for getting crystals into the x-ray beam.
The most direct of these methods is the extraction of crystals from screening devices.
Despite the small volumes, crystals of sufficient size for crystallographic structure
determination may be grown and harvested directly from the chip. Figure 47 shows a highresolution diffraction pattern for a single thaumatin crystal grown from only 5nL of protein
solution (29). Crystals were exposed by separating the microfluidic device from a glass

121

substrate containing microfabricated reaction chambers, cryo-protectant was dispensed on
the reaction wells, and the crystals were harvested using conventional cryo-loops.

Figure 47: X-ray diffraction pattern (resolution < 1.35 A°) from a single thaumatin

crystal grown from 5 nL of sample in chip. The inset shows a clean reflection at 1.35 A°
resolution. Diffraction data was collected at station 8.3.1 of the Advanced Light Source
(ALS) at an incident wavelength of 1 Å, with a 20 s exposure and 1° oscillation.

The high-resolution data obtained from chip-grown thaumatin crystals exceeds that
reported of crystals grown by conventional ground-based techniques, and is comparable to
that obtained from thaumatin crystals grown in space (85). In general crystallization

122

experiments in space have suggested that microgravity environments may be well suited
for the growth of large, high-quality crystals (48, 85-87). The mechanism for the increased
order of space-grown crystals is not completely known but is largely attributed the lack of
buoyancy-driven convection during crystal growth, an effect also present in terrestrial
microfluidic devices. (88-90).

High-resolution diffraction data has been collected from crystals of several protein models
extracted directly from chip (lysozyme, glucose isomerase, ferritin, bovine liver catalase).
Despite this success, the direct extraction of protein crystals from screening devices is a
delicate and time-consuming procedure that has not proven to be generally applicable. For
instance, large single crystals of a type II topoisomerase ATPase domain extracted from a
screening device diffracted to only 3.5 Ǻ; crystals grown from the same condition in
hanging drop experiments diffracted to 2.0 Ǻ (personal communication with K. Corbett).
Several technical problems make this method prone to damaging crystals, thereby
compromising their diffracting power.

Chemical variations and osmotic shock introduced during harvesting can severely reduce
the diffracting power of a crystal. This mechanism is particularly important in nanoliter
volume screening devices due to the large surface to volume ratio of the reactors and the
permeability of the elastomer material.

123

Permeability Effects

In addition to equilibration by free interface diffusion, chip-based reactions are subject to
slow hydration/dehydration due to vapor diffusion through the elastomer chip.

The

magnitude of this effect is determined by a complicated interplay of chemical, material,
geometric, and environmental factors. The transport of water vapor through the elastomer
device is governed by the diffusion equation :

∂P
= K P∇ 2 P ,
∂t

(17)

where P is the partial pressure of water vapor, and KP is the permeability of the elastomer
to water vapor. This equation is valid within the bulk of the elastomer device. An exact
solution to this equation is made difficult due to the three-dimensional geometry and the
complex time-varying boundary conditions. The problem is directly analogous to a heatflux problem and is illustrated in Figure 48 below.

124

Figure 48: Schematic showing boundary conditions influencing the transport of water

vapor through the bulk elastomer. The control lines (blue) are filled with dionized water
and serve as sources of water vapor. The vapor pressures of the reagents (orange and
green) and control fluids are a strong function of temperature. Additionally, the vapor
pressure of the reagents is a function of the concentration of species and hence changes
due to both counter-diffusion and hydration/dehydration. The underlying glass substrate
(black) imposes a no-flux condition.

The partial pressure at the chip surface is determined by the ambient room conditions and
hence may be time-varying. A no-flux condition is present at the bottom of the chip due to
the low permeability of the glass substrate. Additional boundary conditions at the flow
channel, control channel, and microwell surfaces are determined by the vapor pressure of
the various reagents and control fluids. The vapor pressure of the reagents within the flow

125

structure is a function of the identity and concentration of reagents, and hence is time
varying due to diffusive mixing and concentration/dilution effects. The vapor pressure of a
solution is approximated by Raoult’s law:

P = P0 − P0

Σ σi =1 N i
N0

(18)

where P is the vapor pressure of the solution, P0 is the vapor pressure of the pure solvent, Ni
is the molarity of the solute, and N0 is the molarity of the solvent (55.346 mol/L for water).

In normal chip operation the control fluid is chosen to be dionized water and is constantly
replenished through the control line port. The control lines therefore define the boundary
condition of maximal partial pressure and provide a constant source of water vapor. This
ensures a constant flux of water vapor from the control lines into the reagent wells and out
of the chip. As the system evolves towards steady state the reagents within the wells will
asymptotically approach a vapor pressure that gives rise to zero net vapor flux. This
implies that at long times the final vapor pressure of each reaction, and hence the level of
dehydration, will be determined solely by the ambient conditions and the device geometry.
An important point is that the samples do not dehydrate completely, but rather converge to
a condition of dynamic equilibrium in which all the reactors assume the same osmotic
strength irrespective of the mixing ratio or chemistry. For example, screening devices with
crystals of MscL and hdTfR/HFE have been incubated for several months with no apparent
change in hydration and no observed degradation of crystals.

126

It is worth noting that the vapor pressure of an aqueous solution is a strong function of
temperature, varying over four-fold from 5 °C (Pvap = 6.54 mmHg) to 25 °C (Pvap = 27.76
mmHg). This effect results in dramatically different rates and final levels of dehydration
between devices incubated at 4 °C and 20 °C. The rate of evaporation from the control
structure of a screening device was measured by tracking the meniscus of the control input
line over time. Dehydration rates of approximately 8 µL/day were typical of devices
incubated at 20 °C compared to rates of 1 ± 1 µL/day in devices incubated at 4 °C.

In the screening device the timescale for evaporative equilibration is on the order of one to
several days, making it comparable to or slower than the diffusive equilibration of
precipitating agents between wells.

This process therefore results a continued slow

evolution of the conditions through chemical phase-space after diffusive equilibration is
complete.

This continual sampling of phase-space is likely a major factor in the

observation of crystallization events that occur at long incubation times, and hence
increases the number of detected hits.

However, since the rate and final extent of

evaporation depends in a complex way on the chip geometry, reagent chemistry, and
ambient conditions, it is not easily characterized over the large number of unique screening
conditions used in chip. For this reason it may be difficult to ascertain the precise chemical
condition that gave rise to crystallization events in screening devices at long incubation
times.

This uncertainty complicates both the transport of chip-based conditions to

alternative formats and the harvesting of crystals.

127

The transport of water vapor during the crystallization process results in a richer phasespace evolution, giving rise to more crystallization hits, but also introduces uncertainty in
the exact chemical state of each reactor. Uncertainty in the concentration of chemical
species is particularly problematic in the formulation of an appropriate cryo-protectant for
harvesting. This problem is further exasperated by the very small volume of the reagent
wells since the addition of a microliter of mother liquor or cryo-protectant to a nanoliter
volume crystallization mixture results in an abrupt change in the concentration of the
reagents.

Mechanical damage is another cause of reduced crystal diffracting power.

Physical

manipulations during the looping of delicate crystals from solution (common practice in
conventional harvesting) can fracture or crack fragile crystals (especially for thin rods or
plates). The degree of mechanical damage that occurs during the conventional harvesting
of crystals is not well characterized but is thought to be tolerable for all but the most fragile
of crystals.

The additional manipulations required to extract crystals from screening

devices present more severe risks. Peeling away the elastomer to expose the crystallization
wells can result in crystals being carried away with the fluid or crushed between the chip
and the substrate. Furthermore, crystals that adhere to the walls of the chip or the substrate
are difficult to remove without cracking or crushing them.

Finally, harvesting crystals from screening chips necessitates peeling off the entire device
or cutting the control lines. This imposes impractical constraints on harvesting since the
entire device must be sacrificed for the harvesting of a single well; crystals can not be

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harvested from different reactors at optimal times. The potential for inducing chemical and
mechanical damage along with the aforementioned technical complications therefore make
direct extraction from the screening device suitable for only the most robust of crystals.

Transporting Conditions to Conventional Formats

In cases where crystal growth occurs at low supersaturation levels, or where the absolute
concentration of protein is low, it may be necessary to transfer conditions to larger volume
formats in order to produce crystals of sufficient size for diffraction studies. Additionally,
once crystallization conditions are transported to conventional microbatch or vapor
diffusion formats harvesting may be accomplished by well-established conventional
techniques. Since the success and quality of crystal growth is governed both by the
chemistry and the mixing kinetics of an experiment, transferring chip-based crystallization
conditions to conventional formats may not be straightforward. Furthermore the transport
of water vapor through the elastomer may introduce uncertainty in the exact concentration
of reagents that gave rise to crystallization

The success rate of directly transferring crystallization conditions form the chip to hanging
drop vapor diffusion or microbatch techniques was investigated using 4 crystallization
standards (beef liver catalase, proteinase K, glucose isomerase, and bovine pancreas
trypsin) (experiments conducted at Fluidigm corporation). All four proteins were tested in
crystallization trials using a commercially available sparse matrix screen (Crystal Screen;
Hampton Research). The results of these experiments are displayed in Venne diagrams in
Figure 49. In these experiments the rate of successfully transferring conditions directly

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from the chip to hanging drop vapor diffusion format was 66 %. The rate of transferring to
microbatch format was comparable at 56 %. This high success rate reflects the ease with
which these model proteins can be crystallized. Although no systematic study has been
done, the success rate of transferring conditions directly from chip to conventional formats
is estimated by the author to be much lower for more challenging crystallization targets
(approximately 20 %).

Bovine Pancreas Trypsin

Protease K

Glucose Isomerase

Beef Liver Catalase

Figure 49: Venne diagrams showing correspondence between chip, microbatch, and

hanging drop vapor diffusion formats.

130

If directly transporting conditions is not successful, identified chip-based crystallization
conditions nevertheless provide valuable information that can be leveraged for conducting
efficient crystallization trials in conventional formats. Firstly, chip-based experiments
provide an excellent way to efficiently evaluate the crystallizability of a target using small
amounts of sample. This is particularly useful in cases were many othologues or constructs
of a target are being pursued in parallel. Secondly, identifying successful precipitating
agents dramatically reduces the chemical space that must be explored in crystal trials. This
allows for a more refined search of the relevant parameters, greatly increasing the chance
of success. Highly resolved and systematic screening based on crystallization conditions
optimized in chip has been used to successfully transport conditions to microbatch or vapor
diffusion formats. In experiments conducted at UC Berkeley 5 of 6 target proteins that
were initially crystallized in chip were transported to conventional formats (JM Berger,
personal communication).

It is expected that current efforts directed towards more

thorough characterization and modeling of chip equilibration will allow for the
development of systematic protocols for transporting conditions between chip and standard
formats.

Scaling up µFID Reactions

In cases were systematic screening fails to identify crystallization conditions in
conventional formats the success of crystallization may depend on the unique equilibration
kinetics achieved in chip. The slow diffusive mixing achieved in chip provides both a
continuous sampling of chemical phase-space and eliminates rapid initial precipitation.

131

Preserving the mixing kinetics achieved in chip is therefore crucial in attempts to scale up
µFID crystallization reactions with high correspondence.

Conventional free interface diffusion achieves high transient levels of supersaturation but
has a complicated spatial/temporal gradient due to the constant cross section of the
capillary.

This gradient couples the kinetics and thermodynamics of traditional free

interface diffusion assays in a way that µFID does not. In the µFID assay, the fluidic
interface is established between the two wells in a constricted channel where the cross
section is 10 µm x 100 µm. In contrast, the cross section of a well is approximately 300 µm
x 100 µm.

This constriction acts as a high-impedance connection between the two

channels, localizing the concentration gradient only to the length of the connecting channel.
Figure 50 shows a finite difference time domain simulation of the diffusive equilibration of
a low molecular weight dye in two microwells coupled by a constricted channel (PDE
Toolbox, MATLAB®; The MathWorks Inc. of Natick, Mass.). With the exception of the
region in close proximity to the inlet, no appreciable concentration gradient forms in the
microwell itself. In a protein crystallization experiment, this implies that as the wells
equilibrate, the vast majority of the sample evolves simultaneously through a continuum of
thermodynamic conditions.

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Figure 50: Two-dimensional finite element modeling of diffusion of an organic dye in

aqueous solution between two microwells connected by a constricted channel.
Simulation shows the bulk of the concentration drop occurring along the channel with no
appreciable gradient within the microwells. For modeling purposes, constriction of the
channel in the vertical dimension has been represented by a lateral constriction.
Concentrations are normalized to a maximum of 1 (arbitrary units).

In the optimization of crystallization conditions, it is often desirable to slow down the
equilibration process so that favorable conditions are approached more slowly to produce
fewer nucleation events and larger crystals. In vapor diffusion experiments, this can be
achieved by methods such as placing a thin layer of semi-permeable oil over the
precipitant, increasing the size of the crystallization drop to slow equilibration, or by
inclusion of a chemical additive such as glycerol to the crystallization drop in order to
reduce the vapor pressure. While these techniques are effective in slowing down the

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equilibration of the drop with the reservoir, they allow for only coarse control of the
equilibration kinetics. Conversely, microfluidic free interface diffusion allows for precise
and straightforward control of the equilibration rate while decoupling the kinetics and
thermodynamics of crystallization.

The absence of any spatial gradient within the microwells allows for a simple analytical
solution of the time-dependent evolution of the concentration in each chamber. The net
transport of a diffusing species along the channel is equal to the product of the diffusive
current density and the channel cross sectional area. Since the channel is constricted in
both height and width, the problem is one-dimensional and the gradient along the channel
is given by the difference in concentration divided by the channel length. The equation
governing the change of concentration in a well of volume V1 and concentration C1(t) that
is coupled to a second well of volume V2 at concentration C2(t) is therefore given by

dC1 ( t )
C ( t ) − C2 ( t )
= − DA 1
dt
V1 L

where D is the diffusion constant of the species.

(19)

Integration of this equation and

application of the initial conditions C1(0) = C0 , C2(0) = 0, gives

C1 =

C0
C0
V1 + V2 1 A ⎤
t ⎥ . (20)
V2 +
V1 * Exp ⎢ − D
V2 L V1 ⎦
1 + V1 1 + V2

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From this equation, it can be seen that for a given diffusion constant and relative well
volume, the rate of equilibration depends only on two characteristic lengths: the length of
the connecting channel, and the ratio of the well volume to channel cross sectional area.
Thus, modifying the channel geometry allows for intuitive and accurate control over the
kinetics of diffusive equilibration without changing the chemistry of the solutions. For
example, by making the channel twice as long the reaction proceeds at one half the rate,
whereas reducing the channel cross sectional area by a factor of two increases the
equilibration time by the same factor. Furthermore, since these length scales only scale
time in the exponent, the locus of concentrations (path through phase-space) achieved
during a complete equilibration depends only on the diffusion constants of the species and
the relative volume of the wells, and is independent of the channel geometry.

The

decoupling of the kinetics and thermodynamics of diffusive equilibration has important
implications in crystal optimization where it is often desirable to slowly approach
crystallization conditions while conserving the successful thermodynamic variables.

Growth Device

The analysis above suggests that a simple scaling of the reaction well volumes will provide
a high-correspondence method by which screening chip crystallization hits can be
transported to larger volume formats. To test this hypothesis a growth chip device was
designed having larger-volume wells and a variety of connecting channel lengths designed
to explore the effect of varying mixing kinetics on crystallization. The device features 8
reaction sites having 5 different mixing ratios and 4 different connecting channel lengths

135

(Figure 51).

The volume of each well is designed to be approximately 300 nL,

approximately a 30 fold increase over the screening chip format.

Figure 51: Layout of growth device featuring different mixing ratios and connecting

channel geometries.

A series of crystallization experiments were conducted using 7 model proteins that had
been successfully crystallized in the small-volume screening device.

These models

included DNA B/C, Rho, hdTfR/HFE, P450 1-12G (hydroxylase domain), P450 139-3
(hydroxylase domain), DNA D/G/H and MscL.

Of these models, four (DNA B/C,

hdTfR/HFE, P450 1-12G) had resisted attempts at transferring to hanging-drop vapor
diffusion by screening around chip-based conditions. In the case of P450 139-3 vapor
diffusion crystallization was achieved by using solubility information derived from

136

formulator device experiments. Crystallization of the remaining three proteins had been
achieved in hanging drop format.

Rho is a RNA/DNA helicase factor responsible for transcriptional termination in bacteria.
Rho was first crystallized in vapor diffusion format through extensive screening (91) using
conventional methods and then transferred directly to the screening device. In the case of
MscL successful vapor diffusion conditions were discovered and optimized prior to
identifying conditions independently (including some novel conditions) using sparse matrix
chip-based screening experiments. The first crystallization conditions for DNA D/G/H
were found using the screening device after extensive unsuccessful conventional screening.
This condition was eventually used to achieve crystallization in vapor diffusion format by
very refined systematic screening around the identified chip condition. The results of
crystallization trials for these three proteins are summarized in Table 2.

Protein

Vapor Diffusion

Growth Chip

DNA B/C

NO

YES

Rho

YES

YES

hdTfR/HFE

NO

NO

P450 1-12G

NO

NO

P450 139-3

YES

YES

DNA D/G/H

YES

YES

MscL

YES

YES

Table 2: Transfer of crystallization conditions using growth device.

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Screening around chip-based conditions was found to have a success rate that is
comparable to growth chip experiments using the exact chip-based condition. Since no
additional chemical optimization was used in growth-chip experiments (although the
kinetic variable was manipulated) this result supports the hypothesis that the slow diffusive
equilibration between wells allows for more efficient sampling of crystallization phasespace. The overall success rate of the growth chip from this trial was 67 %.

Consistent with the increased reaction volume, the size of crystals grown in the growth chip
was generally larger than that of crystals grown in the screening device. Figure 52 shows
large crystals of DNA B/C, MscL, and P450 139-3 grown in a growth device. The time
required for crystal growth varied substantially, depending on the crystallization target.
Crystals of MscL appeared after two days of incubation in growth device. This incubation
time is similar to that observed in the screening device (1 to 2 days). In contrast, crystals of
DNA B/C appeared after only 2 days of incubation in the screening device, but required
greater than 14 days to appear in the growth device.

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Figure 52: Protein crystallization conditions successfully transported from screening

device (≈ 10 nL) to growth device (≈ 300 nL). (A) Large crystals of DNA B/C grown in
condition identified in screening device (D). (B) Crystals of MscL grown in harvesting
device using successful condition from screening device (E). (C) Large crystal of heme
domain of P450 alkane hydroxylase, MUT 139-3.

Condition was discovered and

optimized in screening device (F). All scale bars are 100 µm.

Another interesting observation was that some crystallization targets exhibited a clear
dependence of crystal size and morphology on connecting channel length. Crystals of
DNA B/C grown by µFID in identical chemical conditions, at the same mixing ratio, but
with different connecting channel lengths are shown in Figure 53. This illustrates the
importance of varying mixing kinetics as an optimization parameter. In contrast, crystals
of MSCL showed similar size and morphology at all connecting channel lengths.

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Figure 53:

geometry.

Dependence of crystal size and morphology on connecting channel
(A)

Crystals of DNA helicase B/C complex.

Mixing ratio of 2:1

(protein:precipitant). Precipitant is 2.0 M (NH4)2SO4, 0.1 M CAPS pH 10.5, 0.2 M
Li2SO4. Connecting channel length: 2000 µm. (B) Crystals of DNA helicase B/C
complex grown in same conditions as (A). Connecting channel length: 250 µm. (C)
Crystals of DNA helicase B/C complex.

Mixing ratio of 4:1 (protein:precipitant).

Precipitant is 2.0 M (NH4)2SO4. Connecting channel length: 500 µm. (D) Crystals of
DNA helicase B/C complex grown in same conditions as (C). Connecting channel
length: 2000 µm. All scale bars are 100 µm.

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Harvesting from the Growth Device

The protocol for extracting crystals from growth chip devices is similar to that used for
extraction from screening devices. The device is flipped upside down and a scalpel is used
to cut around the periphery of the well containing the crystals creating a “patch” of
elastomer that may be removed to expose the well. A drop of cryo-protectant solution into
which the crystals will be transferred is dispensed near the edge of the patch. Peeling the
patch from the rest of the device draws the cryo-protectant onto the exposed well, covering
the crystals. The crystals may then be removed using standard cryo-loops and flash-frozen
in liquid nitrogen. Although cumbersome, this general method (with slight variations) has
allowed for the extraction of crystals for diffraction studies. In the case of robust model
proteins (eg. lysosyme, glucose isomerase, ferritin) high-resolution diffraction data has
been collected using growth chip grown crystals. Additionally, crystals extracted from
growth chips have been used to collect high-resolution data from drug target proteins with
previously unknown structures (personal communication with Fluidigm).

Attempts to harvest more fragile crystals from growth devices have produced varied
results, exhibiting diffracting power equal or inferior to crystals grown and harvested by
conventional techniques.

Chip-grown crystals of DNA D/G/H diffracted to 5.5 Ǻ

resolution. This result is comparable to crystals grown and harvested from hanging drop
formats, indicating that the low resolution may be attributed to the large unit cell, small
size, incorrect cryo-protectant, or poor order of the crystal. In another instance (Rho)
crystals showed evidence of damage during harvesting from chip.

Crystals of Rho

extracted from the growth chip diffracted to approximately 4 Ǻ resolution, while crystals

141

grown from the same condition in hanging drop format diffracted to 3 Ǻ resolution but
displayed increased mosaicity.

Harvesting crystals of DNA B/C from the growth device has been particularly problematic.
A large number of crystals of DNA B/C (approximately 50) harvested from growth chips
showed very poor diffraction, varying between 25 Ǻ and 8 Ǻ. By comparison a very small
(~1000 µm3) single crystal of DNA B/C (that could not be reproduced), grown after
approximately 3 months of incubation in hanging drop format, diffracted to 3 Ǻ and
exhibited the same space group as chip-grown crystals; suggesting that the poor diffraction
of chip-grown DNA B/C crystals is due to damage during harvesting.

Diffraction Device: Membrane-Mediated Vapor Diffusion

The straightforward scaling up of µFID reactions in the form of a growth device has been
successful in producing large diffraction-quality crystals. This strategy has however not
proven to be generally applicable in either the transport of successful conditions to largervolume formats or the harvesting of diffraction-quality crystals. These shortcomings are
attributable to dehydration/hydration effects resulting from the permeation of water vapor
through the bulk silicone elastomer. To realize a high correspondence method of scaling
up crystallization conditions and provide clear path to structure the following criteria must
be met.

1. In order to achieve high correspondence with µFID screening reactions, the device must
preserve the kinetics of microfluidic mixing while providing larger reaction volumes.

142

2. In order to achieve high correspondence with µFID screening reactions, the device must
provide control over permeability effects and must allow for different rates of
hydration/dehydration to be screened.
3. To avoid damaging fragile crystals, the device must allow for harvesting and mounting
with minimal crystals manipulations.
4. In order to asses the quality of crystals independent of any cryo-protectant addition or
freezing process, it is necessary that the device allow for facile room temperature
diffraction studies.
5. The device must allow for the controlled addition of cryo-protectant to the crystal wells.
6. The device must allow for the facile screening of a broad range of cryo-protectants in
order to quickly asses optimal freezing conditions.
7.

The method of crystal harvesting and automation should be amenable to high-

throughput automation and therefore must eliminate the need for delicate crystal
manipulations (i.e., “looping”).
8. To ensure that crystals are harvested at the optimal time the device must allow for the
harvesting of crystals from selective wells without disturbing adjacent reactions.
9. To facilitate alignment of crystals within the X-ray beam the mounting format should
provide minimal optical aberration.
10. The mounting format must allow for the collection of high-quality diffraction data over
a wide range of angles with acceptable background scatter and attenuation.

A diffraction device designed to simultaneously preserve the successful mixing kinetics of
the µFID reactors and allow for precise control over dehydration/hydration effects is shown

143

in Figure 54. The device integrates 20 reaction sites, each containing 5 separate µFID
reactors (inset). Each of the 100 reactors is designed to have a total reaction volume of 200
nL, thereby scaling up the volume of the screening device by a factor of 20. All reaction
sites are connected in parallel to a single protein inlet and a single precipitant inlet. The
connecting channel between the chambers is designed to have lateral dimensions of 150 µm
x 18 µm resulting in a cross sectional area that is approximately 3 fold larger than that of
connecting channels in the screening device.

144
Figure 54: Diffraction chip for scaling up crystallization conditions and harvesting

protein crystals. Protein sample and crystallizing agents are mixed at 20 separate reaction
sites (inset) featuring 5 µFID reactors.

In order to increase the probability of successfully scaling up conditions, different versions
of the device were designed to screen the effect of mixing ratio and channel length. A
layout of a diffraction device designed to allow for optimization of both the mixing ratio
and mixing rate in the initial transport of crystallization conditions to larger volume formats
is shown in Figure 55. Each reaction site has 5 reactors at one of the mixing ratios used in
the screening device (4:1, 2:1, 1:1, 1:2, 1:4). Additionally the connecting channel length is
varied across the device from 200 µm to 1200 µm. Once the optimal reactor geometry is
determined by an initial diffraction chip experiment the condition is repeated on a separate
device that reproduces only this geometry over the 100 reactors. This redundancy allows
for the production of a large number of crystals from identical conditions to be used in
optimizing cryo-protection and freezing protocols.

145

Figure 55: Layout of diffraction device. Two control lines (red) actuate all interface and

containment valves in parallel. Flow structure at each reaction site defines a unique
combination of mixing ratio and connecting channel geometry (blue). 150 µL reagent
reservoirs (black circles) allow for control over rate and extent of dehydration.

In addition to preserving the mixing kinetics of the screening device, the diffraction device
further allows for control over the extent and rate of dehydration/hydration. The key
distinction between the diffraction device and the growth device is that each of the 20
reaction sites is embedded in a 250 µm thick silicone membrane located at the bottom of
separate 150 µL reagent reservoir. A cross section of this membrane showing the enclosed
fluidic structure is shown Figure 56.

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Figure 56: Optical micrograph of cross section of elastomer membrane containing µFID

reactors. 142 µm high reaction wells are enclosed at the top and bottom by two 50 µm
thick elastomer membranes. The image is inverted so that the membrane containing the
constricted connecting channel (in plane), valve membrane, and control channel (cross
section) are visible at the top of the structure.

Efficient vapor transport through the thin membrane may be exploited to exercise control
over the rate and extent of evaporation. The 150 µL wells overlaying each reaction site are
filled with a fluid chosen to control the rate or extent of hydration/dehydration from the
reactors. For example an “osmotic bath protocol” may be used in which a solution of
known concentration may is added to the reservoir and sealed with clear adhesive tape.
During the course of an experiment this solution will equilibrate with the contents of the
reactor through membrane-mediated vapor diffusion, and therefore defines an osmotic bath
that may be used to precisely control the final extent of dehydration from the reactor
(Figure 57). The volume of the osmotic bath is much larger than that of the reactor so the

147

final state is independent of the contents of the well. In order to ensure the reactor
equilibrates to the same osmotic strength as the osmotic bath it is necessary that a low
vapor pressure control fluid (eg. fluorinated silicone oil) be used in the control lines.
Additionally, since slow dehydration through the elastomer may occur (over several weeks)
the osmotic bath solution should be periodically replenished to ensure a well-defined final
state.

Figure 57:

Schematic of diffraction device reaction site illustrating combined

equilibration resulting from µFID reaction and membrane-mediated vapor diffusion.

Control over reagent dehydration provides an additional parameter that may be used in
crystal optimization.

Since the 20 reaction sites of the device may be manipulated

independently

different

using

osmotic

bath

conditions

the

final

level

of

dehydration/hydration to be screened across the device. This is useful both in scaling up
crystallization conditions and in optimizing crystal quality. Figure 58 shows a gallery of
lysosyme crystallization trials using identical chemical conditions and different

148

concentrations of osmotic bath solution. The ease with which the osmotic bath conditions
can be exchanged makes it straight forward to manipulate the concentration of
crystallization reagents over time. This added level of control may be used to transiently
increase the supersaturation for a well-defined time as a means for controlling crystal
nucleation. Additionally, once crystals are formed, the osmotic bath may be exchanged for
progressively more dilute solutions in order to investigate the solubility of crystals information which is extremely valuable in crystal optimization, harvesting, and seeding
experiments.

Figure 58: Influence of osmotic bath solution on crystallization of Lysosyme. Mixing

ratio 2:1 (protein:precipitant). Precipitant is 2 M NaCl, 0.1 M Sodium Acetate, pH 5.2.
Osmotic baths are 0 M NaCl (A), 1.0 M NaCl (B), 2.0 M NaCl (C), and 4.0 M NaCl (D).

149

Concentrated osmotic bath (D) shows pronounced shrinking of wells and coexistence of
tetragonal (second from right) and orthorhombic crystal forms (thin needles). All scale
bars are 800 µm.

Membrane-mediated vapor diffusion may also be used to modify the pH or chemistry of
the reactors over time. Volatile chemicals added to the reagent reservoir will cross the
membrane in vapor phase. This is particularly useful for the addition of volatile cryoprotectants (eg. isopropyl alcohol, ethanol), cross-linking agents (eg. gluteraldehyde,
fomaldahyde), or volatile ligands (eg. ethane). Finally, in cases were crystals grow in the
presence of a modest concentration of cryo-protectant (eg. glycerol, low molecular weight
PEG, MPD, lithium sulfate), the osmotic bath may be used to concentrate these agents
sufficiently so that they freeze into an amorphous glass.

Crystallization Using “Osmotic Bath” Protocol

Initial experiments using the “osmotic bath protocol” described above were successful in
the crystallization of proteins lysosyme, ferritin, glucose isomerase, and MscL. However,
subsequent trials using hdTfR/HFE, DNA B/C and P450 1-12G failed to produce crystals
despite extensive exploration of the final reaction state. Experiments with DNA B/C
further showed evidence of convective transport between the two wells visible as a plume
of protein precipitation. The cause of this convection was determined to be osmotic
differences between the sample and the reagent well during the initial stages of
equilibration. The time constant for equilibration between the osmotic bath and a reaction
chamber may be approximated as

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τ≈

wVρ liq
∆Pvap K P Aρ gas

(21)

where w is the membrane thickness, V is the reactor volume, ρliq is the mass density of
water, ∆Pvap is the difference in vapor pressure between osmotic bath and the reagents, KP
is the permeability of the silicone rubber, A is the area of the membrane, and , ρgas is the
mass density of the water vapor. Assuming an initial concentration difference of one molar
(∆Pvap ≈ 3.5 cmHg), a permeability to water vapor similar to that for CO2 (KP ≈ 5*10-7
cm3·cm/cm2·s·cmHg) (30), a ratio of densities ρliq/ρgas ≈ 1000, and given the reactor and
membrane geometries used in the diffraction chip, this time constant is approximately 12
hours. In comparison the time constant for diffusive equilibration of a salt (D ≈ 1000
µm2/s) between two chambers of 100 nL volume connected by a 500 µm long connecting
channel of 2250 µm2 cross section is on the order of 5 hours. These two timescales are
comparable resulting in an osmotic pumping effect between the coupled wells which
destroys the desired diffusive mixing. In order to preserve diffusive mixing between the
wells the use of the “osmotic bath” protocol was abandoned during the initial diffusive
equilibration phase. The use of an osmotic bath in manipulating the final amount of
dehydration after initial diffusive mixing is however complete is very useful in establishing
a reaction of well-defined chemistry.

Crystallization Using “Permeation Barrier” Protocol

An alternative “permeation barrier” protocol was devised in which permeable oil (FMS oil)
is introduced into the reagent reservoirs overlaying the reaction chambers. Since the oil is

151

immiscible in water it does not induce an osmotic pumping effect between the wells so that
the desired equilibration by diffusion is preserved. The oil creates a barrier to vapor
permeation and therefore allows for the rate of dehydration to be modulated. By varying
the level/amount of oil in each chamber the rate of dehydration may be controlled and
screened across the device, mimicking the permeability effects that are realized in the
screening device.

The effectiveness of this protocol was evaluated in crystallization trials

using the 6 of the 7 protein models that had previously been tested using the growth chip
(P450 139-3 was not tested). All 6 of the model proteins were successfully crystallize on
the first attempt, thereby showing this protocol to be a high correspondence method of
scaling up crystallization conditions identified in the screening device. Figure 59 shows
crystals of Rho grown using this protocol.

152
Figure 59: Crystals of Rho grown in diffraction device. 1:1 mixing ratio of protein

sample (Rho 10 mg/mL, excess RNA (CU)4, 75 mM NaCl, 10 mM TRIS·HCl pH 7.5) to
precipitant (5% w/v PEG 8000, 40% v/v glycerol, 75 mM NaCl). Scale bar is 300 µm.

Diffraction Device: In Silicone Diffraction Studies

Complementary to novel technologies for high-throughput screening and crystal growth is
the need to develop general methods for quickly harvesting and mounting protein crystals.
Traditional techniques for manually mounting crystals by “looping” the crystal out of a
drop of mother liquor require significant skill on the part of the technician and are not
amenable to automation. Furthermore, since the vast majority of diffraction studies are
performed at cryogenic temperatures, harvesting requires the selection and addition of
cryoprotectant. The choice of cryoprotectant, the concentration of cryoprotectant, and the
rate of cryoprotectant addition are parameters that must be optimized to achieve the
maximal diffracting power of the crystal: poorly optimized freezing conditions can result in
greatly reduced crystal diffraction.

In cases where diffraction is poor it can be difficult to ascertain whether the crystal was
inherently disordered or damaged during the mounting and freezing process. Roomtemperature diffraction studies can be used as a diagnostic to evaluate the inherent order of
a crystal form prior to screening freezing parameters. In practice room temperature mounts
in capillaries are difficult to implement, can mechanically damage crystals, and are rarely
used for all but a last resort. Easy methods for performing in situ diffraction studies of
crystals that do not require mechanical manipulations or the exchange of mother liquor are

153

therefore of great value in evaluating the quality of crystals. The extension of these
methods to allow the automated harvesting of crystals, facile cryoprotectant screening, and
low background diffraction studies at cryogenic temperatures will relieve a major obstacle
in the structure determination process.

Beyond allowing for control over dehydration during crystallization, the thin membranes of
the diffraction device allow for direct in silicone diffraction studies. Once a specific
reaction site is selected for harvesting, a thin membrane disk containing the crystals may be
extracted from the device. A punch tool is inserted through the open face of the reagent
reservoirs and used to cut around the periphery of the membrane, creating a “crystal disk”.
Since the reagent reservoirs are located near the center of the membrane there is no risk of
damaging the crystals during this process. The punch tool is designed to fit the orifice of
the reagent reservoir so that it is inherently self-aligning. Crystals may be extracted
without the need for delicate manipulations under magnifying optics so that the extraction
procedure is readily amenable to automation. Furthemore, many crystals within a disk may
be harvested simultaneously in a single procedure, thereby greatly increasing the
throughput of extraction.

After the crystal disk is cut from the surrounding elastomer it is lifted from the reagent
reservoir and mounted using a standard magnetic cap fitted with a small alligator clip
(Figure 60A). Once the crystal disk is positioned in the x-ray beam the crystals may be
easily visualized through the thin transparent membrane.

The crystals may then be

interrogated one by one to asses their quality and to generate statistics on the quality of

154

crystals grown in a given condition. A large savings in time is achieved by eliminating the
need for the separate mounting of each crystal screened. Alpha-numeric indices on each
well allow for easy cataloguing of conditions.

Figure 60: (A) 250 µm thick crystal disk mounted on a cryo-cap fitted with a micro-

alligator clip. Diameter of disk is ¼ inch. (B) Diffraction pattern from a single MscL
crystal showing highest-order reflections at approximately 11.5 Å. Crystals were grown
at 4 °C by µFID at a 1:1 mixing ratio with precipitant (40 % v.v PEG MME 750, 100 mM
nickel chloride, 100 mM imidazole pH 8.0). Image taken at 4 °C with 20 minute
exposure on R-AXIS II home source with 1° oscillation. Characteristic ring diffraction
pattern of the silicone elastomer is visible at approximately 7 Ǻ.

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This technique was used to evaluate the intrinsic order of crystals of MscL grown in
diffraction devices. Approximately 10 crystals were subject to diffraction studies at room
temperature on a Rigaku R-AXIS II home source. Exposure times of 10 to 30 minutes
were taken with 1 ° oscillation at an angle normal to the face of the crystal disks. Of the 10
crystals studied the highest-order reflections were observed at 9 Ǻ resolution.
Representative diffraction data from a crystal of MscL collected in silicone at room
temperature is shown in Figure 60B. The low resolution data collected from these crystals
suggests that the crystals are inherently disordered.

The flash freezing of crystals to cryogenic temperatures (typically -195 °C) is used to
reduce x-ray radiation damage and hence increase the amount of data that can be collected
from a single crystal. The correct choice and controlled addition of cryo-protectant is a
crucial step in achieving the full diffraction potential of a crystal. The diffraction device
allows for both the parallel screening of different cryo-protectants, and the controlled
addition of these agents by free interface diffusion. To introduce cryo-protectant to a µFID
reactor the osmotic bath solution is first replaced with a solution containing the desired
cryo-protectant. The membrane covering the well opposite to the well containing crystals
is then perforated using a micro-knife bringing it into fluidic contact with reservoir
solution. This allows for the cryo-protectant to slowly diffuse into the crystal well over
time. For the current well volume and channel geometry the required time for cryoprotectant addition is approximately 24 hours. The parallel screening of 20 different cryoprotectants is accomplished on a single device having identical reaction sites. Once the
equilibration of cryo-protectant is complete the crystal disks are extracted as described

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above and flash frozen by immersion in a cryogen (liquid nitrogen). As an alternative to
introduction directly from the reagent reservoir the cryo-protectant could be introduced to
the µFID reactors using a separate microfluidic inlet. This arrangement would further
allow for addition of other solutions such as ligands, heavy metals, or fresh protein stock.

Cryogenic in silicone diffraction studies were performed on crystals of 3 crystallization
standards (lysozyme, glucose isomerase, ferritin), and MscL using a variety of
cryoprotectants.

6 crystal disks containing crystals of MscL grown from the same

precipitant (40 % v.v PEG MME 750, 100 mM nickel chloride, 100 mM imidazole pH 8.0)
were harvested from a single device. These disks were frozen in a variety of cryoprotectants (15% PEG 300, 35% PEG 300, 25% propane diol, 20% PEG 300, 28% xylatol,
20 % glycerol). A single oscillation frame was taken of approximately 40 crystals from
these disks. All crystals showed comparable diffracting power with the average resolution
of typically less than 10 Å. The highest-order reflections observed were at approximately 9
Å. This result is consistent with diffraction studies conducted at room temperature and
supports the hypothesis that these crystals are intrinsically poorly ordered.

In contrast, diffraction studies using the three crystallization standards showed very highresolution diffraction.

Three-dimensional glucose isomerase crystals having a

characteristic dimension of 100 µm diffracted to 1.4 Å resolution and exhibited low
mosaicity (0.3). Similarily, ferritin crystals diffracted to 1.6 Å resolution with mosaicity of
0.2. Crystals of lysozyme shot through the crystal disk diffracted to 1.2 Å resolution. This
resolution is very high, particularly in light of the fact that a five-month-old stock of

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lysozyme was used with no optimization of crystallization or harvesting conditions. By
comparison, of the 884 structures of lysozyme deposited in the protein data bank all but 10
are of lower resolution.

Three diffraction patterns from a crystal disk containing a 150 µm x 100 µm x 100 µm
lysozyme crystal taken at -195 °C is shown in
Figure 61. The patterns are taken at 0°, 45°, and 90° from normal to the plane of the disk.
Rotation of the crystal disk changes the thickness of elastomer through which incident and
diffracted x-rays must travel, changing both the attenuation of reflections and the amount of
background scatter. The signal to noise of reflections is still high at a disk angle of 45° to
normal so that data may be collected over a 90° angle. At 90° to normal the incident and
diffracted x-rays must pass through a large amount of elastomer, resulting in the
elimination of all but the strongest reflections and a large and asymmetric background
scatter.

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Figure 61: In silicone diffraction studies of lysozyme. (A) Diffraction pattern take at 0°

from normal to plane of disk: 20 minute exposure with 1° oscillation, detector distance of
250 mm. (B) Diffraction pattern take at 45° from normal to plane of disk: 20 minute
exposure with 1° oscillation, detector distance of 250 mm. (C) Diffraction pattern take
at 90° from normal to plane of disk: 20 minute exposure with 1° oscillation, detector

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distance of 250 mm. (D) Clean reflections at 1.6 Å resolution: 30 minute exposure with
1° oscillation, detector distance of 100 mm. All data taken on R-AXIS IV home source.

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Chapter 9

PRACTICAL CONSIDERATIONS: FABRICATION AND OPERATION

Introduction

Since the first reports of microfluidics for use in analytical chemistry and the biological
sciences, major efforts have focused on achieving highly integrated lab-on-chip devices.
Despite the compelling promise of chip-based fluid-handling and measurement systems,
technical obstacles have until recently made this goal largely unrealized. The fabrication of
true sealing microvalves, a long-standing problem in the field, was addressed by Unger et
al. in the development of Multilayer Soft Lithography. This elegant work represented a
major breakthrough in microfluidics, allowing for the robust and inexpensive integration of
valves in a monolithic silicone elastomer device.

Realizing the potential of MSL in achieving dense integration and high levels of
functionality required that technical problems related to fabrication and device operation to
be overcome. One major advance, the development of a technique for filling elastomeric
microfluidic devices called Pressurized Outgas Priming (POP), is described in Chapter 2.
This technique is the basis for a robust geometric metering scheme, allows for the
suppression of bubble formation, and enables the practical realization of complex largescale fluidic networks.

The first section in this Chapter introduces the technique of

multilayer soft lithography (MSL).

The remaining sections outline the author’s

contribution to the development and refinement of techniques for device priming, substrate
bonding, and layer-layer alignment. Additionally, other fabrication issues and techniques

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for creating multilevel flow structures, and alternate valve geometries are discussed. It is
the author’s intention that this Chapter will provide a useful introduction to several
important considerations for researchers who are interested in MSL technology.

Multilayer Soft Lithography: Background

Multilayer Soft Lithography (MSL), which is an extension of Soft Lithography (26, 92),
enables the facile and inexpensive large-scale integration of valves on chip (13, 27). MSL
describes a process by which consecutive micro-molding and layer bonding steps are used
to generate complex multilayer fluidic devices with active mechanical valves, pumps,
mixers, and flow control logic. Both replica molding from microfabricated masters and the
use of elastomer membranes for actuation of microfluidic valves predates the multilayer
soft lithography. MSL technology seamlessly integrates these ideas in an elegant and
simple fabrication process.

The enormous success of this technique can be largely

attributed to a method developed by Unger et al. for covalently bonding successive layers
of silicone elastomer.

Due to their excellent optical properties, low surface energy (22 mJ/m2), and low Young’s
modulus, silicone rubbers have become the most popular material for multi-layer soft
lithography. Silicone rubbers are typically formed from the combination of two liquid
components that cross-link into a flexible solid upon curing. One such example polymer is
General Electric RTV 615.

Part A of this compound consists polydimethylsiloxane

polymers that have been functionalized with vinyl groups. Part B contains silicon hydride
(Si-H) groups that covalently bond to the vinyl groups of part A, cross-linking the

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polymers. In the presence of a platinum catalyst the silicon hydride groups become
covalently bonded through a direct addition reaction to the vinyl groups, thereby
solidifying the mixture through a cross-linking process (Figure 62). The low curing
shrinkage and absence of gaseous byproducts makes this system ideal for the high-fidelity
reproduction of microfabricated features.

When mixed at the stoichiometric ratio of 10:1 (A:B) there is an equal number of vinyl and
silicon hydride groups, so that all reactive groups are incorporated into a covalent bond.
However, when combined at a different ratio, there remain active groups that do not
participate in a covalent bond, and which instead may be used to permanently bond two
surfaces together, creating a monolithic device (Figure 62).

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Figure 62: MSL bonding process. Cross-linking of polymer through direct addition

reaction of silicon hydride and vinyl groups (top). Off-ratio mixing of silicone results in
excess reactive surface groups for covalent layer-layer bonding.

A process flow diagram illustrating the steps in MSL is shown in Figure 63. Two negative
molds, one defining the flow structure, and the other defining the control structure of
valves, are first patterned on a silicon wafer using conventional photolithography, leaving
10 µm raised features of photo-resist. The flow layer master is then annealed so that the
photo-resist is allowed to re-flow, creating rounded flow channels. Masters are reproduced
by replica molding in silicone rubber. A 30:1 ratio of (A:B) silicone rubber, having excess
vinyl groups, is spun onto the flow mold to a final thickness of 30 µm. A 3:1 silicone
rubber layer, containing excess silicon hydride groups, is cast over the control mold to a
thickness of approximately 7 mm. Once both layers are heated and allowed to partially
cure, the structures solidify. The control layer is then peeled from the mold, punched to
create valve access ports, and aligned to the flow structure. The entire device is then heated
once again, causing the excess vinyl and silicon hydride groups to covalently bond. The
resulting monolithic device is peeled from the flow mold, and channel access ports are
punched into it prior to sealing the multilayer polymer to a glass substrate. The substrate
itself may additionally have structural features, such as microwells that may be accessed
through the molded channels, thus providing larger localized volumes for reactions to
occur.

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Figure 63: Flow diagram illustration technique of multilayer soft lithography.

When a control channel crosses over a flow channel, only a thin square membrane of
elastomer separates the two, forming a valve (Figure 64A). By pneumatic or hydraulic
pressurization of the control channel, the membrane may be deflected down into the flow
channel, causing it to seal against the glass substrate (Figure 64B). Due to the compliance
of the membrane, a hermetic seal may be easily achieved at moderate actuation pressures
even in the presence of particulates or imperfections. The low Young’s modulus of the
elastomer ( ~1 MPa vrs ~100 GPa for crystalline silicon) allows for closing of valves

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having areas as small as 100 µm2, so that many thousands of active valves may be
integrated on a chip smaller then a credit card (27). Just as the transistor is the fundamental
component in modern electronic circuitry, higher level fluidic toolbox of components may
be built up from combinations of valves.

Figure 64: MSL valves. (A) Micrograph of an open valve showing control (horizontal)

and flow (vertical) structures. (B) Closed valve. Application of pressure to control
structure deflects membrane and pinches off flow structure, creating a fluidic seal.

Unger et al. described the serial combination of three separately addressable valves along a
channel to form a peristaltic pump (Figure 65). When operated in the linear regime (below
the cutoff frequency) sequential actuation of these valves through a designated peristaltic
cycle of states moves a fixed volume of fluid across the pump. This pump allows for the
flow direction to be reversed through reversal of the peristaltic sequence. The NavierStokes equations, which describe the flow of a Newtonian fluid at low Reynolds number
are time-reversible so that reversal of the peristaltic sequence causes an exact time-reversal

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of the unsteady flow field due to forward pumping, regardless of symmetry breaking in the
flow structure upstream and downstream of the pump. Interestingly, the cycling of two
valves is sufficient for producing a directional flow if symmetry is broken through the time
sequence (personal communication with Jian Liu). Below the pump cutoff frequency the
flow rate is proportional to the peristaltic cycling rate, thereby allowing for programmable
control of the mass flux.

Figure 65: Peristaltic pump.

Chu et al. described a rotary mixer which features the integration of a peristaltic pump in a
contained circular flow structure to accelerate the mixing of reagents. Batch mixing is
achieved through the dispersion of the reagents within the flow structure as they circulate
through the ring. Using this method the time required for the mixing of two solutions was
reduced from many hours to minutes. Chapter 5 describes the incorporation of this mixing
structure as a key element in achieving true combinatorial mixing on chip. An analysis of

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the scaling laws that govern the mixing speed, numerical simulations of mixing, and the
optimization of this element for ultra-fast mixing are presented in Chapter 6.

The actuation pressure required to close a valve is dependent on the geometry of the valve
junction and the material properties of the elastomer. For elastomer membranes fabricated
from 20:1 GE RTV bonded to 5:1 GE RTV, and a standard geometry of a 10 µm high flow
channel, a 20 µm thick membrane, and a 100 µm x 100 µm valve, the required actuation
pressure is approximately 6 psi. The strong dependence of actuation pressure on the
channel and valve geometry may be exploited to engineer bridges (valves with very high
actuation pressure) by simply tapering the thickness of a control channel in the vicinity of a
flow channel that is not to be closed. By applying an intermediate actuation pressure, a
single control channel may be used to close a plurality of selected flow channels without
significantly impeding flow in adjacent lines.

Chou proposed the use of bridges in realizing a microfluidic multiplexing element. This
element uses an array of complementary valve pairs organized in binary-tree architecture to
selecting 1 of N flow lines using 2log2N control lines (Figure 66). This element enables the
realization of increasingly complex fluidic structures with only a modest rise in control
complexity. The straightforward implementation of this design was first demonstrated in
early protein crystallization designs. More complex multiplexing structures have been
instrumental in realizing large-scale fluidic integration (27), and on-chip combinatorial
mixing.

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Figure 66: Parallel-channel multiplexing structure. Each pair of complementary valves

comprises a bit.

Elastomer Shrinkage

The polymerization of poly(dimethyl-siloxane) does not require the removal of a solvent,
and does not produce bi-products. These properties ensure that very little elastomer
shrinkage occurs during curing when compared to other elastomer systems (typically with
volume shrinkage on the order of 10% - 30%).

Nevertheless, even slight intrinsic

deformation of a molded structure, when integrated over the full length of a device, can
result in unacceptable feature registration errors. Although this problem was tolerated in
early MSL devices (cell and DNA sorters), by maintaining small active device areas
(approximately 10 mm2), few valves (less than 10), and large registration tolerances, it
placed unacceptable constraints on early screening device designs that necessitated larger

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areas (10 cm2) and higher levels of integration (approximately 200 valves). A linear
shrinkage of 1% over the typical length of a device results in misalignment between
features that is large (300 µm) compared to the feature dimensions (100 µm).

Initial curing of the elastomer layers prior to bonding results the isotropic shrinkage of the
structures. Since both layers are supported by a silicon substrate during curing, this
shrinkage is manifested as an expansive strain in the thick layer (7 mm) and thin film
(approx 25 µ). Release of the thick layer prior to alignment releaves this strain causing a
compression of the molded features. This compression was found to be reproducible and
can therefore be compensated for by a complementary expansion of the mold features. A
systematic study of a silicone elastomer system (GE 615 RTV) was carried out to
determine the degree of shrinkage during polymerization.

A microfabricated ruler

consisting of an array of lines spaced at 100 µm intervals was fabricated for the
measurement of elastomer shrinkage. The elastomer was mixed at a ratio of 5 part A : 1
part B, cast to approximately 7 mm, degassed, and cured at 80 °C for 1.25 hours. The 3 cm
molded elastomer part was aligned at one end to the original mold and inspected using an
optical microscope. The total shrinkage of the molded part over the 3 cm pattern was
determined to be 450 ± 50 microns, corresponding to a linear compression of
approximately 1.5 %. The molded part was subsequently cured overnight (approximately
20 hours) and compared to the master once more. The final shrinkage after full curing was
determined to be approximately 2.5 %. Correct registration of features over 3 cm with 10
µm alignment tolerances was achieved by the compensatory expansion of appropriate
master molds by these factors.

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Layer-Layer Registration

As the complexity of devices has increased techniques for the precise alignment of
complex molded elastomer parts have been developed in parallel by many members of our
lab, most notably by Todd Thorsen, Sebastian Maerkl, Jian Liu, and myself.

This

discussion is intended to elucidate the process by which micromolded structures can be
manually aligned to micron precision over a large active area; a task that will seem unlikely
to readers with little experience in this area.

Ignoring leveling considerations, correct alignment of part to a substrate requires the
simultaneous control of two translational degrees of freedom and one rotational degree of
freedom.

Techniques for the alignment of hard planar substrates for wafer bonding

applications are well established and can achieve alignment tolerances below 1 µm. In
contrast, soft structures present a nontrivial alignment problem due to curing shrinkage,
elastic deformation, and unlevel cast parts. This problem is accentuated in the manual
alignment of large compliant parts where physical manipulations invariably introduce
mechanical deformations which are large compared to the feature sizes. Furthermore, the
precision with which an average person can perform manipulations is limited to several
tens of microns.

Nevertheless a technique of iterative alignment and mechanical force-motion transduction
enables the manual alignment of features over a large working area with micron-scale
precision. The part is first aligned to the substrate as precisely as possible, creating a
reversible bond. Typically this will result mechanical deformations of the piece (warping),

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translational misalignment errors of approximately 100 µm, and rotational errors on the
order of a few degrees. One side of the part is then peeled from the substrate and, with the
opposite side fixed to the substrate, is realigned by pushing or pulling the piece. During
this process the elastomer part acts as a force-motion transducer. The strain imparted to the
elastomer is distributed evenly over the length of the unsupported elastomer. This results
in a large mechanical reduction so that a 100 µm translation at the end of a 1 cm
unsupported section produces a 1 µm translation of features located 100 µm from the fixed
point. Slowly advancing the contact front and iterating this process allows for micron scale
alignment to be achieved over a large working area. The use of elastic materials for force
transduction and mechanical reduction may find applications in other areas where
inexpensive micromanipulations are required.

Substrate Adhesion

Glass-elastomer hybrid flow structures eliminate the need for an additional elastomer
bonding step and allow for the incorporation substrate features such as electrodes or
microwells. Additionally, hybrid structures may exploit the plethora of well-characterized
surface modifications and functionalization protocols for glass. Crucial to the operation of
these devices is the ability to create a strong silicone-glass bond. Early hybrid devices
relied exclusively on Vanderwhaals interactions between the glass and the elastomer for
device sealing. This resulted in a weak bond that could not withstand fluid pressures in
excess of approximately 3 psi, and that was easily compromised by mechanical strain
during the insertion of fluidic input/ouput connectors. The limited operation pressure of
these devices necessitated the use of surface modification protocols to increase

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hydrophillicity and facilitate filling (98). Using this bonding protocol it was found that
delamination was the overwhelming device failure mode, ultimately resulting in the failure
of approximately 50% of tested devices.

A method for achieving high-strength silicone-glass bonds by oxygen plasma treatment of
silicone has been previously described (99). It is thought that oxygen plasma treatment
produces reactive groups on the suface that can then covalently bond to the glass substrate.
Contact angle measurements of oxygen plasma treated silicone give clear evidence of a
chemical modification that makes the elastomer more hydrophilic. Efforts to reproduce
this work in our lab using GE 615 RTV elastomer have resulted in inconsistent and
incomplete bonding over large surface areas. Although inconsistent with the proposed
bonding mechanism, bonding appears to be dependent upon the material system (personal
communication R. Ismagilov); reported results use Silgard silicone rubbers. Results with
Silgard are apparently also inconsistent with variations attributed to contaminants
introduced in the plasma chamber (personal communication R. Ismagilov).

Another

practical consideration that makes this technique less attractive is that the surface
modification is temporary so that bonding must be done shortly after plasma treatment.
This requirement places impractical time constraints on device alignment and assembly.
Finally, the bonding is instantaneous so that “one-touch” alignment of devices to substrate
features is required.

In order to resolve this fundamental problem a new bonding protocol was developed for
reversible and robust bonding of Silgard and GE silicone rubber to glass substrates. To

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achieve a strong reversible bond the device and substrate are rinsed with ethanol, dried
under a stream of nitrogen, and aligned to one another. The assembled device is then
baked overnight at 80 °C. It was found that this procedure reliably produced seals that
could withstand greater than 10 psi flow pressures with some seals holding in excess of 30
psi. The bonding procedure was shown to work with both Silgard and GE silicones, and
was compatible with borosilicate crown, soda lime and quartz substrates. Robust bonding
with epoxy and BSA functionalized slides has also been achieved (personal communication
with S. Maerkl). The mechanism for this bonding is unclear and has not been thoroughly
investigated. It is however probable that the ethanol does not participate directly in the
glass-silicone bonding interaction and that other organic solvents would be equally
effective. Limited investigation has showed that ethanol was necessary for bonding, and
that bond strength increased with bake time. Furthermore, fully cured elastomers appear to
bond as well as partially cured elastomers. Since this technique has been instrumental in
improving device yield, and has been universally accepted in our lab as a standard protocol,
the mechanism of bonding warrants further investigation.

Robust Multilayer Bonding

Multiple elastomer bonding steps are required for the fabrication of MSL devices that do
not use hybrid glass-elastomer channels, use push-up valve geometries, or that incorporate
two control layers (see below). The original protocol for bonding successive elastomer
layers utilizes alternating mixing ratio compositions of 3:1 and 30:1 (13). This protocol
works well for the bonding of thick layers but produces weak bonds for the thin layers that
are used to create channel and valve structures. This poor bonding can be attributed to the

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diffusion of reactive species through the polymer during curing steps (in personal
communication with Mark Unger). FTIR studies of cross sections of bonded silicone
elastomer suggest that as a thick elastomer layer containing excess vinyl groups is bonded
to a thin silicon hydride-rich layer the short silicon hydride chains can diffuse up into the
bulk material (personal communication K. Self). The final material properties of the thin
film are therefore dominated by the thicker elastomer layer, resulting in a chemical
composition on the bottom surface that resembles 5:1 silicone. A strong second bond can
be formed between a thin film of 20:1 elastomer and a thin film of 20:1 elastomer
previously bonded to a thick 5:1 layer.

Although this protocol works well for the

successive bonding of two thin layers, it fails if the thickness of the first bonded film is
large (greater than 50 µm). This failure is likely due to incomplete diffusion of the silicon
hydride groups from the bottom surface of the first layer.

Bubble Formation

Early MSL devices relied exclusively on pneumatic actuation for implementing valve
control. This actuation scheme created problems due to bubble formation resulting from
permeation of gas across the elastomer membrane.

This mechanism is particularly

problematic in applications where valves must be operated at high pressures, or actuated for
prolonged periods of time.

In principal, since the control lines must necessarily be

maintained at a pressure higher than the working fluid bubble formation can appear
instantaneously. In practice surface tension at the channel wall suppressed this process
until a nucleation event occurs. The onset of this nucleation can be postponed by initially
priming the device at high pressure (to ensure no nucleation sites remain).

Once a

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nucleation event occurs the bubble continues to grow, filling the entirety of the channel or
breaking off into a string of satellite bubbles. This phenomena severely limits reliability
and performance in pneumatically actuated devices.

As an alternative to pneumatics, hydraulic actuation may be used to completely eliminate
the problem of bubble formation. The POP technique allows for control structures to be
“dead-end” filled with a hydraulic fluid without any modification of control channel
design. Due to the high gas permeability of silicone and the generally large surface to
volume ratios of control structures, complete filling of control lines can be achieved in less
than a minute at modest filling pressures (10 psi). The choice of hydraulic fluid will be
application specific, and will be governed by the fluid properties. The use of dionized
water as a control fluid has become standard in applications involving aqueous chemistry.

Controlling Reagent Dehydration

The use of water as hydraulic fluid has the added advantage of reducing reagent
dehydration issues. The high permeability of silicone rubber to water vapor implies that
reagents are constantly subject to dehydration through the bulk material. This effect is
pronounced in applications that require long incubation times and can result in complete
drying of the flow structure. The rate of dehydration depends on the relative vapor pressure
of the reagent solution, and hence on it’s composition, and on the partial vapor pressure in
the surrounding polymer matrix. The presence of a water-filled control structure in close
proximity to the reagent line mediates this effect by elevating the partial pressure of water
vapor near the channels. At short times this acts to dramatically reduce the rate of

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dehydration.

This effect has been exploited to reduce dehydration in numerous

applications including cell-screening arrays (27), PCR devices (32), and protein
crystallization (29). At long times a state of dynamic equilibrium is achieved in which the
rates of vapor transport to and from the reagents are equal. This equilibrium depends on a
number of factors including the osmotic strength of the reagents, the proximity and density
of the control structure, and the ambient temperature and humidity. The complicated
interplay of these effects makes the long time dehydration of reagents a difficult parameter
to control. This issue is further discussed in Chapter 8 along with methods for controlling
dehydration.

In some applications it may be advantageous to use alternative control fluids. In such cases
material compatibility issues must be considered. Many common organic solvents such as
toluene, isopropyl alcohol, and acetone will quickly swell the elastomer, constricting
control channels. Other volatile organic solvents such as alcohol will quickly diffuse in gas
phase through the bulk material and contaminate reagents. This may be used to advantage
as a means of slowly introducing chemical species into a reaction; for example in inducing
cells with ethanol. Oils may be used as control fluids if no transport of vapor from the
control lines is desired. Many oils, including paraffin oil and poly(dimethyl-siloxane) are
incompatible with silicone rubber and will quickly swell channels. Highly fluorinated
silicone oils (FluoroguardTM Dupont, FMS oil Hampton Research) are however compatible
with silicone rubber and can be used for prolonged periods without detrimental effects.
Many of these compounds have very high viscosity (approximately 1000 cP), and are
therefore not suitable for applications requiring fast control response.

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Push-up Valves

In the original valve configuration described by Unger et al. the control structure is bonded
on top of a membrane that is deflected down into a hybrid silicon-glass flow channel
structure. In this push-down geometry the membrane is not of constant thickness since the
flow channel has a rounded cross section. The difference in valve membrane thickness
between the center and the edge of the flow channel is equal to the channel height. The
added thickness increases the flexural rigidity of the valve. This increased stiffness results
in a faster valve recovery time but limits the maximum channel height that can be closed at
achievable actuation pressures.

The lack of a robust technique for fabricating inter-layer vias implies that all valves must
connected to a planar continuous control structure terminating at a control input port. In
some applications this constraint creates routing problems that are fundamentally
unavoidable (topologically entangled). One example of this is the design of a microfluidic
matrix form combinatorial polymerase chain reactions in which every flow junction must
be controlled by three separately addressable valves. The integration of valve structures
both on the top and the bottom of a flow structure allows for crossing control lines, thereby
obviating the routing constraints imposed by planar structures.

To this end, an alternative valve-geometry was investigated in which a membrane of
constant cross section is deflected up into the flow structure. This push-up geometry is
more optimal in that a membrane is deflected into a curved shape that matches that of the

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top of the flow structure. Push up valves 50, 100, and 200 µm thickness where fabricated
and tested in the closing of a 10 µm high and 100 µm thick flow channel. The membrane
thickness was designed to be approximately 30 µm. It was confirmed that these valves
closed at lower actuation pressures than push-down valves of equal lateral dimensions and
similar minimum membrane thickness. This solution to the routing problem was ultimately
abandoned for a planar solution using designed differential actuation pressures (discussed
below). Nevertheless, the push-up geometry has been used for the fabrication of valves in
high channel structures (100), alleviating routing problems (F. Balagadde, personal
communication) (32), and for the integration of multilevel fluidic flow structures (in
review, PNAS). The closure of a 40 µm high flow channel by 200 µm x 200 µm push-up
valves is shown in Figure 67.

Figure 67: Integrated push-up valves for the closure of tall (40 µm) channel structures.

Figure courtesy of J. Marcus. One vertex of the matrix is shown in the inset.

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Variable Pressure Valves

If control valves have a consistent logical relationship during operation it may be still be
possible to implement planar control structures despite fundamental routing problems due
to topological entanglement. In the case of the microfluidic matrix structure shown in
Figure 68 operation requires that valve X always be actuated when valve Y is actuated. In
this case both valves may be controlled by a single pressure source if the valves are
designed to have differential actuation pressure thresholds. The strong dependence of the
threshold actuation pressure of a valve on valve width may be exploited to tune valve
actuation pressures, thereby allowing for the selective actuation of certain valves at
intermediate pressures. Application of 110 KPa psi pressure causes the closure of valve X
(width 270 microns) while valve Y (width 96 microns) remains open. At pressures above
260 KPa both valves are closed.

This design was used to implement an N by N

combinatorial PCR microfluidic matrix that amortizes a single slug of polymerase reagent
over N2 reactions.

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Figure 68: Microfluidic matrix structure using variable pressure valves to eliminate

wiring constraints.

Multilevel Molds

The ability to combine channel structures having varying height into a single fluidic
network greatly increases design control and flexibility. For instance, tall channels can be
used to create a low-impedance fluidic bus, or to increase flow through long i/o
connections.

Tall reaction wells can be used to increased reaction volumes while

minimizing diffusion lengths and surface to volume ratios (see below). Additionally,
vertically constricted channel sections can be used as size-specific filters for bead and cell
capture or column stacking.

The incorporation of valves into multilevel mold structures imposes additional design
constraints that must be adhered to. Regardless of whether a push-up or push-down valve
geometry is used, achieving a good seal requires that the flow channel have a rounded cross
section. The fabrication of molds having a rounded flow structure is achieved by thermal
re-flow of the patterned photo-resist. Negative photo-resists such as SU8 rely on thermal
polymerization of UV-exposed regions, and therefore can not be reflowed. In order to be
compatible with membrane valves, flow channel sections must therefore be defined using a
positive photoresist such as Shipley 5740.

For features that do not require rounded cross sections negative photoresists such as the
SU8 series are superior to positive resists in that they are more mechanically robust, allow a

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broad range of channel heights (100 nm to 1000 µm), and can achieve very high aspect
ratios (up to 50:1).

For these reasons SU8 resists are preferable for the fabrication of

control structures molds. The higher achievable channel heights result in a dramatic
decrease in the fluidic impedance of the control structure network, thereby allowing for
faster valve response (6). Furthermore, SU8 resist allow for molding/curing temperatures
up to approximately 200 °C compared to approximately 90 °C for 5740. A negative master
of a control structure patterned in a 25 µm high SU8 2025 film is shown Figure 69.

Figure 69: Negative master of 25 µm high control features fabricated in SU8 2025.

Furthermore, in some applications such as the fabrication of removable filters (see below)
and observation windows for absorbance and fluorescence measurements, it may be desired
to maintain a rectangular channel cross section in specific locations within the flow
structure. Multiple lithography steps can be used to create hybrid SU8-5740 molds. If SU8
features are shorter than 5740 features this process is straightforward. Features are first

182

defined in SU8 by conventional processing. The wafer is then coated with 5740 photoresist
and processed in the conventional way. Initial soft-baking of the 5740 planarizes the film
so that height perturbations due to spin-coating over the SU8 features are minimized. Since
SU8 features as small as 1 µm in height are easily visible through 10 µm of 5740,
alignment is easily achieved. Once the 5740 features have been developed they are
thermally annealed to generate a rounded profile amenable to the integration of valves. A
molded replica of a mixing ring featuring a 10 µm high observation window of rectangular
cross section incorporated in a 13 µm high section of channel having rounded cross section
is shown in Figure 70.

Figure 70: Optical micrograph of mixing ring structure molded from hybrid 5740-SU8

master. 10 µm high observation windows of rectangular cross section allow for precise
absorption measurements.

183

SU8 resists are the most practical option if feature heights in excess of 40 µm are needed in
combination with relatively thin (10 µm - 20 µm) valve-compatible channels. In such cases
the SU8 features must be added after 5740 processing is complete since the spin-coating of
5740 onto the high SU8 features would result in a poor quality film of uneven thickness.
The requirement that the SU8 be added after the 5740 presents a non-trivial technical
problem in that the SU8 processing is incompatible with 5740 photo-resist; SU8 developer
quickly dissolves 5740 features. After considerable investigation it was found that a
standard reflow of 5740 features followed by hard-baking at temperatures above 180 °C for
1 hour resulted in a permanent chemical change to the 5740 photo-resist. Films baked at
this elevated temperature exhibit a pronounced change in color, going from dark red to
black, but remain optically smooth. Provided that a sufficiently long reflow bake (120 °C
for 1.5 hrs) is done prior to hard baking no significant deformation of features is observed.

Hard-baked films were not damaged by SU8 processing, and were further found to be
extremely resistant to a variety of solvents including acetone, isopropyl alcohol, and cyclobenzene; in fact a solvent was not discovered that would remove the film. The elevated
bake temperature is crucial to the success of this process. Hard-baking overnight at 150 °C,
the first protection protocol that was tried, did not produce chemically resilient films. An
important point is that thick SU8 films are highly stressed and are prone to cracking so that
thermal shock due to rapid heating or cooling should be avoided. In practice this is easily
achieved by temperature ramping protocols or by simply using the thermal mass of the
oven/hot-plate to achieve gradual temperature changes. A microfabricated mold featuring

184

and array of 50 µm high SU8 channels joined to rounded 13 µm high 5740 channels is
shown in Figure 71.

Figure 71: Hybrid 5740-SU8 negative master with 50 µm tall SU8 features fabricated on

top of rounded 13 µm high 5740.

Microfluidic Filters

Many applications require the capture of beads or cells during buffer exchange steps or
column stacking. This may be achieved by a simple size filter formed by a section of
channel that is constricted in height or width. Since beads may be less than 1 µm in radius,
very high-resolution lithography is required to implement filters based on lateral
constrictions.

Alternatively, vertical constrictions may be easily implemented using

multilevel molds as described above.

A significant consideration in the design and

fabrication of features that are highly constricted in the vertical dimension is the possibility
of channel collapse during MSL processing. It was found that channel structures having

185

aspect ratios of 1:10 and heights of 10 µm spontaneously collapsed during alignment of
elastomer layers. This process was observed to nucleate in a section of channel and then
propagate along the channel length, “zipping up” the channel feature. This problem was
eventually overcome by increasing the channel aspect ratio and by optimizing elastomer
curing times.

Vertical constrictions due to multilevel mold features are “hard-wired” into a device,
creating permanent filters. Removable filters are useful in many applications, such as
buffer exchange or cell capture, that only require particles to be impeded intermittently.
Such a filter can be easily realized by the partial actuation of a membrane valve. Precise
control of the pressure applied to a valve may be used to sufficiently constrict but not close
a channel so that particles may not pass. Tuning the actuation pressure of such a filter
allows for the filter cutoff size to be dynamically controlled. This strategy has been
implemented in the capture of cells for CDNA analysis (31). A major disadvantage to this
scheme is that the filter cutoff size is very sensitive to the actuation pressure, making it
inconvenient and difficult to automate. Furthermore, perturbations to the pressure in the
flow or control structure arising from peripheral valve actuations can result in the escape of
trapped particles.

To circumvent these limitations removable filters that are insensitive to actuation pressure
can be formed by membrane actuators located in sections of channel with rectangular cross
section. Deflection of a membrane into a square channel results in incomplete closure of
the channel with small gaps remaining at the channel corners. Sub-micron gaps are easily

186

achieved in these structures over a broad range of actuation pressures so that no analogue
control of the actuation pressure is required. These filters may be molded from masters
made using multi-step lithography to include sections of channel made from SU8 (Figure
72). These filters have been used for column stacking in applications including on-chip
chemical synthesis and single cell CDNA analysis (J. Marcus in personal communication).

Figure 72: Section of a microfluidic device designed for mRNA capture. Removable

filter (blue) is used to stack functionalized beads for affinity capture (inset). Figure
courtesy of J. Marcus.

Microwell Fabrication

The integration of microwell structures with increased feature heights allows for reaction
volumes to be increased while maintaining small component footprint and minimizing

187

diffusion times.

Tall microwell structures also allow for improved sensitivity in

fluorescence and absorbance measurements by providing increased optical path length.
Multilevel molds may be used in conjunction with push-up valves to fabricate channel and
well structures in a single molding step. An optical micrograph of a multilevel mold
having an array of 65 µm high microwells connected by 13 µm high flow channels is
shown in Figure 73. The incorporation of microwells or other tall features in the flow
channel mold implies that only the push-up valve geometry may be used since a silicone
film thick enough to cover the features will result in membranes that are too thick for
actuation at reasonable pressures.

Figure 73: Negative master with 65 µm high microwells fabricated in SU8 2075 resist

on top of 10 µm high rounded 5740 channels.

The simultaneous molding of microwells and channel structures has the advantage that no
subsequent elastomer alignment step of the channels to the wells is required. Alternatively,

188

the flow structure may be aligned and bonded to a substrate in which microwells have been
separately fabricated. This scheme allows for push-down valve geometry to be used and
has the advantage that a reversible substrate bond can be formed that allows for access to
the microwells for the recovery of reaction products. In particular, a robust reversible bond
can be formed between an elastomer flow structure and a glass substrate with etched
microwells. An important advantage of this geometry is that the reagents are in direct
contact with the substrate, allowing for the straightforward integration of sensing elements
including electrodes, waveguides, ligands, and metallized films for surface plasmon
resonance.

A procedure was developed for etching microwells in soda lime and borosilicate crown
microscope slides. The glass slides are patterned with photoresist (Shipley SJR 5740)
using a negative high-resolution transparency film as a mask. The back of the slides are
then masked with an additional layer of photo-resist and hard-baked at 125 °C for 20
minutes to protect them during etching. Etching is performed at 25 °C with propeller
agitation in equal parts of dionized water, 1 N hydrochloric acid, and buffered oxide
etchant (6 ammonium fluoride: 1 hydrofluoric acid, Transene Company). The addition of
hydrochloric acid prevents the re-deposition of insoluble fluoride salts formed by impurity
elements in the soda lime and borosilicate crown glass substrates (101). Figure 74: Optical
micrographs of features etched in soda lime glass. (A) Rough etch surface due to the
formation of insoluble fluoride salts. (B) Addition of 1 N HCl to etchant results in smooth
etch. shows a comparison between borosilicate crown glass slides etched with straight
buffered oxide etchant and in the presence of 1 N hydrocholoric acid. Etching for 90

189

minutes at 25 °C yields a maximum well depth of approximately 80 µm. The slides are
then washed in acetone to remove the photoresist, and then cleaned in an acid bath
(NanoStripTM Cyantek Corp.).

Figure 74: Optical micrographs of features etched in soda lime glass. (A) Rough etch

surface due to the formation of insoluble fluoride salts. (B) Addition of 1 N HCl to
etchant results in smooth etch.

190

APPENDIX A: FABRICATION PROTOCOLS
Fabrication Protocol: Screening Device
3” silicon wafer substrate
Mold Fabrication:
I.

Flow Mold

Priming:

HDMS vapor 1 min in tuperware container (STP)

Spin 5740:

2000 rpm x 60 s / 15 s ramp
Film thickness = 11 microns

Soft Bake:

contact bake hotplate
110 C x 90 s

Expose Wafer:

define channel structure
45 at 7 mW/cm2

Develop:

5:1 dilution of Shipley 2401 developer
rinse DI H2O
dry under nitrogen

Reflow:

contact hotplate
110 C x 40 min

Hard Bake:

in oven
ramp 120 C to 180 C
hold 1 hr
ramp 180 C to 120 C

Spin SU8 50:

500 rpm x 15 s / 15 s ramp
2000 rpm x 40 s / 15 s ramp
Film thickness = 60 microns

Pre-Exposure Bake:

contact bake hotplate
5 min x 65 C / 20 min x 95 C

Expose Wafer:

define microwells and low impendence i/o
50 s at 7 mW/cm2

191

II.

Post-Exposure Bake:

1 min x 65 C / 12 min x 95 C / 1 min x 65 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Control Mold

Spin SU8 2025:

3000 rpm x 45 s / 15 second ramp up
film thickness = 13 microns

Pre-Exposure Bake:

contact bake hotplate
1 min x 65 C / 5 min x 95 C

Expose Wafer:

define control structure
25 s at 7 mW/cm2

Post-Exposure Bake:

1 min x 65 C / 5 min x 95 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Hard Bake:

contact hotplate
150 C x 60 min

MSL Fabrication

Priming:

all molds
TMCS vapor 1 min in tuperware container (STP)

Cast Flow Layer:

combine 5:1 GE 615 RTV (30 g A: 6 g B)
mix hybrid mixer: 2 min mix / 2 min degas
30 g onto flow mold (petri dish lined with Al foil)

Degas Flow Layer:

pull vacuum in bell jar (approx 30 minutes)

Spin Control Layer:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on control layer
1800 rpm x 60 s / 15 s ramp*
film thickness = 28 microns

Spin Blank Layer:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas

192

dispense 5 mL on blank wafer
2000 rpm x 60 s / 15 s ramp
film thickness = 30 microns
1st Cure Flow Layer:

convection oven
80 C x 60 min

1st Cure Control Layer:

convection oven
80 C x 40 min

1st Cure Blank Layer:

convection oven
80 C x 40 min

Control/Flow Bonding:

peel flow layer from mold
align to control layer
bake in convection oven
80 C x 90 min

Puncing I/O Ports:

peel bonded device from control mold
punch all flow and control ports

Blank/Control Bonding: place control/flow structure on blank
ensure no air bubbles
ensure no collapsed valves
bake in convection oven
80 C x 3 hours
Dicing:

cut around periphery of thick layer
peel from substrate
dice into separate devices

Substrate Mounting:

rinse bottom of devices with ethanol
dry under nitrogen
rinse glass slides with ethanol
dry under nitrogen
put device on slide
ensure no air bubbles
bake in convection oven
80 C x 12 hours

* spin parameters need to be optimized for each batch.

193

Fabrication Protocol: Formulator Device
3” silicon wafer substrate
Mold Fabrication:
I.

Flow Mold

Spin SU8 2015:

3000 rpm x 70 s / 15 second ramp up
film thickness = 13 microns

Pre-Exposure Bake:

contact bake hotplate
1 min x 65 C / 3 min x 95 C

Expose Wafer:

define observation windows
25 s at 7 mW/cm2

Post-Exposure Bake:

1 min x 65 C / 4 min x 95 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Wash:

spin and rinse with acetone and isopropyl alcohol

Hard Bake:

contact bake hotplate
150 C x 60 min

Priming:

HDMS vapor 1 min in tuperware container (STP)

Spin 5740:

1500 rpm x 60 s / 15 s ramp
Film thickness = 12.5 microns

Soft Bake:

contact bake hotplate
110 C x 90 s
define channel structure
45 at 7 mW/cm2

Expose Wafer:
Develop:

5:1 dilution of Shipley 2401 developer
rinse DI H2O
dry under nitrogen

Reflow:

contact hotplate
110 C x 40 min

Hard Bake:

in oven

194

ramp 120 C to 180 C
hold 1 hr
ramp 180 C to 120 C

II.

Spin SU8 50:

500 rpm x 15 s / 15 s ramp
3000 rpm x 40 s / 15 s ramp
Film thickness = 42 microns

Pre-Exposure Bake:

contact bake hotplate
5 min x 65 C / 15 min x 95 C

Expose Wafer:

define low impendence i/o
50 s at 7 mW/cm2

Post-Exposure Bake:

1 min x 65 C / 7 min x 95 C / 1 min x 65 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Control Mold

Spin SU8 2025:

3000 rpm x 45 s / 15 second ramp up
film thickness = 13 microns

Pre-Exposure Bake:

contact bake hotplate
1 min x 65 C / 5 min x 95 C

Expose Wafer:

define control structure
25 s at 7 mW/cm2

Post-Exposure Bake:

1 min x 65 C / 5 min x 95 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen
contact hotplate
150 C x 60 min

Hard Bake:

MSL Fabrication

Priming:

all molds
TMCS vapor 1 min in tuperware container (STP)

Cast Flow Layer:

combine 5:1 GE 615 RTV (30 g A: 6 g B)

195

mix hybrid mixer: 2 min mix / 2 min degas
30 g onto flow mold (petri dish lined with Al foil)
Degas Flow Layer:

pull vacuum in bell jar (approx 30 minutes)

Spin Control Layer:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on control layer
1800 rpm x 60 s / 15 s ramp*
film thickness = 28 microns

Spin Blank Layer:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on blank wafer
2000 rpm x 60 s / 15 s ramp
film thickness = 30 microns

1st Cure Flow Layer:

convection oven
80 C x 60 min

1st Cure Control Layer:

convection oven
80 C x 40 min

1st Cure Blank Layer:

convection oven
80 C x 40 min

Control/Flow Bonding:

peel flow layer from mold
align to control layer
bake in convection oven
80 C x 90 min

Puncing I/O Ports:

peel bonded device from control mold
punch all flow and control ports

Blank/Control Bonding: place control/flow structure on blank
ensure no air bubbles
ensure no collapsed valves
bake in convection oven
80 C x 3 hours
Dicing:

cut around periphery of thick layer
peel from substrate
dice into separate devices

Substrate Mounting:

rinse bottom of devices with ethanol
dry under nitrogen

196

rinse glass slides with ethanol
dry under nitrogen
put device on slide
ensure no air bubbles
bake in convection oven
80 C x 12 hours
* spin parameters need to be optimized for each batch.

197

Fabrication Protocol: Diffraction Device
3” silicon wafer substrate
Mold Fabrication:
I.

II.

Reservoir Molds

Spin SU8 2025:

3000 rpm x 45 s / 15 second ramp up
film thickness = 13 microns

Pre-Exposure Bake:

contact bake hotplate
1 min x 65 C / 5 min x 95 C

Expose Wafer:

define reservoirs
25 s at 7 mW/cm2

Post-Exposure Bake:

1 min x 65 C / 5 min x 95 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Flow Mold

Priming:

HDMS vapor 1 min in tuperware container (STP)

Spin 5740:

900 rpm x 50 s / 5 s ramp
Film thickness = 16 microns

Soft Bake:

contact bake hotplate
110 C x 100 s

Expose Wafer:

define channel structure
70 at 7 mW/cm2

Develop:

7:1 dilution of Shipley 2401 developer
rinse DI H2O
dry under nitrogen

Reflow:

contact hotplate
115 C x 25 min

Hard Bake:

in oven
ramp 120 C to 180 C
hold 1 hr

198

ramp 180 C to 120 C

III.

Spin SU8 100:

1500 rpm x 60 s / 15 s ramp
Film thickness = 150 microns
sit for 15 minutes on flat level surface

Pre-Exposure Bake:

contact bake on level hotplate
5 min x 65 C / 30 min x 95 C / 1 min 65 C
cool to room temperature

Expose Wafer:

define microwells and high i/o
130 s at 7 mW/cm2

Post-Exposure Bake:

2 min x 65 C / 12 min x 95 C / 1 min x 65 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Control Mold

Spin SU8 2025:

3000 rpm x 45 s / 15 second ramp up
film thickness = 13 microns

Pre-Exposure Bake:

contact bake hotplate
1 min x 65 C / 5 min x 95 C

Expose Wafer:

define control structure
25 s at 7 mW/cm2

Post-Exposure Bake:

1 min x 65 C / 5 min x 95 C

Develop:

100 % Shipley Nanodeveloper
rinse with fresh developer
dry under nitrogen

Hard Bake:

contact hotplate
150 C x 60 min

MSL Fabrication

Priming:

all molds
TMCS vapor 5 min in tuperware container (STP)

Cast Through Layer:

combine 5:1 GE 615 RTV (36 g A: 7 g B)

199

mix hybrid mixer: 2 min mix / 2 min degas
36 g onto flow mold (petri dish lined with Al foil)
Degas Through Layer:

pull vacuum in bell jar (approx 30 minutes)

Spin Flow Layer 1:

combine 5:1 GE 615 RTV (30 g A: 6 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on flow layer
350 rpm x 60 s / 10 s ramp*
film thickness = 180 microns

Degas Flow Layer:

pull vacuum in bell jar (approx 30 minutes)

Spin Control Layer:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on control layer
1800 rpm x 60 s / 15 s ramp*
film thickness = 28 microns

Spin Blank Layer:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on blank wafer
2000 rpm x 60 s / 15 s ramp
film thickness = 30 microns

1st Cure Through Layer: convection oven
80 C x 80 min
1st Cure Flow Layer:

convection oven
80 C x 60 min

Spin Flow Layer 2:

combine 20:1 GE 615 RTV (40 g A: 2 g B)
mix hybrid mixer: 2 min mix / 2 min degas
dispense 5 mL on blank wafer
2000 rpm x 60 s / 15 s ramp
film thickness = 30 microns

2nd Cure Control Layer: convection oven
80 C x 20 min
Punching Reservoirs:

peel through layer from mold
punch reservoir through holes

Through/Flow Bonding: peel through layer from mold
align to flow layer
bake in convection oven

200

80 C x 60 min
1st Cure Control Layer:

convection oven
80 C x 40 min

Control/Flow Bonding:

peel flow layer from mold
take care to not rip membranes
align to control layer
ensure no air bubbles under membranes
ensure no collapsed valves
bake in convection oven
80 C x 70 min

1st Cure Blank Layer:

convection oven
80 C x 40 min

Puncing I/O Ports:

peel bonded device from control mold
punch all flow and control ports

Blank/Control Bonding: place control/flow structure on blank
pull vacuum to ensure no air bubbles
ensure no collapsed valves
bake in convection oven
80 C x 12 hours
Dicing:

cut around periphery of thick layer
peel from substrate
cut device to shape

Substrate Mounting:

rinse bottom of device with ethanol
dry under nitrogen
rinse glass slides with ethanol
dry under nitrogen
put device on slide
pull vacuum to ensure no air bubbles
bake in convection oven
80 C x 12 hours

* spin parameters need to be optimized for each batch.

201

APPENDIX B: MATLAB SCRIPT FOR MIXING SIMULATIONS

Program for simulating dispersion in tube or rotary mixer for a %
given flow
velocity profile.

data input

filename = input('enter function filename: ','s');
fid = fopen(filename, 'w'); % open functionfile
dif = input('diffusion constant(um*um/s): ');
fprintf(fid, 'Diffusion constant (um*um/s): %6f\n', dif);
inic = input('initial concetration: ');
fprintf(fid, 'Initial concentration: %6f\n', inic);
vel = input('max velocity(um/s): ');
fprintf(fid, 'Max velocity (um/s): %6f\n', vel);
xl = input('length of tube (nodes): ');
fprintf(fid, 'Number of nodes in x-dir: %6f\n', xl);
yl = input('width of tube (nodes): ');
fprintf(fid, 'Number of nodes in y-dir: %6f\n', yl);
time = input('simulationb time: ');
fprintf(fid, 'Simulation time (s): %6f\n', time);
dx = input('um pr node x-dir: ');
fprintf(fid, 'Spatial step size in x-dir (um/node): %6f\n', dx);
dy = input('um pr node y-dir: ');
fprintf(fid, 'Spatial step size in y-dir (um/node): %6f\n', dy);
dt = input('timesteps (s): ');
fprintf(fid, 'Time step (s) %6f\n', dt);
slugl = input('slug length(nodes): ');
fprintf(fid, 'Initial length of slug (x-dir nodes): %6f\n', slugl);
numpic = input('number of pictures saved in matrix ct: ');
fprintf(fid, 'Number of events saved (i.e. matrices below): %6f\n',
numpic);
inicond = (x1, y1, time,dx,dy,dt,slug);

calculation of timeresolution and initial matrix

stepcount = 1;
lastcount = time/dt;
channelnl = xl + 100;

202
c = zeros(channelnl,yl);
inidom = (100+slugl);
c(101:inidom,:) = ones;
c = c*inic;
ctemp = c;
ct = zeros(channelnl,yl*10);

discretize velocity profile

v = zeros(yl,1);
n = 1;
while n <= yl
v(n,1) = -vel*(4/((yl-1)*(yl-1)))*((n-1)*(n-1) - (n-1)*(yl-1));
n=n+1;
end

do calculations

q=1;
while stepcount <= lastcount

lower noflux boundary y-1 = y+1
y = 1;
x = 2;
n = y;
while x < (xl + 97)
ctemp(x,y) = (dif*dt/(dx*dx))*(c(x+1,y) - 2*c(x,y)
+ c(x-1,y)) + (dif*dt/(dy*dy))*(c(x,y+1) -2*c(x,y)
+ c(x,y+1)) + (v(n,1)*dt/dx)*(-c(x,y) + c(x-1,y))
+ c(x,y);
x = x+1;
end

high noflux boundary y+1 = y-1
y = yl;
x = 2;
n = y;
while x < (xl + 98)
ctemp(x,y) = (dif*dt/(dx*dx))*(c(x+1,y) - 2*c(x,y)
+ c(x-1,y)) + (dif*dt/(dy*dy))*(c(x,y-1) -2*c(x,y)
+ c(x,y-1)) + (v(n,1)*dt/dx)*(-c(x,y) + c(x-1,y))
+ c(x,y);
x = x+1;
end
y = 2;
n = 2;
while y < yl
x = 2;
while x < (xl + 98)
ctemp(x,y) = (dif*dt/(dx*dx))*(c(x+1,y) - 2*c(x,y)
+ c(x-1,y)) + (dif*dt/(dy*dy))*(c(x,y+1) -2*c(x,y)

203
+ c(x,y-1)) + (v(n,1)*dt/dx)*(-c(x,y) + c(x-1,y))
+ c(x,y);
x = x+1;

end
y = y+1;
n = y;

end
c = ctemp;

if stepcount > q*lastcount/numpic
ct(:,(q*yl-(yl-1)):q*yl)=c;
tau = dt*q*lastcount/numpic
x=1;
while x<=channelnl
y=1;
while y <=yl
fprintf(fid, '%6f\n', c(x,y));
y=y+1;
end
x=x+1;
end
q = q+1;
fprintf(fid,'\n');
end
stepcount = stepcount + 1

end
fclose(fid);

204

APPENDIX C: PHASE-SPACE DIAGRAMS

205

206

207

208

APPENDIX D: CRYSTALLIZATION RESULTS FOR OPTIMAL SCREENING
Optimal Xylanase Crystallization Screen Based on Phase-space Mapping

Buffer

pH

10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48

NaCitrate
NaCitrate
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
NaCitrate
NaCitrate
NaCitrate
Tris/HCL
Tris/HCL
Tris/HCL
NaCitrate
Tris/HCL
Tris/HCL
NaCitrate
NaCitrate
Tris/HCL
NaCitrate
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL
Tris/HCL

4.6
4.6
6.5
6.5
8.45
8.45
4.6
4.6
4.6
6.5
6.5
8.45
4.6
6.5
8.45
4.6
4.6
8.45
4.6
6.5
6.5
8.45
8.45
8.45
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
8.2
7.6
7.6
7.6
7.6
7.6
7.6
7.6
7.6
7.6

Conc
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1

Prec1
NaCitrate
NaCitrate
NaCitrate
NaCitrate
NaCitrate
NaCitrate
Na/K Tart
K2HPO4
K2HPO4
K2HPO4
Na/K Tart
K2HPO4
(NH4)2SO4
(NH4)2SO4
(NH4)2SO4
K2HPO4
Na/K Tart
K2HPO4
(NH4)2SO4
Na/K Tart
(NH4)2SO4
Na/K Tart
Na/K Tart
(NH4)2SO4
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000
P8000

Conc
0.65
0.475
0.7
0.5
0.425
0.475
1.1
0.8
1.8
0.6
0.75
2.8
1.08
1.89
0.81
2.8
0.75
0.4
0.945
1.4
1.35
0.9
0.7
1.755
16
23
15
24
28
19
14
20
14
16
24
24
10
16
18
12
28
30
22
16
18
28
16
30

Prec2
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
none
NaCl
NaCl
None
None
Am Aoc
Am Aoc
Am Aoc
K Citrate
K Citrate
K Citrate
(NH4)2SO4
(NH4)2SO5
MgSO4
MgSO4
MgSO4
NaCl
NaCl
K2HPO4
K2HPO5
K2HPO6
NH4AOc
K Citrate
(NH4)2SO4
MgSO4

Conc
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
0.1
0.1
N/A
N/A
0.1
0.1
0.1
0.05
0.05
0.05
.0675
.0675
0.05
0.05
0.05
0.1
0.1
0.1
0.1
0.1
0.1
0.05
.0675
0.05

Prot.
mg/mL
17
19
9.5
6.5
6.75
24.75
21
6.75
4.5
24.75
3.5
17
31.5
23.62
4.5
6.75
13.5
4.5
42
21
54
30
18
33
60
42
60
36
18
66
30
36
66
18
12
12
42
36
18
54
12

209

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