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Contaminant-induced current decline in capillary array electrophoresis Coope, Robin 2006

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Contaminant-Induced Current Decline in Capillary Array Electrophoresis By Robin Coope BASc , The University of British Columbia 1993 MASc, The University of British Columbia 1996 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Physics) THE UNIVERSITY OF BRITISH COLUMBIA April 2006 © Robin Coope,2006 Abstract This research clarifies, for the first time, the mechanism and impact of current decline in capillary array electrophoresis ( C A E ) . High throughput capillary array electrophoresis instruments for D N A sequencing suffer to varying degrees from failure associated with electrophoretic current decline and inhibition or delay in the arrival of fragments at the detector. This effect is known to be associated with residual quantities of large, slow moving fragments of template or genomic D N A carried through from sample preparation and sequencing reactions. Here, we document and investigate the existence of an expanding ionic depletion region induced by overloading the capillary with low-mobility D N A fragments, and the effect of growth of this region on electrophoresis run failure. This depletion region forms upstream of the smaller sequencing fragments, and its expansion was found not to affect the quality of the sequencing peaks at the detector. Rather the current decline associated with depletion region growth reduces the velocity of the downstream sequencing fragments, so fewer fragments arrive at the detector during the run. It is shown, through analytical and numerical models, how increasing quantities of slow moving D N A cause the concentration of background electrolyte downstream to decline. With the concentration of such fragments beyond a threshold quantity, the anode-side boundary of the nascent depletion region is shown to propagate toward the anode at a rate faster than the contaminant D N A migration. Under such conditions the depletion region expands, the current declines, and the electrophoresis run suffers from a reduced yield of sequence data or fails completely. While the upstream boundary of the depletion region propagates with the D N A , the propagation rate of the downstream boundary is found to be inversely proportional to the amount of ionic depletion, and independent of the motion of the D N A . Observations suggest that these downstream boundaries may propagate as a result of an imbalance in current carriers brought about by the exposure of bound charges in the matrix or capillary wall, which may be coupled to a rise in p H . iv Table of Contents Abstract ii Table of Contents iv List of Tables vii List of Figures viii Symbols, Nomenclature and Abbreviations xi Acknowledgements xiii Chapter 1 Introduction 1 1.1 T h e Continued Importance of de novo Sequencing and Capillary Electrophoresis 1 1.2 Matrix selectivity is the next parameter to push for increased performance 3 Chapter 2 The Principles of Capillary Electrophoresis 5 2.1 Principles of Electrophoresis 5 2.2 D N A Propagation in Matrices 8 2.3Other Properties of Electrophoresis 9 2.4Electrokinetic Injection and Sample Stacking 11 2.5Capillary Sequencing for D N A 13 2.6Current Decline and Mitigation Efforts 19 Chapter 3 Apparatus and Methods to Investigate Current Decline 22 3.1 T h e M e g a B A C E 24 3 .2The Single Capillary Instrument 26 3.2.1 Mechanical Design 26 3.2.2 Fluorescence Detection 30 3.2.3 Thermal and Visible Light Cameras 32 3.2.4 Capillaries, Matrix and Buffer 33 3 .3Samples and Methods 34 3.3.1 M e g a B A C E Samples 34 V 3.3.2 MegaBACE Experimental Parameters 35 3.3.3 Electropherogram Analysis 35 3.3.4 Single Capillary Instrument Samples 38 3.3.5 Single Capillary Instrument Parameters 40 3.3.6 Cut Capillary and Thermal Image Analysis 41 Chapter 4 Experiment 43 4.1 Relationship between read failure and capillary current decline 43 4.2Bubbles "... 45 4.2.1 The Contribution of Bubbles to Current Decline 45 4.2.2 Bubble Formation and Growth 48 4.3 Ion Distribution during Current Decline 49 4.3.1 Formation of a Depletion Region 49 4.3.2 A Threshold for Current Decline 53 4.4Temporal evolution of Ion Depletion Boundaries 54 4.4.1 Cathode Boundary and DNA Movement 56 4.4.2 Boundary velocity and its relation to depletion region depth 57 4.5A Mechanism for Current Decline 62 Chapter 5 Analysis of Boundary Propagation 64 5.1 Formation of the Depletion Region 65 5.2 Numerical Modeling of Ionic Depletion 68 5.3 DNA and Cathode Boundary Propagation 80 5.4Anode-Side Boundary Movement 86 5.4.1 The Theory of Moving Boundaries 86 5.4.2 Common Ion Boundaries 91 5.4.3 Boundary Movement by Bound Charge 95 5.4.4 Experimental Evidence for pH Changes in the Depletion Region 101 5.4.5 Boundary Movement by OH" Propagation 106 Chapter 6 Conclusion 111 vi Bibliography 114 Appendix A Properties of D N A and D N A Sequence Methods 125 A . 1 Properties of D N A 125 A.2 Library Construction 126 A .3 D N A Purification 128 A.4 Cycle Sequencing 129 A . 5 B C G e n o m e Sciences Center Sample Preparation 131 Appendix B The Effect of Sample Resuspension in Agarose 134 B. 1 Effects of Injection from Agarose 134 Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour 140 C . 1 Permanent Effects of DNA-lnduced Depletion Regions 140 C.2 Matrix ion depletion from anode-side buffer 146 C . 3 Bubbles' Effect on Current 150 Appendix D L P A and Buffer Properties 156 D. 1 Conductivity and pH of T r i s / T A P S Buffer Under Dilution 156 D.2 The Thermal Expansion Coefficient of L P A 158 Appendix E Temperature Measurement 160 Vll List of Tables Table 1 Data for concentration and solution conductivity for different D N A samples 39 Table 2 Physical data for the numerical model 75 Table 3 Signal strength of the first - 5 0 D N A bases in capillaries resuspended in Dl H 2 0 and Agarose 138 VIII List of Figures Figure 1 Schematic description of electrophoretic properties of D N A , reprinted from [18] 9 Figure 2 T h e original confocal array developed by the Mathies group. Reprinted from [35] 15 Figure 3 T h e airbox in the M e g a B A C E showing the capillary array, anode pressure vessel and cathode array 24 Figure 4 A front view schematic of the single capillary sequencer 26 Figure 5 A schematic of the confocal fluorescence detector system. 30 Figure 6 M e g a B A C E electropherogram data 37 Figure 7 A typical successful electropherogram 38 Figure 8 Read length vs total loaded charge 44 Figure 9: Total loaded charge of capillaries with and without bubbles. 47 Figure 10 Local conductivity and resistance profiles for four cut capillaries 51 Figure 11 Current at the end of runs of varying duration inferred from ionic concentration profiles 53 Figure 12 Total loaded charge vs. quantity of injected D N A 54 Figure 13 A series of infrared images of the capillary taken eight seconds apart and displayed side by side 56 Figure 14 Fits to the first five minutes of anode and cathode boundary data using x(t) = dQ(t)+C2 58 Figure 15 Two examples of ionic depletion boundaries propagating in from a low conductivity cathode 60 Figure 16 Measured propagation rates for boundaries of different depletion depths 61 IX Figure 17 Rate of anode-side boundary propagation vs. quantity of injected D N A 62 Figure 18 1-D discretization of the capillary showing ion flows in the upwind scheme 71 Figure 19 Decay of a peak in ion concentration due to numerical diffusion 76 Figure 20 Effect of a fixed D N A peak on the background electrolyte concentration 78 Figure 21 The effect of a 20 ng D N A peak of varying width 79 Figure 22 Fit of equation (5-29) to a cathode boundary position 84 Figure 23 Adjacent ionic regions forming a moving boundary 87 Figure 24. T h e effect of the regulating function on the distribution of ions in the capillary .89 Figure 25 Simulation of a leading and trailing negative ion 90 , Figure 26 C o m m o n ion boundary motion in buffered and unbuffered systems 94 Figure 27: Bound charge driven boundary movement 98 Figure 28 Comparison of experimental data and simulation of boundary propagation due to bound charges 99 Figure 29 pH details of bound charge driven depletion regions 100 Figure 30 Nickel particles in a capillary crossing into the depletion region 103 Figure 31 Progress of a nickel particle as a depletion boundary crosses its path 104 Figure 32 A five minute simulation with [TAPS]=0 at cathode. T h e retreating T A P S " ion is replaced by OH" ions, raising the p H . 108 Figure 33 Comparison of simulation and experiment for pH driven boundaries 109 Figure 34 Read length vs total loaded charge for samples resuspended in dHaO and agarose 135 X Figure 35 Electropherograms of 1 kb ladder resuspended in Dl H 2 0 and 0.08% Agarose 137 Figure 36. Infrared images (left) of a surface charge induced depletion region (SCIDR) 141 Figure 37 Creation of a S C I D R by addition of A, D N A 142 Figure 38 T h e effect of clipping off the capillary entrance on the movement of a S C I D R 143 Figure 39: Current decline associated with using buffer at the anode. : 146 Figure 40 Conducitivity changes from matrix depletion 147 Figure 41 Effect of a S C I D R boundary meeting a matrix depletion boundary 150 Figure 42: Infrared and visible images of the capillary showing simultaneous growth of a hot region and bubble 151 Figure 43 A histogram showing observed bubble positions after one run 152 Figure 44. A histogram of the data in Figure 8(a), binning the capillaries by total loaded charge 154 Figure 45 Current traces from one plate from the M e g a B A C E 155 Figure 46 Conductivity of the T r i s - T A P S buffer 157 Figure 47 Temperature dependence of pH and conductivity in 50mmol/L T r i s - T A P S 158 Figure 48 A thermal of the capillary and temperature references.... 160 Figure 49 Thermal maps of the capillary depletion region 162 Figure 50 T h e rise in temperature in the depletion region over the course of a run 163 xi Symbols, Nomenclature and Abbreviations Term Definition F Faraday's Constant: 96800 coulombs/mol a Conductivity of a solution, (Qm)"1 = 10"4 uS/cm W Ionic mobility of the ith species (rn^A/s) Q Concentration of the ith species. 1 mol/mJ = 1 mmol/L s Siemens = Q"1 . e Elementary charge 1.6x10"19 C J Current density (Amps/m2) 1 Current (Amps) V lon velocity (m/s) Q Charge (coulombs) tr Run time (s) FWHM Full width-half maximum of a gaussian peak. D Diffusion constant (m2/s) X DNA A 48kb double stranded non-circular phage DNA. Phred The most common algorithm for identifying DNA bases from raw fluorescent sequence data. [1] Read length The number of contiguous nucleotides identified at satisfactory quality, typically Phred quality > 20, in a single sequence run. (see Phred) Aliquot To distribute volume of fluid to multiple sites Phage A virus, including a DNA strand, that infects bacteria Plasmid A circular DNA strand that can reproduce in bacteria Vector A more general term for a plasmid or phage. Insert DNA of interest ligated into a vector dH 20 Deionized water a=0.05 uS/cm TLC Total Loaded Charge Transference Number T = M~ , T+=l T Electropherogram Raw data from an electrophoresis machine. Anode The positive end of the capillary electrophoresis apparatus XII Cathode The negative end of the capillary electrophoresis apparatus Electrophoresis T h e process of ions migrating through solution in response to an electric field. Co-ion A n ion of like charge Counter ion A n ion of opposite charge %w/v Percent weight/volume (usually g/ml). This is a literature convention for polymer concentrations. L P A Linear Polyacrylamide - the D N A separation polymer used in this research P D M A Polydimethylacrylamide. A popular polymer for D N A separations. P C R Polymerase Chain Reaction - the protocol used to amplify D N A fragments by up to 10 6x ABI Applied Biosystems Inc. Manufacturer of the family of D N A sequencers (310, 3100,3700,3730) which dominates the market. LIF Laser Induced Fluorescence B C G S C The B C Cancer Agency G e n o m e Sciences Center. Tris Tris(hydroxymethyl)aminomethane) T h e weak base commonly used in D N A sequencing buffer T A P S [(2-Hydroxy-1,1-bis (hydroxymethyl)ethyl)amino]-1-propanesulfonic acid. T h e weak acid commonly used in D N A sequencing buffer P M T Photomultiplier Tube . T h e fluorescence detector used in many capillary sequencers In silico A term, found in life science, meaning "using a computer". It follows from in vivo and in vitro E O F Electro-osmotic flow. T S R Template Suppression Reagent - an additive to prevent large D N A fragments from being co-injected with sequencing samples bp/kbp/Mbp Measurement of the length of a D N A strand in number of base pairs, or kilo or mega base pairs. C E Capillary Electrophoresis C Z E Capillary Zone Electrophoresis. T h e broader category of electrophoresis which covers D N A separations XIII Acknowledgements I am indebted to numerous people who made my P h D possible. First amongst these is, of course, Andre Marziali, whose support, guidance and commitment was, and is, second to none. T h e absolute master of the rapid and critical insight, Dr. Marziali was able to help the research forward when I got stuck, keep it going in the right direction, and provide the ever-necessary optimism. Speaking of which, Dr. Marziali's development of the Physics 253 robotics course which I had the privilege to help teach will go down as the most fun anyone will ever have in a classroom. I challenge anyone to find a more effective, inspirational or generous thesis supervisor in any field anywhere. Another great source of assistance was the staff of the B C Cancer Agency G e n o m e Sciences Center and in particular, Duane Smailus. Duane prepared many of the'samples used herein, always with dispatch, good humour and his usual standards of quality and consistency. I must thank my colleagues in the lab, and in particular second year co-op student Peter Eugster. Peter, some of whose data appears in this thesis, completed a large number of bubble and infrared experiments in a short period of time and remains my gold standard for efficient execution in the laboratory. Itinerant biochemist Trevor Pugh also provided samples, as did Mary Pines, late of the Sadowski lab. Co-op student Stefan Avail worked on numerical modeling early on, and together we certainly found some blind alleys to avoid! I must also thank fellow graduate students Jon Nakane and Matthew Wiggin for, respectively, their mathematical and biochemical insights and the general good times. Thanks also to the Tiedje lab crew of Anders Ballestad, Eric Nodwell and Scott Webster for letting me use Berserk and the Steamengine cluster, as well as the xiv mathematical, Linux and Matlab insights. Thanks to Boye Ahlborn for translating parts of Kohlrausch's paper, written in the difficult classical scientific German of 1897. Thanks also to Barb Grossman, then of Amersham Biosciences, who ferreted out the object files that allowed me to properly analyse M e g a B A C E data. I am also grateful to my parents, John and Marian Coope , who in addition to everything else, read this thesis at the very end and found that last 300 or so errors. A n d of course Stacey Lobin, for being mom to Ben, who may be the most beautiful child ever, although it seems impossible to design an experiment to test this. Finally I thank my thesis committee, L o m e Whitehead, Jeff Young and Matt Choptuik for taking the time to participate in this intellectual journey which I have so very much enjoyed. XV / am no poet, but if you think for yourselves as I proceed, the facts will form a poem in your minds. Michael Faraday Chapter 1 Introduction 1 Chapter 1 Introduction 1.1 The Continued Importance of de novo Sequencing and Capillary Electrophoresis A s of the close of the twentieth century, large-scale D N A sequencing has emerged as a revolutionary scientific technique. Sequencing may come to be seen as akin to the development of the telescope or the particle accelerator in its impact on understanding of the world and our place in it. Data from the human genome project and other species' genomes have already begun to modify our understanding of the roles of genes and gene regulation and the regulatory role of non-coding D N A . Availability of genomes of multiple species has aided in locating genes associated with disease. More than one commentator has argued that biology is only now entering its golden era [2]. Genomics in the post-human genome project era is branching along several paths. O n e of these is the gathering of more species' genomes for comparative genomics, or comparison of sequence similarities between various organisms and human D N A , to increase our understanding of gene function, and of evolution of sequence information. Another recently embarked-upon endeavour is the sequencing of thousands of human cancer genomes to study cancer progression and the role of genetic mutations in this disease. Clearly these projects will require orders of magnitude more sequencing capacity than the entire human genome project, and will be limited by cost. Although the cost of sequencing has declined from $10/base in 1990 [3] to about $0.004/base in 2005 [4], a human-sized genome of 3x10 9 bases currently costs (with multiple coverage) about $50 million. NIH director Francis Collins has called for the development of Chapter 1 Introduction 2 technologies for the "$1000 Genome" or about $3x10"7 /base. Promising candidates thus far use fluorescently labeled D N A extension reactions [5] [6] [7] to generate short (<100 base) continuous reads in a massively parallel manner. A s a result, these methods are likely to be restricted to resequencing individual organisms for which there already exists a species genome to which the short fragments can be compared. De novo sequencing, on the other hand, requires the sequenced fragments be assembled into a continuous whole without the benefit of a reference sequence. Because of repeated sequence and other factors, the completeness of the assembled genome is dependent on the length of the fragments to a great degree [8], and large scale de novo sequencing is only practical with average read lengths of several hundred bases (see Appendix A.1). Presently, and for the foreseeable future, the dominant technique for large-scale de-novo sequencing is capillary array electrophoresis ( C A E , or C E ) . In C E , separation of D N A strands of different lengths is performed in an array of 96 or 384 75um ID, 60 cm long, discrete glass capillaries. This approach has a combination of advantages over on-chip C E or slab gel electrophoresis, including improved heat dissipation, long read lengths, speed, and ease of automation. In order to justify the continued commitment of resources at existing levels, the cost of de novo sequencing must continue to fall. In the context of C E , this means lower reagent costs and longer read lengths from each capillary. A s patent protection has maintained relatively high polymerase reagent costs, reaction dilution has recently been the biggest source of cost reduction. The B C Cancer Agency G e n o m e Sciences Center ( B C G S C or G S C ) for example, is in the process of introducing 1/256 reaction dilutions in their sequence pipeline, and has shown 1/1024 dilutions to work. 1/256 dilution, with median reads in excess of 800 bases, reduces the reagent cost from Chapter 1 Introduction 3 $6000 to $22.00 per million bases [9]. This source of cost reduction is reaching its limit however. At t h e . G S C ' s current rate for customer sequencing of $4500 per million bases, sequencing reagents represent about 35% of the total, the remainder being labour, operations costs other consumables and bioinformatics support. Even infinite dilution could only reduce that cost another $1500. [4]. Between 1990 and 2000, improved sequencer throughput through automation and increased read lengths was a big source of cost reduction. In 1990, the ABI 370 slab gel sequencer was capable of sequencing 12,000 bases per day. By 1998, the ABI 3700 capillary machine could produce 196,000 bases per day, and by 2002, the 3730x1 had been pushed over 900,000 bases per day. This represents a plateau however, and subsequently, no new separation matrices or buffers have been introduced. Since 1998, improved sample purification and more selective separation matrices have allowed median production read lengths to rise from 500 to 800 bases per capillary This is still well below literature values from as early as 1998 [10], where reads up to 1300 bases per capillary were reported. 1.2 Matrix selectivity is the next parameter to push for increased performance T h e main source of this read length plateau is in limitations of the polymer matrices used in capillaries to separate D N A . Denser matrices with better separating power tend to suffer from increased read failure in the form of loss of capillary current during the run [11]. This current decline manifests itself right after the sample is introduced into the capillary, with the current declining to less than 20% of its initial value after thirty minutes [12]. D N A bands are slowed down and arrive late at the detector, leading to the term "late starts" to describe this phenomenon. Current decline has been shown to correlate with the Chapter 1 Introduction 4 presence of large, low mobility D N A fragments in the sequencing sample which are a byproduct of the sample preparation protocol [13]. T h e frequency and severity of the problem varies with the type of matrix used, and it is more common with the use of less stringent, and typically less expensive, sample preparation techniques [14]. Address ing the issue of current decline is one of the few avenues of continued cost reduction available for capillary electrophoresis. While the causes of current decline had been elucidated during the development of C E separation matrices, the mechanism by which current decline occurs has never been properly explained. It is thus the objective of this thesis to understand why long D N A fragments cause current decline, and to investigate possible methods of mitigation. In the following chapters, the background of capillary electrophoresis for D N A sequencing is developed, along with a review of previous research into the current decline problem. Two pieces of equipment for studying current decline are then described, a single capillary instrument developed specifically for this investigation, and the commercial M e g a B A C E 1000, a 96 capillary sequencer. Results are presented showing the causal relationship of long fragments to current decline and of current decline to reduced D N A "read length". It is then demonstrated for the first time that current decline results from a growing depletion region caused by the presence of long fragments. It is further shown that current decline only occurs if the quantity of long fragments injected is beyond a threshold level. In chapter five, a model is developed to explain the formation and growth of the ionic depletion region, and the reason for the threshold behaviour. Chapter 2 T h e Principles of Capillary Electrophoresis 5 Chapter 2 The Principles of Capillary Electrophoresis T h e modern science of electrophoresis is generally regarded to have begun with Arne Tiselius, in the 1930's. He showed that proteins in human serum could be separated by electric current flow in a liquid-filled tube on the basis of charge and mass. A s Joule heating in free solution electrophoresis causes convective diffusion leading to a loss of resolution in the separation, workers adopted liquid-permeated solid supports such as paper, starch, cellulose, acetate, agarose and polyacrylamide in slabs or sheets. T h e significance of narrow bore (<100um) capillaries to control convection was first recognized by Stellan Hjerten in 1967 who introduced the concept of capillary zone electrophoresis [15]. C E development accelerated in the 1980's with the commercial availability of polyamide coated drawn glass capillaries [16]. This culminated in the extraordinarily successful development of C E for D N A sequencing in the 1990's. Today, C E is also gaining popularity as an analytical tool alongside mass spectrometry (MS) and liquid chromatography (LC), particularly for separating species of different chirality, highly polar species, and as a front end for M S separations [17]. 2.1 Principles of Electrophoresis T h e sheer number of different configurations of analytes, electrolytes, additives and detection schemes possible in electrophoresis and the interdisciplinary nature of the subject has led to an extensive and diverse literature. Sub-categories such as D N A sequencing, peptide separations and inorganic analytical chemistry approach the same phenomena with different vocabularies. Chapter 2 The Principles of Capillary Electrophoresis 6 Electrophoresis has been also influenced by the related field of chromatography, which uses a different vocabulary still. From a physics perspective, it seems easiest to begin with a mathematical description. Electrophoresis is the process of separating charged species in a fluid by differences in electrically induced migration velocity. To perform electrophoresis, a potential difference must be set up across an ionic solution, which can be in a tube, capillary, or open box. Since many analytes are sensitive to pH, a buffer solution is normally used, with an adequate reservoir at each electrode so that a stable pH is maintained throughout the run. Through conservation of mass, it can be shown that such a system is governed by the Einstein-Smoluchowski equation for particle diffusion in the presence of a potential: ^ = A a ^ + a ( 2 , ) dt ox ox where C,, D,, z,, and //,are respectively the concentration, diffusion constant, charge and mobility of the ith ionic species, and E is the local electric field: E(x,t) = -M-; a(x,t) = £ / f y , |C , '(2-2) a(x,t) where J(t) is the current density and a(x,t) is the local conductivity and F is Faraday's constant (96800 Coulomb/mol). In turn, the current is: dx (2-3) <j(x,t)A where V is the voltage and L is the capillary's length. For a given ion in a constant field, and neglecting diffusion, each ion's average drift velocity is: Vi=MtE (2-4) Chapter 2 T h e Principles of Capillary Electrophoresis 7 Electrophoresis works by exploiting the difference in mobility of different analytes. According to the Debye-Huckel theory, the surface charge of the ions or analytes is screened beyond the Debye length. where er is the permittivity of the solution, e is the fundamental charge and / is the ionic strength of the solution. In the presence of an electric field, the analyte ion and counter ions will be pulled in opposite directions, and interact with each other hydrodynamically. Where the Debye layer is much thicker than the particle radius, R, the mobility is given by where the ion has charge Q and r\s is the solvent viscosity. Equation (2-6) applies to small ions and because each ion has a unique value of Q / R , these ions can be separated using electrophoresis in free solution. D N A , however, is much larger and has charge proportional to its length. D N A takes on a globular conformation in free solution such that internal charges are shielded by counterions that do not feel hydrodynamic effects, and the surface charge density and viscous drag thus both scale with the radius. This "free draining" property means that, to a first approximation, fragments of all lengths propagate with the same mobility given by (2-7) rather than (2-6). where p is the D N A globule's surface charge density [18]. D N A must therefore be separated in a viscous medium which can interact with the D N A polymer and produce a length-dependent drag, preventing this (2-5) P (2-7) AKT]SK Chapter 2 The Principles of Capillary Electrophoresis 8 free draining behaviour and breaking the length scaling degeneracy between driving force and drag. 2.2 DNA Propagation in Matrices There are several regimes for D N A molecule propagation in polymer matrices; these are shown in Figure 1, reprinted from [19]. For polyacrylamide matrices, it is thought that the equilibrium reptation regime (C) holds for D N A strands up to several hundred bases in length [20]. There is evidence that longer fragments may propagate in the regime of oriented reptation as, at high driving fields, electropherograms are concluded with a large peak followed by no signal, suggesting all the larger peaks are propagating at the same rate. Though reptation regimes and the governing equations are typically the central point of interest in electrophoresis, much of the work presented here hinges instead on properties of ions and the background electrolyte, and therefore additional background will be provided in this area. . Chapter 2 The Principles of Capillary Electrophoresis 9 Log (strand length) ^ A B C D E F G Figure 1 Schematic description of electrophoretic properties of DNA, reprinted from [19]. [A] Ogston regime - DNA stays coiled and is sieved. [B] Entropic Trapping: The random coil jumps between larger pores. [C] Near equilibrium reptation: The random coil migrates head first through the matrix. [D] Reptation trapping: The DNA is slowed by both ends pulling though the matrix and forming U-shapes. [E] Oriented Reptation: The DNA uncoils and goes through the matrix with one end leading. [F] Geometration: High fields may be characterized by hernias and "bunching" instabilities. [G] Very long molecules may not migrate through matrices at all, possibly because they form knots around gel fibers. 2.3 Other Properties of Electrophoresis Amongst the properties of electrophoretic systems which must be taken into account is the relationship of temperature and solution conductivity. T h e viscosity of aqueous solutions varies according to r/~exp(Ea/kT), where Ea is the activation energy for the viscous flow [21]. This means that ion mobility and therefore buffer conductivity, is dependent on temperature. A widely employed rule of thumb is that between 2 0 - 6 0 ° C the conductivity changes by 2 % / ° C . This is true in the present case, and experimental data is presented in Appendix D Chapter 2 T h e Principles of Capillary Electrophoresis 10 which shows this rule to be quite accurate. Temperature acts as a limiting factor in the separation speed as the temperature gradient between the center and wall of the capillary caused by Joule heating will result in a parabolic conductivity profile which contributes to band broadening [22]. A feature of all capillary electrophoresis is electroosmotic flow ( E O F ) . Under aqueous conditions glass possesses an excess of negative charge. This results in a net positive charge along the surface of the aqueous region. W h e n an electric field is applied, the mobile counterions to this surface charge drift with the fields, but there is no equivalent motion of the fixed surface charges. Consequently, bulk fluid flow is established towards the cathode (negative electrode). E O F differs from hydrostatic flow in that flow is generated within the charged region next to the capillary wall, so the radial velocity profile is flat, and analytes are not dispersed. The E O F velocity is nominally v = ^ E (2-8) where e\s the permittivity of the solution, and <^ is the electric potential at the surface where shear occurs, commonly called the zeta potential. In a real capillary, (2-8) is potentially misleading as it assumes that the E O F driving force is constant throughout the capillary [23]. Different local conditions and defects in the capillary walls could cause different local driving forces for E O F , potentially leading to non-flat flow profiles and analyte dispersion. E O F is also highly dependent on solution pH, particularly in fused silica capillaries and can rise by an order of magnitude with pH increase from 2 to 12. At pH 8 where D N A sequencing takes place, the E O F "mobility" (sC/t]) in an uncoated capillary is on the order of 60x10"9 m 2 A/s [24], much higher than, and in the opposite direction to mobility of D N A sequencing fragments which range from 3 to 20x10"9 m 2 A/s . E O F must therefore be suppressed for Chapter 2 T h e Principles of Capillary Electrophoresis 11 D N A sequencing, using capillary surface treatment or self-coating matrices. Suppression of E O F also prevents dispersion from inhomogeneities in the E O F mobility [25]. In modes of C E where a more acidic buffer can be used, E O F can be used to advantage: increasing the effective length of the capillary or allowing positive and negative analytes to be separated together. T h e latter is done by hydrostatically introducing the sample plug and then conducting an electrophoretic separation while the entire contents of the capillary are flowing past the detector under the influence of E O F . E O F is in fact an integral part of almost all types of C E except for D N A sequencing. 2.4 Electrokinetic Injection and Sample Stacking In sequencing applications, D N A is injected into the capillary by electrophoresis rather than hydrostatic pressure as in some other forms of C E . A well containing the sample is placed at the cathode end of the capillary and the electric field is applied. T h e sample well is then removed and replaced with running buffer so the run can proceed. This "electrokinetic injection" enables sample compression, also known as stacking, which is crucial to the success of capillary sequencing as resolution is inversely proportional to injection peak width [26]. Sample compression affects both the concentration and width of the injected sample slug. The free solution mobility of D N A fragments is 37x10"9 m 2 A / s [27], whereas in the matrix it drops to between 20 and 3 x10"9 m 2 A / s for fragments from 30 bp to 1000 bp. This causes an increase in concentration from C s a m p / e to Ccapiiiary by the amount C =C <V 3 7 x l ( T 9 (2_9) capillary sample ^sample MDNA where the sample conductivity asampie of sequencing fragments is typically one hundred times lower than the background electrolyte conductivity in the matrix ob g e - This does not however compress the Chapter 2 T h e Principles of Capillary Electrophoresis 12 bands in time, so that if electrokinetic injection is done for ten seconds, one would expect the resulting D N A bands to take ten seconds to cross the detector, plus the time attributable to diffusional broadening. In fact, peak width compression of up to a factor ten has been observed [28] immediately after injection, and a factor of three compression was consistently observed in our work with the M e g a B A C E sequencer, using standard sample purification procedures and resuspension of the sample in d H 2 0 . Temporal sample stacking requires that the high field/low field boundary initially present at the capillary entrance move with the D N A so that D N A arriving later in the injection slows down later, and therefore closer to the leading edge of the injection peak. While it has been shown experimentally that lower sample salt concentration promotes stacking [13], and that adding fast-moving OH" ions after injection can also compress the sample [29], no mechanism by which the boundary moves has been hitherto proposed. Of interest to the present discussion is the amount of D N A injected into the capillary. While attempts were made at direct measurement of the D N A injected into the capillary via spectrophotometric measurement of the eluted sample, the quantities involved were too low to give meaningful results. T h e mass of injected fragments in the following experiments was therefore calculated according to: where crsampie is the sample conductivity (Sieverts*m"1 or (Qm)"1), CQNA in (mol*m 3 ) is the D N A concentration in the sample, MWDNA - 295 g/mol for one nucleotide, and l(t) is the capillary current (Amps), integrated over the injection time t. The mass of injected D N A is proportional to its fraction of all the charge carriers, so injection from sample (2-10) Chapter 2 T h e Principles of Capillary Electrophoresis 13 lower conductivity electrolytes results in larger quantities of injected D N A . Note that in this scheme D N A is treated as a group of individual nucleotides: the lengths of the actual fragments are unimportant in this calculation. Two related formulas are also relevant here. The integral in (2-10) is actually the total charge flowing into the capillary during injection. This can be extended to the total loaded charge over the run where tr is the electrophoresis run time. In order to characterize changes in current, we similarly define the normalized total loaded charge as: where 1(0) is the current at the start of the run. 2.5 Capillary Sequencing for DNA T he details of D N A properties, sample preparation and sequencing protocols are contained in Appendix A . Here we suffice to say that D N A sequencing requires creating a quantity of D N A fragments of a common starting point in the sequence and monotonically increasing length from 20 bases to 1000 bases such that there is enough D N A of each length to be detected (typically 10 8 molecules per size band). E a c h fragment terminates with an A , C , G , or T nucleotide that is labeled with one of four different fluorescent dyes, so sequencing involves separation by size and detection of the end-label emission wavelength. This method, developed by Sanger, (2-11) o (2-12) Chapter 2 T h e Principles of Capillary Electrophoresis 14 Gilbert and Maxam in 1977 [30, 31], initially used four separate lanes on a polyacrylamide slab gel with radio-labeled fragments for detection. Hood et. al. improved this with four-color florescent labeling [32] in 1986, enabling sequencing in one lane per sample. This led to the first generation of semi-automated slab-gel sequencers, such as the Applied Biosystems 370 family. Despite read lengths of over 600 bases per lane, these machines were limited by manual intervention in gel casting, and were limited to low field strengths because of excessive joule heating. Inhomogeneities in the gel also caused lane alignment problems, limiting lane densities and making automated base calling difficult. Capillary electrophoresis for D N A sequencing was introduced in 1990 [33] [34] [35, 36], although technical obstacles delayed the appearance of commercially available array sequencers until 1997. T h e principal motivation was a potential increase in separation speed of an order of magnitude through improved heat dissipation, and superior lane tracking. A less obvious advantage is the design flexibility allowed by a discrete capillary array. T h e cathode end can be arranged to match standard 96 or 384-well reaction plates while the anode and detector regions can have any physical layout the designer desires. Samples can be injected directly from 96 or 384-well reaction plates and matrix replacement can be performed by hydrostatic pumping from the anode. It is also possible to replace sample, matrix and buffer containers so only the capillaries themselves have to be cleaned between runs. This continues to be a notable advantage over lab-on-a-chip electrophoresis systems, where the capillaries and buffer wells are all in one monolithic structure. Chapter 2 T h e Principles of Capillary Electrophoresis 15 COMPUTER [— LOW PASS FILTER MIRROR 555rtm LONG PASS FILTER PMT-BANO PASS FILTER LASER INPUT {488 nm) DICHROIC BEAM SPLITTER OBJECTIVE CAPILLARY ARRAY MIRROR DICHROIC 8EAM SPLITTER Outlet Reservoir HIGH VOLTAGE I POWER SUPPLY p Figure 2 The original confocal array developed by the Mathies group. Reprinted from [37] T h e biggest technical challenges in C E sequencing were multicapillary fluorescence detection and development of suitable separation matrices. T o address the former, Mathies et. al. developed a scanning confocal microscope system [37] [38], shown in Figure 2, which led to the introduction of the M e g a B A C E 96 channel sequencer in 1997. This system scanned a microscope objective across the capillaries which were lined up side by side, while the rest of the optics remain fixed. Although it had to scan 96 capillaries every 1.7 seconds, it could devote full laser power to each capillary. This approach was Chapter 2 T h e Principles of Capillary Electrophoresis 16 later scaled to 384 capillaries in the M e g a B A C E 4000. Dovichi and others [39] concurrently developed a sheath flow approach where upon exiting the capillary, fragments were imaged as they were hydrodynamically focused by matrix flowing past the outlet. The laser was aimed down the line of eluting samples from one end, and the resulting fluorescent spots were diffracted off a grating and onto a C C D array. Different colors produced different positions on the C C D . This system gained flexibility with fluorophores at the expense of reagent consumption and signal strength. While it was proven successful on the 3700, the ABI 3730 that followed, imaged its capillaries from one end directly through the capillary glass. This uses only a thirtieth as much buffer and matrix [9], and provides improved uniformity in the fluorescence signal from one capillary to another. T h e biggest obstacle to developing viable capillary array sequencers was in finding a separation matrix that was selective, electrically stable, replaceable and resistant to E O F . Cross linked polyacrylamide matrices which had worked well in the slab format and could be covalently bonded to the capillary wall to prevent E O F were initially employed. Both sample-related and sample-independent matrix instability [33, 35, 39-41] was reported however. Moderate sample-independent current decline was observed that could be periodically reset by clipping a small portion of the cathode end of the capillary. Bubbles were also observed to form spontaneously near the cathode end of the capillary, particularly at fields over 300 V / c m . This work was well reviewed and expanded by Swerdlow et al. in 1992 [42]. They found that sample-independent current decline stemmed from the formation of a resistive region at the cathode end of the capillary, thought to be due to a change in the relative conductivity of the ions across the matrix/buffer boundary (this is known as the transference number). Figeys et al. likewise used capillary cutting to reveal the axial Chapter 2 The Principles of Capillary Electrophoresis 17 conductivity profile after running for up to 280 minutes [43]. Their results appear to be consistent with a change in relative conductivity of the different ionic species across the matrix/buffer interface coupled with diffusion of the depletion region into the capillary. Changing buffer constituents, particularly adding unpolymerized matrix monomers to the buffer ameliorated these effects [44]. T h e mechanism put forth by Swerdlow et al. [42] for this current stabilization is that the monomers equalize the relative mobility (transference number) of the ionic species across the gel/buffer boundary. Spontaneous bubble formation likewise seems to have been largely mitigated by the switch to non-crosslinked matrices. Figeys [44] did not report bubble formation with such matrices, even with runs of hundreds of minutes at 300 V / c m and notwithstanding the high fields associated with the depletion region. T h e M e g a B A C E adopted linear polyacrylamide ( L P A 2-4% w/v) [45-47] with average molecular weights of ~10 6 Da. E O F is suppressed using a surface treatment [48] [49] which suppresses surface charge and binds the linear polyacrylamide to the capillary wall. ABI introduced its proprietary Performance Optimized Polymer (POP) line of matrices for the 3700, based on poly(dimethylacrylamide) P D M A [50]. T h e P D M A polymer suppresses E O F though a moderate degree of hydrophobicity. This allows the polymer to bind to the capillary wall but keep much of its length off the wall, leading to a so-called "loopy" conformation [51]. P M D A based matrices, therefore, allow ABI to use non-coated capillaries. Both systems used T r i s / T A P S as a running buffer because it was found to produce better quality separations than Tris Borate, the traditional slab-gel buffer. It is thought that the latter may be prone to formations of complexes with residual glycerol from cycle sequencing reactions [45]. Tris and T A P S , respectively a large organic acid and base, in equal concentration only Chapter 2 T h e Principles of Capillary Electrophoresis 18 dissociate about 50% each so the solution also has a comparatively high buffering capacity [52]. The exact content of the commercial matrices is not known, but it is clear that sample independent current stability has been attained through judicious selection of buffer and matrix components. Current decline from large fragments, however, continues to be a concern [53] [12] for both L P A and P D M A based matrices. T h e introduction of the M e g a B A C E and 3700, combined with efforts to automate upstream sample preparation resulted in a dramatic increase in the pace of sequencing for the human genome project. A big factor may have been Celera Genomics' 1998 entry into the "race" to sequence the human genome using 300 of the new 3700s. The scientific significance of Celera's contribution remains the subject of debate [54, 55], but it is clear that it stimulated the uptake of large numbers of sequencing machines by all the major genome centers. From the beginning of the H G P in 1990, to 1998, about 3% of the genome had been sequenced[5, 56], while from 1998 to 2001, the other 97% was completed. It is easy to understand how, in the context of the time, both sequencers were introduced to market in haste. The 3700 experienced up to 30% downtime for various mechanical maladies and the sheath flow detector system consumed large quantities of polymer. The M e g a B A C E was somewhat more reliable but required considerable operator involvement for plate exchanges. Under ideal circumstances, however, the M e g a B A C E was capable of read lengths of up to 800bp in 1998, whereas the 3700 could only manage up to 600bp [9]. It is reasonable to suppose that with development of dilute reaction protocols, the sensitive detector and low matrix usage of the M e g a B A C E might have made it the sequencer of choice early on, and allowed the manufacturer to develop a next generation machine with Chapter 2 The Principles of Capillary Electrophoresis 19 better automation. In the end however, the sequencing community largely rejected the M e g a B A C E for one significant reason. Under real conditions, using D N A samples prepared using E. coli growth protocols, the M e g a B A C E had up to a 20% capillary failure rate. T h e s e failures were characterized by declining capillary current and the delayed onset of peaks at the detector. While the 3700 also displayed the same failure mode [53], the rates were considerably lower.- E a c h read failure represents not only a loss of sequencing time, but a loss of the very expensive cycle sequence reaction, as well as all the upstream sample preparation steps. Combined, these failures represented at least 10% of the cost of sequencing at the time, so the cost of read failure to the human genome project was perhaps as high as three hundred million dollars. This is in addition to the fact that using P D M A based matrix to mitigate the problem forced workers to live with lower average read lengths. While the ABI machines always had superior automation, it is likely that the issue of run failure due to current decline decisively cost the M e g a B A C E its initial lead in sequencing. T h e result is that today, virtually all major genome centers only use ABI sequencers. 2.6 Current Decline and Mitigation Efforts Swerdlow et a/.[42] studied the effect of D N A sequencing sample characteristics on current stability, and explicitly showed that rapid current decline was associated with the injection of a sufficient quantity of fragments longer than 1300bp, and that smaller quantities did not cause the effect to occur. After Swerdlow, further discussion of current decline was limited, although it was addressed in the important pair of papers from the Karger lab which point out that, "Indeed the problem of sample cleanup for the successful operation of C E has not been sufficiently emphasized" [14]. Karger's lab developed a Chapter 2 Th e Principles of Capillary Electrophoresis 20 purification method based on centrifugation through filters, which, while effective, proved too expensive for sequencing centers to consider implementing. In the second paper, they reported that quantities of 8kb M13 D N A added back to sequencing samples after filtration and then de-salted did cause current decline. They also demonstrated that adding salt back to de-salted but template laden sample would prevent the current decline, albeit at the cost of reduced loading and separation efficiency. Other techniques found to prevent current decline include multiple sample injections [53] and resuspending reaction products in template suppression reagent (TSR) such as dilute agarose [57, 58]. While filtering reduces the amount of template without reducing the quantity of short sequencing fragments, adding salt or multiple sample injections is likely to reduce the total quantity of D N A injected, including the template, below the threshold for current decline. Results are shown Appendix B which demonstrate that using Agarose as T S R reduces the total quantity of D N A injected, by reducing the injected template below the threshold for current decline. All these methods have drawbacks however. More stringent cleanup adds cost. Increased ionic strength in the sample reduces the total amount of D N A loaded which may result in inadequate signal strength as processes move toward smaller volumes and lower quantities of sequencing fragments. T S R may further reduce the quantity of loaded sequencing fragments, and also presents viscosity-related liquid handling issues. At present, current decline in the ABI sequencers is controlled through a combination of more dilute reactions with less starting D N A , and use of the fault tolerant P O P - 7 matrix (believed to be a combination of P D M A and L P A which is still self-coating). In the future, more selective matrices will evolve from a better understanding Chapter 2 T h e Principles of Capillary Electrophoresis of the current decline problem; it is hoped that the present work will contribute to that understanding. Chapter 3 Apparatus and Methods to Investigate Current Decline 22 Chapter 3 Apparatus and Methods to Investigate Current Decline Initial experiments on current decline and its relationship to read length degradation were carried out on M e g a B A C E D N A sequencers located at the B C Cancer Agency G e n o m e Sciences Center. While the M e g a B A C E s generated 96 channels of current and fluorescence signal data at once, it was not possible to observe other characteristics of the capillaries while the machine was operating. A custom single capillary instrument was therefore constructed, mimicking the M e g a B A C E as much as possible by using the same capillaries, separation matrix and buffer. This instrument was configured with the detection instrumentation at the cathode end of the capillary, rather than the anode end as in conventional sequencers, as it was known from the literature that the source of current decline was likely to be at or near the cathode. Experiments with the single capillary instrument revealed considerable variability in the injection quantity of highly purified samples. The reason for this variability is unknown, but it made it impossible to get reproducible current decline behaviour with purified samples. It was concluded therefore that extensive experiments on a capillary array machine were also required, so a M e g a B A C E was procured and installed at U B C . In this chapter the M e g a B A C E , the custom-built single capillary instrument, and associated methods are described. All capillary separation devices operate on the same physical principles. A capillary must be positioned between two baths of Chapter 3 Apparatus and Methods to Investigate Current Decline 23 electrolyte, which should be level with each other to prevent siphoning. There must be a high voltage power supply connected to electrodes in each bath so that current can pass through the capillary. There must also be some sort of analyte detection scheme, be it through the capillary wall or as the analytes elute from the end of the capillary. T h e detector needs to be far enough from the cathode to allow enough separation, and near to the anode so that the capillary isn't unnecessarily long. There must also be some reasonably straightforward way of replacing the anode and cathode wells to switch between sample, buffer and matrix, and some system for pumping the matrix and rinse water through the capillary. Finally, there must be a system for heating and stabilizing the capillary temperature so as to prevent secondary structure formation in the D N A or thermal band broadening [22]. In light of the foregoing, it is not surprising that commercial sequencers share many similarities. The differences between machines are mostly in the degree of automation, and layout issues related to the number of capillaries in the machine. Chapter 3 Apparatus and Methods to Investigate Current Decline 24 3.1 The MegaBACE Figure 3 The airbox in the MegaBACE showing the capillary array, anode pressure vessel and cathode array The M e g a B A C E 1000 is the first generation 96 channel D N A sequencer from Molecular Dynamics (Subsequently A m e r s h a m Biosciences and now part of General Electric Healthcare). Figure 3 shows the interior of the M e g a B A C E ' s air box, which is kept closed throughout operation. Use of an air box for heating is more or less mandated by the use of capillary arrays, and ABI's current 3730 machine still uses one, albeit smaller than the M e g a B A C E ' s . O n the left, six bundles of sixteen capillaries are arrayed to match the 96 well plates which are positioned below the air box. A platinum electrode hangs next to each capillary. T h e electrodes are grounded across 100kQ resistors and the resulting voltage drop is used to measure Chapter 3 Apparatus and Methods to Investigate Current Decline 25 current. T h e capillaries are O D 225 um, ID 75um and 60cm long. T h e y are coated with a polyamide resin rendering them highly resistant to breakage. A detector window is etched into the coating 40cm from the cathode end, of each capillary, and each array of sixteen detector windows is held together with a plastic clip. All six of the detector window arrays are brought together in a linear array to be scanned by the confocal microscope. T h e microscope's objective scans the array at -1 .7 scans/sec. Four colour flourescent detection is achieved in the following manner: Flourescent light is routed back through a dichroic mirror to separate it from the laser light, then through another dichroic mirror which divides the four flourescent signals into two pairs of lower and higher frequency. Each beam passes through a scanner which switches between two final filters in phase with the objective scan. Two channels are detected on the outbound scan and two on the inbound scan. In this way the four fluorescent wavelengths can be detected using only two photomultiplier tubes. Note that this is different from the original Mathies' design shown in Figure 2, page 15, where the light is sequentially separated into four channels. At the lower right in Figure 3 is the anode, where each bundle comes together and enters the high pressure chamber from where matrix is pumped from six 1 ml microcenterfuge tubes. T h e entire chamber is at high voltage during operation. The L P A matrix used in the M e g a B A C E is quite viscous, so the M e g a B A C E operates with 1000 psi of matrix injection pressure. O n e modification that the G S C made to the standard sequencing protocol was to replace the microcenterfuge tubes of L P A with running buffer at the anode after injection of the L P A into the capillaries but before sample injection. This was done to save money as tubes of L P A uncontaminated with D N A could be used for three runs rather than one, saving $40.00 per Chapter 3 Apparatus and Methods to Investigate Current Decline 26 96 well plate. This produced a significant effect however: upon replacing the L P A vial with buffer, and without injecting D N A , the capillary current would decline by about 50% over fifteen minutes and remain constant at that value. No equivalent relationship between buffer contents and capillary current was observed at the cathode. This effect, which did not affect sequencing performance, is discussed further in Appendix C.2 . 3.2 The Single Capillary Instrument 3.2.1 Mechanical Design Vessel Figure 4 A front view schematic of the single capillary sequencer. Note the position of the laser Induced fluorescence detector close to the cathode, rather than the anode on the MegaBACE. T h e single capillary instrument we developed is schematically depicted in Figure 4. T h e layout of the machine was influenced by the Chapter 3 Apparatus and Methods to Investigate Current Decline 27 need for clearance below the capillary's ends, and a desire to keep the detector optics compact and on one level. T h e solution was to mount the C E apparatus and detector assembly on a small optical breadboard on 15 cm posts above the main breadboard. This gave enough room under the capillary to position the cathode sample/buffer holder using a lab jack. This layout is essentially the same as the M e g a B A C E , which has the whole optical detector assembly midway up the machine, behind the capillary air box which is above the pneumatically driven anode and cathode exchange mechanisms. In order to focus and align the capillary vertically and horizontally, the entire capillary assembly, anode and cathode caps, main deck and heater plate were mounted on a three-axis stage, while the detector optics were fixed. This design sought to limit the unheated or uninsulated portions of the capillary as much as possible to prevent bubble formation through matrix shrinkage. 26 cm of the 36 cm capillary was taped to an aluminum plate heated on the other side by a kapton heater (Omega). T h e 5cm of capillary at the anode was inside a pressure vessel and insulated from temperature changes and only 5cm at the cathode was exposed to room temperature. This arrangement was stable enough that matrix shrinkage-induced bubbles could be avoided if sample and buffer wells were changed in a timely manner. T h e pressure vessel containing the anode consists of a stainless steel cap into which screws a cylinder containing a microcenterfuge tube which contains the desired reagent: polymer matrix, buffer or rinse water. The cap is plumbed for the high pressure and voltage input lines, the platinum anode electrode, and the capillary pressure fitting. T h e two sections are screwed together (13tpi, 1.25" diameter, factor of safety under maximum pressure is 100) and are sealed with an O-ring. A n Upchurch F*150 steel compression fitting Chapter 3 Apparatus and Methods to Investigate Current Decline 28 surrounding a 1/16" O D , 250um ID P E E K tube is used to seal to the capillary. T h e fitting compresses a ferrule into the P E E K tubing which in turn squeezes the close-fitting capillary. T h e high pressure input line, also P E E K tubing, is attached to the chamber cap in the same way. T h e steel cap is secured with four nylon screws to the main deck of the C E instrument which is made from acrylic. T h e lower half of the pressure chamber is also held in an acrylic cylinder so when the system is assembled, only the capillary's steel pressure fitting and a part of the surrounding cap are exposed at high voltage. Voltage was limited by the proximity of the top of the pressure fitting to the heater plate which caused electrical discharges above 5000 V , the result of a compromise between minimizing the exposed region of capillary and proximity of the cap to the heater plate. A maximum voltage of 5000 V was adequate for these experiments. High pressure was delivered to the anode pressure vessel from a nitrogen cylinder with a high pressure regulator through stainless steel tubing to an exhaust valve and then a high pressure quick connect fitting. A length of 5000 psi P E E K tubing connected the latter to the anode pressure vessel cap. In principle, P E E K tubing could be used right from the regulator, but integrating the three-way exhaust valve to vent the system after filling the capillary was most elegantly accomplished with fixed plumbing. T h e quick release fitting proved valuable in that other devices could be attached to the pressure line in order, for example, to flush complete M e g a B A C E capillary bundles offline. T h e L P A polymer can be pumped into the capillary at a pressure as low as 300 psi, but in order to clear occasional blockages which can form if the capillary is allowed to dry out with polymer inside, it was convenient to have higher pressure available. This instrument could apply up to 1500 psi to the anode pressure chamber. Chapter 3 Apparatus and Methods to Investigate Current Decline 29 T h e cathode end of the capillary ran though the same stainless steel cap and ferrule assembly as the anode, originally built to test the hypothesis that bubbles might re-dissolve by pressurizing the whole capillary. While bubbles ultimately proved to be of secondary importance, the ferrule clamp held the capillary in very good alignment with the detector. Samples and buffers were contained in wells drilled in a rotating acrylic disk mounted on a lab jack. T h e sample holder had 200 uL buffer wells and 25 ul_ sample wells. T h e electric field was supplied by a high voltage Spellman power supply connected to the anode pressure vessel directly. The anode electrode was a length of platinum soldered to the pressure cap and hanging close to the capillary. T h e platinum cathode electrode was connected to the Spellman's ground through a 1 M Q resistor. T h e voltage was measured across that resistor to find the capillary current. Both this signal and the P M T output were acquired by the computer's Labview software though an National lnstruments-6025E A / D card. Chapter 3 Apparatus and Methods to Investigate Current Decline 30 520nm post filter Eyepiece J 480nm prefiIter Capillary PMT w/ Pinhole i Moveable Mirror ichroic Mirror 150mm f.I lens Figure 5. A schematic of the confocal fluorescence detector system. In the actual system, the laser was mounted below the apparatus and the input beam arrived with a series of mirrors. 3.2.2 Fluorescence Detection A schematic of the laser induced fluorescence (LIF) detector is shown in Figure 5. It is based on the design of Mathies et al. which was used in the M e g a B A C E [59]. In this case there is only one fluorescent dye colour, rather than four, and therefore only one filter set and detector. Th e principle of confocal laser induced fluorescence microscopy is to focus the laser beam on the capillary, and then form an image of the resulting fluorescent signal by sending the output of the microscope objective through a dichroic mirror and on to the detector. T h e dichroic mirror, pre and post filters, are chosen to match Chapter 3 Apparatus and Methods to Investigate Current Decline 31 the characteristics of the chosen fluorophor, so the laser light is reflected and fluorescent light transmitted. The present work was done using Sybr Green intercalating dye (Molecular Probes), which is excited near 488 nm and emits at 520 nm, and a Sybr Green filter set (Chroma Inc.). The microscope objective was 10X (Roylin Optics). After passing through the 520 nm post-filter the beam passed through a biconvex lens with a focal length of 150 mm which formed a real image on a pinhole plate in front of the photomultiplier tube (PMT). The pinhole could then be moved in the image plane via a small X - Y stage so that the fluorescent spot induced by the laser fell exactly on the pinhole. A moveable mirror was also mounted in the light box which could be interposed in the beam after the lens, so as to redirect it upward where it was confocal with a 26 mm Plossl eyepiece. This feature proved invaluable in aligning the capillary at the laser beam focus before doing a run. The mirror itself moved on a linear stage actuated by a pneumatic cylinder connected to a manual five-way valve outside the light-box. Optical detection was done with a Hamamatsu HC-120 photomultiplier tube. It was driven through a variable gain circuit as per Hamamatsu's schematic, and the output was filtered at 1 kHz, before going to the A / D card. Initial alignment of the optics required aligning the pinhole so that it was confocal with the fluorescent spot from the objective. Coarse alignment was done by removing the cover of the light box and illuminating the capillary with a bright light so as to make the capillary image visible to the naked eye. O n c e the capillary was in approximately the right position, the light box was closed up and then the fluorescent spot was centered on the pinhole by changing the position of the P M T manually and observing the resultant output signal, which was to be maximized. Sybr Green in water was initially used as a flourophor, but without D N A , the signal intensity was low and subject Chapter 3 Apparatus and Methods to Investigate Current Decline 32 to photobleaching. It was subsequently discovered that moving the capillary so the laser was focused on the polyamide coating produced a strong, consistent fluorescent spot which was easy to align. T h e capillary could then be repositioned so the capillary window was centered over the laser focus, and experiments could commence. 3.2.3 Thermal and Visible Light Cameras Thermal and visible light images were used to observe the movement of ionic concentration boundaries, bubbles and metal particles in the capillary. Thermal images were obtained with a 10.6 um Raytheon Control IR2000AS Silicon Bolometer camera. This unit has a fixed focal length and automatic brightness control. A n IR transparent A M T I R polymer lens of 38 mm focal length (Oriel) was placed in front of the camera as a magnifier, giving a field of view of 25 mm. Images were taken every eight seconds, and the Labview data acquisition program was configured to prompt the user to select the region of the IR image containing the capillary at the beginning of the run. Those regions were then cropped out of subsequent images and stored side by side. This image was saved along with separate files containing current and time data, and P M T detector data. Visible light images were obtained with a C a n o n Elura D V video camera. For observations of bubble evolution it was aimed through the camera port of a Leica binocular microscope, giving a field of view of about 9 mm. The nickel particles (section 5.4.4) were imaged through the eyepiece of the C E instrument's on-board microscope, giving a field of view of about 3 mm. Data acquisition for the thermal and D V cameras used their N T S C video outputs and a NI-1025 IMAQ card (National Instruments). Two cards were used for simultaneous imaging. T h e visible light images were cropped and assembled in the same manner as the thermal images. Chapter 3 Apparatus and Methods to Investigate Current Decline 33 3.2.4 Capillaries, Matrix and Buffer Single capillaries extracted from M e g a B A C E capillary bundles were used so as to closely simulate the M e g a B A C E itself. Unless otherwise noted, all experiments were conducted with 36 cm long capillaries, of 75 Lim diameter, with the detector window 2 c m from the cathode. While ant i -EOF coatings could have been applied to in-house new capillaries, it was believed the commercial capillaries would be more consistent. T h e M e g a B A C E capillary windows were all 5 ± 0.2 mm long, knowledge of which was useful for alignment purposes. Had these capillaries not been adaptable for our purposes, windows would have had to be burnt in raw capillaries with nichrome wire, and then the surface treatment performed, with the attendant risk of breakage during these steps. Fortunately for our purposes, a large number of M e g a B A C E capillary bundles were made available when the G S C retired two M e g a B A C E s so many capillaries were available for cut capillary experiments. T h e choice was made to use matrix and buffer from Amersham Biosciences (Part # US79676), rather than make it from scratch despite uncertainty as to the exact contents. Polymerization of small batches of L P A in-house according to [45] gave highly variable viscosity despite identical starting conditions from batch to batch. T h e Amersham L P A by contrast was very consistent. The buffer concentration in the matrix was believed to be 50 mmol/L of each of Tris and T A P S ) respectively [60]. What is not known is the type and concentration of neutral denaturant (such as urea) which is normally present in these reagents according to the literature, or what other ions were present in the L P A from the polymerization. This topic is taken up again in C.2 . Chapter 3 Apparatus and Methods to Investigate Current Decline 34 Tris and T A P S refer, respectively, to the weak base Tris(hydroxymethyl)aminomethane) and the weak acid [(2-Hydroxy-1,1 -bis (hydroxymethyl)ethyl)amino]-1-propanesulfonic acid. T h e s e buffer components were originally introduced by the Karger lab, who developed L P A for use in sequencing [45]. T r i s / T A P S was found to produce better sequence data than the traditional biological buffer TrisBorate, possibly because the former is less likely to cause band broadening by interacting with reagents left over from D N A purification. Tris and T A P S are part of a larger class of "Good's buffers" which exhibit this benign behaviour [52], and which have the further advantage that they are only 50% dissociated in equilibrium and so have high buffering capacity. 3.3 Samples and Methods 3.3.1 MegaBACE Samples Detailed explanations of E. coli based D N A amplification, cell lysis, the cycle sequencing reaction and sample cleanup are given in Appendix A . 5 . T h e s e protocols are used by the G S C preparation and in the Marziali lab. Briefly, a D N A insert from the Mammalian gene collection (MGC-10790) was ligated into a circular M-13 vector (a piece of D N A capable of reproducing inside cells) was grown in E. coli. T h e cells were then lysed and the insert D N A isolated. T h e cycle sequencing reaction was then performed to produce fluorescently labeled single stranded copies of the original template of monotonically increasing size. Th e D N A was then purified out and the sample dried down. Before injection on the M e g a B A C E , samples were resuspended in 20 uL of d H 2 0 , and briefly vortexed and centerfuged. T h e same sample preparation protocols were used for bubble propagation experiments conducted in the Marziali lab as well as in the agarose resuspension experiments described in Appendix B.1. In the Chapter 3 Apparatus and Methods to Investigate Current Decline 35 latter experiments, the samples were pooled and realiquoted several times to ensure consistency. Sizing these samples in agarose showed them to consist of 20-1000 bp single stranded sequencing fragments as well as 7.5 kb M-13 template D N A and some quantity of unseparated long fragments, presumably E. coli genomic D N A left over from colony growth. E. coli's genome is 3 Mb, so these genomic fragments may be in the kilobase to megabase range. In the experiments on bubble propagation, the control consisted of M e g a B A C E 4-Color Sequencing Standard (Amersham Biosciences (US79678), which agarose sizing showed to be free of large fragments. Plates with no D N A , consisting simply of M e g a B A C E running buffer, were also used as controls. 3.3.2 MegaBACE Experimental Parameters M e g a B A C E runs were performed in the following manner, except where noted. L P A was injected at 1000psi for 2 minutes with a buffer plate (100 uL of buffer per well) at the cathode. T h e L P A -containing microcentrifuge tubes were then replaced with tubes containing 2 ml of buffer and a 15 minute prerun performed at 9000V. T h e buffer plate was then removed, and the cathode array rinsed in d H 2 0 . Samples resuspended in 20 uL d H 2 0 were then injected for 10 s at 3 kV and the cathode array rinsed again. T h e original buffer plate was restored to the cathode and the electrophoresis ran for 240 minutes at 6 kV (100V/cm in the 60 cm capillaries). Typical capillary current at the start of the run was 4 uA. 3.3.3 Electropherogram Analysis Electropherograms from sequencers such as the M e g a B A C E are evaluated in terms of read length, which represents the number of Chapter 3 Apparatus and Methods to Investigate Current Decline 36 bases that can be identified with a given level of confidence. Processing of the fourfluorecence data signals is shown in Figure 6. T h e basecalling algorithm accepted as standard in most sequencing facilities is called the Phred algorithm [1, 61]. T h e algorithm accounts for the differences in mobility shifting of the four colours because of differential drag from the different fluorophors and fitting a Gauss ian to each peak based on the expected peak frequency. T h e "quality" of each base is given by Q = -10 log10(Pe), where P e is the probability that the base is incorrectly scored. PhredIO bases represent a 90% confidence that the base has been correctly identified and Phred20, represents a 99% confidence value. The read length is the number of bases above a desired Phred value. A generally accepted minimum is Phred20, although some assembly algorithms use the lower quality parts of the sequence to aid construction of the contiguous "tiling paths" that make up the genome sequence. Chapter 3 Apparatus and Methods to Investigate Current Decline 37 m wrfH03 SbTOTB RunC2 o H03 welH03 2004-01 05 Run02 1288 120 1 30 140 150 160 1 70 180 CGGAGCGTGTTCCGGTGTGTTGTCTGATAH5MTTAGTCTTTACACTTT&GGCAAAACAGGCTTCATAC (b) 2900 3000 3100 3200 Time (scan number) 3300 Figure 6 (a) Raw MegaBACE electropherogram fluorescence data, and (b) basecalled with the Phred algorithm. The latter has been normalized, curve-fit and mobility shifted. A typical example of a successful sequencing run from the M e g a B A C E is shown in Figure 7. Beyond about 700 bp, the peaks become diffusion-broadened enough that base quality drops below the Phred20 cutoff. T h e M e g a B A C E software as shipped did not allow separate files of raw current and P M T signal data to be extracted in order to do detailed analysis. T h e software's exportable data for basecalling had the initial 20 minutes of pre-DNA-arrival data truncated. Proprietary object files were fortunately obtained from Amersham Biosciences which, in conjunction with a Perl script, allowed extraction of raw current and P M T signal strength data. Chapter 3 Apparatus and Methods to Investigate Current Decline 38 70 60 50 8 40 w T 3 0) h 30 20 0 X O « X X X X*SKXX38aaKX X X XX&3E$£ X X xx X X X * X X X X X X X X X X X X X X X £ X X X . > ^ > < X » 0 $ C < X . X X 200 400 600 Peak Number 800 1000 Figure 7 Data from a typical successful electropherogram (Phred20 = 704) showing the tailing off of peak quality as the reads become diffusion limited. 3.3.4 Single Capillary Instrument Samples T h e challenge with the single capillary instrument was finding a sample capable of producing current decline in a reproducible manner. Cycle sequencing products produced highly variable results. This is true in the M e g a B A C E as well: Figure 8, page 44, shows a large range of current decline and Table 3, page 138, shows a factor of two range in fluorescent signal strength from identically prepared samples. A characteristic of ethanol-precipitated cycle sequence products is relatively low concentrations of D N A with extremely low background electrolyte concentrations. Purification in 96 well plates includes hard-Chapter 3 Apparatus and Methods to Investigate Current Decline 39 to-reproduce steps such as manually tapping the plates against the bench, and variations in time in the introduction of different reagents A s a result, there may be considerable variability in samples across individual plates and from plate to plate [13]. Sample Conductivity L i S / c m [DNA] ug/ml Injection Coefficient ug/Q 20 to > 50kb Cycle Sequence Products 25 10 148 0.5-50kb B A C Fragments 300 130 160 48kb X D N A 700 500 265 500 to 23 kbp X -Hind III Ladder 700 500 265 500bp P C R Fragments 15 9 250 Table 1 Data for concentration and solution conductivity for different DNA samples. The injection coefficient was calculated from equation (2-10) M ° N A = VMACDNAMWDNA Qinj ^sample In the search for injection consistency, various other D N A fragments were evaluated. Conductivity and concentration data is shown in Table 1. Two polydisperse samples of high buffer conductivity and D N A concentration were found to cause reproducible current decline. These were 0.5 to 30 kb bacterial artificial chromosome (BAC) digest fragments from the G S C and 0.5 kb to 25 kb X Hind III restriction digest (New England Biolabs). The success of these samples then led to the use of undigested X D N A (New England Biolabs N3011L) for the experiments reported here. At 48 kb, this double stranded, linear phage D N A represents a compromise between ~8kb template and Chapter 3 Apparatus and Methods to Investigate Current Decline 40 longer double stranded genomic D N A fragments found in actual sequencing samples and which are believed to be the source of current decline. This commercial product was found to be very consistent and stable, and reproducible results were obtained over a period of three years using samples from three separate lots. In these experiments, 20 uL aliquots of 500 ug/mL X D N A with 5 uL of 5x Sybr Green intercalating dye were used throughout, although X D N A produced current decline with or without Sybr Green. O n e experimental result which lends weight to the use of X D N A as a model fragment was that the time evolution of current decline was found to be similar for all of the fragments tested. In other words, the high concentration, high conductivity X and X Hind III samples exhibited the same behaviour as low concentration, low conductivity cycle sequencing products. This is of significance as it was not initially known whether current decline was an intrinsic property of the enhanced sample stacking associated with the low conductivity of the sequencing samples. T h e similarity in behaviour of the low and high conductivity samples suggests that the current decline is independent of the degree of sample stacking. 3.3.5 Single Capillary Instrument Parameters A s noted, 36 cm long, 75 um diameter capillaries cut from M e g a B A C E bundles were used for all experiments. L P A was injected for 60 s at 500 psi. Where noted, a 15 minute prerun was performed with 1x buffer at the anode rather than L P A . This reduced the starting current from 8-9 uA to 4-5 uA at 5000 V . The temperature of the heater plate was 5 5 ° C and both injection and runs were performed at 5000 V . For runs other than threshold experiments, the injection time was 20 s. T h e reduced length of the capillary, higher injection voltage, Chapter 3 Apparatus and Methods to Investigate Current Decline 41 heater temperature and longer injection time were all designed to promote current decline or exacerbate any effects such as spontaneous bubble formation which might occur. 5000 V was also the maximum operating voltage of the machines. 3.3.6 Cut Capillary and Thermal Image Analysis T he conductivity distribution in single capillaries was determined by the method of successive cutting and resistance measurement [43] [62]. First, one centimeter of capillary at the anode end was cut off to remove any void caused by matrix shrinkage as the capillary was removed from the heater. T h e capillary's resistance was then measured by placing it across two buffer baths at 400 V and measuring the resulting current. Each measurement lasted about three seconds, minimizing changes in the ion distribution profile in the capillary. T h e measurement was repeated with successive removals of Ax = 1 mm segments from the cathode end of the capillary. O n c e past the region where the resistance was observed to change rapidly, cut segments were increased to Ax = 10 mm. This approach was found to be fast, have good resolution and be much more accurate than pre-cutting the capillary into segments and measuring each individually. T h e conductivity of the n t h segment of capillary was found from (3-1) where A is the capillary area (m 2), V and l n are the capillary voltage and current respectively: (j(n\ = — \ T where 7? = — . ( 3 _ 1 ) A(Rn+,-Rn) In Capillaries were cut by pushing the edge of a glass slide onto the capillary. (N.B. The slides were prone to shattering; for safety, readily available ceramic cutters should be used in future) Cuts were measured against lines marked on the lab bench, with an estimated error of about 0.25 mm. T h e length of the capillary was measured Chapter 3 Apparatus and Methods to Investigate Current Decline 42 before and after the series of 1 mm cuts, and again after the 10 mm cuts and then the average spacing of each was calculated based on the number of measurements taken. Thus the uncertainties in boundary positions are ± 0 . 5 m m . A s noted, thermal images were assembled by placing cropped images of the capillary side by side to show the temporal evolution of thermal fluctuations. After each run, the average brightness across each individual capillary image was calculated, and the edge(s) of the hot region boundary(ies) were found by comparing the image to a threshold value. A complicating factor was that current decline causes overall cooling, changing the threshold value for the depletion boundary in the image. This was only significant for the longest depleted buffer runs, such as Figure 15(b) but in those cases, the image contrast was adjusted across the time axis so as make the image brightness even. For the visual images, positions of bubbles and nickel particles were determined manually, using a Matlab script. O n e data point was obtained for each image (every eight seconds) and matrices of these data were saved with the current and run time for each data point. Position and current data were then fitted using Matlab (The Mathworks) and Microsoft Excel , as described further in section 4.4.2. Chapter 4 Experiment Chapter 4 Experiment 43 The experiments presented in this chapter constitute a systematic investigation of the mechanism underlying observations of read length degradation with associated current decline. T h e first goal of this investigation was to establish the relationship between read length and current decline. Having established that current decline directly affects read length, the next objective was to investigate the source of the current decline. The formation of gas bubbles in the capillaries was explored as a possible source and was largely discounted, leaving inhomogeneity in matrix conductivity as the most likely mechanism for current variation. Conductivity profiles of affected capillaries were examined, leading to the discovery of regions of ionic depletion. Further investigation revealed that depletion region formation is linked to propagation velocities of the regions' boundaries, leading to a highly non-linear relationship between quantity of contaminant D N A present and the formation of the depletion region. Experiments were also performed demonstrating that suppression of long contaminant fragments by sample resuspension in agarose improves the success rate of D N A sequencing. 4.1 Relationship between read failure and capillary current decline. In collaboration with the G e n o m e Sciences Center, the correlation between read length and integrated current throughout the run (total loaded charge) was measured for D N A sequencing samples prepared according to section 3.3.1. The samples were resuspended in d H 2 0 , injected for 10 seconds at 3 kV, and run for 240 minutes at 6 kV. Figure 8(a) shows that there are many shortened reads in this sample set, and that read length increases with increasing total loaded Chapter 4 Experiment 44 charge (TLC) until 700-800bp at which point read length is diffusion limited [63]. 120 <fl 0) <n ro CD TD JD " r o o ro c (D O i _ <D 0_ o CM A TD <D i JZ 0_ 100 0 20 40 60 Total Loaded Charge (mC) 0 20 40 60 Total Loaded Charge (mC) Figure 8 (a) Read length vs total loaded charge for samples resuspended in dH20. Each "x" is one capillary - approximately 200 capillaries are represented, (b) The same data shown as percentage of all called bases with Phred quality values > 20 vs. total loaded charge (TLC) after a 4h run. Each (x) represents one capillary and (•) are mean values for TLC binned into 2 mC increments. Figure 8 (b) shows the same data as Figure 8(a) but is presented as read quality vs. total loaded charge. Read quality is expressed as the number of bases called with Phred (confidence) values > 20 as a percentage of all called bases. Runs with TLC < 15 mC, show either poor basecalling of very broad, late-arriving peaks, or spurious basecalls where no real peaks are present. Between 15 and 40 mC, the number of Phred>20 bases is directly proportional, and nearly Chapter 4 Experiment 45 equal, to the number of bases passing the detector. In this range, reduced read lengths resulting from low electrophoresis current are not associated with poor base quality, but simply fewer fragment bands arriving at the detector. Runs with TLC > 40mC are resolution limited above 700 Phred>20 bases. These runs, like the run shown in Figure 7, have a tail of lower quality bases beyond 700bp which is why the percentage of good reads declines despite the actual Phred20 read length being very good. We conclude that decreasing current during electrophoresis is directly responsible for poor read lengths by decreasing the number of DNA fragment bands arriving at the detector, but that detrimental effects of current decline do not include direct degradation of the analyte band quality. Virtually all called bases in runs with TLC between 15 and 40 mC have scores of Phred20 or higher, indicating that lower current reduces the number of fragment bands passing the detector, but does not significantly decrease the quality of those bands. This is consistent with the source of current decline being upstream of, i.e. nearer the cathode than, the sequencing fragments. 4.2 Bubbles 4.2.1 The Contribution of Bubbles to Current Decline As discussed in section 2.5, spontaneous bubble nucleation seems to have been mitigated by sequencing through use of non cross-linked matrices and lower fields [43] [10]. Anecdotal evidence for bubbles in commercial capillary array machines has been reported more recently however. In particular, the MegaBACE showed current variability on the timescale of seconds (see Figure 46 (b)), consistent with bubble behaviour observed in our single capillary instrument and reported by Swerdlow [42]. We, therefore, undertook to find out if bubbles were to be found in MegaBACE capillaries, whether they Chapter 4 Experiment 46 were, in fact, spontaneously nucleating, how they might otherwise appear, and how they might propagate. In order to observe bubble effects in the M e g a B A C E , four plates of samples made according to Section 3.3.1, were injected at 3000 V for 10 s and run at 6000V for 240 minutes in the M e g a B A C E in the Marziali Lab. Control plates of Amersham D N A size standard and DNA-free running buffer were also injected and run in the same manner. It should be emphasized that the sequencing samples contain sequencing fragments and long D N A fragments, whereas the size standard contains sequencing fragments but no long contaminant D N A . After each run, the air box door was opened, and with both ends of the capillary still submerged in buffer, the capillaries were cooled from 4 0 ° C to room temperature in less than a minute. E a c h sixteen-capillary bundle was then removed for inspection. Bubble lengths were estimated by visual comparison to a ruler under a binocular microscope. A variety of bubbles were observed, including unbroken bubbles of 5 to 70 mm length, "bubble trains" of one or two capillary diameter bubbles spaced a few diameters apart over up to 100mm, and single scattered bubbles at various points in the capillary. For the purposes of this analysis, however, only the presence or absence of bubbles was noted. Chapter 4 Experiment 47 80 70 J 60 50 Z. 40 E 30 20 10 Total Loaded Charge in Capillaries With and Without Bubbles • Sequence Fragments, No Bubbles 0 Sequence Framents with Bubbles s Buffer Only, No Bubbles s s i z e Standard, No Bubbles 10 15 20 25 • 30 35 Total Loaded Charge (milli-Coulombs) 40 45 50 Figure 9: Total loaded charge of capillaries with and without bubbles. See text below for details Figure 9 shows a histogram of the capillaries binned by total loaded charge. The mean TLC for the size standard control was 42mC and 43 mC for the buffer-only control. None of the capillaries in either of the two control plates showed any post-run bubbles. Capillaries with sequencing fragments (380 working capillaries total) were divided into those which contained bubbles and those that did not. As 97% of the buffer control samples showed a TLC of 40mC and above we chose this as a figure of "normal" TLC and values below that represent "reduced" TLC For plates containing sequencing samples - the black and striped bars in Figure 9 - 51% of the runs showed normal loaded charge, while 22% showed reduced TLC and bubble formation, and 26% showed reduced TLC without bubble formation. Clearly, there is a process unrelated to bubble formation that is also capable of Chapter 4 Experiment 48 reducing the total loaded charge. This process may furthermore be the dominant source of current decline even for the capillaries containing bubbles. Experiments with artificially introduced bubbles indicate that the bubbles alone are probably not sufficient to produce the observed current decline. This topic is taken up again in Appendix C . 4.2.2 Bubble Formation and Growth Though it was expected that heat dissipation and thermal gradients in the capillaries might allow bubbles to grow or migrate, it remained unclear whether these bubbles formed spontaneously, or were externally introduced. This question was addressed with the single capillary instrument. With the capillary positioned so the cathode end could be observed through the flat wall of a 100uL square well cut from a 384 well polystyrene culture plate, the state of the capillary entrance could be observed before, during and after sample injection. X D N A samples, as per section 3.3.4, were injected and run for periods from 5 to 120 minutes, and the capillary was afterward removed for inspection under the microscope. In thirty-nine consecutive runs, if no bubbles were observed immediately before injection of long D N A fragments, no bubbles were observed after injection or at the end of the runs. In the absence of spontaneous bubble formation, bubbles must form while the capillary entrance is exposed to air, and this was indeed found to occur. Bubbles could be reliably introduced by allowing the capillary to cool with the cathode exposed. The matrix would shrink, forming a meniscus at the cathode, and a bubble would then form when the cathode was returned to buffer. Critically, such a thermal fluctuation with exposed capillaries was found to occur in the M e g a B A C E during normal cathode plate exchanges. Thermocouple measurements at the M e g a B A C E ' s cathode plate holder revealed that Chapter 4 Experiment 49 through the matrix injection and pre-run stage, with all machine doors closed, the temperature in the cathode plate holder rose to 2 4 ° C as a result of heat transfer from the air box immediately above the cathode plate which circulates air around the capillaries at 4 0 ° C . Upon lowering the cathode plate and opening the drawer to exchange the buffer and sample plates, the air around the exposed capillary array dropped back to room temperature within ten seconds. 22mm of each capillary is exposed to this temperature change. Based on a measured coefficient of thermal expansion for the matrix (see Appendix D.2), it was calculated that the matrix would shrink by at least 40 um, enough to form a bubble half a capillary diameter in size. Bubbles of such a size were observed to be capable of expansion during sample injection in the single capillary instrument. It is clear from the these results that local cooling is the most likely mechanism by which bubbles form in sequencers, and could therefore be mitigated through improved temperature control. A s current decline is shown to occur in the absence of bubbles, we conclude that a second effect, unrelated to the presence of bubbles, is the principal cause of current decline. Further analysis of bubble behaviour, particularly the relationship of bubbles to ionic depletion regions and the effect of bubbles on current is presented in Appendix C . 4.3 lon Distribution during Current Decline 4.3.1 Formation of a Depletion Region In the absence of bubbles, current decline was reliably produced through injection of sufficient quantities of A, D N A . Figure 10 shows cumulative resistance and local conductivity profiles obtained by Chapter 4 Experiment 50 the capillary cutting method introduced in section 3.3.6, for four representative capillaries: one control with no D N A injected and three with X D N A run for the times indicated. Approximately 25ng of X D N A was injected in each case. The conductivity profiles indicate that the presence of the X D N A caused the formation of an expanding region of ionic depletion which locally decreased the conductivity of the capillary. This local decrease in conductivity is an excellent candidate cause of the current decrease observed during runs. A striking feature of these plots is the abruptness of the conductivity boundaries, and the low conductivity of the depletion region. For clarity, we refer to the part of the capillary between the cathode (injection end) and the depletion region as the "cathode region", and the remainder of the capillary between the depletion region and the anode as the "anode region". Capillaries cut after varying run times showed the leading and trailing edge of the depletion region (anode and cathode boundary respectively) moving into the capillary with the leading edge moving faster, causing the depletion region to expand. Though the width of the depletion region increased with time during electrophoresis, there was no observed correlation between the length of the run and the actual conductivity value in each region. In other words, variations in conductivity in the background or depletion regions appeared to arise from properties of individual capillaries and did not evolve in time. Only the relative sizes of the different regions changed. Chapter 4 Experiment 51 16r D 1 £ 8 cd ' u i a: 4 . Conductivity No DNA, 20 Min Run Resistance 10 15 20 25 30 35 10 15 20 25 30 35 16r n1000 16r 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Distance to Cathode (cm) Distance to Cathode (cm) Figure 10 Local conductivity (dashed line) and capillary resistance (solid line) profiles for four cut capillaries. The capillary resistance is the electrical resistance of the remaining capillary, and therefore must decrease as the capillary is cut from the cathode end, and should go to zero at 36 cm. Conductivity is found from making a least-squares fit to each straight segment of the resistance and using that slope as AR/Ax in equation 3. 25 ng of A, DNA was injected and run for the times indicated. T h e resolution of the capillary cutting method was 1 mm and transitions at each boundary of every run were abrupt enough that the change in slope between two straight regions could be localized to one data point. This indicates that the boundaries are self sharpening: the boundary.propagation mechanism works against diffusion. A Gauss ian peak widens according to [64] Chapter 4 Experiment 52 FWHM2 =161n(2)Df (4-1) Given a diffusion constant of D~5x10" 1 0 m2s"1 for the background electrolyte ions, an infinitely sharp transition would be expected to spread to ~3 mm wide by 30 minutes and -4 .5 mm after an hour. Instead, sharp boundaries of less than 1mm in width were found for runs up to 320 minutes. There are of course differences between measuring capillary resistance while the capillary is running at high voltage and measuring resistance using a lower voltage while cutting it up. In the former case the capillary is warmer from both internal joule heating and the instrument heater, so the capillary resistance is lower. A s a test of the validity of the measured conductivity values, the final experimentally measured resistance could be reconstructed by integrating the measured conductivity over the length of the capillary using the conductivity values found by capillary cutting: where cb is the cathode boundary of the depletion region and ab is the anode boundary. A is the capillary cross-sectional area and Tc is a correction factor for temperature-induced conductivity change. The current was experimentally found to rise 30% as the heater raised the central 25cm of capillary from 2 0 ° C to 5 5 ° C so the value of Tc was set at 1.3. Figure 11 shows the expected final currents from (4-2) (immediately before removal of the capillary), compared to an experimentally observed temporal current profile which is typical of these experiments. The calculated and measured values were indeed found to be in close agreement for runs from five to 320 minutes in length. Likewise the initial current of each run could be correctly inferred by extrapolating the anode-side conductivity back to the full R final dx anode (4-2) Chapter 4 Experiment 53 length of the capillary (not shown). Clearly, in these capillaries the formation of the depletion region is the source of the current decline. 5.00, y 4.50 ~ 0.00 H i r- 1 ; i - i 1 1 0 50 100 150 200 250 300 350 Time (min) Figure 11 Current at the end of runs of varying duration (A) inferred from ionic concentration profiles for 12 capillaries. The current plot is a continuous 320-minute run on a single capillary. 4.3.2 A Threshold for Current Decline T o establish the relationship between quantity of injected D N A and depletion region formation, X D N A and 500 bp control samples generated by P C R (see section 3.3.4) were injected for periods of five to twenty seconds at 5000 V , and run for five minutes at 5000 V . T h e results, shown in Figure 12 display a striking threshold in the onset of current decline with the injection of more than approximately 10 ng of X D N A . Below this value, current decline was not observed, and no quantity of 500 bp control D N A caused current decline. Current decline was also not observed when no D N A was injected, save Chapter 4 Experiment 54 specific circumstances such as replacing L P A with buffer at the anode, as described in Appendix C.2 1.15 1.1 1.05 TO O T 3 -a 1 ra o _ i ro 0.95f o r— "S 0.9 N " r o § 0.85 o 0.8 0.75 0 ..4...." ± + + .' + • . + • + 10 15 20 DNA Injected (ng) 25 30 Figure 12 Total loaded charge vs. quantity of injected DNA over a five minute run. The charge in each run was normalized to its initial current value to correct for variability in capillary resistance. For X DNA (•) the current remains stable up to 10 ng injected DNA, but above this threshold the current begins to fall. 500 bp PCR fragments (+) do not cause current decline at any quantity tested. (• - on the y-axis) 18 runs where no DNA was injected show no current decline. Dashed lines represent mean values for the X DNA above and below the threshold and for the 500 bp control fragments. 4.4 Temporal Evolution of Ion Depletion Boundaries. While cutting the capillaries provided excellent spatial data on the depletion region, thermal imaging made it possible to observe the Chapter 4 Experiment 55 depletion region evolving in time. A s a nondestructive technique, it also allowed repetitive observations with the same capillary, where cutting required a new capillary for each observation. It was initially hypothesized that the temperature change itself might cause boundary propagation. It is shown in section 5.4 that this is unlikely to be the case. Here we discuss only the observed movement of the region of elevated temperature. A discussion of temperature measurement techniques is found in Appendix E , and Figure 49 shows an individual image of the capillary with a region of elevated temperature. T o produce Figure 13 below, multiple images of the capillary collected at eight second intervals were cropped, aligned and joined, as explained in section 3.2.3, forming a composite image of the temporal evolution of the thermal profile. Concurrently recording the fluorescent signal allowed determination of the location of the D N A with respect to the elevated temperature region. Chapter 4 Experiment 56 1 201 Distance from Cathode 3 tn o cn Anode Boundary \ < Cathode Boundary 0 5 10 15 20 25 0 5 10 15 20 25 Time (min) Figure 13 (Top) A series of infrared images of the capillary taken eight seconds apart and displayed side by side. The warmer (brighter) region (initially elevated by about 7°C) corresponding to the depletion region can clearly be seen. The horizontal dotted line corresponds to the position of the fluorescence detector along the capillary. The vertical dotted line represents the point in time the fluorescence peak appeared on the detector. (Bottom) The fluorescence signal acquired simultaneously with the infrared images. The DNA peak appears as the cathode boundary crosses the fluorescent detector's position in the thermal image. 4.4.1 Cathode Boundary and DNA Movement Figure 13 shows a series of thermal images of the capillary over time, displayed side by side. The region of elevated temperature in the Chapter 4 Experiment 57 capillary associated with increased Joule heating in the ionic depletion region is clearly visible. In nineteen runs, (four with D N A , and the rest with depleted cathode buffer as in section 4.4.2) the capillary was cut up after being imaged with the thermal camera. In all of these cases, the position of the ionic depletion region found by capillary cutting was the same as seen in the last thermal images, given allowances for thermal shrinkage as the capillary was removed for cutting. T h e fluorescence detector was also used with thermal imaging to determine the location of the X D N A within the conductivity profile. T h e X D N A was consistently found to be at the cathode-side depletion region boundary, also shown in Figure 13. In some cases a small fluorescence peak was observed at the anode-side depletion region boundary, but no signal was observed in the depletion region. W e conclude therefore that the cathode boundary propagates with the D N A . 4.4.2 Boundary velocity and its relation to depletion region depth. A s a first step in understanding the temporal evolution of the depletion region, we investigated the role that the depletion depth plays in this region's motion. In particular, we investigated the relationship between boundary velocity and depletion region depth. Since boundary velocity evolves with time, for the purposes of this comparison, boundary motion is characterized by the dependence of the velocity on the capillary current. In the simplest model, we assume the boundary propagation rate is expected to be linear with current and assign it a mobility //. It should be noted that this, for now, is simply a useful characterization of the motion and is not intended to describe an Chapter 4 Experiment 58 underlying mechanism. For a capilary with a local conductivity cr, the boundary velocity is dx _ /jl(t) dt oA This can be integrated to (4-3) x(t) = ^-Jl(r)dTx(t)^Q{t) + X o (4-4) crA * oA The boundary propagation is then characterized by the coefficient Ci which can be found by a least squares fit to the data x{t)=ClQ{t)+C2 (4_5) where C, = — , C 2 = x0 is an offset related to the camera position, oA and Q(t) is the total loaded charge. Ci is expressed in m/C. 10 15 Time (min) Figure 14 Fits (in white) to the first five minutes of anode and cathode boundary data (in black) using x(t) = dQ(t)+C2. The divergence Chapter 4 Experiment 59 of the cathode boundary from linearity is taken up in detail in section 5.3. This model is a good fit to the anode boundary, but a relatively poor fit to the cathode boundary. Figure 14 shows equation (4-5) fitted to the first five minutes of anode and cathode boundary data. T h e distance traveled by the cathode boundary is clearly not linear with total loaded charge; its mobility must have some field dependence. The latter is taken up in greater detail in section 5.3. In contrast, the anode boundary propagation distance is close to linear with charge. Eleven fits to X DNA-induced anode boundaries gave x(t) oc Q(t)a97±-15. Propagation of the DNA-induced anode-side boundaries varied from 5.4 to 11 m/C for normal matrix, and 10 to 21 m/C when the matrix was depleted by running the anode in buffer (see section 3.3.5). T h e variation was greatest from capillary to capillary, with individual capillaries exhibiting relatively constant propagation rates over multiple runs. Cut capillary measurements showed that injection of X D N A produced very low depletion region conductivities, on the order of 2-5% of the initial conductivity. In order to understand the relationship between depletion region depth and boundary propagation rate, different degrees of depletion were needed. This was achieved by running the capillary with normal L P A in the capillary and anode, but diluted cathode buffers and no D N A . With buffers diluted by at least 50x, a moving boundary was visible with the infrared camera. Data was obtained for 1/50x and 1/1 OOx T r i s / T A P S buffer, and d H 2 0 . T h e s e capillaries were also cut up to find the actual conductivity profile. Representative examples are shown in Figure 15. Chapter 4 Experiment 60 Like the D N A induced anode boundaries, propagation rates are linear with charge. Thirteen such runs with run times of 5 to 25 minutes gave a mean exponent of x(t) <x Q(t)agg±-3. o = 1030/112 jiS/cm o = 1126/212 M-S/cm 0 5 10 15 0 5 10 15 20 25 30 Time (min) Time (min) Figure 15 Two examples of ionic depletion boundaries propagating from a low conductivity cathode with no DNA present, (a) The cathode well has dH20 and the boundary propagates at 3.5 m/C and (b) the well has 0.02x Tris/TAPS buffer and the boundary propagates at 1.8m/C. Figure 16 shows the relationship between the anode boundary propagation rate and depth of various depletion regions. T h e propagation rate of X D N A in the absence of current decline is also shown. The only anode-side boundaries which move faster than the X Chapter 4 Experiment 61 DNA are at the front of deep depletion regions, beyond anything achievable by running depleted buffers at the cathode. 14 o E, 12 <D CO * 10 c o ro ra ° o ra TD C i - 4 CD (1) 8 2 < 0 A A A A Typical X D N A Mobility, • Depleted Buffer @ Cathode A /„ D N A "0 50 100 150 200 250 300 350 Depletion Region Conductivity (uS/cm) 400 Figure 16 Measured propagation rates for boundaries of different depletion depths. The background conductivity in each case is 1100 uS/cm. As an extension of the discovery of a threshold for DNA injection to cause current decline, thermal imaging was used to investigate the relationship between boundary propagation and the amount of DNA injected. Eighteen X DNA aliquots were injected for varying times using the same capillary, and the rate of anode boundary propagation recorded. The results are shown in Figure 17. As in Figure 12, the threshold for the onset of depletion is between 10 and 2 0 ng of DNA, but once established, the anode boundary propagation rate is constant. Chapter 4 Experiment 62 10 20 30 40 50 60 70 80 Injected X, DNA (ng) Figure 17 Rate of anode-side boundary propagation vs. quantity of injected DNA. Beyond the threshold for depletion region formation, the anode-side boundary moves at a constant rate. All runs were approximately five minutes. 4.5 A Mechanism for Current Decline. Figure 16 suggests a mechanism for current decline in the presence of large fragments. Even if any quantity of D N A may be capable of locally depleting the background carriers, if the depletion is not deep enough, the D N A moves faster than any induced anode-side boundary so the depletion region cannot form. The expanding depletion region can only form if there is sufficient depletion of the background electrolyte so that the anode-side boundary takes off and runs away from the D N A . Figure 17 suggests that the sufficiently fast anode boundary propagation may only occur when depletion region Chapter 4 Experiment 63 reaches some limit of "total" depletion. That is why adding more X D N A does not cause the anode boundary to propagate faster. A notable property of this mechanism is that the long D N A fragments do not prevent the movement of small ions by mechanically plugging the capillary, nor by virtue of being a principal current carrier with very low mobility. Nor is the D N A observed to precipitate in the capillary [13]. Rather, the long fragments propagate with their usual mobility, but current decline occurs because of the runaway anode-side boundary, the propagation of which is independent of, though driven by, the long D N A fragments. Chapter 5 Analysis of Boundary Propagation 64 Chapter 5 Analysis of Boundary Propagation W e have shown in the previous chapter that current decline is caused by the D N A forming a depletion region which, having reached sufficient depth, is able to expand because the anode-side boundary starts to propagate faster than the D N A and cathode-side boundary. W e have also demonstrated a relationship between the depth of the depletion region and the rate of anode boundary propagation in the absence of D N A . It remains then to be understood why the depletion region forms and why the anode and cathode side boundaries move as they do. In this chapter, analytic arguments are used to show how slow moving ions can form a depletion region downstream. A numerical model is introduced by which the quantity of D N A required to completely deplete the background electrolyte is calculated. The movement of the boundaries is analyzed, starting with the cathode boundary. Comparison of the anode and cathode boundaries allows us to discard variable electroosmotic flow as a mechanism for the cathode boundary non-linearity. Fits to the cathode-side boundary movement shows the D N A to transition between two modes of migration as the field declines. Analysis of the anode boundary propagation mechanism is less conclusive as the experimental evidence is not definitive. The theory of moving boundaries for different electrolyte types is therefore introduced to provide a framework for possible mechanisms. A numerical model is introduced to test various possibilities. It is shown that the like-ion conductivity gradient mechanism which has been cited as the likely source of these slow moving, low conductivity boundaries Chapter 5 Analysis of Boundary Propagation 65 [43, 62, 65] is not in fact likely to be at work, and it is concluded that the most likely mechanism requires some combination of fixed charge in the matrix and/or a rise in pH in the depletion region so O H " ions become principle carriers. Experimental evidence for pH changes, via changes observed in the electrophoretic behavior of nickel particles, is presented in section 5.4.4. 5.1 Formation of the Depletion Region T he common approach to analytical models of capillary zone electrophoresis is to assume that the conductivity of background electrolyte is - 100 times higher than the conductivity of macromolecules being analyzed [66]. This permits the assumption that the electric field in equation (5-1) is constant, and thus linearized, the governing equations become tractable. If the electrophoresis scheme does not involve a high degree of sample concentration, such an assumption is quite reasonable, but this is not true of the present case. If, for example, the 20 s wide peak in Figure 13 contains ~10 ng of D N A , the concentration is - 7 0 mmol/L, comparable to the concentration of the electrolyte, and enough to significantly perturb the conductivity. It is still instructive, however, to examine the perturbation of a small quantity of slow-moving charged species on the background carriers. Consider again the 1-D Smoluchowski equation to describe the time evolution of ion concentrations in the presence of diffusion and electric drift: dt ox ox where C,, D, and JUJ(C) are respectively the concentration, diffusion coefficient and electrophoretic mobility of the i t h charged species. In Chapter 5 Analysis of Boundary Propagation 66 the present case, the buffer ions are all univalent, so the charge z is not included. CT(*,0 = Z F N C , - (5_2) J(t) = V ei dx J{t) 0 (5-3) E M = ^ U - m (5-4) a(x,t) T h e local field E(x,t) is found by first calculating the local conductivity, o(x,t), where F is the Faraday constant and the summation is over all ion species, and then the current density J(t) from (5-3). For ionic polymers such as D N A , Cdna refers to the concentration of charges, not individual particles, and thus includes the multiplicity of charges per molecule. The fact that these are long molecules is reflected in the low mobility but not in the concentration. T h e matrix buffer is 50 mmol/L T r i s - T A P S , initially at pH = 8.3, (see section 3.2.4, page 33 for more detail). They dissociate to give 25mmol/L of T A P S " and T r i s H \ so the contribution of H + and OH" (5x10" 6mmol/L and 2x10"3 mmol/L respectively at pH 8.3) can be ignored and we model a two-ion system plus D N A . Charge conservation dictates C+=C+Cdna-For further simplification, we consider the system in the frame of reference of the D N A , so that Cdna(x) is not time dependent. In reality, the mobility of the large D N A is of order 1/10 that of the carrier ions so we can assume the D N A is fixed. Let us now consider the quantity of interest - the concentration of mobile ions C = C.+C+. From charge conservation, C(x, t) = 2C_ (x, t) + Cdm (x) (5_5) dC(x,t) _2dC_(x,t) dt ~ dt Chapter 5 Analysis of Boundary Propagation 67 Re-writing (5-1) for all mobile ions, taking advantage of (5-5) and assuming the quantity of injected D N A is small, and that ju = ju. = -//+, we can write 1 3 / - ^ ( 5 - 6 ) dC_=Dd2C_ , Z ) 9 2 Q M • + -2 ox dt dx2 2 dx2 For initial conditions of a uniform anion concentration, and ignoring diffusion for now, the drift term of (5-6) will initially tend to increase C. on the cathode side of the D N A peak (where dCdna/dx >0) and decrease C . on the anode side of the peak. Note also that a larger carrier ion mobility will exacerbate this effect. Assuming that Cdna and the resulting perturbation to C . (defined as SC.) is also small we can follow a perturbation analysis similar to that used in the study of membranes with fixed charges [66]: C_(x,t) = C°_+SC_(x,t) and 8SC_ = D-82SC D d2C dna + -J 8 C. dna 2 C ° ( 5 - 7 ) ( 5 - 8 ) 8t dx2 2 8x2 2F 8x\ At steady state, using boundary conditions at the ends of the capillary, and assuming that Cdna(x) is nonzero over a finite length xi< x <x 2 and SC_(0) = SC_(L) = 0, (5_9) where L is the length of the capillary. This yields: SC (x) = ^— fl - -Tf(r>/z-. V ' 4FC°_D{ L)l d n a K ' (5 -10) for all x > X2 downstream of the Cdna peak. Although (5-10) is an approximation for small perturbations only, it sheds light on what drives the initial formation of the depletion region, and, as is shown below, on the threshold behaviour of current decline as a function of increasing injected D N A . In qualitative agreement with observations and Chapter 5 Analysis of Boundary Propagation 68 numerical results shown below, (5-10) predicts increasing ionic depletion downstream of the low mobility D N A , with the amount of depletion proportional to the total number of low mobility fragments. A s we shall see in section 5.2, numerical solutions to (5-6) indicate that the depletion SC., once it becomes a significant fraction of C.° , grows rapidly in magnitude with increasing amounts of injected D N A as a result of the growing electric field in the depleted region. Therefore, formation of a deep depletion region tends to occur rapidly once a critical quantity of low mobility fragments is reached. Estimates of this critical number using (5-10) where we set SC. ~ C° and given typical run parameters: C . = 25 mmol/L, D = 5 x 1 0 1 0 m 2 /s , J = 1000 A / m 2 gives C D N A ~ 1 0 1 2 nucleotides, or ~ 1 ng of large (i.e. slow moving) D N A fragments. Beyond this critical number, increasing D N A injection will rapidly deepen the depletion region to the point where, as demonstrated in Figure 12, the depletion region boundary mobility exceeds the fragment mobility and the depletion region expands. Experimental results from Figure 12 indicate that this threshold occurs at ~ 10 ng of injected D N A . 5.2 Numerical Modeling of Ionic Depletion W e turn now to numerical modeling of the C E system. Complete models of C E are difficult to produce as the system's behaviour is dependent on properties which vary widely with chemical components. Most schemes are also subject to numerical diffusion, which can result from errors in transport due to the finite size of the discretization and can dominate over Brownian diffusion. T h e difficulty in removing numerical diffusion without making models somewhat opaque has been mentioned as a limitation [67]. Models are likely to be most useful where, such as in the present case, they are used to better understand a limited set of observed phenomena, or predict to Chapter 5 Analysis of Boundary Propagation 69 first order the behaviour of well-understood analytes in well-buffered systems [68]. C E has been modeled with both continuum and molecular dynamics equations [69]. A n attempt was made here to remove numerical diffusion by calculating electric fields based on charge imbalances. This worked until proper constants were applied at which point the model became totally unstable. Such an approach is discussed in [70] where it is pointed out that the discretization step size must be on the order of the Debye length which is impractically small for real simulations. The following simulation uses a first order finite difference approximation (FDA) to the continuum Smoluchowski equation. The purpose of the present model is to show the effect of D N A on background ions and to test hypotheses related to moving boundaries. This of course means that the background electrolyte concentration and resulting electric fields are not constant. It also means that acid base equilibrium must be maintained, which represents the majority of computation time in this simulation. Several simplifying assumptions can be made however. Electroosmotic flow is neglected as it has been shown experimentally to first order to be unaffected by evolution of the depletion region as discussed in 5.4.4. Diffusion shall also be neglected, for two reasons. It is on the order of 100 times slower than the drift terms in the transport equations [71], and in this model, Brownian diffusion is actually overwhelmed by numerical diffusion. Fortunately, the experimental results we seek to explain here, such as in Figure 10, show that the boundaries of interest are self-sharpening, so in these cases, the system will act to negate the effect of numerical diffusion. In the absence of electroosmotic flow or any other hydrostatic effects, the flow profile is taken to be flat across the capillary so the discretization can be one dimensional. Chapter 5 Analysis of Boundary Propagation 70 T h e behaviour of ions under changes in concentration, temperature and pH is complex and varies from species to species. Of greatest concern are relationship of mobility to temperature and concentration: /u(T) and ju(C), and pH(T), the variation of pH with temperature. In a localized region of the capillary, T ex 1/a oc 1/C so ju(T) and ju(C) are coupled (see Appendix E), which may be of significance in the case, addressed in section 5.4.2, of motion of boundaries between identical solutions of different concentrations. In the simulations presented in section 5.4.2, ionic mobilities are made functions of concentration. In the case that changes in pH mediate boundary movement, discussed in section 5.4.3, pH(T) could become significant. In fact, dpH/dTfor 50 mmol/L T r i s - T A P S was experimentally found to be - 0 . 0 2 / ° C . Given that the largest temperature increase measured in the depletion region was about 7 ° C , this represents a fall of 0.14 pH units which is not significant compared to rise in pH of 2-3 units believed to be occurring in the depletion region. For this reason the temperature dependence of the pH is not included in the simulation. Chapter 5 Analysis of Boundary Propagation 71 Cathode Reservoir ~ & Left Right Boundary Boundary Cell 1 Cell n 7 * k-1 Cells k k+1 cathode [- ions] [+ ions] anode JJH/2 Jt+1/2 •fc-1/2 Jt+1/2 Figure 18 1-D discretization of the capillary showing ion flows in the upwind scheme. Figure 18 shows how the capillary is discretized in such a way as to preserve the charge neutrality required by equation (5-1). W h e n voltage is applied, the positive ions move to the left and the negative ions move to the right. T h e charge flux per unit time of a given ion is defined as 0 , = y.iCiEA (5-11) where A is the area of the capillary. Charge neutrality is explicitly preserved by defining the electric field at the cell boundaries Ek±i/2 such that the net charge from the movement of ions into and out of Chapter 5 Analysis of Boundary Propagation 72 each cell is zero. Equating the negative and positive species flowing into and out of cell k gives £ M , C ^ _ 1 / 2 - XMi :CtE k + l l 2 = 5 > / + O w - Sn+C?+E k_V 2 (5-12) i- i- ;'+ i+ where each sum is over the /' species of each charge. Combining like fields and expressing in terms of the conductivity gives j (5-13) J J °*-l/2 '£+1/2 Given a constant current j at each time step, this expression holds if (5-14) °"*-l/2 = F 0"A+l/2 = ^ T h e left side of equation (5-1) is written in discrete form as k * = v(^c) At Here we define the field gradient for positive ions as ^E _ Ek+]/2 ~ Ek_l/2 Ax Ax and the concentration gradient for positive ions as ±c_ck+l-ck Ax Ax Applying (5-16) and (5-17) to (5-15)and simplifying gives: At Ax For positive species and for negative species: (5-15) (5-16) (5-17) (5-18) Chapter 5 Analysis of Boundary Propagation 73 Q Ck _ Mk+\Ek-\nCk-\ f^k^k+xn^k (5-19) At Ax Equations (5-18)and (5-19) preserve charge neutrality throughout. Chemical equilibrium is often ignored in C E simulations, because the assumption C 0 » C a n a iyte implies that the pH is constant and under normal conditions, H + and OH" ions can be ignored. In the present case however, the contribution of these species must be taken into account as buffer capacity may be exceeded and water ions potentially become significant current carriers. A s discussed in section 3.2.4, the buffer solution consists of a mixture of Tris, a weak monovalent base, and T A P S , a weak monovalent acid. T h e coupled equations of chemical equlibrium can then be written as _ [Tris + X[H+ + x + y + z] (5-20) Tristi+ ~ [TrisH+-x\ _ [TAPS' + y\H+ + x + y + z] (5-21) TAPS~ [TAPS-y] kw = [H+ +x + y + z\pH~ + z] (5-22) Here K T r i S H + is the conjugate acid dissociation constant for Tris, k T A P s is the acid dissociation constant for T A P S and x, y and z are the contributions to the H+ concentration arising from the dissociation of T r i s H + , T A P S and H 2 0 respectively. The initial conditions are applied as concentrations of neutral Tris, T A P S and H + and OH" at 10"7 M , This system of non-linear equations is solved for x, y and z using Newton's method at each iteration, and the concentrations of the species are updated with the new values of x,y and z. T h e requirement to simulate acid-base equilibrium makes the model both more and less complicated. It can be assumed that because H2O is present at 55M, it is in infinite supply everywhere. T h e Chapter 5 Analysis of Boundary Propagation 74 mobility of water ions is also not well defined and while H+ and OH" mobilities are nominally given in Table 2, ion hopping makes those values difficult to define precisely [72]. Because the supply of water is infinite however, the concentrations of the water ions can be calculated by the chemical equilibrium equations. This is convenient as the mobility of those ions is so high as to make numerical stability difficult to achieve without impractically small time steps. In fact, the same results were obtained when the water ions were moved with finite difference equations, as when chemical equilibrium calculations were used to determine their concentrations. T h e chemical equilibrium calculation appears to correct for any instability introduced by the finite difference scheme for the water ions. This approach might break down if all the buffer ions were truly depleted, but in fact even when the capacity of the buffer to maintain a stable pH is exceeded, the conductivity is still dominated by the movement of one or other of the main ions and the distribution of neutral species. T h e capillary was divided into n = 256 cells, of 0.1 mm each, using the natural 1-D discretization following from the radial symmetry of the system in the absence of bulk flow such as E O F . T h e time step was then chosen as 10ms so the maximum movement of the T r i s H + ions is less than 0.07mm per time step. This was found to produce stable simulations at any degree of ionic depletion. T h e cathode reservoir then naturally represents the left boundary, the contents and volume of which can be either held constant or altered as needed. T h e anode side boundary is held at the initial conditions as it is assumed that conditions there remain fixed throughout the simulation. T h e algorithm was implemented in both Matlab and Fortran77 with data presentation performed in Matlab. T h e algorithm was as follows 1. Initialize concentration matrix with undissociated buffer Chapter 5 Analysis of Boundary Propagation 75 2. Set initial D N A conditions, balancing D N A charge with added T r i s H + . 3. Calculate ionic equilibrium in each cell 4. Calculate total capillary resistance and current 5. Calculate conductivity, electric field and molecule velocity. 6. Apply upwind and downwind F D A equations to positive and negative species 7. Calculate chemical equilibrium in each cell. Repeat steps 4-7 as needed. All simulations were run with a 36 cm capillary of 75 um diameter, at 5000V. lon properties are listed in Table 2: Species Electrophoretic Mobility Equlibrium T r i s + 30.1x10' 9 mzNs [73] pKb = 8.1 [74] T A P S " 25x10 _ y m / W s [ * ] pK=8.4 (Sigma Aldrich) H + 363x10"9 rrVWs [74] pKw =14 OH" 205 x10"9 m 2 A / s [74] pKw = 14 D N A (free solution) . 37 x10"9 m 2 /Vs[27] N.B: This is for any length D N A Table 2 Physical data for the numerical model. Measurement of TAPS mobility is show in D.1 Two versions of the model were developed, one with all the carrier ions and neutral species [ T r i s H \ TAPS", H + , O H - , Tr i s 0 , T A P S 0 ] and D N A - in which acid-base equilibrium is maintained, and another with two or three ions (i.e., one ion of each charge or two ions of like charge and a counterion) behaving as fully dissociated strong electrolytes. The ions' mobilities and concentrations were then chosen to resemble T r i s H + , T A P S " and/or faster and slower ions as needed. T h e latter, non-buffered model, which runs much faster due to the Chapter 5 Analysis of Boundary Propagation 76 absence of the chemical equilibrium calculation, serves as an approximation for when the electrolyte is not depleted, the pH is near neutral and the water ions do not play a major role. Peak Position Time (s) Figure 19 Non-buffered simulation of the decay of a peak in ion concentration over 250 seconds due to numerical diffusion. T h e first order finite difference approximation used in this model exhibits numerical diffusion. T he effective diffusion constant can be found by initially setting the concentration of the ions so that there is a gaussian peak. A s the simulation proceeds, the center remains fixed but the peak shrinks and spreads out maintaining a constant area. A diffusion constant [22] can be found through the evolution of the peak width over time: 2 FWHM2 • N (5-23) Chapter 5 Analysis of Boundary Propagation 7 7 Figure 19 shows a plot of cr2 vs. time from which the numerical diffusion constant is found to be Dnd = 12x10"9 m 2 /s . The diffusion constant of ions can be found from the Einstein diffusion relation: e where e is the elementary electronic charge. At room temperature, we find D ~ 0.025/^ which gives values of D ~ 5x10" 1 0 m 2 / s for the main carrier ions and 5x10" 1 1m 2/s for X D N A . While this dominance of numerical diffusion does not negate the usefulness of the model for qualitative experiments, care must be taken to ensure the numerical diffusion does not produce significant errors. If, for example, a D N A peak is introduced as in Figure 20, but given a non-zero mobility, numerically diffused D N A will "leak" into the downstream depletion region and cause the anode side boundary to propagate away in accordance with equation (5-41), giving an incorrect result. T h e solution in this case is to run the simulation in the frame of reference of the, D N A peak, as was done in the analytic case. In this manner the D N A position will not be recalculated using the F D A , so it does not have a chance to diffuse. Chapter 5 Analysis of Boundary Propagation 78 4000 Position (mm) Figure 20 Effect of a fixed DNA peak on the background electrolyte conductivity. Near total depletion (a ~ 5 uS/cm) is achieved after 20 s run time with 16 ng of DNA Figure 20 shows the effect of a series of fixed Gauss ian D N A peaks of varying height on the background electrolyte after 20 seconds. The D N A peaks have a width of 200 um, typical of those observed (eg Figure 13). A s expected, the ion distribution shows a more extreme analog to the perturbation approximation in equation (5-10). The simulation was run under the same conditions as those used for the data in Figure 12, and as in Figure 12, near total depletion occurs with between 10 and 20 ng of D N A present, in good agreement with experiment. Figure 21 shows the effect on the ion profile when the peak is broadened. The degree of depletion is independent of the width of the D N A peak. This agrees with equation (5-10) and explains the experimental observation that more conductive samples which Chapter 5 Analysis of Boundary Propagation 79 exhibit a lesser degree of sample stacking have the same depletion behaviour as less conductive, and consequently more compressed, samples. 4000 , , , r — 1 r — r - , . Position (mm); Figure 21 The effect of a 20 ng DNA peak of varying width, after 20 s. The degree of depletion is the same for each width. Finally Figure 22, shows how reducing the mobility of the D N A deepens the depletion region. This simulation was again run in the frame of reference of the D N A so its mobility was subtracted from the T A P S " mobility and added to the T r i s H + mobility. W h e n the D N A mobility decreases, the T A P S - ion gets relatively faster, and the perturbation caused by the D N A peak gets more severe. Chapter 5 Analysis of Boundary Propagation 80 200 Mobility of DNA (*10s mWs) Figure 22 The effect of DNA mobility on depletion depth. This simulation was performed in the frame of the DNA, with the DNA's nominal mobility subtracted from the TAPS' ion's and added to the TrisH+ mobility. X DNA in LPA has a mobility of ~2.5x10"9 m2/Vs. 18ng of DNA was used and the simulation was run for 20 s. 5.3 DNA and Cathode Boundary Propagation T o understand why the depletion region boundaries propagate, we turn now to their movement in the frame of the capillaries. In section 4.4 it was noted that the anode boundary propagation velocity depends linearly on current while the cathode boundary does not. W e also note that the presence of the D N A peak at the cathode boundary implicates the D N A mobility in the cathode boundary velocity, and note that the absence of D N A at the anode boundary points to imbalance in Chapter 5 Analysis of Boundary Propagation 81 ion flow as the driving mechanisms for that boundary. T h e following discussion expands on these arguments. Before considering a mechanism for cathode boundary movement, it should be considered whether, as in Figure 13 beyond the range of the IR camera, the anode boundary diverges from linearity as much as the cathode boundary. There is no reason to suppose from the IR images that this is not happening, as both boundaries appear linear over the first five minutes, and some variable E O F could in principle exist. T o check this, four runs were conducted where D N A was injected, the run was thermally imaged and the capillaries were then cut up. T h e actual anode boundary position could then be compared with one extrapolated from the thermal image, where x(tfinai) = C1Qfinai+C2. Ci was determined by fitting to the anode boundary, and the offset C 2 was found by comparing the cut capillary and thermally imaged positions of the cathode boundary, which remained in view throughout. From this it was found that the difference between the actual and extrapolated anode positions was no more than 1.3% for the runs of 5, 6 and 13 minutes and 10% f o r a run of 41 minutes. In the 41-minute run the cathode boundary, by comparison, lagged its linearly extrapolated position by 50%. W e conclude therefore that the anode boundary maintains its linearity of position with respect to charge throughout the run while the cathode boundary diverges from linearity. E O F , if it is present, must therefore remain relatively constant. Given the hypothesis that the cathode boundary is driven by the propagating D N A , the nonlinearity of the boundary movement must be intrinsic to the D N A migration. It is known that in agarose, the mobility of long fragments has a field dependent term [75] v = p:0E + julE2. (5-25) Chapter 5 Analysis of Boundary Propagation 82 Using the present system of fitting position against charge, this would take the form of (5-26) Such a function can only be fitted to the observed cathode boundary data if the coefficient u 0 is negative, i.e. the D N A is positive, which doesn't agree with any electrophoresis mechanism hitherto reported. There is evidence however that at low fields, large fragments, which normally propagate under the biased reptation regime, fall into an entropic trapping regime where mobility is reduced [76]. T h e D N A is trapped in larger pores in the matrix, but within the influence of the force field generated by the applied voltage, thermal energy imparted to the D N A allows it to migrate through the constrictions to the next trapping site. This is modeled as an Arrhenius process of energy barrier crossing between trapped states, with negligible probability of a reverse reaction (i.e. backward migration induced by thermal motion), and is characterized by a Boltzmann factor that includes the energy barrier height associated with crossing between trapped states, together with the applied potential: v _ (QxE-U0)/kT (5-27) Here, E is the local field and Qx is a parameter to be found that combines the effective number of elementary charges available to move the D N A despite screening, multiplied by the length scale of the energy barrier. At higher fields (E> E 0 = U 0 /Qx), enough force is applied to the D N A to remove the barrier entirely, and migration is constant. In this regime, normal electrophoretic behaviour characterized by (5-25), is expected to apply. T o accommodate the threshold behaviour between the two regimes, the sigmoid function is used Chapter 5 Analysis of Boundary Propagation 83 Y = 1 (5-28) where x t is the threshold and x 0 is a measure of the steepness of the transition from 0 to 1. Combining (5-25) and (5-27) with the sigmoid function, and putting all driving parameters in terms of currents gives f 1 \ ( V 1- 1 1 + e - ( / - / o ) / * „ 1 +£-('-'.)". V i - i - e j This is a 6 parameter fit: u.0, uy.are the two mobility terms l 0 , the threshold for trapping; l c which is related to the effective charge of the X D N A and the trap escape distance, and temperature; v 0, related to the relaxation time of X D N A in L P A ; and x 0 , the sigmoid steepness parameter. Here we set the steepness parameter x 0 to 0.1 so that the fit requires five parameters. In effect though, this is two separate fits of two parameters, one in the low field and one in the high field regime, with a threshold value to be found between them. Chapter 5 Analysis of Boundary Propagation 84 30.00 0.00 5.00 10.00 "15.00 20.00 25.00 30.00 Time (min) Figure 23 Fit of equation (5-29) to a cathode boundary position. Parameters at 293 K are U 0 = 6 kT, un = 1x10'9 m 2/Vs, u-, = 1.2x10"13 m 3/V 2s, v 0 = 2x10 2 mm/s, Qx/kT = 8x10"4 m/V. Viewed independently, the parameters of the fit for the two regimes are quite reasonable. In the biased reptation regime, the linear term u 0 = 1x10"9 m 2 /Vs is close to measured values of u for X DNA in the absence of depletion regions. It is also very close to the value for agarose reported in [75] although the nonlinear term in this case is an order of magnitude smaller. The entropic barrier U0 = E0Qx can be overcome when the field is strong enough that the electric forces are comparable to the thermal forces acting on the DNA. This occurs when E0 = kT/qb [77], where b ~ 100nm is the Kuhn length (twice the persistence length) for dsDNA, and q is the effective charges per Kuhn length - about 20e" for dsDNA [78]. Q, the number of charges available to move the DNA, is q multiplied by the number Chapter 5 Analysis of Boundary Propagation 85 of Kuhn lengths n k ~ 150 for X DNA. The length parameter x can be taken as the pore size of the matrix, which is ~ 3nm [20]. This gives an expression for U 0 : Up = nkqx (5.30) kT qb " Using the numbers for rik , x and b, gives Uo ~ 6kT, as was found in the fit. Qx/kT itself can be estimated from the data above as Qx = nkqx (5.31) kT kT which gives an estimated value of Qx/kT = 4x10"4 mA/, compared to 8x10" 4mA/ from the fit. The parameter v0 is the velocity of D N A as it falls into the entropic regime. In this case the midpoint of the sigmoid is found to be at 2.24 uA, which, if (5-25) is used, also gives .02 mm/s. This makes intuitive sense as the velocities in the two regimes must match at the transition point. No experimental confirmation of this effect in polymer matrices has been found in the literature, but the absence of such data was noted by Jean Louis Viovy in 2000: it is somewhat surprising that it [entropic trapping] has been overlooked for quite a long time in the context of gel electrophoresis. This is probably due to the conditions necessary for its appearance, and in particular the requirement of low fields: such conditions are not very interesting as far as separation is concerned, and they were avoided by experimentalists on a pragmatic basis. [76] W e have shown here that the behaviour of D N A in the entropic trapping regime may in fact be interesting, but from a high-throughput, low-cost D N A sequencing perspective, it would be generally desirable if entropic trapping of large fragments, and in fact, large fragments themselves, were entirely avoided! Chapter 5 Analysis of Boundary Propagation 86 5.4 Anode-Side Boundary Movement Experimental results show that anode-side boundaries in both the DNA-induced and depleted buffer cases are not associated with the presence of D N A . The ions at the anode side boundary must therefore be the background Tris and T A P S ions as well as H + and OH" ions. There could conceivably be other ions from the buffer or matrix present, but their behaviour should in principle be typical of small ions and therefore predictable. A configuration and behaviour of these ions on both sides of the boundary must then be found which can explain the boundary movement. In order to do this, it is best to start with the basic theory of moving boundaries in systems of multiple ions. T h e proposed models for anode boundary propagation can then be best understood in the context of the failure of this theory in describing the observed propagation 5.4.1 The Theory of Moving Boundaries T h e behaviour of ionic boundaries has been the subject of research for over a century [79]. There are several types of ionic boundaries, including those between two strong electrolytes sharing a common counterion, weak electrolytes where H + and OH" may play a role, and concentration boundaries with the same positive and negative ions on both sides but at different concentrations. W e begin by examining the simplest system: two different ion populations in adjacent regions, with a common counterion [80]. For thematic continuity, we shall assume the adjacent ions are negative and the common counterion is positive. Consider a system where ion 2, with concentration C 2 moves with velocity v 2 into a region which is being vacated by ion 1, of concentration Ci and velocity vi as shown in Figure 24. W e also make the assumption for now that ^>[i2- T h e counterion, Chapter 5 Analysis of Boundary Propagation 87 of course, has concentrations C i and C2 to balance the negative ions everywhere, and a mobility f n "A v2C2 I I I Figure 24 Adjacent region of ion 1 (dashed lines) and 2 (solid lines) forming a moving boundary with velocity v b . It will be shown below that conservation of ion flux requires certain values of C 2 in order for the boundary to move but we assume for the moment that this moving boundary satisfies that condition. T h e change in concentration overt ime between boundaries I and II is equal to the difference in flux across the two boundaries and also equal to the difference in concentration multiplied by the movement of the boundary swept out between them. A0 = v2C2 vxCx =vhC, -vhQ . b^2 Solving for vt> and given v = juE = juJ/crwe get T( - - v Mi yC2 C, J (5-32) (5-33) KJU2+JU ju, +ju J T h e mobilities can be rewritten as T Mn (5-34) Mn +M T n is known as the transference number and represents the relative conductivity of the ion and counterion. Then v b becomes Chapter 5 Analysis of Boundary Propagation 88 vt = J T2~Tx (5-35) F C2 - C, ' Conservation of charge flux everywhere in the capillary requires that only certain values of C 2 are allowed in (5-35). This was first pointed out by Friedrich Kohlrausch in 1897 [79]. Assuming for the time being that the mobilities are constant with respect to ionic concentration, we write them as u, = Z\/A\ where Zj is the charge of the ions. Neglecting diffusion, the sum over all the ions gives: (5-36) |//;| dt dx' but charge neutrality requires that everywhere YJZiCi(x,t)=0 (5-37) thus yJ_dCj{x1t) = 0 ( 5 . 3 8 ) and integrating gives yc^)=co{x) <5-39> i \M,\ Equation (5-39) implies that after initial conditions are established by, say, hydrostatically injecting some combination of electrolytes into the capillary, the value of co(x) remains constant in time. This equation is known as the Kohlrausch Regulating Function, and once electrophoresis starts, it determines the concentrations of species that follow moving boundaries between species. Equation (5-39) requires that as ion 2 moves into the region vacated by ion 1 in Figure 24, it has concentration Chapter 5 Analysis of Boundary Propagation 89 C = C v. (5-40) J Applying (5-40) to (5-33) gives, after some simplification, J fix MA (5-41) so the boundary moves at the speed of the leading ion. Measuring such a boundary between strong electrolytes of different mobilities and combining and obtaining conductivity data for the leading solution turns out to be the best way to measure the transference number (5-34) of the leading electrolyte at different ion concentrations [80] v2C2 v b2 Figure 25. The effect of the regulating function on the distribution of ions in the capillary. Initial conditions are as in Figure 24 and ion 1 (dashed lines) is leading ion 2 (solid lines). The regulating function (5-39) requires that lon 2 takes on concentration C 3 to conserve total ion flux. The new concentration boundary in ion 2 remains fixed. Th e actual picture for strong electrolytes is shown in Figure 25, which represents what would happen if the system were initialized at t = 0 as shown in Figure 24 and then run for some time. The regulating function automatically adjusts the concentration of the region following ion 1 giving a new concentration for ion 2 of C 3 . This then gives the C h a p t e r 5 A n a l y s i s o f B o u n d a r y P r o p a g a t i o n 90 c o r r e c t v e l o c i t y o f t he t ra i l ing i o n s to m a t c h t he l e a d i n g i o n . T h e n e w b o u n d a r y vb1 b e t w e e n r e g i o n s of d i f ferent c o n c e n t r a t i o n s o f ion 2 h o w e v e r , s h o u l d b e s ta t i ona ry . T h e s e t h r e e r e g i o n s r e p r e s e n t d i f ferent " z o n e s " , h e n c e t he g e n e r a l t e r m "cap i l l a r y z o n e e l e c t r o p h o r e s i s " in c o m m o n u s e in a n a l y t i c a l c h e m i s t r y . t = 0 sec t = 40 sec 100 (a) 50 10 20 30 100 10 20 30 100 (b) 50 10 20 Position (mm) 30 100 10 20 Position (mm) Figure 26 Simulation of a leading (dashed line, u. = u.{) and trailing (solid line, u. = m) negative ion. Initial states are at left and, after 40 sec, at right, (a) (it < W so the moving boundary remains sharp, (b) Lit > w so moving boundary smears out. S i m u l a t i o n s o f two s t r o n g e l e c t r o l y t e s w i th a c o m m o n c o u n t e r i o n a n d v a r y i n g mob i l i t i es a r e s h o w n in Figure 26 . In (a) t he l e a d i n g ion h a s a h i g h e r mob i l i t y t h a n t he t ra i l ing ion a n d in (b) t he t ra i l ing ion h a s a h i g h e r mob i l i t y . T h e a d j u s t m e n t of the t ra i l ing ion c o n c e n t r a t i o n to c o n s e r v e c h a r g e f lux c a n b e o b s e r v e d . T h e m o b i l e a n d s t a t i o n a r y Chapter 5 Analysis of Boundary Propagation 91 boundaries are visible, though the fixed boundary at the original interface location is subject to numerical diffusion. If the classical moving boundary model were to apply, there would have to be another negative ion following the T A P S " in the depletion region. While there is no evidence for such a hypothetical ion, it can also be shown that the physical properties required by theory make it unlikely that such an ion could exist. Consider the depletion region as region 3 in Figure 25 page 89. For such a boundary to be self sharpening, the ion in the depletion region must have lower mobility than the leading T A P S ions' mobility of 25x10"9 m 2 A/s. In that case the boundary would propagate at the speed of the T A P S ion, but in reality the boundary actually propagates at, at most, one fifth that speed. T h e regulating function can be used to solve for the mobility of the hypothetical ion, given the experimentally measured concentrations on either side of the boundary. This gives a mobility of 4x10"9 m 2 A/s, which is much lower than any ionic species save very large D N A fragments. T h e only species present which might be negatively charged and might have such a mobility would be fragments of acrylamide polymers, but conservation of mass would prevent any bulk flow of such ions so this is unlikely. 5.4.2 Common Ion Boundaries Previous work on anomalous conductivity in electrophoresis [43, 62, 65] has cited Michael Spencer's three 1983 papers on the subject [81] [82] [83] as providing a possible explanation for current decline. Building on the prewar ion boundary work of Longsworth and others [80], Spencer argued that a change in transference number from differential retardation of ions could induce a depletion region at the gel buffer boundary. If the transference number was dependent on ion concentration, the newly formed boundary could then propagate into Chapter 5 Analysis of Boundary Propagation 92 the matrix. T h e first part of this theory has been experimentally verified by Swerdlow [42] and Figeys [43] et al. as noted in section 2.5, page 16. It has not, however, been shown that a transference number change alone is responsible for boundary movement into the matrix without an accompanying pH change or involvement of another ion species. Analytic arguments and simulations are presented here which suggest that this boundary movement is unlikely to come from a concentration dependent transference number in general, and particularly not in the present case with T r i s / T A P S buffer. T h e extant literature on these "common-ion" boundaries consists of two papers. Smith, in 1931 [84], reproduced the correct magnitude and direction of a 200/100 mmol/L LiCI boundary, which has a notably large change in transference number, though did not report boundary motion for other species with a smaller dT/dC values. Spencer's own experimental results [83] show boundaries accompanied by pH changes. Prediction of the direction of boundary propagation based on the transference number gave the right direction, but more quantitative agreement could not be shown. Spencer also shows how the pH would change with depletion for a typical single ion weak electrolyte, but no prediction of boundary velocity is given in the case where water ions become significant carriers [82]. Elsewhere, Chien [85] suggests common-ion boundaries are stationary to at least first order, and Beckers and Bocek [86] assert that the only known moving common-ion boundaries are accompanied by a change in pH, or are multivalent ions near pKa. Spencer's prediction for common-ion boundary movement was tested via simulation. Spencer derived an expression for boundary movement dependent on a change in relative mobility (transference number) of two ionic species with concentration dependent mobilities. Chapter 5 Analysis of Boundary Propagation 93 J dT (5-42) F dC If d T / d C * 0, the boundary can move and will be self-sharpening, as the point of lowest concentration has the highest velocity. T h e simulation was done for both buffered and unbuffered systems. d T / d C * 0 is satisfied if the mobility of the carrier ions vary with concentration by different amounts. A common empirical formula for p(C) for strong electrolytes such as KCI and NaCl in the range of 1-100 mmol/L is given in (5-43) where the coefficient 0.5 is found to be typical for univalent ions [87]. Assuming that the constant would be slightly different for different ions, we arbitrarily assign T h e s e are for the principal carrier ions. W e assume that in the buffered system, the water ions have their usual mobilities. T h e s e are arbitrary ions, but for the sake of comparison, their initial mobilities are the same as the Tris and T A P S ions. (5-43) Chapter 5 Analysis of Boundary Propagation 94 rjl '— ' 1 01 1 ' '8.34 0 10 20 30 0 10 20 30 Position (mm) Position (mm) Figure 27 (a) Initial (solid line) and final (dashed line) ion distributions for two unbuffered ions over 60 seconds, (b) The same simulation in a buffered electrolyte, showing a change in pH near the boundary. Figure 27 shows the results of the simulation for two and four ions. T h e boundaries show numerical diffusion and in both cases the center of the final concentration profile moves to the right at a rate of ~0 .5m/C. T h e boundaries move the same direction irrespective of the sign of d T / d C however, so the observed movement is likely an artifact of the numerical diffusion. W h e n water ions are included there is a small change in pH, as shown, but the same pH change occurs for both variable and constant ion mobility. Numerical diffusion appears to dominate any actual movement of the boundary, and may in fact obscure changes in boundary movement due to nonzero d T / d C . T h e model cannot, therefore, give a definitive answer to the question of whether such a like-ion boundary moves, but certainly does not Chapter 5 Analysis of Boundary Propagation 95 reproduce observed propagation rates even with large changes in transference number. T h e possibility of the observed boundaries propagating because of changes in transference number appears equally unlikely when considered analytically. T h e fastest moving boundaries we see in normal matrix propagate at 10 m/C. The conductivity falls from 1100 LiS/cm in the background to 70 LiS/cm in the depletion region. Absent a pH change, the concentration of T r i s + and T A P S " would be 3 mmol/L in the depletion region compared to 50mmol/L in the background. If this were a common-ion moving boundary, equation (5-42) would require a change in transference number of 20% to give 10m/C. This seems implausible as typical transference number changes are more like 5% over 1-100 mmol/L [87] [88] for strong electrolytes. T h e s e are accompanied by changes in molar conductivity (conductivity/concentration) of 20%. Figure 47, page 157, of a vs. [Tris T A P S ] in fact shows no measurable change in molar conductivity at all, so it is very unlikely that changes in transference number can explain this boundary. Finally, the clipped capillary data shown in C.1 shows that it is definitely possible for a concentration boundary to exist in the capillary, as seen by thermal imaging, but which remains stationary because its upstream driving source has been removed. It must be concluded therefore, it is not the case that these boundaries move because of changes in relative conductivity brought on by concentration dependent mobilities, and that the explanation must lie in some system involving more than two-ions. 5.4.3 Boundary Movement by Bound Charge There are two other possible mechanisms which, when simulated, produce behaviour similar to that observed experimentally. T h e first is that a change in pH across the boundary allows extra OH" Chapter 5 Analysis of Boundary Propagation 96 ions from the depletion region to neutralize acid species at the boundary, causing it to advance. The second is that some small quantity of bound charge may exist on the acrylamide or capillary surface which might produce a moving boundary. Simulations and analytical analysis of the pH mismatch model, shown below, show boundary propagation and depletion depths comparable to experiment. What is lacking however is a mechanism by which the pH may rise sufficiently to explain the observed boundary movement. T h e bound charge model, which also produces pH changes, does have a realistic source so we focus on this model first. There is ample evidence from the literature that polyacyliamide can become charged overtime as the monomers become hydrolyzed. [89, 90]. Chiari et a/,for example, found more that 30% of polyacrylamide monomers became hydrolyzed in 0.1 Molar N a O H in less than an hour. [91]. While the present L P A is at a much lower p H , it is reasonable to assume that it has some small degree of bound negative charge, Given that 4% w/v L P A has approximately 500mmol/L acrylic monomers, we will make the assumption that of the order of 1 mmol/L of the chain components are charged. It is also possible that the L P A might become charged only when the electrolyte is depleted. This would be quite possible if the acrylamide were behaving as a weak acid, but this behaviour has not been reported in the literature and will again require a pH change. A velocity for a boundary driven by fixed charge can be derived in similar manner to the derivation in section 5.4.1. Without bound charge, such a like-ion concentration boundary should not move. T h e bound charge introduces a change in the proportion of the positive and negative mobile species however, so effectively the transference number changes. Consider again the ion-plus-counterion situation in Figure 24, page 87. Here, we assume a constant concentration Cf of Chapter 5 Analysis of Boundary Propagation 97 bound negative charges throughout the system. Th e ions have a constant mobility and we assume for simplicity that LL = T h e negative ion has concentrations C i and C2 but the bound negative charges give the positive ions concentrations C-i+Cf and C2+Cf. T h e flux of negative ions in the two regions is again given as A 0 = v 2 C 2 - v A = vbC2 - vbCx. now however, the velocity becomes v. = or J_ F juC. juCx V juC2+ ju(C2+Cf) yCx + M(CX + CF) (5-44) (5-45) c, 2C, +CT 2 C 1 + C / J ^ C 2 - C 1 (5-46) Propagation rates for a range of bound charges and degrees of depletion is shown below in Figure 28. Chapter 5 Analysis of Boundary Propagation 98 30 n l . i i i : 1 1 0 200 400 600 800 1000 Depletion Region Conductivity (uS/cm) Figure 28: Plots of equation (5-45) for different densities of bound charge. The background conductivity was 950 uS/cm. Simulations were next performed with the full chemical equilibrium model plus bound charge. T h e s e bound negative charges were initialized simply by adding the equivalent concentration of Tr i s + throughout the capillary. The concentration of buffer at the cathode end was then diluted by various fractions to give a range of conductivities typical of those observed experimentally in the depletion region. A comparison of these results with experiment is shown in Figure 29 below. Chapter 5 Analysis of Boundary Propagation 99 20 r 0 • A — Bound Charge = 0.5 — Bound Charge = 1 H— Bound Charge = 2 •©— Bound Charge = 4 • Experimental Data 0 100 200 300 400 Depletion Region Conductivity (>iS/cm) 500 600 Figure 29 Experimental boundary propagation compared to simulation of boundary propagation due to bound charges. Bound charges are in mmol/L. Simulated cathode buffer concentrations are (0.5,1, 2, 4, 8,16) mmol/L and background electrolyte = 50 mmol/L. Zero bound charge failed to produce a moving boundary This model approximately reproduces the behaviour of the boundary observed experimentally. Unlike the pH variation model discussed below, the boundary movement arises naturally from the decline in carrier ions. A n interesting piece of data from Chiari et al is that P D M A appears to hydriolize about 500 times more slowly than L P A [91]. This may explain why P D M A is less prone to current decline than L P A . A curious feature of these simulations is that for bound charge up to 1 mmol/L, the pH rises in the depletion region whereas for 2 mmol/L and above, the pH falls. T h e comparison is shown in Figure 30 Chapter 5 Analysis of Boundary Propagation 100 below. The cause of this change is not understood but is likely to be related to the limited buffer capacity in the depletion region. If there are not sufficient positive ions to counter the negative bound charge, the charge may act as an acid and drive the pH down, whereas where there is excess basic buffer, the pH may rise. In section 5.5 we present evidence of what appears to be a sustained rise in p H . T h e present simulations do not show a sustained rise in pH while such behaviour is displayed by boundaries driven by larger pH mismatches. T h e latter mechanism is described below and while it may not be at work in the present situation, a definitive answer may have to await a more precise measurement of pH changes in the capillary. 40 35 30 •5 g 25 • 20 10 • [TAPS -] •[Tris0] -pH 8.9 8.8 8.7 8.6 8.5 8.4 8.3 8.2 8.1 40 35 30 h 25 20 15 10 • [TAPS"] •[Tris0] pH 0 10 20 30 Distance from Cathode (mm) 0 10 20 30 Distance from Cathode (mm) 8.9 8.8 H8.7 8:6 8.5 £ 8.4 8.3 8.2 H8.1 8 Figure 30 A comparison of behaviour between a bound charge of 1 mmol/L on the left and 4 mmol/L on the right. The variation in pH is apparent. Cathode buffer concentration and background electrolyte were 2 mmol/L and 50 mmol/L in both cases. Chapter 5 Analysis of Boundary Propagation 101 5.4.4 Experimental Evidence for pH Changes in the Depletion Region. The preceding simulations using bound charges reproduced the boundary movement, but do not suggest a substantial change in p H . There are a couple of issues here. The first is that, as discussed in Appendix C . 1 , deep depletion regions can permanently damage the capillary surface coating so that depletion regions subsequently arise without special buffer conditions or D N A . Such an effect could arise from adsorbed D N A , a change in p H , or the high fields associated with the depletion region. It is hard to understand how anything but a pH change could affect the chemical structures at the capillary surface. A high enough electric field would have to be strong enough to affect the physical structure of the matrix. Second, it is shown in this section that nickel particles seem to respond to the depletion region in a manner consistent with a sustained rise in p H . T he following experiments were motivated by a desire to measure any residual E O F in capillaries. Such measurements are normally done with neutral E O F markers such as dimethylsulfoxide ( D M S O ) [92] and mesityl oxide [93]. T h e s e are detected via U V absorption, not available on our instrument. Instead, two other techniques were devised: solid particle propagation and matrix-buffer boundary movement. T h e solid particle approach was applied as follows: Approximately 200mg of nickel powder (Novamet 4SP-400) with a mean diameter of 10 Lim was mixed with 1 ml of L P A by vortexing, centrifuged briefly to remove air bubbles, then pumped into the capillary. T h e movement of the particles could be observed in the instrument's onboard microscope, and images of the capillary were obtained with the video camera as described in section 3.2.3. T h e Chapter 5 Analysis of Boundary Propagation 102 particle locations were recorded manually on the images and the resulting position vs. time and current data used to find the propagation coefficients using equation (4-5). The limitation of this technique was that the surface charge of the particles was unknown. It was, therefore, unclear whether the particles were moving because of E O F or electrophoresis. In order to check this, the position of the LPA/buffer boundary at the anode was recorded. T h e moving L P A boundary method was based on the assumption that under normal well buffered conditions, the L P A itself did not gain significant charge so that any capillary wall-induced E O F would pump both the L P A and buffer towards the cathode. T o observe this effect, the L P A at the anode was replaced with buffer at the start of the run, to make an LPA-liquid boundary. After the run, the capillary was cut up from the anode end and at each cutting, the end of the capillary was prodded with a piece of 50Lim wire. Buffer by itself did not adhere to the wire, whereas the extremely sticky L P A would. Three capillaries from three different bundles were tested with the nickel powder/matrix mixture and the particles were found to move between -1.2 and -1.5 m/C (the negative sign refers to the particles moving towards the cathode, the opposite of DNA) . T h e rates were the same for all particles observed, and constant over runs up to 25 minutes long. T h e cut capillary method was subsequently used on one of the capillaries which showed the particles moving -1 .2m/C. After a 160 minute run, the buffer/LPA interface was found 4 cm from the anode, again giving -1 .2m/C. T h e fact that the particles move at the same rate as the L P A supports the hypotheses that the particles and L P A are uncharged. T h e direct effect of the depletion region on the particles was then observed, and Figure 31 reveals the surprising result: crossing an anode boundary causes the particles to reverse direction. T h e particle Chapter 5 Analysis of Boundary Propagation 103 tracked in Figure 31 initially moves towards the cathode at -1.3 m/C. After the anode boundary passes through at 8 m / C , the same particle reverses and propagates towards the cathode at 4.6 m/C. T h e depletion depth in this region was estimated using equation (C-2), (Appendix C) at 85 uS/cm. The anode boundary moves faster than the particles, so they do not stack against the boundary. A similar effect is shown in Figure 32 where a dilute-buffer depletion region, estimated at 200 uS/cm, caused particles to slow from -1.2 m/C to -0.2 m/C. Figure 31 (a) images of nickel particles in the capillary. The falling and rising white lines are tracks of one particle before and after being passed by the depletion boundary. The left particle track moves -1.3m/C and the right one moves 4.6m/C. The dark horizontal line in (a) is an artifact, (b) A thermal image of the same capillary. The horizontal while lines delineate the field of view of the visible images in (a). Chapter 5 Analysis of Boundary Propagation 104 Time (min) Time (min) Figure 32 (a) Progress of nickel particles as a depletion boundary crosses their paths. Particles are visible as rows of black dots above and below the white lines, which track a third particle. Its propagation rate changes from -1.2 m/C to -0.2 m/C. Note the lowest particle changes direction first and the upper ones follow in order, (b) A thermal image of the same capillary. The horizontal while lines delineate the field of view of the visible images in (a). T h e behaviour of the particles as they cross into the depletion boundary is only consistent with a change in electrophoretic behaviour of the particles. Conservation of mass requires that it cannot be some local change in E O F direction. Figure 32 also shows that the downstream particles clearly change direction later than the particles closer to the cathode, the direction from which the depletion boundary is coming. This implies that the surface charge of the particles must Chapter 5 Analysis of Boundary Propagation 105 change from neutral to negative. The nickel particles are likely to have a surface layer of nickel oxide. Nickel oxide, as other oxides, is known to have an isoelectric point where surface groups are charged. Parks [94] gives the isoelectric point for NiO as 10.3. It is possible to estimate if these groups are becoming charged, assuming the particles are moving at a terminal velocity, balanced between the electrophoretic force and viscous drag, Fe = Fd (5-47) where the electrophoretic force is Fe=Eq = fAppE, ( 5 _ 4 8 ) and where E is the local field in the depletion region, estimated at 1.8x105 V/m and q, the charge on the particle, is the maximum change density p multiplied by the particle area A p and a surface charge density factor f. If the spacing of atoms at the surface is 3A, p = 1.7 Coul/m 2 1 , the viscous drag force is given by Stokes Law: Fd = 67rr]rv ( 5 _ 4 9 ) where r; is the viscosity, and r is the particle radius of 10Lim. The particle velocity was found from Figure 31 (a) as velocity of the left-hand particle track added to the velocity of the right-hand particle track as the former represents the EOF. This gives v = 4x10"5 m/s or a shear rate of about 0.5s"1. This corresponds to an LPA viscosity of about 50Pa s [47, 95]. Solving for the fraction of sites f which would have to be singly ionized to give the observed velocity, gives f = 0.4% which is certainly reasonably small. Without knowing more about details of the particles' surface chemistry we cannot accurately determine the rise in pH. It suffices to say here that there is reasonable evidence that the pH does indeed rise in the depletion 1 Published values for silanol groups on glass are 0.6-0.8 Coul/m2 [23] Chapter 5 Analysis of Boundary Propagation 106 region, and that the degree of increase is proportional to the depth of depletion. 5.4.5 Boundary Movement by OH" Propagation In light of the evidence for rising pH in the depletion region, we examine one other possible model for the observed moving boundaries. Rising pH can occur naturally where the concentration of the acid component of a buffer solution is reduced while the basic component is maintained. In the case of a 50 mmol/L T r i s / T A P S solution, the pH will rise from 8.3 to 10 as [TAPS] declines to zero. In an electrophoretic system, the boundary between high and normal pH regions can move because extra OH" ions impinging on the background region cause neutral T A P S to be ionized. This draws down the T A P S ion concentration and the boundary moves It is possible to derive a boundary velocity in this system. First, note that this velocity is different from that described in section 5.4.1 because in the present case of a buffer, ionic species are not conserved. Here, OH" ions from the depletion region travel into the undepleted region effectively adding extra base to the undepleted region. T h e excess OH" ions are neutralized by the ionization of T A P S 0 to TAPS". This is normal buffer behaviour, but because the system is under electrophoresis, the newly created T A P S " ions move. Thus the T A P S 0 concentration is drawn down at a rate proportional to the flux of OH" ions. T h e boundary remains sharp: OH" diffusing forward are neutralized and T A P S 0 ions diffusing backward become T A P S ; and move forward again. T o calculate the expected boundary propagation rate, we make the assumption that the excess OH" ions in the depletion region can ionize the neutral T A P S on the undepleted side. Chapter 5 Analysis of Boundary Propagation 107 vdOH[OH]dA = vb[TAPS]bA (5-50) T h e subscript d refers to the depletion region and b to the nondepleted (background) region. Equation (5-52) shows that deeper depletion will produce a faster moving boundary and the boundary moves faster if the background region is less conductive (Experimental evidence for the latter involving depleted matrices is shown in Appendix C.2). T o actually use (5-52) requires knowledge of [OH"] and the depletion conductivity. Just calculating the ion concentrations from initial conditions does not take into account the increased concentration of Tris as it is transported into the depletion region and neutralized. Obtaining realistic values of these quantities requires actual simulation. Simulations were done using the finite difference model with buffering, as described in 5.2, with initial capillary conditions [Tris] = [TAPS] = 50mmol/L and the cathode boundary set to [Tris] = 50 mmol/L and [TAPS] from .1 to 10 mmol/L. Data from a three minute simulation with [TAPS] = 0.8 mmol/L is shown in Figure 33. T h e boundary is self-sharpening, and propagates at 12 m/C. T h e rise in neutral Tris from about 25mmol/L in the background to 100 mmol/L in the depletion region can be seen, accompanied by a rise in pH from 8.3 to 10.2. (5-51) T he boundary propagation rate in m/C is therefore I ad[TAPS]bA (5-52) Chapter 5 Analysis of Boundary Propagation 108 10 15 20 Distance from Cathode (mm) Figure 33 A five minute simulation with [Tris] = 50 mmol/L and [TAPS]=0 at cathode. As the boundary moves from left to right, the retreating TAPS" ion is replaced by OH' ions, raising the pH. T h e comparison of calculated, simulated and experimental boundary propagation rates are shown in Figure 34. T h e calculated values were obtained (5-52) by using values for [OH"]d and aa obtained by simulation, and those results closely match. A n interesting effect of the simulations is that as [TAPS] drops below 0.4 mmol/L, the conductivity actually rises. This is not observed in the experimental data. Chapter 5 Analysis of Boundary Propagation 109 18 16h 14 12 10 £• 8 CQ 6 • 6 o Calculated Boundary Propagation • Simulated Boundary Propagation • Experimental Results 50 100 150 200 250 300 Depletion Region Conductivity (u.S/cm) 350 400 Figure 34 Simulations of the depleted cathode-side buffer for [TAPS] = 0.4 to 8 mmol/L compared to experimental data. The capillary has [Tris]=[TAPS] = 50 mmol/L giving a conductivity of 1130u.S/cm. The obvious difficulty of this model is that it is not clear how such a large elevation in pH can arise. In the model, the cathode buffer is arbitrarily assigned to have a normal Tris concentration and depleted T A P S , which raises the pH. In the case where DNA is present, the Tris and T A P S carrier ions should be depleted to the same degree unless the DNA is able to selectively block the T A P S ion and allow OH" through. Such behaviour is seen in macroions at membranes but is unlikely to operate with a small ion such as T A P S . Likewise depleted cathode buffers produce moving boundaries right away, not giving enough time for the inbound Tris to raise the pH in the buffer well itself. As we showed in the previous section however, there does appear to be a rise in the pH in the depletion region, so while the Chapter 5 Analysis of Boundary Propagation 110 fixed charge model is more likely to be correct, the mismatched pH model cannot be completely disregarded until more is known about the pH in the depletion region. Chapter 6 Conclusion 111 Chapter 6 Conclusion This research has clarified for the first time the mechanism of current decline in D N A sequencing in capillary array electrophoresis. First, by analyzing current and fluorescence data from capillary array electropherograms, it was shown that current decline was the primary cause of reduced D N A read length rather than direct interference from contaminant fragments. Although the quality of the D N A peaks was preserved, current decline caused the velocity of the peaks to drop, meaning that fewer peaks arrived at the detector during the run. It was also shown that while bubbles were found in sequencing capillaries, they were not the primary driving mechanism of current decline, and in fact, expanding bubbles are likely an effect rather than a cause of current decline. It was also shown that local capillary -cooling, associated with opening the machine for buffer and sample exchanges, allowed small voids to form which permitted, in many cases , runaway bubble growth. Resuspending samples in agarose gel had previously been shown to prevent current decline. Further experiments here suggest that agarose reduces the overall quantity of injected D N A , without reducing the sample stacking efficiency, rather than preferentially reducing the loading of long fragments. In order to study current decline in more detail, a single capillary apparatus was constructed. Using 48 kb double stranded X D N A as a model molecule and commercial linear polyacrylamide matrix with T r i s / T A P S buffer, it was shown that there was a threshold for current decline of 10-15 ng of injected D N A . Capillary cutting and resistance measurement revealed that beyond the threshold, D N A induced an expanding region of ionic depletion. A novel technique of infrared imaging of the capillary was introduced enabling differences in conductivity to be observed, since the more depleted side was at Chapter 6 Conclusion 112 elevated temperature. This enabled observation of the propagating concentration boundaries in real time. T h e D N A was found to propagate with the trailing edge of the depletion region while the leading edge propagated away. Combining these data with experiments with depleted buffers and no D N A revealed that the propagation rate of the leading boundary was proportional to the depth of the depletion region. This led to a hypothesis that the threshold for current decline occurred when enough D N A was injected to cause the leading boundary to propagate faster than the D N A itself. Sub-threshold quantities of D N A would produce a smaller depletion in the downstream electrolyte so any leading boundary movement would be overtaken by the D N A itself. Analytic and numerical models were introduced to demonstrate how semi-fixed charges - approximating D N A - cause a depletion region to form in the downstream background electrolyte. A numerical simulation showed that about 16 ng of D N A was required to completely deplete the background electrolyte, in good agreement with experiment. Models of anode and cathode boundary propagation were developed. T h e D N A , propagating with the cathode boundary, was found to change propagation regimes, from biased reptation to entropic trapping, with declining field. This explained the D N A and cathode boundary's propagation rate which was non-linear with current. T h e anode boundary was found to have a linear propagation rate with current, but the mechanism by which it moved was more difficult to determine. It was shown via simulation that the most likely propagation mode involved a mismatch in positive and negative carriers in the depletion region brought on by the presence of bound charges either on the capillary surface or in the matrix. This model, Chapter 6 Conclusion 113 however, did not produce significant changes in pH, which may in fact be present. Indirect experimental evidence for a rise in pH was found through the observation of nickel particles in the matrix, which were found to change propagation direction upon entering the depletion region. This was believed to be due to a rise in p H . For that reason, another model was proposed to explain the situation where the depletion region propagates because it has an elevated p H , where OH" ions became principle current carriers. At the present time, current decline in D N A sequencing seems to be mostly under control through the injection of smaller sample quantities with better purification, and more fault tolerant, though less efficient, matrices. A s the era of single molecule sequencing draws near, the share of capillary sequencing in the overall market will best be maintained by extending continuous average read lengths as far as possible. This will require more selective matrices, however, but these matrices must maintain a good tolerance to large fragments without exhibiting current decline. It is clear that there is still much to learn about moving ionic boundaries. 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Birren, B. , Personal Communication. 2005. 99. Burgi, D. , K. Solomon, and R . L . Chien, Methods for Calculating the internal temperature of capillary collumns during capillary electrophoresis. Journal of Liquid Chromatography, 1991. 14(5): p. 847-867. Appendix A Properties of D N A and D N A Sequence Methods 125 Appendix A Properties of DNA and DNA Sequence Methods A. 1 Properties of DNA In order to understand the constraints on D N A sequencing machines and protocols, the properties of D N A needs to be understood in detail. D N A has numerous properties that can be ingeniously employed to facilitate selective cutting, copying and amplification. It is the most stable of the major biomolecules to work with and, in contrast to proteins and metabolites, D N A fragments of different sequences have the same key properties such as shape and charge density. A s a result, genomics, the large scale study of D N A , has advanced far and fast in comparison to "proteomics" or "metabolomics". Following are general descriptions of the useful properties of D N A , clone library construction and cycle sequencing and a detailed description of the methods of sample preparation used in this work. Double stranded D N A is comprised of two polymeric helices made from four deoxynucleotides: Adenine, Guanine, Thymine and Cytosine (A, G , T and C ) attached to a sugar phosphate backbone. A and T and G and C are each structurally complementary and non-covalently bond to each other, so in the double helix, A is always opposite T and G opposite C . This creates excellent binding specificity as the probability of a sequence of N random nucleotides being complementary to another is N" 4. Long double strands of D N A can be melted at 9 5 ° C into single strands, and annealed again at 5 0 ° C . D N A can be copied by polymerase enzymes which extend a complementary copy along one of the single strands. T h e deoxyribose backbone of Appendix A Properties of D N A and D N A Sequence Methods 126 the D N A has 5 carbon atoms with hydroxyl groups on the 3' and 5' carbons and extension always occurs from the 3' end of the extending fragment towards the 5' end of the complementary fragment. There also exist restriction enzymes, which cut D N A at sites with D N A sequence unique to each enzyme. G e n o m e s of different organisms vary in size, from a few million D N A base pairs for bacteria to a few gigabases for mammals to ten gigabases for certain plants. The D N A is packed into chromosomes which can be extracted from cells and purified for analysis. Near random sequences of D N A are easiest to sequence, but the high binding strength of the G and C nucleotides make so-called " G C rich regions" difficult to sequence. Regions with many short repeated sequences are also difficult as single stranded copies can loop back and undergo complementary binding with themselves. Special reaction conditions can be used to overcome these difficult regions. A. 2 Library Construction There are directed and random strategies for dividing a genome up for sequencing, but all ultimately require the production of fragments a few kilobases in length. These must then be separated and individually amplified to produce enough starting material to perform the cycle sequencing reaction to produce the 20 to 1000 bp fragments which will actually reveal the sequence. Overlapping sequence data from these individual fragments are then reassembled into the genome in silico. Th e lowest cost and most bias-free method of genome sequencing involves preparing libraries of randomly sheared fragments which are stored in E. coli cells which can be amplified as needed. T h e s e are called clone libraries. T o make clone libraries, randomly sheared fragments are ligated into a break in a circular piece of D N A called a vector (either a Appendix A Properties of D N A and D N A Sequence Methods 127 plasmid or a phage), capable of reproducing in bacterial cells. T h e unknown fragment plus vector, ligated back into a circle, is called the template, because copies will be made from it for sequencing. T h e template is then incorporated into E . coli cells by creating holes in the cell walls, either chemically, or through an electrical process called electroporation, which allows the template to diffuse into the cells - a process called transformation for prokaryotic cells. The concentration of template and E. coli are adjusted so that essentially all the successful transformations involve one vector only entering a cell. The cells are then "plated out" on agar gel based growth media. Surviving cells capable of reproduction can then establish individual colonies, where each daughter cell has a common ancestor, and contains a common template. The original vector into which the inserts were ligated contains one gene with resistance to antibiotics and another, (usually Lac-Z) which makes a blue pigment. The colony growth media contains ampicillin, so only the cells which incorporated a vector with the antibiotic gene survive. T h e inserts are actually ligated right into the middle of the L a c - Z gene so the cells that incorporated a vector containing no insert survive, but appear blue, while the vector-plus-insert colonies have a non-functioning L a c - Z gene and are white. The white colonies, each containing about 10 6 cells, can then be picked from the growth media using a robot. Those colonies are grown further in 384 well incubation plates so enough of each colony exists that the insert can be extracted. These arrays of cell colonies in 384 well plates, each well containing one vector and D N A fragment of interest are called clone libraries. The advantage of maintaining the library as template in E . coli cells is that cells from each colony can be stored, re-plated, grown and sequenced as needed. T h e best common approach to large scale sequencing today is to actually construct the libraries in two steps. A clone library of Appendix A Properties of D N A and D N A Sequence Methods 128 random fragments of order 100kb are ligated into bacterial artificial chromosome (BAC) vectors and grown in a similar way to the shorter plasmid vectors. These B A C s , whose locations with respect to each other are found through a process called restriction fragment mapping, are then sheared into random fragments, to make sequencing clone libraries. A.3 DNA Purification The next step in preparing sequence fragments is taking some of the clone libraries and extracting the template. A typical low-cost protocol, and one used in the present experiments, is the alkaline-lysis approach [96]. First, some cells are transferred from the clone library to new plates which are incubated again produce more D N A . T h e s e cells are then centrifuged into a pellet, the supernatant discarded and the cells resuspended in buffer (usually Tris-HCI) and E D T A (ethylenediaminetetraacetic acid). E D T A chelates divalent metals ions, which inhibits D N A s e s (enzymes that cut DNA) . T h e cells are then lysed with sodium hydroxide (NaOH) and sodium dodecyl(lauryl)sulfate (SDS , a common detergent). T h e S D S makes holes in the cell membranes and the N a O H denatures the cellular D N A , separating it into single stranded fragments (ssDNA). T h e template D N A is circular however, so is topologically constrained. Potassium acetate (KAc) is then added, which does three things: T h e circular D N A is allowed to renature but sheared cellular D N A remains denatured. The s s D N A is precipitated, since large s s D N A molecules are insoluble in high salt. Adding K A c to the S D S also forms K D S , which is insoluble. This allows for the easy removal of the S D S from the plasmid D N A . T h e sample is again centrifuged to remove cell debris, K D S and cellular s s D N A . T h e template, and potentially some Appendix A Properties of D N A and D N A Sequence Methods 129 genomic D N A , is in the supernatant, while all other unwanted material is in the pellet. The supernatant containing the D N A of interest must then be cleaned of excess salts. Ethanol or isopropanol and a salt - usually ammonium acetate - are added to the solution causing the D N A to precipitate out of solution while other ions remain. Centrifugation collects the D N A in a pellet at the bottom of the well at which point it can be resuspended in buffer, ready for cycle sequencing. A.4 Cycle Sequencing T h e method of D N A sequencing by electrophoresis was developed by Sanger [30] and independently by Gilbert and Maxam [31], in 1977. Although the original protocol is still in use in low throughput settings, it involves radio-labelled nucleotides and a separate separation must be done for each of the four bases. A significant advance occurred in 1986 when Hood et al. [32] reported laser-induced fluorescence (LIF) detection methods for D N A . With four different flourophores, separation was now possible in one lane rather than four, with no radiation handling issues. This sequencing protocol is in wide use, and is carried out in the following way: Template (the vector plus insert described above) D N A is mixed with deoxyneucleotides (dNTPs: , A , C , G , and T) , dideoxyneucleotides (ddNTPs) , D N A polymerase (enzymes which add complementary d N T P s and d d N T P s to a strand of DNA) and a ~20bp primer. T h e primer is complementary to a region on the template strand immediately adjacent to the insert, so any insert can be copied regardless of sequence. T h e key to this method is the d d N T P s , which differ from d N T P s by the lack of a 3' hydroxyl group. This prevents another nucleotide being added after a d d N T P is incorporated. T h e Appendix A Properties of D N A and D N A Sequence Methods 130 d d N T P s are also fluorescently labeled, with a different colour for each of the four nucleotides. T h e reaction occurs at three temperatures. Above 9 0 ° C , the D N A denatures, becoming single stranded. The temperature is then lowered to 5 0 ° C , and primers bind to the template. The temperature is then raised to 6 0 ° C and the polymerases begin extending the primer with the available d N T P s , making a complementary copy of the insert. Crucially, the d N T P s and d d N T P s are mixed in a proportion of about 100:1. A s a result, some fragments of each size are produced, each sharing a common starting point but terminated at a different nucleotide. A s each terminating nucleotide has a dye molecule specific to its type, A , C , G or T , when the fragments are separated by length, the terminating nucleotides can be identified by colour. Cycle sequencing reactions typically use thirty thermal cycles to generate enough D N A for sequencing. After thermal cycling, samples are again cleaned up with ethanol precipitation, and then dried down in their reaction plates, ready for sequencing. Just before loading the plates onto the sequencers, the samples are resuspended in d H 2 0 . T h e full protocol normally involves aliquoting the ethanol purified template into two new plates before cycle sequencing and then performing the cycle sequencing reactions using one primer specific to each end of the template in each plate. T h e two sequences that result are complementary to each other, and may or may not overlap, depending on the length of the insert. Sequencing data is assembled into actual D N A sequence by comparing different pieces of sequence to find where they overlap. Overlapping pieces can be assembled into contigs of continuous overlapping data. For a purely random genome, the assembly error probability is Appendix A Properties of D N A and D N A Sequence Methods where N is the number of reads, L is the average read length, and G is the total length of D N A to be reassembled [8]. Clearly longer read lengths L and a greater number of reads N are desirable. In fact for high quality genome sequencing, at least five times overlap is required. Sequencing via B A C maps, where the location in the genome of each 100-200 kb B A C is known, reduces the value of G from order 10 9 to 10 5 . This is in fact a principle source of contention in the C e l e r a / H G P debate as it has been argued that Celera Genomic's "whole genome shotgun" approach would never have worked had they not used the Human G e n o m e Project's framework to enhance their accuracy. Interestingly, the error probability for real genomes, which are up to 10% repeats, has not be been formally studied. It is postulated that as many key repeat intervals in genomic D N A are on the order of 1 kb, so read lengths of 1.5 kb would provide a significant advantage, but this has never been quantified [97],[98]. A.5 Genome Sciences Center Sample Preparation T he samples prepared for experiments performed on the M e g a B A C E were prepared in the following manner. This protocol is reproduced from Watcher et al. [58] which details experiments in resuspending samples in dilute agarose to prevent current decline. Further results stemming from this work are reported in section 4.1 and Appendix B.1. Bacteria containing a single clone from the Mammalian G e n e Collection (MGC-10790) were inoculated into each well of a 96-well culture block (Beckman Coulter) in 1.2 mL of 2xYT media (Becton Dickinson) supplemented with Chloramphenicol (Sigma) at 12.5 jug/mL. T h e block was sealed with a sheet of A i r P o r e ™ tape (Qiagen) and incubated for 16 hours at 3 7 ° C with agitation at 290 rpm in a New Appendix A Properties of D N A and D N A Sequence Methods 132 Brunswick Scientific shaking-incubator fitted with custom holders. Following growth, cell pellets were collected by centrifugation for 20 minutes at 1400 g and the media decanted. T h e plasmid D N A was then isolated using the modified alkaline lysis procedure described above. Cycle sequencing was performed using D Y E n a m i c energy transfer (ET) dye brew mix (Amersham Biosciences). T o increase the speed and efficiency of fluid transfers and decrease well-to-well variability all fluid transfer steps were performed with Hydra 96-channel microdispensers (Robbins Scientific). All solutions and reactions were prepared with deionized 18 M Q c m water. 6 uL of the homogenized template D N A (164 ug/mL) was sequenced in each well of 28 96-well P C R plates. E a c h 20 ul_ reaction contained 8 uL of D Y E n a m i c E T brew mix, 5 pmol o f - 2 1 M 1 3 forward primer, and 6 ul_ of D N A , the remaining volume was d H 2 0 . Cycle sequencing was performed in a P T C - 2 2 5 D N A engine tetrad (MJ Research) with a ramp speed of 3 ° C / s e c using 30 cycles of 9 5 ° C for 20 s, 4 8 ° C for 15 s, 6 0 ° C for 1 min, followed by incubation at 4 ° C . For the experiments in agarose resuspension, the sequencing reactions from all plates were collected by centrifugation after thermal cycling, pooled and re-aliquoted into 28 fresh 96-well Robbins plates. T o concentrate the sequenced products and remove extra salts and dye-terminators, the reactions were ethanol precipitated. 60 uL of 95% ethanol and 2 uL of 7.5 mol/L ammonium acetate (pH 7.5) were added to each well and, after mixing by repeated pipetting with a Robbins Hydra, D N A precipitates were collected by centrifuging the cycle plate for 30 min at 2750 g at 4 ° C . The ethanol/salt mixture was decanted immediately following centrifugation by inverting and vigorously shaking the plates to remove the liquid from the wells. Following a wash with 150 uL of 70% ethanol the plates were spun inverted at 700 Appendix A Properties of D N A and D N A Sequence Methods 133 g over paper towelling for 1 min to remove any residual ethanol. The reaction pellets were dried in a S p e e d V a c with the rotor removed, on high heat for 2 minutes. T h e plates were sealed with foil tape and the precipitated sequencing reactions were stored at - 2 0 ° C in plastic bags. For the experiments in bubble growth and propagation reported in section 4.2 and Appendix C , 96 well plates with ethanol purified template dried down and stored at - 2 0 ° C were received at the Marziali lab, and cycle sequencing and ethanol precipitation were performed as described above. T h e only difference was that reagents were added manually using a single channel Gilson Distriman manual pipettor and an eight channel electric pipettor instead of a Robbins Hydra. T h e samples were also not pooled and realiquoted after cycle sequencig Appendix B T h e Effect of Sample Resuspension in Agarose 134 Appendix B The Effect of Sample Resuspension in Agarose B.1 Effects of Injection from Agarose A n initial motivation for research into current decline was to find methods to mitigate current decline with minimal added cost in sample preparation steps, reagents or hardware. Reducing the concentration of long fragments through restriction digests or filtration had been reported [14, 42, 57] but none had been widely adopted by genome centers, presumably for cost reasons. Resuspending the sample in agarose prior to electrokinetic injection was instead suggested as a low cost method to preferentially reduce the concentration of long fragments during electrokinetic injection. This method was investigated at the Marziali lab and at the G e n o m e Sciences Center and ultimately adopted as standard procedure on the M e g a B A C E 1000 at the G S C . T he G S C proved the agarose resupension technique by resuspending identical pooled and realiquoted samples from a single clone from the mammalian genome collection (MGC-10790) in d H 2 0 and various concentrations of Agarose [58]. Sample preparation is described in detail above in Appendix A . 5 Pairs of identical plates were resuspended in 20 u l dO.02% to 0.6% (SeaKem Gold Agarose -F M C Bioproducts). O n e plate from each pair was sequenced on each of the two M e g a B A C E s at the G S C . With agarose resuspension, average read lengths rose from 198 to 653 bp and "successful" runs, Appendix B T h e Effect of Sample Resuspension in Agarose 135 classified as more than 50 Phred20 bases, increased from 47% to 98.4% of reads. 20 40 60 Total Loaded Charge (mC) 800 700 600 500 400 300 200 100 (b) Agarose 20 40 60 Total Loaded Charge (mC) Figure 35 Read length vs total loaded charge for (a) Samples resuspended in dH20 as shown in Figure 8. (b) The same samples resuspended in 0.06% agarose. Each "x" is one capillary. The cause of the improvement with agarose was made clear by analyzing the raw current and signal data. Figure 35 compares total loaded charge after injection from water resuspension, (also shown Figure 8), with T L C after agarose resuspension. While in section 4.1 a correlation between T L C and read length was shown, the agarose almost completely prevented current decline from occurring. Almost all capillaries after agarose resuspension show a T L C over 40 m C . Appendix B T h e Effect of Sample Resuspension in Agarose 136 While the efficacy of loading from agarose was demonstrated, it was not known if the reduction in incidence of current decline was due to preferential suppression of large fragments or an overall suppression of fragments. This was investigated in the Marziali lab using the single capillary instrument. Samples of 1 kb ladder (New England Biolabs N3232S) consisting of 0.5 to 10 kb double stranded fragments was used as a sample with a representative size range, but with more a consistent injection behaviour then cycle sequence products, which likewise led to the choice of X D N A for current decline experiments. 20 u.L of ladder was mixed into 20 u.L 5x Sybr Green and 60 u,L d H 2 0 to make 10 x 10 uJ_ aliquots. These were dried down and resuspended in either 10 uL d H 2 0 or 10 ul. of 0.08% Agarose (Seakim Gold, F M C Bioloabs) dissolved in d H 2 0 . The samples were then injected for 15 sec at 5 (j,A and run at 2 jaA. Representative electropherograms are shown in Figure 36. T h e ratio of the areas of the 3-10 kb peaks to the 500/517 bp peaks for each electropherogram was then found. T h e average ratio for three samples resuspended in d H 2 0 was 9.6 and the average for three samples resuspended in Agarose was 8.9, a difference of about 7%. T h e reduction in peak area for the 500/517 bp peaks were about 12% from water to agarose, and 18% for the 3-10 kb peaks from water to agarose. In other words, the overall reduction in injected D N A was larger than the preferential reduction in longer fragments. Figure 36 Electropherograms of 1kb ladder resuspended in Dl H20 and 0.08% Agarose Although long fragments could not be seen at the detector of the M e g a B A C E , the signal intensity of the first fragments could be measured. Data from the four plates shown in Figure 35b was analyzed in the following way. Capillaries with a total loaded charge over 3 0 m C , were isolated, as capillaries with lower T L C exhibited inconsistent florescence data. T h e flour channels of fluorescence data in the high T L C capillaries were summed and the first fifteen minutes of that data starting from the onset of peaks at the detector was integrated to get a signal strength value for each capillary. T h e s e were then averaged over all high T L C capillaries on that plate. T h e results, shown in Table 3, indicate that, the quantity of small fragments was Appendix B T h e Effect of Sample Resuspension in Agarose 138 reduced by about 20% by the agarose. T h e large variation in injected fragment quantity can also be seen in the range of values obtained. Machine Integrated Fluorescence Arb. Units % Drop d H 2 0 0.06% Agarose MB1 2 2 0 ± 1 2 0 1 6 4 ± 7 5 25% M B 2 1 1 5 ± 3 5 9 8 ± 2 1 15% Table 3 Signal strength of the first -50 DNA bases in capillaries resuspended in Dl H20 and Agarose. Machines refer to the two MegaBACE sequencers at the GSC. Taken together, the M e g a B A C E and single capillary data for the effect of Agarose resuspension indicate that some preferential reduction in injection of large fragments is accompanied by a comparable reduction in the quantity of all fragments injected. This would tend to militate against the use of agarose in current sample preparation protocols even with a more sensitive but fault prone gel as dilutions have reduced the quantity of sample to near detection limits. (It was in fact found that the surface tension of liquid agarose made pipetting into 384 well plates impractical). T h e curious aspect of these results is that if agarose merely reduced the quantity of fragments across the board, the same result ought to be achievable by reducing injection time. This has never been reported as a viable option and it is not known why. Perhaps the most plausible explanation is that the agarose works by preferentially retarding very long genomic fragments and that in fact these very long fragments are the primary culprit in current decline. T h e quantity of shorter (<10kb) fragments may not be so critical in this matrix formulation, despite published reports in the past Appendix B The Effect of Sample Resuspension in Agarose showing current decline to occur with template sized fragments. [14, 42]. Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 140 Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. There are two effects which were observed in the course of this research which do not contribute to the main current decline effect, but should be of interest in understanding secondary current effects observed in capillaries. The first of these is the permanent effect depletion region formation has on the capillary. It is believed that a buildup of surface charge at the entrance to the capillary appears, which cannot be removed by replacing the matrix, and results in a mild depletion region formation every time the capillary is subsequently run. The second phenomenon is the rapid current decline occurring when the tube of matrix at the anode is replaced by buffer, as per the G S C ' s cost saving protocol. This is consistent with some positively charged species being removed from the matrix and is an example of the moving boundary equation in action. Finally, bubbles are revisited and it is shown how, despite bubbles not being the principle cause of major current decline, bubbles do contribute to the problem. C. 1 Permanent Effects of DNA-lnduced Depletion Regions. It was observed that after formation of a DNA-induced depletion region, subsequent running of the capillary with new matrix and buffer would produce a depletion region at the cathode end without DNA or any other modifying agents. This phenomenon was found to occur consistently after the formation of a DNA-induced depletion region, but Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. not after injection of D N A below the threshold for depletion region formation and not after the formation of depletion regions with depleted buffers. W e tentatively call these "surface charge-induced depletion regions" (SCIDRs) as the formation mechanism survives matrix replacement so must be on the capillary surface, and it was shown in chapter 5 that the presence of bound charges is likely to be the cause of boundary movement of this type. A typical S C I D R is shown in Figure 372. Distance From Cathode (mm) Distance From Cathode (mm) Figure 37. Infrared images (left) of a surface charge induced depletion region (SCIDR) propagating at 2 m/C. The conductivity profile (right), obtained by capillary cutting after the run finished, represents the capillary at the bottom edge of the left image at time t=23 min. 2 If it is established that pH changes are the principle cause of boundary movement, these boundaries could be known as SpHIDRs! Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. T h e driving mechanism for S C I D R s was found to be localized at the entrance of the capillary as shown in Figure 38. Here, X D N A and its depletion region were allowed to propagate into the capillary about 10mm. T h e matrix was then pumped out and the cathode buffer replaced. The subsequent S C I D R propagated right past the area affected by the D N A and depletion region. Neither the quantity of injected D N A nor the DNA's run time was found to correlate with the subsequent degree of S C I D R depletion or its propagation rate. Time (min) Time (min) Figure 38 A fresh capillary with (a) X DNA injected to form a depletion region, and (b) running the same capillary with fresh LPA and cathode buffer. Current is shown, unsealed, in black. The depletion region in (b) propagates right past the area affected by the depletion region in (a). Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 143 Even more direct evidence for changes at the capillary entrance being the source of S C I D R s is shown in Figure 39 where a S C I D R was allowed to grow to about 10mm. T h e first millimeter of capillary was then clipped off. T h e S C I D R boundary traveled forward another two millimeters and then came to a halt. W h e n the L P A was again pumped out and electrophoresis restarted, no depletion region formed, which indicates that the part of the capillary causing the S C I D R had been permanently removed. This same experiment was repeated with D N A (not shown) where the IR image was used to locate the cathode boundary which was clipped off after five minutes. T h e anode boundary continued in another two millimeters and again came to a halt. 2 4 6 8 Time (min) 2 4 6 Time (min) Figure 39 (a) A SCIDR advancing into the capillary at 2.1 m/C. (b) After clipping the first millimeter of capillary, the boundary advances at the same rate for a further 2-3 mm and then holds stationary. Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 144 T h e observations described above are intriguing and shed some light on how S C I D R s may form as well as, more generally, how the anode boundaries may propagate. A s this is a surface effect, it must involve interactions with the surface coating. The ant i -EOF coating in these capillaries is made by replacing the easily hydrolyzed S i - 0 bonds at the surface with S i - C . T h e s e are then linked to acrylamide polymers which remain fixed in place at the wall and presumably interact with L P A as it is pumped in to prevent it from moving under E O F [48]. Deterioration of the coating is believed to manifest itself through some combination of shearing of the fixed acrylamide, hydrolysis of exposed S i - 0 groups and adsorbtion of charged species onto the capillary wall. The fact that S C I D R s are driven by some wall modification close to the entrance of the capillary suggests either a localized pH rise resulting in rapid hydrolysis or adsorbtion of D N A onto the capillary wall. It is not clear why either of these effects should occur only at the entrance of the capillary. T h e fact that the boundaries come to a halt and the depletion regions remain fixed after the source of the depletion region is removed is to be expected. O n c e a change in concentration is established and the ionic species in each region are restored to the same proportions, the regulation function requires that the boundary remain stationary. That this boundary remains fixed also lends strong weight to the notion that the boundary is definitely not driven by a change in transference number as in equation (5-42). T he residual movement of the boundaries after the end of the capillary is clipped is interesting and the reasons why are not clear. If fixed charge was causing the boundary to move, it might be expected to keep moving as further fixed charge would continue to be exposed. If the fixed charge was induced by a change in pH on the capillary surface or in the acrylamide, the restoration of the pH would presumably neutralize this effect. If the S C I D R boundary is driven by a pure change in pH, as described in section 5.4.5, the excess OH" ions in the depletion region will be swept out by T A P S " ions coming in from the newly clipped end of the capillary. If the depletion region is of length ld, the remaining Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 145 OH" ions in the depletion region [OH"]d can move the boundary forward a distance le according to [OH-]d 1=1 d [TAPS0]" ( C - 1 ) where [ T A P S ° ] b is the neutral T A P S concentration in the background region. T h e depletion region conductivity is assumed to be 160 u.S/cm and | T A P S 0 ] b = 25mmol/L. Equation (5-52) then gives the correct propagation rate if the depletion region's pH is 9.3 of [OH"] = 0.02 mmol/L. This, however, gives a residual propagation distance le of 7 urn, more than two orders of magnitude too small. While the nickel particle data suggests the pH does indeed rise, this datum suggests the pH rise itself is not the only mechanism moving the boundary. T h e s e conclusions are not necessarily contradictory: the actual rise in pH is not known and it may not take a large rise in pH to charge the nickel particles enough to change direction. A small rise in p H , not enough to move a boundary, may be enough to charge the relevant species enough to display the observed behaviour. Intuitively, the mechanism that best fits the data is that some pH change does occur which has the effect of locally charging the matrix or capillary wall. How this charge-induced pH change occurs and how the inside of the capillary is affected are unknown. This clearly represents an opportunity for significant future investigation. Future work could involve thermal imaging and capillary cutting as well as online monitoring of pH with U V detectors and indicator solutions as well as the setting up of artifical pH gradients and possibly different matrix polymers. A s an aside, it emerged in the course of this analysis, that the depth of single-sided depletion regions could be calculated from the rate of current decline, assuming a given background conductivity and consistent behaviour at the anode. This was done by fitting the current to the rising resistance: Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 146 1(f) V (C-2) * 0 ( ' - * » ( ' ) ) + off where R 0 is the initial resistance/unit length, I is the capillary length and xb(t) is the measured boundary position. T h e depletion region resistance Rd, and R0ff, an offset for the part of the capillary submerged in the buffer, are free parameters. For Figure 38b this gives a depletion depth of 160 uS/cm, similar to that observed for the cut capillary in Figure 37. This method is only useful when there is only one depletion region and the rest of the capillary is electrically stable. In such circumstances it can be used to nondestructively estimate the depletion region conductivity. C.2 Matrix ion depletion from anode-side buffer. 10 4 0 2 4 6 8 10 Time (min) 12 14 16 18 20 Figure 40: Typical current decline associated with depleted matrix for a 36cm capillary after replacing the LPA matrix at the anode with aqueous buffer and applying 5000V. Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 147 A s discussed in section 3.1, it was observed that replacing the L P A at the anode end with buffer would cause the current to decline by about 50%, and then stabilize. A typical example of this highly repeatable current decline is shown in Figure 40. Assuming a sharp moving boundary between regions of different conductivity, a propagation rate was calculated from the time taken from the beginning of the run to when the current stabilized. This corresponded to a propagation rate of 75 m/C. A capillary was then cut up from the anode end after four minutes run time and a boundary was indeed found at the location predicted by the propagation rate. T h e anode-side conductivity was typical for that of undepleted capillaries and the cathode-side conductivity was typical of that for completely depleted capillaries. 1200 1000 + — 800 I" 600 O 400 200 - • I - -o<x>o ^ o O o ° O Resistance Conductivity 1800 1600 1400 1200 _ E c O 1000 E 800 S in 'i 600 K 400 200 30 25 20 15 10 Distance to A n o d e (cm) Figure 41 Cut capillary data from four minutes into matrix depletion. The anode and cathode sides of the boundary are 958 and 545 uS/cm respectively. Note that this change in conductivity is associated with a very subtle change in the slope of the resistance curve. Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 148 In ignorance of buffer and matrix components, it is not possible to say exactly what process is occurring in the capillary. T h e moving boundary equations and regulation function, however, can give some insight into the properties of the moving ions. This self sharpening boundary must be propagating at the speed of the leading ion. This rate of 75 m/C in the 1200 u,S/cm background electrolyte corresponds to 40x10"9 m 2 / V s . This is faster than Tris and more typical of small positive ions like N a + . This suggests that an ion left over from the polymerization of the L P A is being removed [89]. T h e situation that is believed to arise is similar to that shown in Figure 25 where there is a fixed boundary at the anode entrance to the capillary defined by the regulating function, and a moving boundary with different ionic species on either side. This explains the experimentally observed result that increasing the buffer concentrations at the anode doesn't change the capillary conductivity. A s noted, it is not known what ion is being removed from the matrix, although it is possible that it is excess T E M E D [47]. T E M E D is basic, so would produce a positively ionic species. In fact, equations (5-35) and (5-39) can be solved numerically for the concentrations of Tris and the unknown ion in the undepleted matrix. If the concentration of T r i s + and T A P S " is assumed to be 25 mmol/L on the depleted side, and given mobilities in Table 2, the dissociated [Tris+] = 5 mmol/L and [unknown ion] = 24 mmol/L on the undepleted side. If the L P A had started with 50 mmol/L T r i s / T A P S these concentrations of undissociated species could easily arise in an excess of a positively charge free ion and would give a pH of 8.7. In about 75% of cases where matrix depletion was recorded, two abrupt transition points were visible at the end of the period of current decline. T h e s e are shown, along with what is believed to be their cause, in Figure 42. T h e first point corresponds with the matrix depletion boundary from the anode crossing a S C I D R boundary from Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 149 the cathode. T h e second point corresponds to the matrix depletion boundary exiting the cathode end of the capillary. T h e IR image shows the S C I D R boundary speeding up from 1.7 to 3.1 m/C as the invisible-to-infrared matrix depletion boundary comes past. This is to be expected from equation (5-52) as conductivity drop from (typical values of) 1100 to 600 u.S/cm would predict exactly such a rise. T h e D N A -induced depletion region adjusts its propagation rate in the same way, shown in Figure 42(b). Th e anode-side of its depletion region propagates across the S C I D R at 68 m/C, then slows to 16 m/C, a typical rate in depleted matrix. Inspection of all the matrix depletion data showed that cases where these transitions were observed always corresponded to cases where X D N A had been previously introduced. Fresh capillaries did not show this behaviour. Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 150 Time (min) Time (min) Figure 42 (a) Thermal images of a surface charge induced boundary crossing an invisible-to-IR depleted matrix boundary. The upward traveling SCIDR boundary initially propagates 1.7 m/C, rising to 3.1 m/C as it crosses the downward traveling depleted matrix boundary. Note the change of slope of the thermally imaged depletion region at t = 11 min in (a). Current, falling from 9 uAto 5 uA, is shown in black, (b) After the DNA is injected, the anode boundary races to the edge of the SCIDR boundary at 68 m/C where it slows to 16m/C. C.3 Bubbles' Effect on Current It was found that although bubbles are not a primary source of current decline, they do act to perturb current decline and affect depletion region growth. The relationship between bubble and Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. depletion region growth was examined in detail with thermal and visible light imaging combined with capillary cutting. Bubbles were introduced by capillary cooling and then X D N A was injected. Figure 43 shows a representative example. While bubble growth occurs with the depletion region, the depletion region actually grows faster than the bubble, while the bubble appears to be driven forward with the cathode boundary. This was typical of continuous long bubbles in the single capillary instrument. Time (min) Figure 4 3 : Infrared (top left) and visible (top right) images of the capillary showing simultaneous growth of a hot region and bubble. The positions of the two are superimposed below, showing the hot region advancing substantially ahead of the bubble. The depletion region boundaries are shown with (*) and the bubble boundaries with (•) Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 152 35 | 1 1 1—: 1—: 1 i r Position (mm) Figure 44 A histogram showing observed bubble positions after one run. The bubble's cathode ends line up with the expected location of depletion regions seen in bubble-free measurements, but the bubbles are mostly shorter than the 60-70mm of depletion region that could account for the observed current. Indirect evidence of the same behaviour is seen in the M e g a B A C E . Figure 44 shows data from one plate where continuous long bubbles were isolated and binned by cathode end location and length. Most bubbles begin 25-30 mm into the capillary and are 25 to 30 mm long. T h e bubbles' cathode ends are approximately coincident with cathode side boundaries of ionic depletion regions observed with the single capillary instruments for runs of comparable total loaded charge. T h e s e bubbles are, however, considerably shorter than the Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 153 60-80mm ionic depletion regions at 2-5% of the background conductivity required to produce the observed current in the single capillary experiments. T h e s e 20-30 mm long bubbles would have to have a surrounding conductivity of about 1% of the background electrolyte, lower than any measured depletion region. W e conclude therefore that Figure 44 shows the same effect as Figure 43, and the depletion region expands faster than the bubbles and that the bubbles are definitely not the cause of current decline even where they are well developed. Although bubbles are clearly not the principle cause of current decline, they do manifest themselves in the current data in the form of current variability. Consider again the two plates shown in Figure 8, page 44, and Figure 35(a), page 135. T h e s e were called plate 4105 and plate 4106 in the G S C ' s records and will henceforth be together called 41 Ox. In single capillary experiments, the rate of current decline in bubble-free runs was very repeatable, as shown in Figure 11 and Figure 12. If such behaviour was observed in the M e g a B A C E , one would expect the 41 Ox plates to show a bimodal distribution, with all capillaries showing either no decline and T L C - 5 0 m C or current decline and T L C - 1 0 m C . Figure 45 bins the 41 Ox plates' T L C by frequency. There is biomodal behaviour, with peaks at 10 and 50 m C , but there are a substantial number of capillaries with intermediate charge as well. These are capillaries where bubble growth is causing some degree of current decline without the existence of a depletion region. Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. 154 70 | 1 1 1 r 1 1—: 1 1 1 r Total Loaded Charge (mC) Figure 45. A histogram of the data in Figure 8(a), binning the capillaries by total loaded charge. Some bimodal behaviour is observed. T h e source of these intermediate degrees of current decline can be seen in Figure 46, which shows current traces for the 4105 plate. A menagerie of unusual behaviours is seen. D07 and E10 show the current declining for a time and then rising. A06 and B04 show high frequency dips early on while in A08 the dips persist. D09 shows a profile consistent with bubble-free decline. Column 06 shows various capillaries which experience about 25% decline. High frequency (on the order of minutes or sections) variations have been reported elsewhere [42] and are consistent with our single capillary observations of artificially introduced bubbles. It may be that local heating temporarily pinches off the current, causing it to fall, which in Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour. turn cools the capillary and shrinks the offending bubble. Capillaries such as C02 which experience steady decline at a lower rate are consistent with "bubble trains" seen in the M e g a B A C E and single capillary instrument where one bubble propagates many centimeters into the capillary, leaving a string of small bubbles behind it at regular intervals. These could generate enough resistance to cause current decline but at a rate lower than that associated with the growth of a full blown depletion region. 01 02 03 04 05 06 07 08 09 10 11 12 1" O D -t—' • P"™"»--v», I N - -Time 0-240 min Figure 46 Current traces from one plate from the MegaBACE. The Y-axes are current (0-4 \iA) and the X-axes show time (0-240 minutes). For a description of bubble types see text. Appendix D L P A and Buffer Properties 156 Appendix D LPA and Buffer Properties D. 1 Conductivity and pH of Tris/TAPS Buffer Under Dilution For various reasons, it was necessary to measure the conductivity and pH of the buffer under different temperatures and dilutions. First, no value of the mobility of the T A P S ion was to be found in the literature. Second , the effect of buffer depletion on moving boundaries (section 5.4) or charged particles (section 5.4.4) would be mediated by a change in molar conductivity (o7C) and/or p H . 1.2 g of Tris and 2.4 g of T A P S were dissolved in 200 mL d H 2 0 to give a 50 mmol/L solution. T h e conductivity and pH were measured using a V W R Model 8000 pH meter and a V W R Bench/Portable conductivity meter. The solution was then diluted by factors of two. T h e concentration of the dissociated ions was then calculated using the chemical equilbrium algorithm described in section 5.2 and fit to the observed conductivity data to find the mobility for T A P S , U T A P S was found to be 25x10"9 m 2 A / s . Appendix D L P A and Buffer Properties 157 Figure 47 (a) (•) measured conductivity data fit with U T A P S = 25x10"9 m2/vs. (b) measured (•) and calculated (+) pH values. T h e striking feature of the data in Figure 47 is the linearity of the conductivity over two orders of magnitude of concentration. This is different from the behaviour of most strong electrolytes, whose ions obey the Onsager limiting law near 1 mmol/L [87]. /U = jU0+Ay[C (D-1) Appendix D L P A and Buffer Properties 158 35 Temperature °C 20 25 30 35 40 Temperature °C 45 Figure 48 The temperature dependence of (a) pH and (b) conductivity in 50 mmol/L Tris-TAPS. dpH/dT = -0.02 and da/dT= 0.02. Figure 48 shows the temperature variation of pH and conductivity of the T r i s / T A P S . The former shows that the pH change is relatively small over the range of temperatures seen in this work (up to 7 ° C above ambient). T h e relationship between conductivity and temperature shows the aforementioned 2 % / ° C variation discussed in the text. D.2 The Thermal Expansion Coefficient of LPA T h e thermal expansion coefficient of L P A was measured to test the hypothesis that matrix shrinkage due to cooling could cause bubbles to form in capillaries. This is discussed in section 4.2.2. L P A , Appendix D L P A and Buffer Properties 159 which is about 95% water, was, surprisingly, found to have a thermal expansion coefficient almost twice that of water. Coefficients for water and L P A were measured by heating a filled capillary in the single capillary instrument, removing the anode and cathode buffer wells, and then removing the capillary. T h e distance to the resulting menisci at each end of the capillary was measured, and the coefficient of thermal expansion calculated from AL 1 (D-2) a = AT L where L is the portion of capillary (200 mm) subject to temperature change. In this case the temperature changed from 5 0 ° C to 1 8 ° C , resulting in the d H 2 0 shrinking 2 mm and the L P A shrinking 4 mm. T h e thermal expansion coefficients were respectively: a = 2.7x10"4 °C" 1 for water and a = 5.2x10"4 °C" 1 for L P A . In fact, a for water is irregular and falls from 0 - 4 ° C , is 0 at 4 ° C , 2x10"4 at 2 0 ° C and 4x10"4 at 4 0 ° C . It is probably reasonable to assume that L P A has twice the thermal expansion coefficient as water over the range of 2 0 - 4 0 ° C . T h e average value of a for L P A in the temperature range of interest is therefore taken to be 3.8x10"4 °C" 1 Appendix E Temperature Measurement Appendix E Temperature Measurement It was initially thought that the actual temperature of the capillary might have a significant role to play the propagation rate of depletion regions. T o that end, the temperature of the capillary was measured, first by thermal imaging with a reference temperature and then by direct measurement using a thermocouple bonded to the capillary. While it has been shown that temperature effects were unlikely to play a major role boundary movement, these infrared and thermocouple methods can be checked against literature values Figure 49 A still image from the infrared camera showing the LIF objective on the left, the capillary with the region of elevated temperature at center, and the reference heater on the right. The latter has a piece of capillary glued to an aluminum strip, with thermocouples located top and center. Appendix E Temperature Measurement Figure 49 shows the capillary with hot region, microscope objective on the left and reference temperature device on the right. T h e latter has a piece of capillary glued with epoxy to an aluminum holder. O n the back side of the aluminum, a loop of nichrome wire was glued down with a thermocouple (Omega Type T) bonded in the center. Another thermocouple was glued to the end of the capillary -as seen at the top right of the image. These two data points were then mapped to the apparent brightness of the reference capillary to create a brightness vs. temperature map. The temperature of the actual capillary and depletion region was then calculated from that map. This had to be done for each image as the brightness adjustment of the thermal camera was automatic. For direct measurement, a 0.002" thermocouple (Omega Type T copper-constantin) was bonded to the capillary opposite the microscope objective. Appendix E Temperature Measurement Figure 50 Top: A thermal image with temperature range shown in upper right. The thermocouple is visible as a while streak at across the IR image. Bottom: A comparison of the thermal image and thermocouple temperature data. Both the thermocouple and thermal camera show a rise in temperature of about five degrees, although the peak temperature rise at the start of the run is about seven degrees above ambient. This is in line with literature values. Burgi et al [99] found an empirical formula for the internal temperature rise in a 75|im capillary as T=11.5*Power/Length (W/m). The power loss across the depletion region is l 2/arjA, where I is the current and a d t h e depletion region conductivity estimated to be 100 u.S/cm. The temperature rise can then be found from the experimental current. Appendix E Temperature Measurement 163 Time (min) Figure 51 The rise in temperature in the depletion region according to T= 11.5*l2/odA,. Temperature declines as the current declines. This is the internal rise in temperature in the capillary. T h e external rise is less. Both of these results show however that there the temperature rise is not going to make the capillary get much closer to boiling the buffer. A s such it is understandable that no spontaneous bubble nucleation takes place. 


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