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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 B A S c , The University of British Columbia 1993 M A S c , 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 T h i s research clarifies, for the first time, the m e c h a n i s m a n d impact of current decline in capillary array electrophoresis ( C A E ) .  High  throughput capillary array electrophoresis instruments for D N A s e q u e n c i n g suffer to varying d e g r e e s from failure associated with electrophoretic current decline a n d inhibition or delay in the arrival of fragments at the detector. T h i s effect is known to be a s s o c i a t e d with residual quantities of large, slow moving fragments of template or g e n o m i c D N A carried through from s a m p l e preparation a n d s e q u e n c i n g reactions. Here, we d o c u m e n t and investigate the existence of an expanding ionic depletion region induced by overloading the capillary with low-mobility D N A fragments, a n d the effect of growth of this region on electrophoresis run failure. T h i s depletion region forms upstream of the smaller s e q u e n c i n g fragments, and its e x p a n s i o n w a s found not to affect the quality of the s e q u e n c i n g p e a k s at the detector.  Rather the current decline  a s s o c i a t e d with depletion region growth r e d u c e s the velocity of the d o w n s t r e a m s e q u e n c i n g fragments, so fewer fragments arrive at the detector during the run. It is s h o w n , through analytical a n d numerical models, how increasing quantities of slow moving D N A c a u s e the concentration of background electrolyte downstream to decline. With the concentration of s u c h fragments beyond a threshold quantity, the a n o d e - s i d e boundary of the nascent depletion region is shown to propagate toward the a n o d e at a rate faster than the contaminant D N A migration. U n d e r s u c h conditions the depletion region expands, the current declines, a n d the electrophoresis run suffers from a reduced yield of s e q u e n c e 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, a n d independent of the motion of the D N A . O b s e r v a t i o n s s u g g e s t that these downstream boundaries m a y propagate a s a result of an imbalance in current carriers brought about by the exposure of bound c h a r g e s in the matrix or capillary wall, which m a y be coupled to a rise in p H .  iv  Table of Contents Abstract  ii  T a b l e of Contents  iv  List of T a b l e s  vii  List of Figures  viii  S y m b o l s , Nomenclature and Abbreviations Acknowledgements Chapter 1  Introduction  xi xiii 1  1.1 T h e Continued Importance of d e novo S e q u e n c i n g a n d Capillary Electrophoresis  1  1.2 Matrix selectivity is the next parameter to push for increased performance Chapter 2  T h e Principles of Capillary Electrophoresis  3 5  2.1 Principles of Electrophoresis  5  2.2 D N A Propagation in Matrices  8  2 . 3 O t h e r Properties of Electrophoresis  9  2.4Electrokinetic Injection and S a m p l e Stacking  11  2.5Capillary S e q u e n c i n g for D N A  13  2 . 6 C u r r e n t Decline and Mitigation Efforts  19  Chapter 3  A p p a r a t u s and Methods to Investigate Current Decline  22  3.1 T h e M e g a B A C E  24  3 . 2 T h e Single Capillary Instrument  26  3.2.1  M e c h a n i c a l Design  26  3.2.2  F l u o r e s c e n c e Detection  30  3.2.3  T h e r m a l and Visible Light C a m e r a s  32  3.2.4  Capillaries, Matrix and Buffer  33  3 . 3 S a m p l e s a n d Methods 3.3.1  M e g a B A C E Samples  34 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 4.4.1  Cathode Boundary and DNA Movement  4.4.2  Boundary velocity and its relation to depletion region  depth  56 57  4.5A Mechanism for Current Decline Chapter 5  54  Analysis of Boundary Propagation  62 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  106  Chapter 6  Boundary Movement by OH" Propagation Conclusion  111  vi  Bibliography Appendix A  114 Properties of D N A and D N A S e q u e n c e 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 S c i e n c e s C e n t e r S a m p l e Preparation  131  Appendix B B. 1  T h e Effect of S a m p l e R e s u s p e n s i o n in A g a r o s e Effects of Injection from A g a r o s e  Appendix C  134 134  S e c o n d a r y Effects of Ionic Depletion a n d Bubble  Behaviour  140  C. 1  P e r m a n e n t Effects of D N A - l n d u c e d Depletion R e g i o n s  140  C.2  Matrix ion depletion from a n o d e - s i d e buffer  146  C. 3  Bubbles' Effect on Current  150  Appendix D  L P A and Buffer Properties  156  D. 1  Conductivity a n d p H of T r i s / T A P S Buffer U n d e r Dilution  156  D.2  T h e T h e r m a l E x p a n s i o n Coefficient of L P A  158  Appendix E  Temperature Measurement  160  Vll  List of Tables T a b l e 1 Data for concentration a n d solution conductivity for different D N A samples T a b l e 2 Physical data for the numerical model  39 75  T a b l e 3 Signal strength of the first - 5 0 D N A b a s e s in capillaries r e s u s p e n d e d in Dl H 2 0 and A g a r o s e  138  VIII  List of Figures Figure 1 S c h e m a t i c description of electrophoretic properties of D N A , reprinted from [18]  9  Figure 2 T h e original confocal array d e v e l o p e d 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, a n o d e pressure v e s s e l and cathode array  24  Figure 4 A front view schematic of the single capillary s e q u e n c e r  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 R e a d length vs total loaded charge  44  Figure 9: Total loaded charge of capillaries with and without bubbles. 47 Figure 10  Local conductivity a n d resistance profiles for four cut  capillaries Figure 11  51  Current at the end of runs of varying duration inferred from  ionic concentration profiles Figure 12 Total loaded charge vs. quantity of injected D N A  53 54  Figure 13 A series of infrared images of the capillary taken eight s e c o n d s apart and displayed side by side Figure 14  56  Fits to the first five minutes of a n o d e and cathode boundary  data using x(t) = dQ(t)+C  2  58  Figure 15 T w o e x a m p l e s of ionic depletion boundaries propagating in from a low conductivity cathode  60  Figure 16 M e a s u r e d 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 Figure 18  62  1-D discretization of the capillary showing ion flows in the  upwind s c h e m e  71  Figure 19 D e c a y of a peak in ion concentration d u e to numerical diffusion Figure 20  76  Effect of a fixed D N A peak on the background electrolyte  concentration Figure 21  78  T h e 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 a n d unbuffered systems  94  Figure 27: B o u n d charge driven boundary movement Figure 28  98  C o m p a r i s o n of experimental data and simulation of  boundary propagation d u e to bound charges Figure 29  99  p H details of bound charge driven depletion regions  100  Figure 30 Nickel particles in a capillary crossing into the depletion region Figure 31  103  P r o g r e s s of a nickel particle a s a depletion boundary  c r o s s e s its path  104  Figure 32 A five minute simulation with [TAPS]=0 at cathode.  The  retreating T A P S " ion is replaced by O H " ions, raising the p H . 108 Figure 33 C o m p a r i s o n of simulation and experiment for p H driven boundaries Figure 34 R e a d length vs total loaded charge for s a m p l e s in d H a O and a g a r o s e  109 resuspended 135  X  Figure 35  Electropherograms of 1 kb ladder r e s u s p e n d e d in Dl H 0 2  a n d 0.08% A g a r o s e  137  Figure 36. Infrared images (left) of a surface charge induced depletion region ( S C I D R ) Figure 37  141  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 m o v e m e n t of a S C I D R  143  Figure 39: Current decline associated with using buffer at the a n o d e . : Figure 40 Conducitivity c h a n g e s from matrix depletion Figure 41  147  Effect of a S C I D R boundary meeting a matrix depletion  boundary Figure 42:  146  150  Infrared and visible i m a g e s of the capillary showing  simultaneous growth of a hot region and bubble  151  Figure 43 A histogram showing o b s e r v e d bubble positions after o n e run Figure 44.  152 A histogram of the data in Figure 8(a), binning the  capillaries by total loaded charge  154  Figure 45  Current traces from o n e 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  T e m p e r a t u r e d e p e n d e n c e of p H and conductivity in  50mmol/L T r i s - T A P S  158  Figure 48 A thermal of the capillary a n d temperature references....  160  Figure 49  162  T h e r m a l m a p s of the capillary depletion region  Figure 50 T h e rise in temperature in the depletion region over the c o u r s e of a run  163  xi  Symbols, Nomenclature and Abbreviations Term F a W  Definition Faraday's Constant: 96800 coulombs/mol Conductivity of a solution, (Qm)" = 10" uS/cm Ionic mobility of the ith species (rn^A/s) Concentration of the ith species. 1 mol/m = 1 mmol/L Siemens = Q" . Elementary charge 1.6x10" C Current density (Amps/m ) Current (Amps) lon velocity (m/s) Charge (coulombs) Run time (s) Full width-half maximum of a gaussian peak. Diffusion constant (m /s) A 48kb double stranded non-circular phage DNA. The most common algorithm for identifying DNA bases from raw fluorescent sequence data. [1] The number of contiguous nucleotides identified at satisfactory quality, typically Phred quality > 20, in a single sequence run. (see Phred) To distribute volume of fluid to multiple sites A virus, including a DNA strand, that infects bacteria A circular DNA strand that can reproduce in bacteria A more general term for a plasmid or phage. DNA of interest ligated into a vector Deionized water a=0.05 uS/cm Total Loaded Charge 1  4  J  Q s e J 1  1  19  2  V  Q tr  FWHM D X DNA Phred Read length Aliquot Phage Plasmid Vector Insert dH 0 TLC Transference Number 2  2  T =  ~  M  , T =l +  T  Electropherogram Raw data from an electrophoresis machine. The positive end of the capillary electrophoresis Anode apparatus  XII  Cathode  T h e negative end of the capillary electrophoresis apparatus  Electrophoresis  T h e p r o c e s s of ions migrating through solution in r e s p o n s e to an electric field.  Co-ion  A n ion of like charge  C o u n t e r ion  A n ion of opposite charge  %w/v  Percent weight/volume (usually g/ml). T h i s is a literature convention for polymer concentrations.  LPA  Linear Polyacrylamide - the D N A separation polymer u s e d in this research  PDMA  Polydimethylacrylamide. A popular polymer for D N A separations.  PCR  P o l y m e r a s e C h a i n Reaction - the protocol u s e d to amplify D N A fragments by up to 10 x 6  ABI  Applied B i o s y s t e m s Inc. Manufacturer of the family of D N A s e q u e n c e r s (310, 3100,3700,3730) which dominates the market.  LIF  L a s e r Induced F l u o r e s c e n c e  BCGSC  The B C C a n c e r Agency G e n o m e Sciences Center.  Tris  Tris(hydroxymethyl)aminomethane) T h e w e a k b a s e c o m m o n l y used in D N A s e q u e n c i n g buffer  TAPS  [(2-Hydroxy-1,1-bis (hydroxymethyl)ethyl)amino]-1propanesulfonic acid. T h e w e a k acid c o m m o n l y u s e d in D N A s e q u e n c i n g buffer  PMT  Photomultiplier T u b e . T h e fluorescence  detector  u s e d in m a n y capillary s e q u e n c e r s  In silico  A term, found in life s c i e n c e , meaning "using a computer". It follows from in vivo a n d in vitro  EOF  Electro-osmotic flow.  TSR  T e m p l a t e S u p p r e s s i o n R e a g e n t - an additive to prevent large D N A fragments from being c o injected with s e q u e n c i n g s a m p l e s  bp/kbp/Mbp  M e a s u r e m e n t of the length of a D N A strand in number of b a s e pairs, or kilo or m e g a b a s e pairs.  CE  Capillary Electrophoresis  CZE  Capillary Z o n e Electrophoresis. T h e broader category of electrophoresis which covers D N A separations  XIII  Acknowledgements I a m indebted to numerous people who m a d e my P h D possible. First a m o n g s t these is, of course, A n d r e Marziali, w h o s e support, g u i d a n c e a n d commitment was, and is, s e c o n d to none. T h e absolute master of the rapid and critical insight, Dr. Marziali w a s able to help the research forward w h e n I got stuck, keep it going in the right direction, a n d provide the e v e r - n e c e s s a r y optimism. S p e a k i n g of which, Dr. Marziali's development of the P h y s i c s 253 robotics c o u r s e which I had the privilege to help teach will go down as the most fun a n y o n e will ever h a v e in a c l a s s r o o m . I challenge a n y o n e to find a more effective, inspirational or g e n e r o u s thesis supervisor in any field anywhere. Another great s o u r c e of assistance w a s the staff of the B C C a n c e r A g e n c y G e n o m e S c i e n c e s C e n t e r and in particular, D u a n e Smailus.  D u a n e prepared m a n y of the'samples u s e d herein, always  with dispatch, g o o d humour and his usual standards of quality a n d consistency.  I must thank my colleagues in the lab, and in particular  s e c o n d y e a r co-op student Peter Eugster. Peter, s o m e of w h o s e data a p p e a r s in this thesis, completed a large n u m b e r of bubble a n d infrared experiments in a short period of time a n d remains my gold standard for efficient execution in the laboratory. Itinerant biochemist T r e v o r P u g h also provided s a m p l e s , as did Mary P i n e s , late of the S a d o w s k i lab. C o - o p student Stefan Avail worked on numerical modeling early o n , a n d together we certainly found s o m e blind alleys to avoid! I must also thank fellow graduate students J o n N a k a n e and Matthew Wiggin for, respectively, their mathematical and biochemical insights a n d the general g o o d times. T h a n k s also to the Tiedje lab crew of A n d e r s Ballestad, Eric Nodwell a n d Scott W e b s t e r for letting m e u s e Berserk a n d the S t e a m e n g i n e cluster, a s well as the  xiv  mathematical, Linux a n d Matlab insights.  T h a n k s to B o y e Ahlborn for  translating parts of Kohlrausch's paper, written in the difficult classical scientific G e r m a n of 1897.  T h a n k s also to Barb G r o s s m a n , then of  A m e r s h a m B i o s c i e n c e s , who ferreted out the object files that allowed me to properly a n a l y s e M e g a B A C E data. I a m also grateful to my parents, J o h n a n d Marian C o o p e , who in addition to everything else, read this thesis at the very end and found that last 300 or s o errors. A n d of c o u r s e S t a c e y Lobin, for being m o m to B e n , who m a y be the most beautiful child ever, although it s e e m s impossible to design an experiment to test this. Finally I thank my thesis committee, L o m e W h i t e h e a d , Jeff Y o u n g a n d Matt Choptuik for taking the time to participate in this intellectual journey which I have so very m u c h enjoyed.  XV  / am no poet, but if you think for yourselves facts will form a poem in your  as I proceed,  minds. Michael F a r a d a y  the  1  C h a p t e r 1 Introduction  Chapter 1 Introduction 1.1 The Continued Importance of de novo Sequencing and Capillary Electrophoresis A s of the c l o s e of the twentieth century, large-scale D N A s e q u e n c i n g has e m e r g e d as a revolutionary scientific technique. S e q u e n c i n g m a y c o m e to be s e e n as akin to the development of the t e l e s c o p e or the particle accelerator in its impact on understanding of the world and our place in it. Data from the h u m a n g e n o m e project a n d other species' g e n o m e s have already begun to modify our understanding of the roles of g e n e s and g e n e regulation a n d the regulatory role of non-coding D N A . Availability of g e n o m e s of multiple s p e c i e s has aided in locating g e n e s associated with d i s e a s e .  More  than o n e commentator has argued that biology is only now entering its golden era [2]. G e n o m i c s in the post-human g e n o m e project era is branching along several paths. O n e of these is the gathering of more species' g e n o m e s for comparative g e n o m i c s , or comparison of s e q u e n c e similarities between various organisms a n d h u m a n D N A , to increase our understanding of g e n e function, and of evolution of s e q u e n c e information. A n o t h e r recently e m b a r k e d - u p o n e n d e a v o u r is the s e q u e n c i n g of thousands of h u m a n c a n c e r g e n o m e s to study c a n c e r progression a n d the role of genetic mutations in this d i s e a s e .  Clearly  t h e s e projects will require orders of magnitude more s e q u e n c i n g capacity than the entire h u m a n g e n o m e project, a n d will be limited by cost. Although the cost of s e q u e n c i n g has declined from $ 1 0 / b a s e in 1990 [3] to about $ 0 . 0 0 4 / b a s e in 2005 [4], a human-sized g e n o m e of 3 x 1 0 b a s e s currently costs (with multiple coverage) about $50 million. 9  NIH director Francis Collins has called for the development of  2  C h a p t e r 1 Introduction  technologies for the "$1000 G e n o m e " or about $3x10" / b a s e . 7  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 s p e c i e s g e n o m e to which the short fragments c a n be compared.  De novo s e q u e n c i n g , on the other hand, requires the  s e q u e n c e d fragments be a s s e m b l e d into a continuous whole without the benefit of a reference s e q u e n c e .  B e c a u s e of repeated s e q u e n c e  a n d other factors, the c o m p l e t e n e s s of the a s s e m b l e d g e n o m e is d e p e n d e n t on the length of the fragments to a great d e g r e e [8], a n d large s c a l e  de novo s e q u e n c i n g is only practical with a v e r a g e read  lengths of several hundred b a s e s (see A p p e n d i x A . 1 ) . Presently, and for the foreseeable future, the dominant technique for large-scale  de-novo s e q u e n c i n g 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 7 5 u m ID, 60 c m long, discrete glass capillaries. T h i s a p p r o a c h h a s a combination of a d v a n t a g e s over on-chip C E or slab gel electrophoresis, including improved heat dissipation, long read lengths, s p e e d , and e a s e of automation. In order to justify the continued commitment of resources at existing levels, the cost of  de novo s e q u e n c i n g must continue to fall.  In the context of C E , this m e a n s lower reagent costs a n d longer read lengths from e a c h capillary. A s patent protection has maintained relatively high p o l y m e r a s e reagent costs, reaction dilution has recently b e e n the biggest s o u r c e of cost reduction. T h e B C C a n c e r A g e n c y G e n o m e S c i e n c e s C e n t e r ( B C G S C or G S C ) for example, is in the p r o c e s s of introducing 1/256 reaction dilutions in their s e q u e n c e pipeline, and has shown 1/1024 dilutions to work. 1/256 dilution, with m e d i a n reads in e x c e s s of 800 b a s e s , reduces the reagent cost from  3  C h a p t e r 1 Introduction  $6000 to $22.00 per million b a s e s [9]. T h i s source of cost reduction is reaching its limit however. A t t h e . G S C ' s current rate for customer s e q u e n c i n g of $4500 per million b a s e s , s e q u e n c i n g reagents represent about 35% of the total, the remainder being labour, operations costs other c o n s u m a b l e s and bioinformatics support. E v e n infinite dilution could only reduce that cost another $1500. [4]. Between 1990 and 2000, improved s e q u e n c e r throughput through automation and increased read lengths w a s a big s o u r c e of cost reduction. In 1990, the ABI 370 slab gel s e q u e n c e r w a s c a p a b l e of s e q u e n c i n g 12,000 b a s e s per day. B y 1998, the ABI 3700 capillary m a c h i n e could produce 196,000 b a s e s per day, a n d by 2002, the 3730x1 had b e e n p u s h e d over 900,000 b a s e s per day. T h i s represents a plateau however, and subsequently, no new separation matrices or buffers h a v e b e e n introduced. S i n c e 1998, improved s a m p l e purification a n d more selective separation matrices have allowed median production read lengths to rise from 500 to 800 b a s e s per capillary  T h i s is still well below literature values from as early a s  1998 [10], where reads up to 1300 b a s e s per capillary were reported.  1.2 Matrix selectivity is the next parameter to push for increased performance T h e main s o u r c e of this read length plateau is in limitations of the polymer matrices u s e d 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]. T h i s current decline manifests itself right after the s a m p l e is introduced into the capillary, with the current declining to less than 20% of its initial value after thirty minutes [12].  D N A b a n d s are slowed down a n d arrive  late at the detector, leading to the term "late starts" to describe this p h e n o m e n o n . Current decline has b e e n shown to correlate with the  4  C h a p t e r 1 Introduction  p r e s e n c e of large, low mobility D N A fragments in the s e q u e n c i n g s a m p l e which are a byproduct of the s a m p l e preparation protocol [13]. T h e frequency a n d severity of the problem varies with the type of matrix u s e d , a n d it is more c o m m o n with the u s e of less stringent, a n d typically less expensive, s a m p l e preparation techniques [14]. A d d r e s s i n g the issue of current decline is o n e of the few a v e n u e s of continued cost reduction available for capillary electrophoresis.  While the c a u s e s of current decline had b e e n  elucidated during the development of C E separation matrices, the m e c h a n i s m by which current decline o c c u r s has n e v e r b e e n properly explained.  It is thus the objective of this thesis to understand why long  D N A fragments c a u s e current decline, and to investigate possible methods of mitigation. In the following chapters, the background of capillary electrophoresis for D N A s e q u e n c i n g is d e v e l o p e d , along with a review of previous research into the current decline problem. T w o p i e c e s of equipment for studying current decline are then d e s c r i b e d , a single capillary instrument d e v e l o p e d specifically for this investigation, a n d the commercial M e g a B A C E 1000, a 96 capillary s e q u e n c e r .  Results  are presented showing the c a u s a l relationship of long fragments to current decline a n d 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 c a u s e d by the p r e s e n c e of long fragments. It is further shown that current decline only o c c u r s if the quantity of long fragments injected is beyond a threshold level.  In chapter five, a  model is d e v e l o p e d to explain the formation a n d growth of the ionic depletion region, and the reason for the threshold behaviour.  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  5  Chapter 2 The Principles of Capillary Electrophoresis T h e m o d e r n s c i e n c e of electrophoresis is generally regarded to have begun with A r n e Tiselius, in the 1930's. H e s h o w e d that proteins in h u m a n s e r u m could be separated by electric current flow in a liquidfilled tube on the basis of charge a n d m a s s .  A s J o u l e heating in free  solution electrophoresis c a u s e s convective diffusion leading to a loss of resolution in the separation, workers adopted liquid-permeated solid supports s u c h as paper, starch, cellulose, acetate, a g a r o s e a n d 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 z o n e electrophoresis [15].  C E development accelerated in the 1980's with  the c o m m e r c i a l availability of polyamide coated drawn glass capillaries [16]. T h i s culminated in the extraordinarily successful development of C E for D N A s e q u e n c i n g in the 1990's. T o d a y , C E is also gaining popularity a s an analytical tool alongside m a s s spectrometry ( M S ) a n d liquid chromatography (LC), particularly for separating s p e c i e s of different chirality, highly polar s p e c i e s , and a s a front e n d for M S separations [17].  2.1 Principles of Electrophoresis T h e s h e e r number of different configurations of analytes, electrolytes, additives and detection s c h e m e s possible in electrophoresis and the interdisciplinary nature of the subject has led to an extensive and diverse literature. Sub-categories s u c h a s D N A s e q u e n c i n g , peptide separations and inorganic analytical chemistry a p p r o a c h the s a m e p h e n o m e n a with different vocabularies.  6  Chapter 2 The Principles of Capillary Electrophoresis  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: ^  =  dt  A  a  ^  +  ox  a  (  2  , )  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)  a(x,t) = £ / f y , | C ,  '(2-2)  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: (2-3)  dx <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)  7  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  Electrophoresis works by exploiting the difference in mobility of different analytes.  A c c o r d i n g to the D e b y e - H u c k e l theory, the surface  c h a r g e of the ions or analytes is s c r e e n e d beyond the D e b y e length. (2-5)  where e is the permittivity of the solution, e is the fundamental c h a r g e r  a n d / is the ionic strength of the solution. In the p r e s e n c e of a n electric field, the analyte ion and counter ions will be pulled in opposite directions, and interact with e a c h other hydrodynamically. W h e r e the D e b y e layer is m u c h thicker than the particle radius, R, the mobility is given by  where the ion has charge Q a n d r\ is the solvent viscosity. Equation s  (2-6) applies to small ions and b e c a u s e e a c h ion has a unique value of Q / R , these ions c a n be separated using electrophoresis in free solution. D N A , however, is m u c h larger and has charge proportional to its length. D N A takes on a globular conformation in free solution s u c h that internal c h a r g e s are shielded by counterions that d o not feel hydrodynamic effects, a n d the surface charge density and viscous drag thus both s c a l e with the radius. T h i s "free draining" property m e a n s that, to a first approximation, fragments of all lengths propagate with the s a m e mobility given by (2-7) rather than (2-6).  P  (2-7)  AKT] K S  where p is the D N A globule's surface charge density [18].  D N A must  therefore be separated in a viscous m e d i u m which c a n interact with the D N A polymer and produce a length-dependent drag, preventing this  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  8  free draining behaviour a n d breaking the length scaling d e g e n e r a c y between driving force and drag.  2.2 DNA Propagation in Matrices T h e r e 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 b a s e s in length [20].  T h e r e is evidence that longer fragments m a y propagate in  the regime of oriented reptation as, at high driving fields, electropherograms are c o n c l u d e d with a large peak followed by no signal, suggesting all the larger peaks are propagating at the s a m e rate. T h o u g h reptation regimes a n d the governing equations are typically the central point of interest in electrophoresis, m u c h of the work presented here hinges instead on properties of ions a n d the background electrolyte, and therefore additional background will be provided in this a r e a .  .  9  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  Log (strand length)  ^  A  B  C  D  E  F  G  Figure 1 S c h e m a t i c description of electrophoretic properties of D N A , reprinted from [19]. [A] O g s t o n regime - D N A stays coiled a n d is sieved. [B] Entropic T r a p p i n g : T h e random coil j u m p s between larger pores. [C] Near equilibrium reptation: T h e random coil migrates head first through the matrix. [D] Reptation trapping: T h e D N A is s l o w e d by both e n d s pulling though the matrix a n d forming U - s h a p e s . [E] Oriented Reptation: T h e D N A u n c o i l s and g o e s through the matrix with o n e e n d leading. [F] Geometration: High fields may be characterized by hernias and " b u n c h i n g " instabilities. [G] Very long molecules may not migrate through matrices at all, p o s s i b l y b e c a u s e they form knots around gel fibers.  2.3 Other Properties of Electrophoresis A m o n g s t the properties of electrophoretic s y s t e m s which must be taken into account is the relationship of temperature a n d solution conductivity. T h e viscosity of a q u e o u s solutions varies according to  r/~exp(Ea/kT), where E is the activation energy for the viscous flow a  [21]. T h i s m e a n s that ion mobility and therefore buffer conductivity, is d e p e n d e n t on temperature. A widely e m p l o y e d rule of thumb is that between 2 0 - 6 0 ° C the conductivity c h a n g e s by 2 % / ° C . T h i s is true in the present c a s e , and experimental data is presented in A p p e n d i x D  10  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  which s h o w s this rule to be quite accurate. T e m p e r a t u r e acts a s a limiting factor in the separation s p e e d a s the temperature gradient between the center and wall of the capillary c a u s e d 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 (EOF).  U n d e r a q u e o u s conditions glass p o s s e s s e s an e x c e s s of  negative charge. T h i s results in a net positive charge along the surface of the a q u e o u s 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. C o n s e q u e n t l y , bulk fluid flow is established towards the cathode (negative electrode). E O F differs from hydrostatic flow in that flow is generated within the c h a r g e d region next to the capillary wall, so the radial velocity profile is flat, a n d analytes are not dispersed. T h e 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 s h e a r occurs, commonly called the zeta potential. In a real capillary, (2-8) is potentially misleading as it a s s u m e s that the E O F driving force is constant throughout the capillary [23].  Different  local conditions and defects in the capillary walls could c a u s e 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 p H , particularly in fused silica capillaries and can rise by a n order of magnitude with p H increase from 2 to 12. At p H 8 where D N A s e q u e n c i n g takes place, the E O F "mobility" (sC/t]) in an uncoated capillary is on the order of 60x10" m A / s [24], much higher than, a n d in 9  2  the opposite direction to mobility of D N A s e q u e n c i n g fragments which range from 3 to 20x10" m A / s . E O F must therefore be s u p p r e s s e d for 9  2  11  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  D N A s e q u e n c i n g , using capillary surface treatment or self-coating matrices.  S u p p r e s s i o n of E O F also prevents dispersion from  inhomogeneities in the E O F mobility [25].  In m o d e s of C E where a  more acidic buffer c a n be u s e d , E O F can be u s e d to advantage: increasing the effective length of the capillary or allowing positive a n d negative analytes to be separated together. T h e latter is d o n e by hydrostatically introducing the s a m p l e plug and then conducting a n 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 s e q u e n c i n g .  2.4 Electrokinetic Injection and Sample Stacking In s e q u e n c i n g applications, D N A is injected into the capillary by electrophoresis rather than hydrostatic pressure a s in s o m e other forms of C E .  A well containing the s a m p l e is placed at the cathode  e n d of the capillary a n d the electric field is applied. T h e s a m p l e well is then removed and replaced with running buffer so the run c a n p r o c e e d . T h i s "electrokinetic injection" e n a b l e s s a m p l e c o m p r e s s i o n , also known as stacking, which is crucial to the s u c c e s s of capillary s e q u e n c i n g  as  resolution is inversely proportional to injection peak width [26]. S a m p l e c o m p r e s s i o n affects both the concentration a n d width of the injected s a m p l e slug. T h e free solution mobility of D N A fragments is 37x10" m A / s [27], w h e r e a s in the matrix it drops to between 20 a n d 9  2  3 x10" m A / s for fragments from 30 bp to 1000 bp. T h i s c a u s e s an 9  2  increase in concentration from C  C  s a m p  e  to  <V  =C capillary  /  C piiiary by the amount ca  37xl(T  9  (2_9)  sample ^sample  where the s a m p l e conductivity  MDNA  a mpie of s e q u e n c i n g fragments is sa  typically o n e hundred times lower than the background electrolyte conductivity in the matrix ob - T h i s d o e s not however c o m p r e s s the ge  12  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  b a n d s in time, so that if electrokinetic injection is d o n e for ten s e c o n d s , o n e would expect the resulting D N A b a n d s to take ten s e c o n d s to c r o s s the detector, plus the time attributable to diffusional broadening. In fact, peak width c o m p r e s s i o n of up to a factor ten has b e e n o b s e r v e d [28] immediately after injection, a n d a factor of three c o m p r e s s i o n w a s consistently o b s e r v e d in our work with the M e g a B A C E s e q u e n c e r , using standard s a m p l e purification procedures a n d r e s u s p e n s i o n of the s a m p l e in d H 0 . 2  T e m p o r a l s a m p l e stacking requires that the high field/low field b o u n d a r y initially present at the capillary entrance m o v e with the D N A s o that D N A arriving later in the injection slows down later, a n d therefore closer to the leading e d g e of the injection peak. W h i l e it has b e e n s h o w n experimentally that lower s a m p l e salt concentration promotes stacking [13], a n d that a d d i n g fast-moving O H " ions after injection c a n also c o m p r e s s the s a m p l e [29], no m e c h a n i s m by which the boundary m o v e s has been hitherto p r o p o s e d . O f interest to the present discussion is the amount of D N A injected into the capillary. W h i l e attempts were m a d e at direct m e a s u r e m e n t of the D N A injected into the capillary via spectrophotometric m e a s u r e m e n t of the eluted s a m p l e , the quantities involved were too low to give meaningful results. T h e m a s s of injected fragments in the following experiments w a s therefore calculated according to: (2-10) sample  where  cr mpie is the sa  s a m p l e conductivity (Sieverts*m" or (Qm)" ), CQNA 1  in ( m o l * m ) is the D N A concentration in the sample, MWDNA 3  1  295  g/mol f o r o n e nucleotide, a n d l(t) is the capillary current (Amps), integrated over the injection time t. T h e m a s s of injected D N A is proportional to its fraction of all the charge carriers, so injection from  13  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  lower conductivity electrolytes results in larger quantities of injected DNA.  Note that in this s c h e m e D N A is treated as a group of individual  nucleotides: the lengths of the actual fragments are unimportant in this calculation. T w o related formulas are also relevant here. T h e integral in (2-10) is actually the total charge flowing into the capillary during injection. T h i s c a n be extended to the total loaded c h a r g e over the run (2-11)  o where t is the electrophoresis run time. r  In order to characterize  c h a n g e s in current, we similarly define the normalized total loaded charge as: (2-12)  where 1(0) is the current at the start of the run.  2.5 Capillary Sequencing for DNA T h e details of D N A properties, s a m p l e preparation a n d s e q u e n c i n g protocols are contained in A p p e n d i x A . H e r e we suffice to s a y that D N A s e q u e n c i n g requires creating a quantity of D N A fragments of a c o m m o n starting point in the s e q u e n c e a n d monotonically increasing length from 20 b a s e s to 1000 b a s e s s u c h that there is e n o u g h D N A of e a c h length to be detected (typically 1 0  8  molecules per size band). E a c h fragment terminates with an A , C , G , or T nucleotide that is labeled with o n e of four different fluorescent d y e s , so s e q u e n c i n g involves separation by size and detection of the end-label emission wavelength.  T h i s method, d e v e l o p e d by S a n g e r ,  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  14  Gilbert and M a x a m in 1977 [30, 31], initially u s e d four separate lanes on a polyacrylamide slab gel with radio-labeled fragments for detection.  H o o d et. al. improved this with four-color florescent labeling  [32] in 1986, enabling s e q u e n c i n g in o n e lane per s a m p l e . T h i s led to the first generation of semi-automated slab-gel s e q u e n c e r s , s u c h a s the Applied B i o s y s t e m s 370 family. Despite read lengths of over 600 b a s e s per lane, these m a c h i n e s were limited by manual intervention in gel casting, a n d were limited to low field strengths b e c a u s e of e x c e s s i v e joule heating. Inhomogeneities in the gel also c a u s e d lane alignment problems, limiting lane densities and making automated b a s e calling difficult. Capillary electrophoresis for D N A s e q u e n c i n g w a s introduced in 1990 [33] [34] [35, 36], although technical obstacles d e l a y e d the a p p e a r a n c e of commercially available array s e q u e n c e r s until 1997. T h e principal motivation w a s a potential increase in separation s p e e d of an order of magnitude through improved heat dissipation, a n d superior lane tracking. A less obvious advantage is the d e s i g n flexibility allowed by a discrete capillary array. T h e cathode e n d c a n be arranged to match standard 96 or 384-well reaction plates while the a n o d e and detector regions c a n have any physical layout the designer desires.  S a m p l e s c a n be injected directly from 96 or 384-well reaction  plates a n d matrix replacement c a n be performed by hydrostatic pumping from the a n o d e .  It is also possible to replace s a m p l e , matrix  a n d buffer containers so only the capillaries themselves have to be c l e a n e d between runs. T h i s continues to be a notable advantage over lab-on-a-chip electrophoresis systems, where the capillaries and buffer wells are all in o n e monolithic structure.  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  COMPUTER [—  15  LOW PASS FILTER MIRROR  555rtm LONG PASS FILTER  PMT-  DICHROIC BEAM SPLITTER  BANO PASS FILTER  MIRROR  LASER INPUT {488 nm)  DICHROIC 8EAM SPLITTER  OBJECTIVE CAPILLARY ARRAY  Outlet Reservoir  HIGH VOLTAGE POWER SUPPLY  I p  Figure 2 The original confocal array developed by the Mathies group. Reprinted from [37]  The  biggest technical challenges in C E s e q u e n c i n g were  multicapillary fluorescence detection a n d development of suitable separation matrices. T o a d d r e s s the former, Mathies et. al. d e v e l o p e d a s c a n n i n g confocal m i c r o s c o p e system [37] [38], shown in Figure 2, which led to the introduction of the M e g a B A C E 96 c h a n n e l s e q u e n c e r in 1997.  T h i s s y s t e m s c a n n e d a m i c r o s c o p e objective a c r o s s the  capillaries which were lined up side by side, while the rest of the optics remain fixed. Although it had to s c a n 96 capillaries every 1.7 s e c o n d s , it could devote full laser power to e a c h capillary. T h i s a p p r o a c h w a s  16  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  later s c a l e d to 384 capillaries in the M e g a B A C E 4000. Dovichi a n d others [39] concurrently d e v e l o p e d a sheath flow a p p r o a c h where upon exiting the capillary, fragments were imaged as they were hydrodynamically focused by matrix flowing past the outlet.  T h e laser  w a s a i m e d down the line of eluting s a m p l e s from o n e e n d , a n d the resulting fluorescent spots were diffracted off a grating a n d onto a C C D array. Different colors produced different positions on the C C D .  This  s y s t e m gained flexibility with fluorophores at the e x p e n s e of reagent consumption a n d signal strength. While it was proven successful on the 3700, the ABI 3730 that followed, imaged its capillaries from o n e e n d directly through the capillary glass. T h i s u s e s only a thirtieth a s m u c h buffer a n d matrix [9], a n d provides improved uniformity in the fluorescence signal from o n e capillary to another. T h e biggest obstacle to developing viable capillary array s e q u e n c e r s w a s in finding a separation matrix that w a s selective, electrically stable, replaceable and resistant to E O F .  C r o s s linked  polyacrylamide matrices which had worked well in the slab format a n d could be covalently b o n d e d to the capillary wall to prevent E O F were initially e m p l o y e d .  Both sample-related a n d sample-independent  matrix instability [33, 35, 39-41] w a s reported however.  Moderate  sample-independent current decline w a s o b s e r v e d that could be periodically reset by clipping a small portion of the cathode end of the capillary. B u b b l e s were also o b s e r v e d to form spontaneously near the cathode e n d of the capillary, particularly at fields over 300 V / c m . T h i s work w a s well reviewed a n d e x p a n d e d by Swerdlow et al. in 1992 [42]. T h e y found that sample-independent current decline s t e m m e d from the formation of a resistive region at the cathode e n d of the capillary, thought to be d u e to a c h a n g e in the relative conductivity of the ions a c r o s s the matrix/buffer boundary (this is known a s the transference number). Figeys et al. likewise u s e d capillary cutting to reveal the axial  17  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  conductivity profile after running for up to 280 minutes [43].  Their  results a p p e a r to be consistent with a c h a n g e in relative conductivity of the different ionic s p e c i e s a c r o s s the matrix/buffer interface coupled with diffusion of the depletion region into the capillary. C h a n g i n g buffer constituents, particularly adding unpolymerized matrix m o n o m e r s to the buffer ameliorated t h e s e effects [44].  T h e m e c h a n i s m put forth by  Swerdlow et al. [42] for this current stabilization is that the m o n o m e r s equalize the relative mobility (transference number) of the ionic s p e c i e s a c r o s s the gel/buffer boundary. S p o n t a n e o u s bubble formation likewise s e e m s to have b e e n largely mitigated by the switch to non-crosslinked matrices.  Figeys [44] did not report bubble  formation with s u c h matrices, e v e n with runs of hundreds of minutes at 300 V / c m and notwithstanding the high fields a s s o c i a t e d 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 a v e r a g e molecular weights of ~ 1 0  6  D a . E O F is  s u p p r e s s e d using a surface treatment [48] [49] which s u p p r e s s e s surface charge a n d binds the linear polyacrylamide to the capillary wall. ABI introduced its proprietary Performance Optimized Polymer ( P O P ) line of matrices for the 3700, b a s e d on poly(dimethylacrylamide) P D M A [50].  T h e P D M A polymer s u p p r e s s e s E O F though a moderate  d e g r e e of hydrophobicity. T h i s allows the polymer to bind to the capillary wall but keep m u c h of its length off the wall, leading to a socalled "loopy" conformation [51].  P M D A b a s e d matrices, therefore,  allow ABI to use non-coated capillaries. Both s y s t e m s u s e d T r i s / T A P S a s a running buffer b e c a u s e it w a s found to produce better quality separations than Tris Borate, the traditional slab-gel buffer. It is thought that the latter m a y be prone to formations of c o m p l e x e s with residual glycerol from cycle s e q u e n c i n g reactions [45].  Tris a n d T A P S ,  respectively a large organic acid and b a s e , in equal concentration only  18  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  dissociate about 50% e a c h so the solution also h a s a comparatively high buffering capacity [52]. T h e exact content of the c o m m e r c i a l matrices is not known, but it is clear that s a m p l e independent current stability has b e e n attained through judicious selection of buffer a n d matrix c o m p o n e n t s .  Current decline from large fragments, however,  continues to be a c o n c e r n [53] [12] for both L P A and P D M A b a s e d matrices. T h e introduction of the M e g a B A C E and 3700, c o m b i n e d with efforts to automate upstream s a m p l e preparation resulted in a dramatic increase in the p a c e of s e q u e n c i n g for the h u m a n g e n o m e project. A big factor m a y have been C e l e r a G e n o m i c s ' 1998 entry into the "race" to s e q u e n c e the h u m a n g e n o m e using 300 of the new 3700s. T h e scientific significance of C e l e r a ' s contribution remains the subject of debate [54, 55], but it is clear that it stimulated the uptake of large n u m b e r s of s e q u e n c i n g m a c h i n e s by all the major g e n o m e centers. F r o m the beginning of the H G P in 1990, to 1998, about 3% of the g e n o m e had b e e n sequenced[5, 56], while from 1998 to 2001, the other 97% w a s completed. It is e a s y to understand how, in the context of the time, both s e q u e n c e r s were introduced to market in haste.  T h e 3700  e x p e r i e n c e d up to 30% downtime for various m e c h a n i c a l maladies a n d the sheath flow detector system c o n s u m e d large quantities of polymer. T h e M e g a B A C E w a s s o m e w h a t more reliable but required considerable operator involvement for plate e x c h a n g e s .  U n d e r ideal  circumstances, however, the M e g a B A C E was c a p a b l e of read lengths of up to 8 0 0 b p in 1998, w h e r e a s the 3700 could only m a n a g e up to 6 0 0 b p [9]. It is reasonable to s u p p o s e that with development of dilute reaction protocols, the sensitive detector and low matrix u s a g e of the M e g a B A C E might have m a d e it the s e q u e n c e r of choice early o n , a n d allowed the manufacturer to develop a next generation m a c h i n e with  19  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  better automation.  In the e n d however, the s e q u e n c i n g community  largely rejected the M e g a B A C E for o n e significant reason. conditions, using D N A s a m p l e s prepared using  U n d e r real  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 a n d the d e l a y e d onset of peaks at the detector.  While the 3700 also  displayed the s a m e failure m o d e [53], the rates were considerably lower.- E a c h read failure represents not only a loss of s e q u e n c i n g time, but a loss of the very expensive cycle s e q u e n c e reaction, a s well a s all the upstream s a m p l e preparation steps. C o m b i n e d , t h e s e failures represented at least 10% of the cost of s e q u e n c i n g at the time, s o the cost of read failure to the h u m a n g e n o m e project w a s p e r h a p s a s high a s three hundred million dollars. T h i s is in addition to the fact that using P D M A b a s e d matrix to mitigate the problem forced workers to live with lower a v e r a g e read lengths.  W h i l e the ABI m a c h i n e s always  had superior automation, it is likely that the issue of run failure d u e 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 g e n o m e  centers only u s e ABI s e q u e n c e r s .  2.6 Current Decline and Mitigation Efforts Swerdlow et a/.[42] studied the effect of D N A s e q u e n c i n g s a m p l e characteristics on current stability, and explicitly s h o w e d that rapid current decline w a s associated with the injection of a sufficient quantity of fragments longer than 1300bp, and that smaller quantities did not c a u s e the effect to occur. After Swerdlow, further discussion of current decline w a s limited, although it w a s a d d r e s s e d in the important pair of papers from the Karger lab which point out that, "Indeed the problem of s a m p l e cleanup for the successful operation of C E has not b e e n sufficiently emphasized" [14].  Karger's lab d e v e l o p e d a  20  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  purification method b a s e d on centrifugation through filters, which, while effective, proved too expensive for s e q u e n c i n g centers to c o n s i d e r implementing. In the s e c o n d paper, they reported that quantities of 8kb M 1 3 D N A a d d e d back to s e q u e n c i n g s a m p l e s after filtration a n d then de-salted did c a u s e current decline. T h e y also demonstrated that adding salt back to de-salted but template laden s a m p l e would prevent the current decline, albeit at the cost of reduced loading a n d separation efficiency.  Other techniques found to prevent current decline include  multiple s a m p l e injections [53] and resuspending reaction products in template s u p p r e s s i o n reagent ( T S R ) s u c h a s dilute a g a r o s e [57, 58]. While filtering r e d u c e s the amount of template without reducing the quantity of short s e q u e n c i n g fragments, adding salt or multiple s a m p l e injections is likely to reduce the total quantity of D N A injected, including the template, below the threshold for current decline. Results are s h o w n A p p e n d i x B which demonstrate that using A g a r o s e a s T S R r e d u c e s the total quantity of D N A injected, by reducing the injected template below the threshold for current decline. All t h e s e methods have drawbacks however.  M o r e stringent  c l e a n u p a d d s cost. Increased ionic strength in the s a m p l e r e d u c e s the total amount of D N A loaded which m a y result in inadequate signal strength as p r o c e s s e s m o v e toward smaller v o l u m e s a n d lower quantities of s e q u e n c i n g fragments. T S R may further reduce the quantity of loaded s e q u e n c i n g fragments, and also presents viscosityrelated liquid handling issues. At present, current decline in the ABI s e q u e n c e r s is controlled through a combination of more dilute reactions with less starting D N A , a n d u s e of the fault tolerant P O P - 7 matrix (believed to be a combination of P D M A a n d L P A which is still self-coating).  In the  future, more selective matrices will evolve from a better understanding  C h a p t e r 2 T h e Principles of Capillary Electrophoresis  of the current decline problem; it is h o p e d that the present work will contribute to that understanding.  C h a p t e r 3 A p p a r a t u s and M e t h o d s 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 s e q u e n c e r s located at the B C C a n c e r A g e n c y G e n o m e S c i e n c e s Center. While the M e g a B A C E s generated 96 c h a n n e l s of current and fluorescence signal data at o n c e , it w a s not possible to observe other characteristics of the capillaries while the machine w a s operating. A custom single capillary instrument w a s therefore constructed, mimicking the M e g a B A C E as m u c h as possible by using the s a m e capillaries, separation matrix and buffer. T h i s instrument w a s configured with the detection instrumentation at the cathode e n d of the capillary, rather than the a n o d e end as in conventional s e q u e n c e r s , as it w a s known from the literature that the source of current decline w a s 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.  T h e reason for this variability is unknown, but it m a d e it  impossible to get reproducible current decline behaviour with purified samples.  It w a s c o n c l u d e d therefore that extensive experiments on a  capillary array m a c h i n e were also required, so a M e g a B A C E w a s 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, a n d associated methods are described. All capillary separation d e v i c e s operate on the s a m e physical principles. A capillary must be positioned between two baths of  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  23  electrolyte, which should be level with e a c h other to prevent siphoning. T h e r e must be a high voltage power supply c o n n e c t e d to electrodes in e a c h bath s o that current c a n p a s s through the capillary. T h e r e must also be s o m e sort of analyte detection s c h e m e , be it through the capillary wall or as the analytes elute from the e n d of the capillary. T h e detector n e e d s to be far e n o u g h from the cathode to allow e n o u g h separation, a n d near to the a n o d e so that the capillary isn't unnecessarily long. T h e r e must also be s o m e reasonably straightforward w a y of replacing the a n o d e and cathode wells to switch between s a m p l e , buffer a n d matrix, a n d s o m e s y s t e m for pumping the matrix a n d rinse water through the capillary. Finally, there must be a s y s t e m for heating a n d stabilizing the capillary temperature so a s to prevent s e c o n d a r y structure formation in the D N A or thermal band broadening [22].  In light of the foregoing, it is not surprising that  c o m m e r c i a l s e q u e n c e r s share m a n y similarities. T h e differences between m a c h i n e s are mostly in the d e g r e e of automation, a n d layout i s s u e s related to the n u m b e r of capillaries in the machine.  C h a p t e r 3 A p p a r a t u s a n d 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  T h e M e g a B A C E 1000 is the first generation 96 c h a n n e l D N A s e q u e n c e r from M o l e c u l a r D y n a m i c s (Subsequently A m e r s h a m B i o s c i e n c e s and now part of G e n e r a l Electric Healthcare).  Figure 3  s h o w s the interior of the M e g a B A C E ' s air box, which is kept c l o s e d throughout operation. U s e of an air box for heating is more or l e s s mandated by the u s e of capillary arrays, and ABI's current 3730 machine still u s e s 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 h a n g s next to e a c h capillary. T h e electrodes are grounded a c r o s s 1 0 0 k Q resistors a n d the resulting voltage drop is u s e d to m e a s u r e  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  25  current. T h e capillaries are O D 225 u m , ID 7 5 u m a n d 6 0 c m 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 4 0 c m from the cathode e n d , of e a c h capillary, a n d e a c h 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 s c a n n e d by the confocal m i c r o s c o p e . T h e microscope's objective s c a n s the array at - 1 . 7 s c a n s / s e c .  F o u r 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 a n d higher frequency.  Each  b e a m p a s s e s through a s c a n n e r which switches between two final filters in p h a s e with the objective s c a n . T w o c h a n n e l s are detected on the outbound s c a n a n d two on the inbound s c a n . In this w a y the four fluorescent wavelengths c a n be detected using only two photomultiplier tubes.  Note that this is different from the original  Mathies' design shown in Figure 2, p a g e 15, where the light is sequentially separated into four channels. At the lower right in Figure 3 is the a n o d e , where e a c h bundle c o m e s together and enters the high pressure c h a m b e r from where matrix is p u m p e d from six 1 ml microcenterfuge tubes. T h e entire c h a m b e r is at high voltage during operation. T h e L P A matrix u s e d in the M e g a B A C E is quite viscous, s o 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 m a d e to the standard s e q u e n c i n g protocol w a s to replace the microcenterfuge tubes of L P A with running buffer at the a n o d e after injection of the L P A into the capillaries but before s a m p l e injection. T h i s w a s d o n e to s a v e m o n e y as tubes of L P A uncontaminated with D N A could be u s e d for three runs rather than one, saving $40.00 per  C h a p t e r 3 A p p a r a t u s a n d Methods to Investigate Current Decline  26  96 well plate. T h i s p r o d u c e d 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 a n d remain constant at that value. No equivalent relationship between buffer contents a n d capillary current w a s observed at the cathode. T h i s effect, which did not affect s e q u e n c i n g performance, is d i s c u s s e d further in A p p e n d i x 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 w a s influenced by the  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  27  need for c l e a r a n c e below the capillary's ends, and a desire to keep the detector optics c o m p a c t and on one level. T h e solution w a s to mount the C E apparatus and detector a s s e m b l y on a small optical breadboard on 15 c m posts a b o v e the main b r e a d b o a r d . T h i s g a v e e n o u g h room under the capillary to position the cathode sample/buffer holder using a lab jack. T h i s layout is essentially the s a m e as the M e g a B A C E , which has the whole optical detector a s s e m b l y midway up the machine, behind the capillary air box which is a b o v e the pneumatically driven a n o d e a n d cathode e x c h a n g e m e c h a n i s m s .  In order to focus a n d align  the capillary vertically a n d horizontally, the entire capillary a s s e m b l y , a n o d e and cathode c a p s , main d e c k a n d heater plate were mounted on a three-axis stage, while the detector optics were fixed. T h i s design sought to limit the unheated or uninsulated portions of the capillary as m u c h as possible to prevent bubble formation through matrix shrinkage. 26 c m of the 36 c m capillary w a s taped to a n aluminum plate heated on the other side by a kapton heater ( O m e g a ) . T h e 5 c m of capillary at the a n o d e w a s inside a pressure v e s s e l a n d insulated from temperature c h a n g e s and only 5 c m at the cathode w a s e x p o s e d to room temperature. T h i s arrangement w a s stable e n o u g h that matrix shrinkage-induced bubbles could be a v o i d e d if s a m p l e a n d buffer wells were c h a n g e d in a timely manner. T h e pressure v e s s e l containing the a n o d e consists of a stainless steel c a p into which screws a cylinder containing a microcenterfuge tube which contains the desired reagent: polymer matrix, buffer or rinse water. T h e c a p is plumbed for the high pressure a n d voltage input lines, the platinum a n o d e electrode, and the capillary pressure fitting. T h e two sections are screwed together (13tpi, 1.25" diameter, factor of safety under m a x i m u m pressure is 100) and are s e a l e d with a n O-ring. A n U p c h u r c h F*150 steel c o m p r e s s i o n fitting  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  28  surrounding a 1/16" O D , 2 5 0 u m ID P E E K tube is u s e d to seal to the capillary. T h e fitting c o m p r e s s e s a ferrule into the P E E K tubing which in turn s q u e e z e s the close-fitting capillary. T h e high pressure input line, also P E E K tubing, is attached to the c h a m b e r c a p in the s a m e way. T h e steel c a p is s e c u r e d with four nylon screws to the main d e c k of the C E instrument which is m a d e from acrylic. T h e lower half of the pressure c h a m b e r is also held in an acrylic cylinder s o w h e n the s y s t e m is a s s e m b l e d , only the capillary's steel pressure fitting and a part of the surrounding c a p are e x p o s e d at high voltage. Voltage w a s limited by the proximity of the top of the pressure fitting to the heater plate which c a u s e d electrical discharges a b o v e 5000 V , the result of a c o m p r o m i s e between minimizing the e x p o s e d region of capillary a n d proximity of the c a p to the heater plate. A maximum voltage of 5000 V w a s a d e q u a t e for these experiments. High pressure w a s delivered to the a n o d e pressure v e s s e l 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 c o n n e c t e d the latter to the a n o d e pressure v e s s e l c a p .  In principle, P E E K tubing could be  u s e d right from the regulator, but integrating the three-way exhaust valve to vent the system after filling the capillary w a s most elegantly a c c o m p l i s h e d with fixed plumbing. T h e quick release fitting proved valuable in that other d e v i c e s 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 c a n be p u m p e d into the capillary at a pressure a s low a s 300 psi, but in order to clear o c c a s i o n a l  blockages  which c a n form if the capillary is allowed to dry out with polymer inside, it w a s convenient to have higher pressure available. T h i s instrument could apply up to 1500 psi to the a n o d e pressure c h a m b e r .  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  29  T h e cathode e n d of the capillary ran though the s a m e stainless steel c a p and ferrule a s s e m b l y a s the a n o d e , originally built to test the hypothesis that bubbles might re-dissolve by pressurizing the whole capillary. While bubbles ultimately proved to be of s e c o n d a r y importance, the ferrule c l a m p held the capillary in very g o o d alignment with the detector.  S a m p l e s and buffers were contained in wells drilled  in a rotating acrylic disk mounted on a lab jack. T h e s a m p l e holder had 200 uL buffer wells a n d 25 ul_ s a m p l e wells. T h e electric field w a s supplied by a high voltage S p e l l m a n power supply c o n n e c t e d to the a n o d e pressure v e s s e l directly. T h e a n o d e electrode w a s a length of platinum soldered to the pressure c a p a n d hanging c l o s e to the capillary. T h e platinum cathode electrode w a s c o n n e c t e d to the Spellman's ground through a 1 M Q resistor. T h e voltage w a s m e a s u r e d a c r o s s 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.  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  30  520nm post filter Eyepiece  J  480nm prefiIter Capillary  ichroic Mirror  PMT w/ Pinhole  150mm f.I lens  i  Moveable Mirror 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 s c h e m a t i c of the laser induced fluorescence (LIF) detector is shown in Figure 5. It is b a s e d on the design of Mathies et al. which w a s u s e d in the M e g a B A C E [59].  In this c a s e there is only o n e fluorescent  d y e colour, rather than four, a n d therefore only o n e filter set a n d detector. T h e principle of confocal laser induced fluorescence m i c r o s c o p y is to focus the laser b e a m on the capillary, a n d then form an image of the resulting fluorescent signal by sending the output of the m i c r o s c o p e objective through a dichroic mirror a n d on to the detector. T h e dichroic mirror, pre and post filters, are c h o s e n to match  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  31  the characteristics of the c h o s e n fluorophor, so the laser light is reflected and fluorescent light transmitted. T h e present work w a s d o n e using S y b r G r e e n intercalating dye (Molecular Probes), which is excited near 488 nm and emits at 520 nm, and a S y b r G r e e n filter set ( C h r o m a Inc.). T h e microscope objective w a s 10X (Roylin Optics). After passing through the 520 nm post-filter the b e a m p a s s e d through a biconvex lens with a focal length of 150 m m which formed a real image on a pinhole plate in front of the photomultiplier tube ( P M T ) . T h e pinhole could then be m o v e d 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 m o v e a b l e mirror w a s also mounted in the light box which could be interposed in the b e a m after the lens, so a s to redirect it upward where it w a s confocal with a 26 m m Plossl e y e p i e c e .  This  feature proved invaluable in aligning the capillary at the laser b e a m focus before doing a run. T h e mirror itself m o v e d on a linear stage actuated by a pneumatic cylinder c o n n e c t e d to a m a n u a l five-way valve outside the light-box. Optical detection w a s d o n e with a H a m a m a t s u H C - 1 2 0 photomultiplier tube.  It w a s driven through a  variable gain circuit a s per H a m a m a t s u ' s schematic, and the output w a s filtered at 1 k H z , before going to the A / D card. Initial alignment of the optics required aligning the pinhole s o that it w a s confocal with the fluorescent spot from the objective. C o a r s e alignment w a s d o n e by removing the cover of the light box a n d illuminating the capillary with a bright light so a s to m a k e the capillary image visible to the naked eye.  O n c e the capillary w a s in  approximately the right position, the light box w a s closed up and then the fluorescent spot w a s centered on the pinhole by changing the position of the P M T manually a n d observing the resultant output signal, which w a s to be maximized. S y b r G r e e n in water w a s initially u s e d a s a flourophor, but without D N A , the signal intensity w a s low a n d subject  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  to photobleaching.  32  It w a s subsequently discovered that moving the  capillary s o the laser w a s f o c u s e d on the polyamide coating p r o d u c e d a strong, consistent fluorescent spot which w a s e a s y to align. T h e capillary could then be repositioned so the capillary window w a s centered over the laser focus, a n d experiments could c o m m e n c e .  3.2.3 Thermal and Visible Light Cameras T h e r m a l and visible light i m a g e s were u s e d to o b s e r v e the m o v e m e n t of ionic concentration boundaries, bubbles and metal particles in the capillary. T h e r m a l images were obtained with a 10.6 u m R a y t h e o n Control I R 2 0 0 0 A S Silicon Bolometer c a m e r a . T h i s unit has a fixed focal length a n d automatic brightness control. A n IR transparent A M T I R polymer lens of 38 m m focal length (Oriel) w a s placed in front of the c a m e r a as a magnifier, giving a field of view of 25 mm.  Images were taken every eight s e c o n d s , and the Labview data  acquisition program w a s configured to prompt the user to select the region of the IR image containing the capillary at the beginning of the run. T h o s e regions were then c r o p p e d out of s u b s e q u e n t i m a g e s and stored side by side. T h i s image w a s s a v e d along with separate files containing current a n d time data, and P M T detector data. Visible light i m a g e s were obtained with a C a n o n Elura D V video camera.  F o r observations of bubble evolution it w a s a i m e d through the  c a m e r a port of a L e i c a binocular microscope, giving a field of view of about 9 m m . T h e nickel particles (section 5.4.4) were imaged through the e y e p i e c e of the C E instrument's on-board microscope, giving a field of view of about 3 m m . Data acquisition for the thermal a n d D V c a m e r a s u s e d their N T S C video outputs and a NI-1025 I M A Q card (National Instruments).  T w o cards were used for simultaneous  imaging. T h e visible light i m a g e s were c r o p p e d a n d a s s e m b l e d in the s a m e m a n n e r a s the thermal images.  C h a p t e r 3 A p p a r a t u s and M e t h o d s 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 u s e d s o a s to closely simulate the M e g a B A C E itself.  Unless  otherwise noted, all experiments were conducted with 36 c m long capillaries, of 75 Lim diameter, with the detector window 2 c m from the cathode. W h i l e a n t i - E O F coatings could have b e e n applied to inh o u s e new capillaries, it w a s 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 m m long, knowledge of which w a s useful for alignment p u r p o s e s . H a d these capillaries not been adaptable for our purposes, windows would have had to be burnt in raw capillaries with nichrome wire, a n d then the surface treatment performed, with the attendant risk of b r e a k a g e during these steps. Fortunately for our purposes, a large n u m b e r of M e g a B A C E capillary bundles were m a d e available w h e n the G S C retired two M e g a B A C E s s o m a n y capillaries were available for cut capillary experiments. T h e choice w a s m a d e to use matrix a n d buffer from A m e r s h a m B i o s c i e n c e s (Part # U S 7 9 6 7 6 ) , rather than m a k e it from scratch despite uncertainty as to the exact contents.  Polymerization of small  batches of L P A in-house according to [45] g a v e highly variable viscosity despite identical starting conditions from batch to batch. T h e A m e r s h a m L P A by contrast w a s very consistent. T h e buffer concentration in the matrix w a s believed to be 50 mmol/L of e a c h of Tris and T A P S ) respectively [60]. W h a t is not known is the type a n d 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. T h i s topic is taken up again in C . 2 .  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  34  Tris a n d T A P S refer, respectively, to the w e a k b a s e Tris(hydroxymethyl)aminomethane) a n d the weak acid [(2-Hydroxy1,1 -bis (hydroxymethyl)ethyl)amino]-1-propanesulfonic acid.  These  buffer c o m p o n e n t s were originally introduced by the Karger lab, who d e v e l o p e d L P A for u s e in s e q u e n c i n g [45]. T r i s / T A P S w a s found to produce better s e q u e n c e data than the traditional biological buffer TrisBorate, possibly b e c a u s e the former is less likely to c a u s e band broadening by interacting with reagents left over from D N A purification. Tris a n d T A P S are part of a larger c l a s s of "Good's buffers" which exhibit this benign behaviour [52], and which have the further a d v a n t a g e that they are only 50% dissociated in equilibrium a n d s o have high buffering capacity.  3.3 Samples and Methods 3.3.1 MegaBACE Samples Detailed explanations of  E. coli b a s e d D N A amplification, cell  lysis, the cycle s e q u e n c i n g reaction a n d s a m p l e c l e a n u p are given in A p p e n d i x A . 5 . T h e s e protocols are u s e d by the G S C preparation a n d in the Marziali lab. Briefly, a D N A insert from the M a m m a l i a n g e n e collection ( M G C - 1 0 7 9 0 ) w a s ligated into a circular M - 1 3 vector (a piece of D N A c a p a b l e of reproducing inside cells) w a s grown in E. coli. T h e cells were then lysed and the insert D N A isolated. T h e cycle s e q u e n c i n g reaction w a s then performed to produce fluorescently labeled single stranded copies of the original template of monotonically increasing size. T h e D N A was then purified out and the s a m p l e dried down.  Before injection on the M e g a B A C E , s a m p l e s were r e s u s p e n d e d  in 20 u L of d H 0 , and briefly vortexed a n d centerfuged. 2  T h e s a m e s a m p l e preparation protocols were u s e d for bubble propagation experiments conducted in the Marziali lab as well as in the a g a r o s e r e s u s p e n s i o n experiments d e s c r i b e d in A p p e n d i x B . 1 . In the  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  35  latter experiments, the s a m p l e s were pooled a n d realiquoted several times to e n s u r e consistency.  Sizing these s a m p l e s in a g a r o s e s h o w e d  them to consist of 20-1000 bp single stranded s e q u e n c i n g fragments a s well as 7.5 kb M - 1 3 template D N A and s o m e quantity of unseparated long fragments, presumably E. coli g e n o m i c D N A left over from colony growth. E. coli's g e n o m e is 3 M b , s o these g e n o m i c fragments m a y be in the kilobase to m e g a b a s e range. In the experiments on bubble propagation, the control consisted of M e g a B A C E 4 - C o l o r S e q u e n c i n g Standard ( A m e r s h a m B i o s c i e n c e s (US79678), which a g a r o s e sizing s h o w e d 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 u s e d 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 w a s 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 a n d a 15 minute prerun performed at 9 0 0 0 V . T h e buffer plate w a s then r e m o v e d , a n d the cathode array rinsed in dH 0. 2  S a m p l e s r e s u s p e n d e d in 20 uL d H 0 were then injected for 10 2  s at 3 k V a n d the cathode array rinsed again. T h e original buffer plate w a s restored to the cathode and the electrophoresis ran for 240 minutes at 6 kV ( 1 0 0 V / c m in the 60 c m capillaries). Typical capillary current at the start of the run w a s 4 uA.  3.3.3 Electropherogram Analysis Electropherograms from s e q u e n c e r s s u c h as the M e g a B A C E are evaluated in terms of read length, which represents the n u m b e r of  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  36  b a s e s that c a n be identified with a given level of confidence. P r o c e s s i n g of the f o u r f l u o r e c e n c e data signals is shown in Figure 6. T h e basecalling algorithm a c c e p t e d as standard in most s e q u e n c i n g facilities is called the Phred algorithm [1, 61]. T h e algorithm accounts for the differences in mobility shifting of the four colours b e c a u s e of differential drag from the different fluorophors a n d fitting a G a u s s i a n to e a c h peak b a s e d on the expected peak frequency. T h e "quality" of e a c h b a s e is given by Q =  -10 log (P ),  the b a s e is incorrectly s c o r e d .  10  e  where P  e  is the probability that  P h r e d I O b a s e s represent a 90%  confidence that the b a s e has b e e n correctly identified a n d P h r e d 2 0 , represents a 99% confidence value. T h e read length is the n u m b e r of b a s e s a b o v e a desired P h r e d value. A generally a c c e p t e d minimum is P h r e d 2 0 , although s o m e a s s e m b l y algorithms use the lower quality parts of the s e q u e n c e to aid construction of the contiguous "tiling paths" that m a k e up the g e n o m e s e q u e n c e .  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  SbTOTB  m  wrfH03  H03  welH03 2004-01 05 Run02 MoteculwDynam.es 1288 120  RunC2  1 30  37  o  140  150  160  1 70  180  CGGAGCGTGTTCCGGTGTGTTGTCTGATAH5MTTAGTCTTTACACTTT&GGCAAAACAGGCTTCATAC  (b)  2900  3000  3100  3200  3300  T i m e ( s c a n number)  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 e x a m p l e of a successful s e q u e n c i n g run from the M e g a B A C E is s h o w n in Figure 7. B e y o n d about 700 bp, the p e a k s b e c o m e diffusion-broadened enough that b a s e quality d r o p s below the P h r e d 2 0 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 A m e r s h a m B i o s c i e n c e s which, in conjunction with a Perl script, allowed extraction of raw current a n d P M T signal strength data.  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  38  70 60 X O « X  X  X X*SKXX38aaKX  X X  50 X  XX&3E$£ X  8 40  X  w  X  X  0)  X  30 xx X  X  X  X  X X X X  X  X  £ X  X  T 3  h  X  . ^ >  > < X  »0$C  <  X.  X  X * X X  20  XX  0  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 w a s finding a s a m p l e c a p a b l e of producing current decline in a reproducible manner. C y c l e s e q u e n c i n g products produced highly variable results.  T h i s is  true in the M e g a B A C E as well: Figure 8, p a g e 44, s h o w s a large range of current decline and Table 3, p a g e 138, s h o w s a factor of two range in fluorescent signal strength from identically prepared s a m p l e s .  A  characteristic of ethanol-precipitated cycle s e q u e n c e products is relatively low concentrations of D N A with extremely low b a c k g r o u n d electrolyte concentrations.  Purification in 96 well plates includes hard-  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  39  to-reproduce steps s u c h as manually tapping the plates against the b e n c h , a n d variations in time in the introduction of different reagents A s a result, there m a y be considerable variability in s a m p l e s a c r o s s individual plates and from plate to plate [13].  Sample  Conductivity  [DNA]  Injection  LiS/cm  ug/ml  Coefficient ug/Q  20 to > 50kb C y c l e  25  10  148  0.5-50kb B A C F r a g m e n t s  300  130  160  48kb X D N A  700  500  265  500 to 23 kbp X - H i n d III  700  500  265  15  9  250  S e q u e n c e Products  Ladder 500bp P C R F r a g m e n t s  Table 1 Data for concentration and solution conductivity for different DNA samples. The injection coefficient was calculated from equation  (2-10)  M  °  N  A  Qinj  =  VMA DNA DNA C  MW  ^sample  In the s e a r c h for injection consistency, various other D N A fragments were evaluated. Conductivity a n d concentration data is shown in Table 1. T w o polydisperse s a m p l e s of high buffer conductivity and D N A concentration were found to c a u s e reproducible current decline. T h e s e were 0.5 to 30 kb bacterial artificial c h r o m o s o m e ( B A C ) digest fragments from the G S C a n d 0.5 kb to 25 kb X Hind III restriction digest (New E n g l a n d Biolabs). T h e s u c c e s s of these s a m p l e s then led to the use of undigested X D N A (New E n g l a n d Biolabs N 3 0 1 1 L ) for the experiments reported here. At 48 kb, this double stranded, linear p h a g e D N A represents a c o m p r o m i s e between ~ 8 k b template a n d  C h a p t e r 3 A p p a r a t u s a n d M e t h o d s to Investigate Current Decline  40  longer double stranded g e n o m i c D N A fragments found in actual s e q u e n c i n g s a m p l e s and which are believed to be the s o u r c e of current decline. T h i s commercial product w a s found to be very consistent a n d stable, and reproducible results were obtained over a period of three years using s a m p l e s from three separate lots.  In t h e s e  experiments, 20 uL aliquots of 500 u g / m L X D N A with 5 uL of 5x S y b r G r e e n intercalating dye were u s e d throughout, although X D N A produced current decline with or without S y b r G r e e n . O n e experimental result which lends weight to the u s e of X D N A as a model fragment w a s that the time evolution of current decline w a s found to be similar for all of the fragments tested. In other words, the high concentration, high conductivity X and X Hind III s a m p l e s exhibited the s a m e behaviour as low concentration, low conductivity cycle s e q u e n c i n g products. T h i s is of significance as it w a s not initially known whether current decline w a s a n intrinsic property of the e n h a n c e d s a m p l e stacking associated with the low conductivity of the s e q u e n c i n g s a m p l e s . T h e similarity in behaviour of the low a n d high conductivity s a m p l e s s u g g e s t s that the current decline is independent of the d e g r e e of s a m p l e stacking.  3.3.5 Single Capillary Instrument Parameters A s noted, 36 c m long, 75 um diameter capillaries cut from M e g a B A C E bundles were used for all experiments.  L P A w a s injected  for 60 s at 500 psi. W h e r e noted, a 15 minute prerun w a s performed with 1x buffer at the a n o d e rather than L P A . T h i s reduced the starting current from 8-9 u A to 4-5 u A at 5000 V . T h e temperature of the heater plate w a s 5 5 ° C a n d both injection a n d runs were performed at 5000 V . F o r runs other than threshold experiments, the injection time w a s 20 s. T h e reduced length of the capillary, higher injection voltage,  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  41  heater temperature and longer injection time were all d e s i g n e d to promote current decline or exacerbate any effects s u c h a s s p o n t a n e o u s bubble formation which might occur. 5000 V w a s also the m a x i m u m operating voltage of the machines.  3.3.6 Cut Capillary and Thermal Image Analysis T h e conductivity distribution in single capillaries w a s determined by the method of s u c c e s s i v e cutting a n d resistance m e a s u r e m e n t [62].  [43]  First, o n e centimeter of capillary at the a n o d e end w a s cut off to  r e m o v e any void c a u s e d by matrix shrinkage as the capillary w a s r e m o v e d from the heater. T h e capillary's resistance w a s then m e a s u r e d by placing it a c r o s s two buffer baths at 400 V and measuring the resulting current. E a c h m e a s u r e m e n t lasted about three s e c o n d s , minimizing c h a n g e s in the ion distribution profile in the capillary. T h e m e a s u r e m e n t w a s repeated with s u c c e s s i v e removals of Ax = 1 m m s e g m e n t s from the cathode e n d of the capillary. O n c e past the region where the resistance was observed to c h a n g e rapidly, cut s e g m e n t s were increased to Ax = 10 m m . T h i s a p p r o a c h w a s found to be fast, have g o o d resolution a n d be m u c h more accurate than pre-cutting the capillary into s e g m e n t s and measuring e a c h individually. T h e conductivity of the n  t h  s e g m e n t of capillary w a s found  from (3-1) where A is the capillary area (m ), V and l are the capillary 2  n  voltage a n d current respectively: (j( \ n  =—  \  A(R ,-R ) n+  n  T  where 7? = — .  I  (  3 _ 1  )  n  Capillaries were cut by pushing the e d g e of a glass slide onto the capillary. ( N . B . T h e slides were prone to shattering; for safety, readily available c e r a m i c cutters should be u s e d in future) C u t s were m e a s u r e d against lines marked on the lab bench, with an estimated error of about 0.25 m m . T h e length of the capillary w a s m e a s u r e d  C h a p t e r 3 A p p a r a t u s and M e t h o d s to Investigate Current Decline  42  before a n d after the series of 1 m m cuts, a n d again after the 10 m m cuts a n d then the a v e r a g e s p a c i n g of e a c h w a s calculated b a s e d on the n u m b e r of m e a s u r e m e n t s taken. T h u s the uncertainties in boundary positions are ± 0 . 5 m m . A s noted, thermal images were a s s e m b l e d by placing c r o p p e d images of the capillary side by side to show the temporal evolution of thermal fluctuations. After e a c h run, the a v e r a g e brightness a c r o s s e a c h individual capillary image was calculated, and the edge(s) of the hot region boundary(ies) were found by c o m p a r i n g the image to a threshold value. A complicating factor w a s that current decline c a u s e s overall cooling, changing the threshold value for the depletion boundary in the image. T h i s w a s only significant for the longest depleted buffer runs, s u c h as Figure 15(b) but in those c a s e s , the image contrast w a s adjusted a c r o s s the time axis so a s m a k e the image brightness e v e n .  F o r the visual images, positions of bubbles  a n d nickel particles were determined manually, using a Matlab script. O n e data point w a s obtained for e a c h image (every eight s e c o n d s ) a n d matrices of these data were s a v e d with the current and run time for e a c h data point. Position and current data were then fitted using Matlab (The Mathworks) and Microsoft E x c e l , a s d e s c r i b e d further in section 4.4.2.  C h a p t e r 4 Experiment  43  Chapter 4 Experiment T h e experiments presented in this chapter constitute a systematic investigation of the m e c h a n i s m underlying observations of read length degradation with associated current decline. T h e first goal of this investigation w a s to establish the relationship between read length a n d current decline. Having established that current decline directly affects read length, the next objective w a s to investigate the s o u r c e of the current decline. T h e formation of g a s bubbles in the capillaries w a s explored as a possible s o u r c e a n d w a s largely discounted, leaving inhomogeneity in matrix conductivity a s the most likely m e c h a n i s m for current variation. Conductivity profiles of affected capillaries were e x a m i n e d , 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 a n d the formation of the depletion region. Experiments were also performed demonstrating that s u p p r e s s i o n of long contaminant fragments by s a m p l e resuspension in a g a r o s e improves the s u c c e s s rate of D N A s e q u e n c i n g .  4.1 Relationship between read failure and capillary current decline. In collaboration with the G e n o m e S c i e n c e s C e n t e r , the correlation between read length and integrated current throughout the run (total loaded charge) w a s m e a s u r e d for D N A s e q u e n c i n g s a m p l e s prepared according to section 3.3.1. T h e s a m p l e s were r e s u s p e n d e d in d H 0 , injected for 10 s e c o n d s at 3 k V , a n d run for 240 minutes at 6 2  kV.  Figure 8(a) s h o w s that there are m a n y shortened reads in this  s a m p l e set, a n d that read length increases with increasing total loaded  44  Chapter 4 Experiment  charge (TLC) until 700-800bp at which point read length is diffusion limited [63]. 120  0) <fl  <n  ro  CD 100 TD  JD "ro  o  ro c (D O i _  <D  0_  o  CM A TD  < iD  JZ  0_  0 20 40 60 Total Loaded C h a r g e (mC)  0 20 40 60 Total Loaded C h a r g e (mC)  Figure 8 (a) Read length vs total loaded charge for samples resuspended in dH 0. Each "x" is one capillary - approximately 200 2  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  C h a p t e r 4 Experiment  46  were, in fact, spontaneously nucleating, how they might otherwise appear, and how they might propagate. In order to o b s e r v e bubble effects in the M e g a B A C E , four plates of s a m p l e s m a d e according to Section 3.3.1, were injected at 3000 V for 10 s and run at 6 0 0 0 V for 240 minutes in the M e g a B A C E in the Marziali L a b . Control plates of A m e r s h a m D N A size standard a n d D N A - f r e e running buffer were also injected and run in the s a m e manner.  It should be e m p h a s i z e d that the s e q u e n c i n g s a m p l e s  contain s e q u e n c i n g fragments and long D N A fragments, w h e r e a s the size standard contains s e q u e n c i n g fragments but no long contaminant D N A . After e a c h run, the air box door w a s o p e n e d , a n d with both e n d s of the capillary still s u b m e r g e d in buffer, the capillaries were c o o l e d from 4 0 ° C to room temperature in less than a minute. E a c h sixteencapillary bundle w a s then removed for inspection. B u b b l e lengths were estimated by visual c o m p a r i s o n to a ruler under a binocular m i c r o s c o p e . A variety of bubbles were o b s e r v e d , including unbroken bubbles of 5 to 70 m m length, "bubble trains" of o n e or two capillary diameter bubbles s p a c e d a few diameters apart over up to 1 0 0 m m , a n d single scattered bubbles at various points in the capillary. F o r the p u r p o s e s of this analysis, however, only the p r e s e n c e or a b s e n c e of bubbles w a s noted.  47  Chapter 4 Experiment  Total Loaded Charge in Capillaries With and Without Bubbles 80  70 J  60  50  Z.  • Sequence Fragments, No Bubbles 0 Sequence Framents with Bubbles s Buffer Only, No Bubbles s s i z e Standard, No Bubbles  40  E 30  20  10  10  15  20  25  • 30  35  40  45  50  Total Loaded Charge (milli-Coulombs)  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  48  C h a p t e r 4 Experiment  reducing the total loaded charge. T h i s process m a y furthermore be the dominant source of current decline e v e n for the capillaries containing bubbles.  Experiments with artificially introduced bubbles indicate that  the bubbles alone are probably not sufficient to produce the o b s e r v e d current decline. T h i s topic is taken up again in A p p e n d i x C .  4.2.2 Bubble Formation and Growth T h o u g h it w a s expected that heat dissipation a n d thermal gradients in the capillaries might allow bubbles to grow or migrate, it remained unclear whether these bubbles formed spontaneously, or were externally introduced. T h i s question w a s a d d r e s s e d with the single capillary instrument. With the capillary positioned so the cathode e n d could be o b s e r v e d through the flat wall of a 100uL s q u a r e well cut from a 384 well polystyrene culture plate, the state of the capillary entrance could be o b s e r v e d before, during a n d after s a m p l e injection. X D N A s a m p l e s , as per section 3.3.4, were injected a n d run for periods from 5 to 120 minutes, and the capillary w a s afterward r e m o v e d for inspection under the microscope.  In thirty-nine  consecutive runs, if no bubbles were o b s e r v e d immediately before injection of long D N A fragments, no bubbles were o b s e r v e d after injection or at the e n d of the runs. In the a b s e n c e of s p o n t a n e o u s bubble formation, bubbles must form while the capillary entrance is e x p o s e d to air, and this w a s indeed found to occur. B u b b l e s could be reliably introduced by allowing the capillary to cool with the cathode e x p o s e d .  T h e matrix would shrink,  forming a m e n i s c u s at the cathode, and a bubble would then form w h e n the cathode w a s returned to buffer. Critically, s u c h a thermal fluctuation with e x p o s e d capillaries w a s found to o c c u r in the M e g a B A C E during normal cathode plate e x c h a n g e s . T h e r m o c o u p l e m e a s u r e m e n t s at the M e g a B A C E ' s cathode plate holder revealed that  49  C h a p t e r 4 Experiment  through the matrix injection a n d pre-run stage, with all machine doors c l o s e d , the temperature in the cathode plate holder rose to 2 4 ° C a s a result of heat transfer from the air box immediately a b o v e the cathode plate which circulates air around the capillaries at 4 0 ° C .  Upon  lowering the cathode plate and opening the drawer to e x c h a n g e the buffer a n d s a m p l e plates, the air around the e x p o s e d capillary array d r o p p e d back to room temperature within ten s e c o n d s . 2 2 m m of e a c h capillary is e x p o s e d to this temperature c h a n g e .  B a s e d on a  m e a s u r e d coefficient of thermal expansion for the matrix (see A p p e n d i x D.2), it w a s calculated that the matrix would shrink by at least 40 um, e n o u g h to form a bubble half a capillary diameter in size. B u b b l e s of s u c h a size were o b s e r v e d to be c a p a b l e of e x p a n s i o n during s a m p l e injection in the single capillary instrument. It is clear from the these results that local cooling is the most likely m e c h a n i s m by which bubbles form in s e q u e n c e r s , and could therefore be mitigated through improved temperature control. A s current decline is shown to o c c u r in the a b s e n c e of bubbles, we c o n c l u d e that a s e c o n d effect, unrelated to the p r e s e n c e of bubbles, is the principal c a u s e of current decline.  Further analysis of bubble  behaviour, particularly the relationship of bubbles to ionic depletion regions a n d the effect of bubbles on current is presented in A p p e n d i x C.  4.3 lon Distribution during Current Decline  4.3.1 Formation of a Depletion Region In the a b s e n c e of bubbles, current decline w a s reliably p r o d u c e d through injection of sufficient quantities of A, D N A . Figure 10 s h o w s cumulative resistance and local conductivity profiles obtained by  C h a p t e r 4 Experiment  50  the capillary cutting method introduced in section 3.3.6, for four representative capillaries: o n e control with no D N A injected and three with X D N A run for the times indicated. Approximately 2 5 n g of X D N A w a s injected in e a c h c a s e . T h e conductivity profiles indicate that the p r e s e n c e of the X D N A c a u s e d the formation of an expanding region of ionic depletion which locally d e c r e a s e d the conductivity of the capillary. T h i s local d e c r e a s e in conductivity is an excellent candidate c a u s e of the current d e c r e a s e o b s e r v e d during runs. A striking feature of these plots is the abruptness of the conductivity boundaries, and the low conductivity of the depletion region. F o r clarity, we refer to the part of the capillary between the cathode (injection end) a n d the depletion region a s the "cathode region", a n d the remainder of the capillary between the depletion region a n d the a n o d e as the "anode region". Capillaries cut after varying run times s h o w e d the leading a n d trailing e d g e of the depletion region (anode and cathode boundary respectively) moving into the capillary with the leading e d g e moving faster, c a u s i n g the depletion region to e x p a n d . T h o u g h the width of the depletion region increased with time during electrophoresis, there was no o b s e r v e d correlation between the length of the run and the actual conductivity value in e a c h region.  In other words, variations in conductivity in the background or  depletion regions a p p e a r e d to arise from properties of individual capillaries and did not evolve in time. Only the relative sizes of the different regions c h a n g e d .  51  C h a p t e r 4 Experiment  16r  Conductivity D  1  £ 8 cd  No DNA, 20 Min Run  'ui  a:  4  .  Resistance  10  15  20  25  30  1000  16r  0  35  n  5  10  15  20  25  30  10  15  20  25  30  35  10  15  20  25  30  35  16r  35  Distance to Cathode (cm)  0  5  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 w a s 1 m m a n d transitions at e a c h boundary of every run were abrupt e n o u g h that the c h a n g e in slope between two straight regions could be localized to o n e data point. T h i s indicates that the boundaries are self sharpening: the boundary.propagation m e c h a n i s m works against diffusion. A G a u s s i a n peak widens according to [64]  52  C h a p t e r 4 Experiment  FWHM  2  =161n(2)Df  G i v e n a diffusion constant of D~5x10"  10  (4-1)  m s" for the background 2  1  electrolyte ions, an infinitely sharp transition would be expected to s p r e a d to ~3 m m wide by 30 minutes and - 4 . 5 m m after an hour. Instead, sharp boundaries of less than 1mm in width were found for runs up to 320 minutes. T h e r e are of course differences between measuring capillary resistance while the capillary is running at high voltage a n d measuring resistance using a lower voltage while cutting it up. In the former c a s e the capillary is warmer from both internal joule heating a n d the instrument heater, so the capillary resistance is lower. A s a test of the validity of the m e a s u r e d conductivity values, the final experimentally m e a s u r e d resistance could be reconstructed by integrating the m e a s u r e d conductivity over the length of the capillary using the conductivity values found by capillary cutting:  R final  (4-2)  dx anode  where cb is the cathode boundary of the depletion region a n d ab is the a n o d e boundary. A is the capillary cross-sectional area a n d T is a c  correction factor for temperature-induced conductivity c h a n g e .  The  current w a s experimentally found to rise 30% a s the heater raised the central 2 5 c m of capillary from 2 0 ° C to 5 5 ° C so the value of T w a s set c  at 1.3.  Figure 11 shows the expected final currents from (4-2)  (immediately before removal of the capillary), c o m p a r e d to a n experimentally o b s e r v e d temporal current profile which is typical of t h e s e experiments.  T h e calculated and m e a s u r e d values were indeed  found to be in c l o s e agreement for runs from five to 320 minutes in length. Likewise the initial current of e a c h run could be correctly inferred by extrapolating the anode-side conductivity back to the full  53  C h a p t e r 4 Experiment  length of the capillary (not shown).  Clearly, in t h e s e capillaries the  formation of the depletion region is the source of the current decline. 5.00, y 4.50 ~  0.00 H  0  i  r-  1  50  100  150  ;  i 200  1  1  300  350  -i 250  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 a n d depletion region formation, X D N A and 500 bp control s a m p l e s generated by P C R (see section 3.3.4) were injected for periods of five to twenty s e c o n d s 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 DNA.  Below this value, current decline w a s not o b s e r v e d , and no  quantity of 500 bp control D N A c a u s e d current decline.  Current  decline w a s also not o b s e r v e d when no D N A w a s injected, s a v e  54  C h a p t e r 4 Experiment  specific circumstances s u c h a s replacing L P A with buffer at the a n o d e , a s described in A p p e n d i x C.2  1.15 1.1 TO 1.05  O T 3  -a  ra o _i  ..4...."  1  •  ±  +  +  .  +  +  .'  +  •  ro 0 . 9 5 f o  r—  "S  0.9  N  "ro  § o  0.85 0.8 0.75  0  10  15  DNA Injected (ng)  20  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 m a d e it possible to o b s e r v e the  C h a p t e r 4 Experiment  55  depletion region evolving in time. A s a nondestructive technique, it also allowed repetitive observations with the s a m e capillary, where cutting required a new capillary for e a c h observation. It w a s initially hypothesized that the temperature c h a n g e itself might c a u s e boundary propagation. It is shown in section 5.4 that this is unlikely to be the c a s e . H e r e we d i s c u s s only the o b s e r v e d movement of the region of elevated temperature. A discussion of temperature m e a s u r e m e n t techniques is found in A p p e n d i x E , and Figure 49 s h o w s a n 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 s e c o n d intervals were c r o p p e d , aligned and joined, a s 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.  56  C h a p t e r 4 Experiment  1 1 cn  Anode Boundary  \  tn  o  < Cathode Boundary  3  Distance from Cathode  20  0  5  10  15  20  25  0  5  10  15 Time (min)  20  25  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 s h o w s a series of thermal images of the capillary over time, displayed side by side. T h e region of elevated temperature in the  C h a p t e r 4 Experiment  57  capillary a s s o c i a t e d with increased Joule heating in the ionic depletion region is clearly visible. In nineteen runs, (four with D N A , a n d the rest with depleted cathode buffer as in section 4.4.2) the capillary w a s cut up after being imaged with the thermal c a m e r a . In all of t h e s e c a s e s , the position of the ionic depletion region found by capillary cutting w a s the s a m e as s e e n in the last thermal images, given allowances for thermal shrinkage as the capillary w a s r e m o v e d for cutting. T h e fluorescence detector w a s 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 w a s consistently found to be at the cathode-side depletion region boundary, also shown in Figure 13. In s o m e c a s e s a small fluorescence p e a k w a s o b s e r v e d at the anode-side depletion region boundary, but no signal w a s o b s e r v e d in the depletion region. W e c o n c l u d e therefore that the cathode boundary propagates with the DNA.  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. S i n c e boundary velocity evolves with time, for the p u r p o s e s of this c o m p a r i s o n , boundary motion is characterized by the d e p e n d e n c e of the velocity on the capillary current. In the simplest model, we a s s u m e 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  (4-3)  oA  This can be integrated to x(t) = ^-Jl(r)dTx(t)^Q ) crA * {t  +  (4-4)  X o  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)=C Q{t)+C l  _  2  (4  5)  where C, = — , C = x is an offset related to the camera position, 2  0  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)+C . The divergence 2  59  C h a p t e r 4 Experiment  of the cathode boundary from linearity is taken up in detail in section 5.3.  T h i s model is a g o o d fit to the a n o d e boundary, but a relatively poor fit to the cathode boundary. Figure 14 s h o w s equation (4-5) fitted to the first five minutes of a n o d e 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 s o m e field d e p e n d e n c e . T h e latter is taken up in greater detail in section 5.3.  In contrast, the  a n o d e boundary propagation distance is close to linear with charge. E l e v e n fits to X D N A - i n d u c e d a n o d e boundaries g a v e x(t) oc  Q(t) - . a97±  15  Propagation of the D N A - i n d u c e d anode-side boundaries varied from 5.4 to 11 m / C for normal matrix, a n d 10 to 21 m / C w h e n the matrix w a s depleted by running the a n o d e in buffer (see section 3.3.5). T h e variation w a s greatest from capillary to capillary, with individual capillaries exhibiting relatively constant propagation rates over multiple runs. C u t capillary m e a s u r e m e n t s s h o w e d 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 d e g r e e s of depletion were n e e d e d .  T h i s w a s a c h i e v e d by  running the capillary with normal L P A in the capillary a n d a n o d e , but diluted cathode buffers a n d no D N A . With buffers diluted by at least 50x, a moving boundary w a s visible with the infrared c a m e r a . Data w a s obtained for 1/50x a n d 1/1 OOx T r i s / T A P S buffer, a n d d H 0 . 2  capillaries were also cut up to find the actual conductivity profile. Representative e x a m p l e s are shown in Figure 15.  These  60  C h a p t e r 4 Experiment  Like the D N A induced a n o d e boundaries, propagation rates are linear with charge. Thirteen such runs with run times of 5 to 25 minutes g a v e a m e a n exponent of x(t) <x o = 1030/112 jiS/cm  0  5  10  Q(t) - . agg±  3  o = 1126/212 M-S/cm  15  Time (min)  0  5  10  15  20  25  30  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 dH 0 and the boundary propagates at 3.5 m/C and 2  (b) the well has 0.02x Tris/TAPS buffer and the boundary propagates at 1.8m/C.  Figure 16 s h o w s the relationship between the a n o d e boundary propagation rate a n d depth of various depletion regions.  The  propagation rate of X D N A in the a b s e n c e of current decline is also shown.  T h e only a n o d e - s i d e boundaries which m o v e faster than the X  61  Chapter 4 Experiment  DNA are at the front of deep depletion regions, beyond anything achievable by running depleted buffers at the cathode. 14  o  A  E, 1 2  • A  A  <D CO  Typical X D N A Mobility, Depleted Buffer @ C a t h o d e /„ D N A  * 10 c  o  A  ro  ra ° o  A  ra  TD C  i-  4  CD  (1)  8  2  <  0 "0  50  100 150 200 250 300 Depletion Region Conductivity (uS/cm)  350  400  Figure 16 Measured propagation rates for boundaries of different depletion depths. The background conductivity in each case is 1100 uS/cm.  A s an extension of the discovery of a threshold for D N A 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. A s in Figure 12, the threshold for the onset of depletion is between 1 0 and 2 0 ng of DNA, but once established, the anode boundary propagation rate is constant.  62  C h a p t e r 4 Experiment  10  20  30 40 50 Injected X, DNA (ng)  60  70  80  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 s u g g e s t s a m e c h a n i s m for current decline in the  p r e s e n c e of large fragments.  E v e n if any quantity of D N A m a y be  c a p a b l e of locally depleting the background carriers, if the depletion is not d e e p e n o u g h , the D N A m o v e s faster than any induced a n o d e - s i d e boundary s o the depletion region cannot form. T h e expanding depletion region c a n only form if there is sufficient depletion of the background electrolyte so that the anode-side boundary takes off a n d runs away from the D N A . Figure 17 suggests that the sufficiently fast a n o d e boundary propagation may only o c c u r w h e n depletion region  C h a p t e r 4 Experiment  63  r e a c h e s s o m e limit of "total" depletion. T h a t is why adding more X D N A d o e s not c a u s e the a n o d e boundary to propagate faster. A notable property of this m e c h a n i s m 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 o b s e r v e d to precipitate in the capillary [13].  Rather, the long fragments propagate with their usual  mobility, but current decline o c c u r s b e c a u s e of the runaway a n o d e side boundary, the propagation of which is independent of, though driven by, the long D N A fragments.  64  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  Chapter 5 Analysis of Boundary Propagation W e have shown in the previous chapter that current decline is c a u s e d by the D N A forming a depletion region which, having r e a c h e d sufficient depth, is able to e x p a n d b e c a u s e 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 a n o d e boundary propagation in the a b s e n c e of D N A .  It remains then to be understood why the depletion  region forms and why the a n o d e a n d cathode side boundaries m o v e a s they do. In this chapter, analytic arguments are u s e d to s h o w how slow moving ions c a n 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. T h e m o v e m e n t of the boundaries is a n a l y z e d , starting with the cathode boundary. C o m p a r i s o n of the a n o d e and cathode boundaries allows us to discard variable electroosmotic flow as a m e c h a n i s m for the cathode boundary non-linearity. Fits to the cathode-side boundary m o v e m e n t s h o w s the D N A to transition between two m o d e s of migration as the field declines. A n a l y s i s of the a n o d e boundary propagation m e c h a n i s m is less conclusive as the experimental e v i d e n c e is not definitive. T h e theory of moving boundaries for different electrolyte types is therefore introduced to provide a framework for possible m e c h a n i s m s . numerical model is introduced to test various possibilities.  A  It is s h o w n  that the like-ion conductivity gradient m e c h a n i s m which has b e e n cited a s the likely s o u r c e of these slow moving, low conductivity boundaries  65  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  [43, 62, 65] is not in fact likely to be at work, and it is c o n c l u d e d that the most likely m e c h a n i s m requires s o m e combination of fixed charge in the matrix and/or a rise in p H in the depletion region so O H " ions b e c o m e principle carriers. Experimental evidence for p H c h a n g e s , via c h a n g e s o b s e r v e d in the electrophoretic behavior of nickel particles, is presented in section 5.4.4.  5.1 Formation of the Depletion Region T h e c o m m o n a p p r o a c h to analytical models of capillary z o n e electrophoresis is to a s s u m e that the conductivity of background electrolyte is - 1 0 0 times higher than the conductivity of m a c r o m o l e c u l e s being analyzed [66].  T h i s permits the assumption  that the electric field in equation (5-1) is constant, and thus linearized, the governing equations b e c o m e tractable. If the electrophoresis s c h e m e d o e s not involve a high d e g r e e of s a m p l e concentration, s u c h 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, c o m p a r a b l e to the concentration of the electrolyte, and e n o u g h to significantly perturb the conductivity. It is still instructive, however, to examine the perturbation of a small quantity of slow-moving c h a r g e d s p e c i e s on the background carriers. C o n s i d e r again the 1-D S m o l u c h o w s k i equation to describe the time evolution of ion concentrations in the p r e s e n c e of diffusion a n d electric drift:  dt  ox  ox  where C,, D, and JUJ(C) are respectively the concentration, diffusion coefficient a n d electrophoretic mobility of the i  t h  c h a r g e d s p e c i e s . In  66  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  the present c a s e , the buffer ions are all univalent, so the charge z is not included.  CT(*,0 = Z  ei  J(t) = V  E  M  F  N ,C  ( _2) 5  (5-3)  dx  0 =  ^ J{t) U a(x,t)  (5-4)  m  T h e local field E(x,t) is found by first calculating the local conductivity, o(x,t), where F is the F a r a d a y constant a n d the summation is over all ion s p e c i e s , a n d then the current density J(t) from (5-3). F o r ionic polymers s u c h a s D N A , Cdna refers to the concentration of c h a r g e s , not individual particles, and thus includes the multiplicity of c h a r g e s per molecule. T h e fact that these are long molecules is reflected in the low mobility but not in the concentration. T h e matrix buffer is 50 m m o l / L T r i s - T A P S , initially at p H = 8.3,  (see  section 3.2.4, p a g e 33 for more detail). T h e y dissociate to give 2 5 m m o l / L of T A P S " a n d T r i s H \ s o the contribution of H a n d O H " +  (5x10" mmol/L and 2x10" mmol/L respectively at p H 8.3) c a n be 6  3  ignored and we model a two-ion system plus D N A . C h a r g e conservation dictates  C =C+C +  dna  For further simplification, we consider the s y s t e m 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 s o we c a n a s s u m e the D N A is fixed. Let us now consider the quantity of interest - the concentration of mobile ions C = C.+C+. F r o m charge conservation,  C(x, t) = 2C_ (x, t) + C  dm  dC(x,t) dt  _ dC_(x,t) 2  ~  dt  (x)  (5_5)  67  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  Re-writing (5-1) for all mobile ions, taking advantage of (5-5) and a s s u m i n g the quantity of injected D N A is small, and that  ju = ju. = -//+, we c a n write  ,Z)9 Q 2  dC_ d C_ 2  =D  dt  • + -  dx  2  2  M  dx  2  1  3  2  ox  /  ^  -  (5-6)  For initial conditions of a uniform anion concentration, a n d 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 d e c r e a s e C . on the a n o d e side of the peak. Note also that a larger carrier ion mobility will exacerbate this effect. A s s u m i n g that Cdna and the resulting perturbation to C . (defined as SC.) is also small we c a n follow a perturbation analysis similar to that used in the study of m e m b r a n e s with fixed c h a r g e s [66]:  C_(x,t) = C°_+SC_(x,t)  (5-7)  and  8SC_ 8t  8 SC = Ddx 2  2  D d Cdna 2  2  8x  +-  J  C.dna  8  2F 8x\  2  (5-8)  2C°  At steady state, using boundary conditions at the e n d s of the capillary, and a s s u m i n g that Cdna(x) is nonzero over a finite length xi< x < x a n d 2  SC_(0) = SC_(L) = 0,  _  (5  9)  where L is the length of the capillary. T h i s yields:  SC (x) = V  '  ^— fl - -Tf(r>/z-. 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 s h e d s light on what drives the initial formation of the depletion region, a n d , a s is shown below, on the threshold behaviour of current decline as a function of increasing injected D N A . In qualitative agreement with observations a n d  68  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  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 n u m b e r of low mobility fragments. A s we shall s e e in section 5.2, numerical solutions to (5-6) indicate that the depletion SC., o n c e it b e c o m e s a significant fraction of C . ° , grows rapidly in magnitude with increasing amounts of injected D N A a s a result of the growing electric field in the depleted region. T h e r e f o r e , formation of a d e e p depletion region tends to o c c u r rapidly o n c e a critical quantity of low mobility fragments is r e a c h e d . Estimates of this critical n u m b e r using (5-10) where we set SC. ~ C° and given typical run parameters: C . = 25 mmol/L, D = 5 x 1 0 gives C N A ~ 1 0 D  fragments.  1 2  1 0  m / s , J = 1000 A / m 2  2  nucleotides, or ~ 1 ng of large (i.e. slow moving) D N A  B e y o n d this critical number, increasing D N A injection will  rapidly d e e p e n the depletion region to the point where, a s demonstrated in Figure 12, the depletion region boundary mobility e x c e e d s the fragment mobility and the depletion region e x p a n d s . Experimental results from Figure 12 indicate that this threshold o c c u r s 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 s y s t e m . C o m p l e t e m o d e l s of C E are difficult to produce a s the system's behaviour is d e p e n d e n t on properties which vary widely with c h e m i c a l components.  M o s t s c h e m e s are also subject to numerical diffusion,  which c a n result from errors in transport d u e to the finite size of the discretization and c a n dominate over Brownian diffusion. T h e difficulty in removing numerical diffusion without making m o d e l s s o m e w h a t o p a q u e has b e e n mentioned as a limitation [67].  M o d e l s are likely to  be most useful where, s u c h as in the present c a s e , they are u s e d to better understand a limited set of o b s e r v e d p h e n o m e n a , or predict to  69  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  first order the behaviour of well-understood analytes in well-buffered s y s t e m s [68].  C E has been modeled with both continuum and  molecular d y n a m i c s equations [69]. A n attempt w a s m a d e here to remove numerical diffusion by calculating electric fields b a s e d on charge imbalances. T h i s worked until proper constants were applied at which point the model b e c a m e totally unstable.  S u c h an a p p r o a c h  is d i s c u s s e d in [70] where it is pointed out that the discretization step size must be on the order of the D e b y e length which is impractically small for real simulations. T h e following simulation u s e s a first order finite difference approximation ( F D A ) to the continuum S m o l u c h o w s k i equation. T h e purpose of the present model is to show the effect of D N A on background ions a n d to test h y p o t h e s e s related to moving boundaries. T h i s of course m e a n s that the background electrolyte concentration and resulting electric fields are not constant.  It also  m e a n s that acid b a s e equilibrium must be maintained, which represents the majority of computation time in this simulation. S e v e r a l simplifying assumptions c a n be m a d e however.  Electroosmotic flow is  neglected as it has b e e n shown experimentally to first order to be unaffected by evolution of the depletion region as d i s c u s s e d 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], a n d in this model, Brownian diffusion is actually overwhelmed by numerical diffusion. Fortunately, the experimental results we s e e k to explain here, s u c h as in Figure 10, s h o w that the boundaries of interest are self-sharpening, s o in these c a s e s , the system will act to negate the effect of numerical diffusion. In the a b s e n c e of electroosmotic flow or any other hydrostatic effects, the flow profile is taken to be flat a c r o s s the capillary s o the discretization c a n be one dimensional.  70  C h a p t e r 5 Analysis of B o u n d a r y Propagation  T h e behaviour of ions under c h a n g e s in concentration, temperature and p H is complex a n d varies from s p e c i e s to s p e c i e s . O f greatest c o n c e r n are relationship of mobility to temperature and concentration: /u(T) a n d ju(C), a n d pH(T), the variation of p H with temperature. In a localized region of the capillary, T ex 1/a oc 1/C s o ju(T) and ju(C) are coupled (see A p p e n d i x E ) , which m a y be of significance in the c a s e , a d d r e s s e d 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 m a d e functions of concentration. In the c a s e that c h a n g e s in p H mediate boundary movement, d i s c u s s e d in section 5.4.3, pH(T) could b e c o m e significant. dpH/dTfor -0.02/°C.  In fact,  50 mmol/L T r i s - T A P S w a s experimentally found to be G i v e n that the largest temperature increase m e a s u r e d in the  depletion region w a s about 7 ° C , this represents a fall of 0.14 p H units which is not significant c o m p a r e d to rise in p H of 2-3 units believed to be occurring in the depletion region. F o r this reason the temperature d e p e n d e n c e of the p H is not included in the simulation.  71  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  Cathode Reservoir ~ & Left Boundary Cell 1  Right Boundary Cell n * 7  Cells k  k-1 cathode  k+1 [+ ions] anode  [- ions]  J  JH/2  Jt+1/2 Jt+1/2  •fc-1/2  Figure 18 1-D discretization of the capillary showing ion flows in the upwind scheme.  Figure 18 s h o w s how the capillary is discretized in s u c h a way a s to preserve the c h a r g e neutrality required by equation (5-1). W h e n voltage is applied, the positive ions m o v e to the left a n d the negative ions m o v e to the right. T h e c h a r g e flux per unit time of a given ion is defined a s 0,  =  y. C EA i  i  (5-11)  where A is the a r e a of the capillary. C h a r g e neutrality is explicitly preserved by defining the electric field at the cell boundaries Ek±i/2 s u c h that the net charge from the m o v e m e n t of ions into a n d out of  72  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  e a c h cell is zero. Equating the negative a n d positive s p e c i e s flowing into and out of cell k gives £  M  , C ^ _  1  /  2  -  i-  XMi:CtE  k+ll2  i-  =5>/+Ow  - Sn C? E _ +  +  k  V2  i+  ;'+  where e a c h s u m is over the /' s p e c i e s of e a c h charge. C o m b i n i n g like fields and expressing in terms of the conductivity gives  j  J J °*-l/2  (5-13)  '£+1/2  G i v e n a constant current j at e a c h time step, this e x p r e s s i o n holds if  (5-14) °"*-l/2  =  0" l/2 =  F  ^  A+  T h e left side of equation (5-1) is written in discrete form a s k  At  * = v(^c)  (5-15)  H e r e we define the field gradient for positive ions a s  ^E  _ E ]/ k+  ~  2  Ax  E_ k  l/2  (5-16)  Ax  and the concentration gradient for positive ions a s  ±c_c -c k+l  Ax  (5-17)  k  Ax  Applying (5-16) a n d (5-17) to (5-15)and simplifying gives:  (5-18) At  Ax  For positive s p e c i e s and for negative species:  (5-12)  73  C h a p t e r 5 Analysis of B o u n d a r y Propagation  Ck  Q  _ Mk+\Ek-\nCk-\  At  f^k^k+xn^k  (5-19)  Ax  Equations (5-18)and (5-19) preserve charge neutrality throughout. C h e m i c a l equilibrium is often ignored in C E simulations, b e c a u s e the assumption C » 0  C  ana  i y t e implies that the p H is constant  and under normal conditions, H and O H " ions c a n be ignored. In the +  present c a s e however, the contribution of these s p e c i e s must be taken into account as buffer capacity m a y be e x c e e d e d a n d water ions potentially b e c o m e significant current carriers. A s d i s c u s s e d in section 3.2.4, the buffer solution consists of a mixture of Tris, a w e a k monovalent base, and T A P S , a weak monovalent acid. T h e coupled equations of chemical equlibrium c a n then be written as  _ [Tris + X[H  +  Tristi+  ~  ~  T r  S  +  + x + y + z]  (5-21)  [TAPS-y]  TAPS  Here K i H  (5-20)  [TrisH -x\ +  = [H  +  w  + z]  +  _ [TAPS' + y\H  k  x+y  +  +x  + y + z\pH~  + z]  (5-22)  is the conjugate acid dissociation constant for Tris, k A P s is T  the acid dissociation constant for T A P S a n d x, y a n d z are the contributions to the H+ concentration arising from the dissociation of T r i s H , T A P S a n d H 0 respectively. T h e initial conditions are applied +  2  as concentrations of neutral Tris, T A P S and H a n d O H " at 10" M , T h i s +  7  system of non-linear equations is solved for x, y a n d z using Newton's method at e a c h iteration, and the concentrations of the s p e c i e s are updated with the new values of x,y and z. T h e requirement to simulate acid-base equilibrium m a k e s the model both more and less complicated. It can be a s s u m e d that b e c a u s e H2O is present at 5 5 M , it is in infinite supply everywhere. T h e  74  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  mobility of water ions is also not well defined a n d while H+ a n d O H " mobilities are nominally given in Table 2, ion hopping m a k e s those values difficult to define precisely [72].  B e c a u s e the supply of water is  infinite however, the concentrations of the water ions c a n be calculated by the chemical equilibrium equations. T h i s is convenient as the mobility of those ions is so high a s to m a k e numerical stability difficult to achieve without impractically small time steps. In fact, the s a m e results were obtained when the water ions were m o v e d with finite difference equations, as w h e n chemical equilibrium calculations were u s e d to determine their concentrations. T h e chemical equilibrium calculation a p p e a r s to correct for any instability introduced by the finite difference s c h e m e for the water ions. T h i s a p p r o a c h might break down if all the buffer ions were truly depleted, but in fact e v e n w h e n the capacity of the buffer to maintain a stable p H is e x c e e d e d , the conductivity is still dominated by the movement of o n e or other of the main ions a n d the distribution of neutral s p e c i e s . T h e capillary w a s divided into n = 256 cells, of 0.1 m m e a c h , using the natural 1-D discretization following from the radial symmetry of the s y s t e m in the a b s e n c e of bulk flow s u c h a s E O F .  T h e time step  w a s then c h o s e n a s 10ms s o the m a x i m u m movement of the T r i s H  +  ions is less than 0.07mm per time step. T h i s w a s found to p r o d u c e stable simulations at any d e g r e e of ionic depletion. T h e cathode reservoir then naturally represents the left boundary, the contents a n d volume of which c a n be either held constant or altered a s n e e d e d .  The  a n o d e side boundary is held at the initial conditions a s it is a s s u m e d that conditions there remain fixed throughout the simulation. T h e algorithm w a s implemented in both Matlab and Fortran77 with data presentation performed in Matlab. T h e algorithm w a s as follows 1.  Initialize concentration matrix with undissociated buffer  75  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  2.  Set initial D N A conditions, balancing D N A charge with a d d e d TrisH . +  3.  Calculate ionic equilibrium in e a c h cell  4.  Calculate total capillary resistance and current  5.  C a l c u l a t e conductivity, electric field and molecule velocity.  6.  A p p l y upwind and downwind F D A equations to positive and negative s p e c i e s  7.  Calculate chemical equilibrium in e a c h cell. R e p e a t steps 4-7 as n e e d e d . All simulations were run with a 36 c m capillary of 75 um  diameter, at 5000V.  lon properties are listed in Table 2: Electrophoretic  Species Tris  Equlibrium  Mobility 30.1x10' m Ns z  9  +  m / W s  [73]  25x10  H  363x10" rrVWs [74]  pKw = 1 4  205 x10" m A / s [74]  pKw = 14  9  +  OH"  9  2  N . B : T h i s is for any  D N A (free 37 x10" solution)  [74]  pK=8.4 (Sigma Aldrich)  TAPS"  _y  [*]  p K b = 8.1  9  m /Vs[27] 2  length D N A  .  Table 2 Physical data for the numerical model. Measurement of TAPS mobility is show in D.1  T w o versions of the model were d e v e l o p e d , o n e with all the carrier ions a n d neutral s p e c i e s [ T r i s H \ T A P S " , H , O H , T r i s , T A P S ] +  -  0  0  a n d D N A in which a c i d - b a s e equilibrium is maintained, a n d another -  with two or three ions (i.e., one ion of e a c h charge or two ions of like c h a r g e and a counterion) behaving a s fully dissociated strong electrolytes.  T h e ions' mobilities and concentrations were then c h o s e n  to resemble T r i s H , T A P S " and/or faster and slower ions a s n e e d e d . +  T h e latter, non-buffered model, which runs m u c h faster d u e to the  76  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  a b s e n c e of the chemical equilibrium calculation, serves a s an approximation for when the electrolyte is not depleted, the p H is near neutral a n d 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 u s e d in this model exhibits numerical diffusion. T h e effective diffusion constant c a n be found by initially setting the concentration of the ions s o that there is a g a u s s i a n peak. A s the simulation proceeds, the center remains fixed but the peak shrinks and s p r e a d s out maintaining a constant a r e a . A diffusion constant [22] c a n be found through the evolution of the peak width over time:  FWHM  2  2  •  N  (5-23)  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  7 7  Figure 19 s h o w s a plot of cr vs. time from which the numerical diffusion 2  constant is found to be D  = 12x10" m / s . T h e diffusion constant of 9  nd  2  ions c a n 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"  10  m / s for the main 2  carrier ions and 5x10" m /s for X D N A . While this d o m i n a n c e of 11  2  numerical diffusion d o e s not negate the usefulness of the model for qualitative experiments, care must be taken to e n s u r e the numerical diffusion d o e s not produce significant errors. If, for example, a D N A p e a k is introduced as in Figure 20, but given a non-zero mobility, numerically diffused D N A will "leak" into the downstream depletion region a n d c a u s e the a n o d e side boundary to propagate away in a c c o r d a n c e with equation (5-41), giving an incorrect result. T h e solution in this c a s e is to run the simulation in the frame of reference of the, D N A peak, a s w a s d o n e in the analytic c a s e .  In this m a n n e r the  D N A position will not be recalculated using the F D A , so it d o e s not have a c h a n c e to diffuse.  C h a p t e r 5 A n a l y s i s of B o u n d a r y 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 s h o w s the effect of a series of fixed G a u s s i a n D N A p e a k s of varying height on the background electrolyte after 20 s e c o n d s . T h e D N A peaks have a width of 200 um, typical of those o b s e r v e d (eg Figure 13). A s expected, the ion distribution s h o w s a more extreme analog to the perturbation approximation in equation (5-10). T h e simulation w a s run under the s a m e conditions a s those u s e d for the data in Figure 12, a n d a s in Figure 12, near total depletion o c c u r s with between 10 and 20 ng of D N A present, in good agreement with experiment.  Figure 21 s h o w s the effect on the ion profile w h e n the  p e a k is b r o a d e n e d . T h e d e g r e e of depletion is independent of the width of the D N A peak. T h i s a g r e e s with equation (5-10) a n d explains the experimental observation that more conductive s a m p l e s which  79  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  exhibit a lesser d e g r e e of s a m p l e stacking have the s a m e depletion behaviour a s less conductive, a n d consequently more c o m p r e s s e d , 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 d e e p e n s the depletion region. T h i s simulation w a s again run in the frame of reference of the D N A s o its mobility w a s subtracted from the T A P S " mobility a n d a d d e d to the T r i s H mobility. W h e n the D N A +  mobility d e c r e a s e s , the T A P S - ion gets relatively faster, a n d the perturbation c a u s e d by the D N A peak gets more severe.  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  80  200  Mobility of DNA (*10 m W s ) s  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" m /Vs. 18ng of DNA was used and the simulation was 9  2  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 w a s noted that the a n o d e boundary propagation velocity d e p e n d s linearly on current while the cathode boundary d o e s not. W e also note that the p r e s e n c e of the D N A peak at the cathode boundary implicates the D N A mobility in the cathode boundary velocity, a n d note that the a b s e n c e of D N A at the a n o d e boundary points to imbalance in  81  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  ion flow a s the driving m e c h a n i s m s for that boundary. T h e following discussion e x p a n d s on these arguments. Before considering a m e c h a n i s m for cathode boundary movement, it should be c o n s i d e r e d whether, a s in Figure 13 b e y o n d the range of the IR c a m e r a , the a n o d e boundary diverges from linearity as m u c h a s the cathode boundary. T h e r e is no reason to s u p p o s e from the IR i m a g e s that this is not happening, a s both boundaries a p p e a r linear over the first five minutes, and s o m e variable E O F could in principle exist. T o c h e c k this, four runs were conducted where D N A w a s injected, the run w a s thermally imaged a n d the capillaries were then cut up. T h e actual a n o d e boundary position could then be x(tf i)  c o m p a r e d with o n e extrapolated from the thermal image, where = C Qf nai C2. 1  ina  Ci w a s determined by fitting to the a n o d e boundary, a n d  +  i  the offset C w a s found by comparing the cut capillary a n d thermally 2  i m a g e d positions of the cathode boundary, which remained in view throughout.  F r o m this it w a s found that the difference between the  actual a n d extrapolated a n o d e positions w a s no more than 1.3% for the runs of 5, 6 and 13 minutes a n d 10% f o r a run of 41 minutes.  In  the 41-minute run the cathode boundary, by c o m p a r i s o n , lagged its linearly extrapolated position by 50%. W e conclude therefore that the a n o d e boundary maintains its linearity of position with respect to c h a r g e throughout the run while the cathode boundary diverges from linearity. E O F , if it is present, must therefore remain relatively constant. G i v e n the hypothesis that the cathode boundary is driven by the propagating D N A , the nonlinearity of the boundary m o v e m e n t must be intrinsic to the D N A migration. It is known that in a g a r o s e , the mobility of long fragments has a field dependent term [75]  v = p: E + ju E . 2  0  l  (5-25)  82  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  Using the present system of fitting position against charge, this would take the form of  (5-26)  S u c h a function c a n only be fitted to the o b s e r v e d 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 m e c h a n i s m hitherto reported. T h e r e 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. T h i s is modeled as an Arrhenius p r o c e s s of energy barrier crossing between trapped states, with negligible probability of a reverse reaction (i.e. backward migration induced by thermal motion), a n d 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-U )/kT 0  (5-27)  H e r e , E is the local field a n d Q x is a parameter to be found that c o m b i n e s the effective number of elementary c h a r g e s available to m o v e the D N A despite screening, multiplied by the length s c a l e of the energy barrier. At higher fields (E> E = U /Qx), e n o u g h force is applied to the 0  0  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 a c c o m m o d a t e the threshold behaviour between the two regimes, the sigmoid function is used  83  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  Y =  (5-28)  1  where x is the threshold and x is a m e a s u r e of the s t e e p n e s s of the t  0  transition from 0 to 1. C o m b i n i n g (5-25) and (5-27) with the sigmoid function, a n d putting all driving parameters in terms of currents gives f  1  1-  V  \  (  1 1  i  +  - ( / - / o ) / * „ -ie  e  V  j  1 +£-('-'.)".  T h i s is a 6 parameter fit: u. , uy.are the two mobility terms 0  l , the 0  threshold for trapping; l which is related to the effective c h a r g e of the c  X D N A a n d the trap e s c a p e distance, and temperature; v , related to 0  the relaxation time of X D N A in L P A ; and x , the sigmoid s t e e p n e s s 0  parameter.  H e r e we set the s t e e p n e s s parameter x to 0.1 so that the  fit requires five parameters.  0  In effect though, this is two separate fits of  two parameters, o n e in the low field and one in the high field regime, with a threshold value to be found between them.  84  Chapter 5 Analysis of Boundary Propagation  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 = 6 kT, un = 1x10' m /Vs, u-, = 1.2x10" 9  2  13  0  m /V s, v = 2x10 mm/s, Qx/kT = 8x10" m/V. 3  2  2  4  0  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" m / V s is close to measured values of u for X DNA in the absence of 9  2  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 U = E Qx can be overcome when the field is 0  0  strong enough that the electric forces are comparable to the thermal forces acting on the DNA. This occurs when E = kT/qb [77], where b ~ 100nm is 0  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  85  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  of Kuhn lengths n ~ 150 for X DNA. The length parameter x can be taken as k  the pore size of the matrix, which is ~ 3nm [20]. This gives an expression for U : 0  Up  n qx  =  (5.30)  k  kT  qb "  Using the numbers for rik , x and b, gives U o ~ 6 k T , a s w a s found in the fit. Q x / k T itself c a n be estimated from the data a b o v e a s Qx  =  n qx  (. )  k  kT  5  31  kT  which gives an estimated value of Qx/kT = 4x10" m A / , c o m p a r e d to 4  8x10" mA/ from the fit. T h e parameter v is the velocity of D N A a s it 4  0  falls into the entropic regime.  In this c a s e the midpoint of the sigmoid  is found to be at 2.24 u A , which, if (5-25) is u s e d , also gives .02 mm/s. T h i s m a k e s intuitive s e n s e as the velocities in the two regimes must match at the transition point. N o experimental confirmation of this effect in polymer matrices has b e e n found in the literature, but the a b s e n c e of s u c h data w a s noted by J e a n Louis Viovy in 2000: it is somewhat trapping]  surprising  has been overlooked  context of gel electrophoresis. conditions requirement interesting avoided  necessary  [entropic  for quite a long time in the This is probably  for its appearance,  of low fields: such conditions as far as separation  by experimentalists  that it  due to the  and in particular  the  are not very  is concerned,  on a pragmatic  and they basis.  were  [76]  W e have shown here that the behaviour of D N A in the entropic trapping regime m a y in fact be interesting, but from a high-throughput, low-cost D N A s e q u e n c i n g perspective, it would be generally desirable if entropic trapping of large fragments, and in fact, large fragments t h e m s e l v e s , were entirely avoided!  86  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  5.4 Anode-Side Boundary Movement Experimental results show that anode-side boundaries in both the D N A - i n d u c e d and depleted buffer c a s e s are not associated with the p r e s e n c e of D N A . T h e ions at the a n o d e side boundary must therefore be the background Tris and T A P S ions a s well a s H a n d O H " +  ions. T h e r e could conceivably be other ions from the buffer or matrix present, but their behaviour should in principle be typical of small ions a n d therefore predictable. A configuration and behaviour of these ions on both s i d e s of the boundary must then be found which c a n explain the boundary movement.  In order to d o this, it is best to start with the  basic theory of moving boundaries in s y s t e m s of multiple ions. T h e p r o p o s e d models for a n o d e boundary propagation c a n then be best understood in the context of the failure of this theory in describing the o b s e r v e d propagation  5.4.1 The Theory of Moving Boundaries T h e behaviour of ionic boundaries has b e e n the subject of r e s e a r c h for over a century [79]. T h e r e are several types of ionic boundaries, including those between two strong electrolytes sharing a c o m m o n counterion, weak electrolytes where H a n d O H " m a y play a +  role, a n d concentration boundaries with the s a m e positive and negative ions on both s i d e s but at different concentrations.  W e begin  by examining the simplest system: two different ion populations in adjacent regions, with a c o m m o n counterion [80].  F o r thematic  continuity, we shall a s s u m e the adjacent ions are negative a n d the c o m m o n counterion is positive.  C o n s i d e r a system where ion 2, with  concentration C m o v e s with velocity v 2  2  into a region which is being  v a c a t e d by ion 1, of concentration C i a n d velocity vi as shown in Figure 24. W e also m a k e the assumption for now that ^>[i2- T h e counterion,  87  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  of course, has concentrations C i and C2 to balance the negative ions everywhere, a n d a mobility  n  f  "A  vC 2  2  II  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 m o v e but we a s s u m e  for the moment that this moving boundary satisfies that condition. T h e c h a n g e in concentration o v e r t i m e between boundaries I and II is equal to the difference in flux a c r o s s the two boundaries and also equal to the difference in concentration multiplied by the m o v e m e n t of the boundary swept out between them.  A0 = v C 2  2  vC x  x  =v C, b^2 -v Q h  h  .  (5-32)  Solving for vt> a n d given v = juE = juJ/crwe get  -  T(  -  v  (5-33)  Mi  JU +JU  K  2  ju, +ju  J yC2  C, J  T h e mobilities c a n be rewritten a s  Mn  T  Mn  T  n  (5-34)  +M  is known a s the transference number and represents the relative  conductivity of the ion a n d counterion. T h e n v  b  becomes  88  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  2~ x  J  t=  T  v  (5-35)  T  F C - C, ' 2  C o n s e r v a t i o n of c h a r g e flux everywhere in the capillary requires that only certain values of C are allowed in (5-35). T h i s w a s first pointed 2  out by Friedrich K o h l r a u s c h in 1897 [79]. A s s u m i n g for the time being that the mobilities are constant with respect to ionic concentration, w e write them a s u, = Z\/A\ where Zj is the c h a r g e of the ions. Neglecting diffusion, the s u m over all the ions gives: (5-36)  |// | ;  dt  dx'  but charge neutrality requires that everywhere  Y Z C (x,t)=0 J  i  (5-37)  i  thus  yJ_dC {x t) j  1  =  0  (5.  3 8  )  a n d integrating gives  y ^)=co{x) c  i  <- > 5  39  \M,\  Equation (5-39) implies that after initial conditions are established by, s a y , hydrostatically injecting s o m e combination of electrolytes into the capillary, the value of co(x) remains constant in time. T h i s equation is known a s the Kohlrausch Regulating Function, a n d o n c e electrophoresis starts, it determines the concentrations of s p e c i e s that follow moving boundaries between s p e c i e s . Equation (5-39) requires that a s ion 2 m o v e s into the region v a c a t e d by ion 1 in Figure 24, it h a s concentration  89  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  C  (5-40)  =C v.  J  Applying (5-40) to (5-33) gives, after s o m e simplification,  J  fi  x  (5-41)  MA  s o the boundary m o v e s at the s p e e d of the leading ion. M e a s u r i n g s u c h a boundary between strong electrolytes of different mobilities a n d combining and obtaining conductivity data for the leading solution turns out to be the best way to m e a s u r e the transference number (5-34) of the leading electrolyte at different ion concentrations  vC 2  2  [80]  vb2  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 to conserve 3  total ion flux. The new concentration boundary in ion 2 remains fixed.  T h e actual picture for strong electrolytes is shown in Figure 25, which represents what would h a p p e n if the system were initialized at t = 0 a s shown in Figure 24 a n d then run for s o m e time. T h e regulating function automatically adjusts the concentration of the region following ion 1 giving a new concentration for ion 2 of C 3 . T h i s then gives the  90  C h a p t e r 5 A n a l y s i s of B o u n d a r y P r o p a g a t i o n  c o r r e c t v e l o c i t y of t h e trailing i o n s to m a t c h t h e l e a d i n g i o n . T h e n e w boundary v  b1  b e t w e e n r e g i o n s of different c o n c e n t r a t i o n s of ion 2  however, s h o u l d be stationary.  T h e s e three r e g i o n s r e p r e s e n t different  " z o n e s " , h e n c e t h e g e n e r a l t e r m " c a p 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 = 4 0 sec 100  100  (a) 5 0  10  20  30  10  20  10  20  30  100  100  (b) 5 0  10  20  Position (mm)  30  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 of two strong electrolytes with a c o m m o n counterion a n d v a r y i n g m o b i l i t i e s a r e s h o w n in F i g u r e 2 6 . In (a) t h e l e a d i n g i o n h a s a h i g h e r m o b i l i t y t h a n t h e t r a i l i n g i o n a n d in (b) t h e t r a i l i n g i o n h a s a higher mobility.  T h e a d j u s t m e n t of the trailing 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 flux 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 stationary  91  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  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. W h i l e there is no evidence for s u c h a hypothetical ion, it c a n also be shown that the physical properties required by theory m a k e it unlikely that s u c h a n ion could exist. C o n s i d e r the depletion region as region 3 in Figure 25 page 89.  F o r s u c h 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" m A / s . 9  2  In that  c a s e the boundary would propagate at the s p e e d of the T A P S ion, but in reality the boundary actually propagates at, at most, o n e fifth that speed.  T h e regulating function c a n be u s e d to solve for the mobility of  the hypothetical ion, given the experimentally m e a s u r e d concentrations on either side of the boundary. T h i s gives a mobility of 4x10" m A / s , 9  2  which is m u c h lower than any ionic s p e c i e s s a v e very large D N A fragments. T h e only s p e c i e s present which might be negatively c h a r g e d a n d might have s u c h a mobility would be fragments of acrylamide polymers, but conservation of m a s s would prevent any bulk flow of s u c h ions s o this is unlikely.  5.4.2 Common Ion Boundaries Previous work on a n o m a l o u s conductivity in electrophoresis [43, 62, 65] has cited Michael Spencer's three 1983 papers on the subject [81] [82] [83] a s providing a possible explanation for current decline. Building on the prewar ion boundary work of Longsworth a n d others [80], S p e n c e r argued that a c h a n g e in transference number from differential retardation of ions could induce a depletion region at the gel buffer boundary. If the transference number w a s dependent on ion concentration, the newly formed boundary could then propagate into  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  92  the matrix. T h e first part of this theory has been experimentally verified by Swerdlow [42] and F i g e y s [43] et al. as noted in section 2.5, p a g e 16.  It has not, however, been shown that a transference number  c h a n g e alone is responsible for boundary movement into the matrix without an a c c o m p a n y i n g p H c h a n g e or involvement of another ion s p e c i e s . Analytic arguments and simulations are presented here which s u g g e s t that this boundary movement is unlikely to c o m e from a concentration d e p e n d e n t transference number in general, a n d particularly not in the present c a s e 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 a n d direction of a 200/100 mmol/L LiCI boundary, which h a s a notably large c h a n g e in transference number, though did not report boundary motion for other s p e c i e s with a smaller dT/dC values. S p e n c e r ' s own experimental results [83] show boundaries a c c o m p a n i e d by p H c h a n g e s .  Prediction of the direction of boundary  propagation b a s e d on the transference number g a v e the right direction, but more quantitative agreement could not be s h o w n . S p e n c e r also s h o w s how the p H would c h a n g e with depletion for a typical single ion w e a k electrolyte, but no prediction of boundary velocity is given in the c a s e where water ions b e c o m e significant carriers [82].  E l s e w h e r e , C h i e n [85] suggests c o m m o n - i o n boundaries  are stationary to at least first order, and B e c k e r s a n d B o c e k [86] assert that the only known moving c o m m o n - i o n boundaries are a c c o m p a n i e d by a c h a n g e in p H , or are multivalent ions near p K a . S p e n c e r ' s prediction for c o m m o n - i o n boundary m o v e m e n t w a s tested via simulation. S p e n c e r derived an expression for boundary m o v e m e n t d e p e n d e n t on a c h a n g e in relative mobility (transference number) of two ionic s p e c i e s with concentration d e p e n d e n t mobilities.  93  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  J dT  (5-42)  F dC If d T / d C * 0, the boundary c a n m o v e a n d will be self-sharpening, a s the point of lowest concentration has the highest velocity. T h e simulation w a s d o n e for both buffered and unbuffered systems.  dT/dC  * 0 is satisfied if the mobility of the carrier ions vary with concentration by different amounts. A c o m m o n empirical formula for p(C) for strong electrolytes s u c h as KCI and N a C l in the range of 1-100 m m o l / L is given in (5-43) where the coefficient 0.5 is found to be typical for univalent ions [87]. A s s u m i n g that the constant would be slightly different for different ions, we arbitrarily assign  (5-43)  T h e s e are for the principal carrier ions. W e a s s u m e that in the buffered system, the water ions have their usual mobilities. T h e s e are arbitrary ions, but for the s a k e of c o m p a r i s o n , their initial mobilities are the s a m e a s the Tris and T A P S ions.  94  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  rjl  0  '—  '  10 20 Position (mm)  1 30  0  1  0  ' 10 20 Position (mm) 1  '8.34 30  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 a n d four ions. T h e boundaries show numerical diffusion and in both c a s e s the center of the final concentration profile m o v e s to the right at a rate of ~ 0 . 5 m / C . T h e boundaries m o v e the s a m e direction irrespective of the sign of d T / d C however, so the o b s e r v e d movement is likely an artifact of the numerical diffusion. W h e n water ions are included there is a small c h a n g e in p H , a s shown, but the s a m e p H c h a n g e o c c u r s for both variable and constant ion mobility. Numerical diffusion a p p e a r s to dominate any actual movement of the boundary, and m a y in fact o b s c u r e c h a n g e s in boundary movement d u e to nonzero d T / d C . T h e model cannot, therefore, give a definitive a n s w e r to the question of whether s u c h a like-ion boundary m o v e s , but certainly d o e s not  95  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  reproduce o b s e r v e d propagation rates e v e n with large c h a n g e s in transference number. T h e possibility of the observed boundaries propagating b e c a u s e of c h a n g e s in transference number a p p e a r s equally unlikely when considered analytically. T h e fastest moving boundaries we s e e in normal matrix propagate at 10 m / C . T h e conductivity falls from 1100 LiS/cm in the background to 70 LiS/cm in the depletion region. A b s e n t a p H c h a n g e , the concentration of T r i s and T A P S " would be 3 mmol/L +  in the depletion region c o m p a r e d to 50mmol/L in the background. If this were a c o m m o n - i o n moving boundary, equation (5-42) would require a c h a n g e in transference number of 20% to give 1 0 m / C . T h i s s e e m s implausible a s typical transference number c h a n g e s are more like 5% over 1-100 mmol/L [87] [88] for strong electrolytes. T h e s e are a c c o m p a n i e d by c h a n g e s in molar conductivity (conductivity/concentration) of 20%.  Figure 47, page 157,  of a vs.  [Tris T A P S ] in fact shows no measurable c h a n g e in molar conductivity at all, so it is very unlikely that c h a n g e s in transference n u m b e r c a n explain this boundary. Finally, the clipped capillary data shown in C.1 s h o w s that it is definitely possible for a concentration boundary to exist in the capillary, a s s e e n by thermal imaging, but which remains stationary b e c a u s e its upstream driving s o u r c e has b e e n r e m o v e d . It must be concluded therefore, it is not the c a s e that these boundaries m o v e b e c a u s e of c h a n g e s in relative conductivity brought on by concentration dependent mobilities, a n d that the explanation must lie in s o m e s y s t e m involving more than two-ions.  5.4.3 Boundary Movement by Bound Charge T h e r e are two other possible m e c h a n i s m s which, when simulated, produce behaviour similar to that o b s e r v e d experimentally. T h e first is that a c h a n g e in p H a c r o s s the boundary allows extra O H "  96  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  ions from the depletion region to neutralize acid s p e c i e s at the boundary, causing it to a d v a n c e . T h e s e c o n d is that s o m e small quantity of bound charge m a y exist on the acrylamide or capillary surface which might produce a moving boundary. Simulations and analytical analysis of the p H mismatch model, shown below, s h o w boundary propagation a n d depletion depths c o m p a r a b l e to experiment. W h a t is lacking however is a m e c h a n i s m by which the p H m a y rise sufficiently to explain the o b s e r v e d boundary movement.  T h e bound  charge model, which also produces p H c h a n g e s , d o e s have a realistic s o u r c e so we focus on this model first. T h e r e is ample evidence from the literature that polyacyliamide c a n b e c o m e c h a r g e d o v e r t i m e as the m o n o m e r s b e c o m e hydrolyzed. [89, 90].  Chiari et a/,for example, found more that 30% of  polyacrylamide m o n o m e r s b e c a m e hydrolyzed in 0.1 Molar N a O H in less than an hour. [91]. W h i l e the present L P A is at a m u c h lower p H , it is r e a s o n a b l e to a s s u m e that it has s o m e small d e g r e e of bound negative charge, G i v e n that 4% w/v L P A has approximately 5 0 0 m m o l / L acrylic m o n o m e r s , we will m a k e the assumption that of the order of 1 m m o l / L of the chain c o m p o n e n t s are c h a r g e d . It is also possible that the L P A might b e c o m e c h a r g e d only w h e n the electrolyte is depleted.  T h i s would be quite possible if the acrylamide were  behaving a s a w e a k acid, but this behaviour has not been reported in the literature a n d will again require a p H c h a n g e . A velocity for a boundary driven by fixed charge c a n be derived in similar m a n n e r to the derivation in section 5.4.1. Without bound charge, s u c h a like-ion concentration boundary should not move.  The  bound charge introduces a c h a n g e in the proportion of the positive a n d negative mobile s p e c i e s however, s o effectively the transference number changes. Figure 24, p a g e 87.  C o n s i d e r again the ion-plus-counterion situation in Here, we a s s u m e a constant concentration Cf of  97  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  bound negative c h a r g e s throughout the system. T h e ions have a constant mobility a n d we a s s u m e for simplicity that LL =  The  negative ion has concentrations C i and C2 but the bound negative c h a r g e s give the positive ions concentrations C-i+Cf a n d C2+Cf. T h e flux of negative ions in the two regions is again given as A0 = v C 2  v A =vC  -  2  b  -  2  vC.  (5-44)  V  (5-45)  b  x  now however, the velocity b e c o m e s  v. =  F  juC  juC.  J_  x  yC + M(C + C )  juC + ju(C +C ) 2  2  f  X  x  F  or  2C,  +C  T  c,  (5-46)  2C +C J^C -C 1  /  2  1  Propagation rates for a range of bound c h a r g e s and d e g r e e s of depletion is shown below in Figure 28.  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  98  30  nl  .  0  i  i  i  :  1  1  200 400 600 800 Depletion Region Conductivity (uS/cm)  1000  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 c h a r g e s were initialized simply by adding the equivalent concentration of T r i s  +  throughout the capillary. T h e concentration of buffer at the cathode e n d w a s then diluted by various fractions to give a range of conductivities typical of those o b s e r v e d experimentally in the depletion region. A c o m p a r i s o n of these results with experiment is shown in Figure 29 below.  99  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  20  r  •A— — H— •©— •  0 0  100  Bound Charge = 0.5 Bound Charge = 1 Bound Charge = 2 Bound Charge = 4 Experimental Data  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  T h i s model approximately reproduces the behaviour of the boundary o b s e r v e d experimentally.  Unlike the p H variation model  d i s c u s s e d 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 a p p e a r s to hydriolize about 500 times more slowly than L P A [91]. T h i s m a y 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 c h a r g e up to 1 mmol/L, the p H rises in the depletion region w h e r e a s for 2 m m o l / L a n d above, the p H falls. T h e c o m p a r i s o n is shown in Figure 30  100  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  below. T h e c a u s e of this c h a n g e 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 c h a r g e m a y act as a n acid and drive the p H down, w h e r e a s where there is e x c e s s basic buffer, the p H m a y rise. In section 5.5 we present e v i d e n c e of what a p p e a r s to be a sustained rise in p H . T h e present simulations do not show a sustained rise in p H while s u c h behaviour is displayed by boundaries driven by larger p H m i s m a t c h e s . T h e latter m e c h a n i s m is d e s c r i b e d below a n d while it m a y not be at work in the present situation, a definitive answer m a y h a v e to await a more precise m e a s u r e m e n t of p H c h a n g e s in the capillary. 40  40  • [TAPS"]  • [TAPS ] -  •[Tris ] 0  35  8.9  -pH  •[Tris ] 0  35  8.8 30  8.9  pH 8.8  30 h  H8.7  8.7 •5 g 25  8.6  8.5  • 20  25  8:6  20  8.5  8.4  8.4  15 8.3  10  £  8.3 10  0  10 20 Distance from Cathode (mm)  8.2  8.2  8.1  H8.1  30  0  10 20 Distance from Cathode (mm)  8 30  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.  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  101  5.4.4 Experimental Evidence for pH Changes in the Depletion Region. T h e preceding simulations using bound charges reproduced the boundary movement, but do not suggest a substantial c h a n g e in p H . T h e r e are a couple of issues here. T h e first is that, as d i s c u s s e d in A p p e n d i x C . 1 , d e e p depletion regions c a n permanently d a m a g e the capillary surface coating s o that depletion regions subsequently arise without special buffer conditions or D N A .  S u c h a n effect could arise  from a d s o r b e d D N A , a c h a n g e in p H , or the high fields associated with the depletion region. It is hard to understand how anything but a p H c h a n g e could affect the chemical structures at the capillary surface.  A  high e n o u g h electric field would have to be strong e n o u g h to affect the physical structure of the matrix. S e c o n d , it is shown in this section that nickel particles s e e m to respond to the depletion region in a m a n n e r consistent with a sustained rise in p H . T h e following experiments were motivated by a desire to m e a s u r e any residual E O F in capillaries. S u c h m e a s u r e m e n t s are normally d o n e with neutral E O F markers s u c h as dimethylsulfoxide ( D M S O ) [92] a n d 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 a p p r o a c h was applied as follows: Approximately 2 0 0 m g of nickel powder (Novamet 4 S P - 4 0 0 ) with a m e a n diameter of 10 Lim w a s mixed with 1 ml of L P A by vortexing, centrifuged briefly to remove air bubbles, then p u m p e d into the capillary. T h e movement of the particles could be o b s e r v e d in the instrument's o n b o a r d microscope, and images of the capillary were obtained with the video c a m e r a as described in section 3.2.3. T h e  102  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  particle locations were recorded manually on the i m a g e s a n d the resulting position vs. time and current data used to find the propagation coefficients using equation (4-5). T h e limitation of this technique w a s that the surface charge of the particles w a s unknown. It was, therefore, unclear whether the particles were moving b e c a u s e of E O F or electrophoresis.  In order to c h e c k this, the position of the  LPA/buffer boundary at the a n o d e w a s recorded. T h e moving L P A boundary method w a s b a s e d 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 p u m p both the L P A a n d buffer towards the cathode.  T o observe  this effect, the L P A at the a n o d e w a s replaced with buffer at the start of the run, to m a k e an LPA-liquid boundary. After the run, the capillary w a s cut up from the a n o d e e n d and at e a c h cutting, the e n d of the capillary w a s prodded with a piece of 50Lim wire. Buffer by itself did not a d h e r e to the wire, w h e r e a s the extremely sticky L P A would. T h r e e 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 D N A ) . T h e rates were the s a m e for all particles o b s e r v e d , and constant over runs up to 25 minutes long. T h e cut capillary method w a s subsequently u s e d on o n e of the capillaries which s h o w e d the particles moving - 1 . 2 m / C . After a 160 minute run, the buffer/LPA interface w a s found 4 c m from the a n o d e , again giving - 1 . 2 m / C . T h e fact that the particles m o v e at the s a m e rate a s the L P A supports the hypotheses that the particles a n d L P A are u n c h a r g e d . T h e direct effect of the depletion region on the particles w a s then o b s e r v e d , and Figure 31 reveals the surprising result: crossing an a n o d e boundary c a u s e s the particles to reverse direction. T h e particle  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  103  tracked in Figure 31 initially m o v e s towards the cathode at -1.3 m / C . After the a n o d e boundary p a s s e s through at 8 m / C , the s a m e particle reverses a n d propagates towards the cathode at 4.6 m / C . T h e depletion depth in this region w a s estimated using equation (C-2), (Appendix C ) at 85 u S / c m . T h e a n o d e boundary m o v e s faster than the particles, s o they do not stack against the boundary. A similar effect is s h o w n in Figure 32 where a dilute-buffer depletion region, estimated at 200 u S / c m , c a u s e d 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).  C h a p t e r 5 A n a l y s i s of B o u n d a r y 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 c r o s s into the depletion boundary is only consistent with a c h a n g e in electrophoretic behaviour of the particles. C o n s e r v a t i o n of m a s s requires that it cannot b e s o m e local c h a n g e in E O F direction. Figure 32 also s h o w s that the d o w n s t r e a m particles clearly c h a n g e direction later than the particles closer to the cathode, the direction from which the depletion boundary is c o m i n g . T h i s implies that the surface charge of the particles must  105  Chapter 5 Analysis of Boundary Propagation  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, e  (5-47)  = d  F  F  where the electrophoretic force is F =Eq e  = fA pE, p  ( 5  _  4 8 )  and where E is the local field in the depletion region, estimated at 1.8x10 V/m and q, the charge on the particle, is the maximum change 5  density p multiplied by the particle area A and a surface charge p  density factor f. If the spacing of atoms at the surface is 3A, p = 1.7 Coul/m , the viscous drag force is given by Stokes Law: 21  F  d  = 67rr]rv  where r; is the viscosity, and r is the particle radius of  ( 5  10Lim.  _  4 9 )  The  particle velocity was found from Figure 31 (a) as velocity of the lefthand particle track added to the velocity of the right-hand particle track as the former represents the EOF. This gives v = 4x10" m/s or a 5  shear rate of about 0.5s" . This corresponds to an LPA viscosity of 1  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/m [23] 2  106  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  region, and that the d e g r e e of increase is proportional to the depth of depletion.  5.4.5 Boundary Movement by OH" Propagation In light of the e v i d e n c e for rising p H in the depletion region, we examine o n e other possible model for the o b s e r v e d moving boundaries. Rising p H c a n o c c u r naturally where the concentration of the acid c o m p o n e n t of a buffer solution is reduced while the basic c o m p o n e n t is maintained. In the c a s e of a 50 mmol/L T r i s / T A P S solution, the p H will rise from 8.3 to 10 as [ T A P S ] declines to zero. In an electrophoretic system, the boundary between high a n d normal p H regions c a n m o v e b e c a u s e extra O H " ions impinging on the background region c a u s e neutral T A P S to be ionized. T h i s draws down the T A P S ion concentration and the boundary m o v e s  First,  It is possible to derive a boundary velocity in this system. note that this velocity is different from that described in section  5.4.1  b e c a u s e in the present c a s e of a buffer, ionic s p e c i e s are not conserved.  Here, O H " ions from the depletion region travel into the  undepleted region effectively adding extra b a s e to the undepleted region. T h e e x c e s s O H " ions are neutralized by the ionization of TAPS  0  to T A P S " . T h i s is normal buffer behaviour, but b e c a u s e the  s y s t e m is under electrophoresis, the newly created T A P S " ions move. T h u s the T A P S  0  concentration is drawn down at a rate proportional to  the flux of O H " ions. T h e boundary remains sharp: O H " diffusing forward are neutralized a n d T A P S  0  ions diffusing backward b e c o m e  T A P S ; and m o v e forward again. T o calculate the expected boundary propagation rate, we m a k e the assumption that the e x c e s s O H " ions in the depletion region c a n ionize the neutral T A P S on the undepleted side.  107  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  v [OH] A d  d  OH  =  v [TAPS] A  (5-50)  b  b  T h e subscript d refers to the depletion region a n d b to the nondepleted (background) region. (5-51)  T h e boundary propagation rate in m / C is therefore (5-52)  I  a [TAPS] A d  b  Equation (5-52) s h o w s that d e e p e r depletion will produce a faster moving boundary a n d the boundary m o v e s faster if the background region is less conductive (Experimental e v i d e n c e for the latter involving depleted matrices is shown in A p p e n d i x C.2). T o actually use (5-52) requires knowledge of [OH"] and the depletion conductivity.  Just  calculating the ion concentrations from initial conditions d o e s not take into account the increased concentration of Tris a s it is transported into the depletion region and neutralized. Obtaining realistic v a l u e s of t h e s e quantities requires actual simulation. Simulations were d o n e using the finite difference model with buffering, as d e s c r i b e d in 5.2, with initial capillary conditions [Tris] = [ T A P S ] = 5 0 m m o l / L and the cathode boundary set to [Tris] = 50 mmol/L a n d [ T A P S ] from .1 to 10 mmol/L.  Data from a three minute  simulation with [ T A P S ] = 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 2 5 m m o l / L in the background to 100 m m o l / L in the depletion region c a n be s e e n , a c c o m p a n i e d by a rise in p H from 8.3 to 10.2.  108  C h a p t e r 5 A n a l y s i s of B o u n d a r y Propagation  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 c o m p a r i s o n of calculated, simulated a n d experimental boundary propagation rates are shown in Figure 34. T h e calculated v a l u e s were obtained (5-52) by using values for [OH"] and aa obtained d  by simulation, and those results closely match. A n interesting effect of the simulations is that a s [ T A P S ] drops below 0.4 mmol/L, the conductivity actually rises. T h i s is not o b s e r v e d in the experimental data.  109  Chapter 5 Analysis of Boundary Propagation  18  o • •  16h  Calculated Boundary Propagation Simulated Boundary Propagation Experimental Results  14  12 10  £•  8  CQ  6  50  •  6  100  150  200  250  300  350  400  Depletion Region Conductivity (u.S/cm)  Figure 34 Simulations of the depleted cathode-side buffer for [TAPS] = 0.4 to 8 mmol/L c o m p a r e d to experimental data. T h e 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. A s 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.  111  Chapter 6 Conclusion  Chapter 6 Conclusion T h i s research has clarified for the first time the m e c h a n i s m of current decline in D N A s e q u e n c i n g in capillary array electrophoresis. First, by analyzing current a n d fluorescence data from capillary array electropherograms, it w a s shown that current decline w a s the primary c a u s e of reduced D N A read length rather than direct interference from contaminant fragments.  Although the quality of the D N A p e a k s w a s  preserved, current decline c a u s e d the velocity of the p e a k s to drop, meaning that fewer peaks arrived at the detector during the run. It w a s also shown that while bubbles were found in s e q u e n c i n g capillaries, they were not the primary driving m e c h a n i s m of current decline, and in fact, expanding bubbles are likely an effect rather than a c a u s e of current decline.  It was also shown that local capillary  -  cooling, a s s o c i a t e d with opening the machine for buffer a n d s a m p l e e x c h a n g e s , allowed small voids to form which permitted, in m a n y c a s e s , runaway bubble growth. R e s u s p e n d i n g s a m p l e s in a g a r o s e gel had previously b e e n shown to prevent current decline. Further experiments here s u g g e s t that a g a r o s e 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 w a s constructed. Using 48 kb double stranded X D N A a s a model molecule a n d commercial linear polyacrylamide matrix with T r i s / T A P S buffer, it w a s shown that there w a s a threshold for current decline of 10-15 ng of injected D N A . Capillary cutting a n d resistance m e a s u r e m e n t revealed that beyond the threshold, D N A induced an expanding region of ionic depletion. A novel technique of infrared imaging of the capillary w a s introduced enabling differences in conductivity to be o b s e r v e d , since the more depleted side w a s at  112  Chapter 6 Conclusion  elevated temperature. T h i s enabled observation of the propagating concentration boundaries in real time. T h e D N A w a s found to propagate with the trailing e d g e of the depletion region while the leading e d g e propagated away.  C o m b i n i n g these data with  experiments with depleted buffers a n d no D N A revealed that the propagation rate of the leading boundary w a s proportional to the depth of the depletion region. T h i s led to a hypothesis that the threshold for current decline occurred w h e n e n o u g h D N A w a s injected to c a u s e the leading boundary to propagate faster than the D N A itself. S u b threshold quantities of D N A would produce a smaller depletion in the downstream electrolyte s o any leading boundary movement would be overtaken by the D N A itself. Analytic a n d numerical models were introduced to demonstrate how semi-fixed c h a r g e s - approximating D N A - c a u s e a depletion region to form in the downstream background electrolyte.  A numerical  simulation s h o w e d that about 16 ng of D N A w a s required to completely deplete the background electrolyte, in good agreement with experiment. M o d e l s of a n o d e and cathode boundary propagation were developed.  T h e D N A , propagating with the cathode boundary, w a s  found to c h a n g e propagation regimes, from biased reptation to entropic trapping, with declining field. T h i s explained the D N A a n d cathode boundary's propagation rate which w a s non-linear with current. T h e a n o d e boundary w a s found to have a linear propagation rate with current, but the m e c h a n i s m by which it m o v e d w a s more difficult to determine.  It w a s shown via simulation that the most likely  propagation m o d e involved a mismatch in positive a n d negative carriers in the depletion region brought on by the p r e s e n c e of bound c h a r g e s either on the capillary surface or in the matrix. T h i s model,  Chapter 6 Conclusion  113  however, did not produce significant c h a n g e s in p H , which may in fact be present. Indirect experimental evidence for a rise in p H w a s found through the observation of nickel particles in the matrix, which were found to c h a n g e propagation direction upon entering the depletion region. T h i s w a s believed to be d u e to a rise in p H . F o r that r e a s o n , another model w a s p r o p o s e d to explain the situation where the depletion region propagates b e c a u s e it has an elevated p H , where O H " ions b e c a m e principle current carriers. At the present time, current decline in D N A s e q u e n c i n g s e e m s to be mostly under control through the injection of smaller s a m p l e quantities with better purification, and more fault tolerant, though less efficient, matrices. A s the era of single molecule s e q u e n c i n g draws near, the share of capillary s e q u e n c i n g in the overall market will best be maintained by extending continuous a v e r a g e read lengths as far a s possible.  T h i s 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 m u c h to learn about moving ionic boundaries. 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Journal of Liquid Chromatography, 1991. 14(5): p. 847-867.  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  Appendix A Properties of DNA and DNA Sequence Methods A. 1 Properties of DNA In order to understand the constraints on D N A s e q u e n c i n g m a c h i n e s a n d protocols, the properties of D N A n e e d s to be understood in detail. D N A has numerous properties that c a n be ingeniously e m p l o y e d to facilitate selective cutting, copying a n d amplification.  It is the most stable of the major biomolecules to work  with a n d , in contrast to proteins and metabolites, D N A fragments of different s e q u e n c e s have the s a m e key properties s u c h a s s h a p e a n d c h a r g e density. A s a result, g e n o m i c s , the large s c a l e study of D N A , h a s a d v a n c e d far and fast in c o m p a r i s o n to "proteomics" or "metabolomics".  Following are general descriptions of the useful  properties of D N A , clone library construction a n d cycle s e q u e n c i n g a n d a detailed description of the methods of s a m p l e preparation u s e d in this work. D o u b l e stranded D N A is c o m p r i s e d of two polymeric helices m a d e from four deoxynucleotides: A d e n i n e , G u a n i n e , T h y m i n e a n d C y t o s i n e (A, G , T a n d C ) attached to a s u g a r phosphate b a c k b o n e . A a n d T a n d G a n d C are e a c h structurally complementary a n d noncovalently bond to e a c h other, s o in the double helix, A is always opposite T a n d G opposite C . T h i s creates excellent binding specificity a s the probability of a s e q u e n c e of N random nucleotides being c o m p l e m e n t a r y to another is N" . L o n g double strands of D N A c a n be 4  melted at 9 5 ° C into single strands, and a n n e a l e d again at 5 0 ° C . D N A c a n be copied by  polymerase enzymes which extend a c o m p l e m e n t a r y  c o p y along o n e of the single strands. T h e deoxyribose b a c k b o n e of  125  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  the D N A h a s 5 c a r b o n atoms with hydroxyl groups on the 3' a n d 5' c a r b o n s a n d extension always o c c u r s from the 3' e n d of the extending fragment towards the 5' end of the complementary fragment. T h e r e also exist restriction enzymes, which cut D N A at sites with D N A s e q u e n c e unique to e a c h e n z y m e . G e n o m e s of different organisms vary in size, from a few million D N A b a s e pairs for bacteria to a few g i g a b a s e s for m a m m a l s to ten g i g a b a s e s for certain plants. T h e D N A is p a c k e d into c h r o m o s o m e s which c a n be extracted from cells and purified for analysis. N e a r random s e q u e n c e s of D N A are easiest to s e q u e n c e , but the high binding strength of the G and C nucleotides m a k e so-called " G C rich regions" difficult to s e q u e n c e . R e g i o n s with m a n y short repeated s e q u e n c e s are also difficult a s single stranded copies c a n loop back a n d undergo complementary binding with themselves.  Special  reaction conditions c a n be u s e d to o v e r c o m e these difficult regions.  A. 2 Library Construction T h e r e are directed and random strategies for dividing a g e n o m e up for s e q u e n c i n g , but all ultimately require the production of fragments a few kilobases in length. T h e s e must then be separated a n d individually amplified to produce e n o u g h starting material to perform the cycle s e q u e n c i n g reaction to produce the 20 to 1000 bp fragments which will actually reveal the s e q u e n c e .  Overlapping  s e q u e n c e data from these individual fragments are then r e a s s e m b l e d into the g e n o m e  in silico. T h e lowest cost and most bias-free method  of g e n o m e s e q u e n c i n g involves preparing libraries of randomly s h e a r e d fragments which are stored in  E. coli cells which c a n be  amplified a s n e e d e d . T h e s e are called clone libraries. T o m a k e clone libraries, randomly s h e a r e d fragments are ligated into a break in a circular piece of D N A called a vector (either a  126  127  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  plasmid or a phage), c a p a b l e of reproducing in bacterial cells. T h e unknown fragment plus vector, ligated back into a circle, is called the template, b e c a u s e copies will be m a d e from it for s e q u e n c i n g . template is then incorporated into E .  The  coli cells by creating holes in the  cell walls, either chemically, or through an electrical p r o c e s s called electroporation, which allows the template to diffuse into the cells - a p r o c e s s called  transformation for prokaryotic cells. T h e concentration  of template and  E. coli are adjusted so that essentially all the  successful transformations involve o n e vector only entering a cell. T h e cells are then "plated out" on a g a r gel b a s e d growth media. Surviving cells c a p a b l e of reproduction can then establish individual colonies, where e a c h daughter cell has a c o m m o n ancestor, a n d contains a c o m m o n template.  T h e original vector into which the inserts were  ligated contains o n e g e n e with resistance to antibiotics and another, (usually L a c - Z ) which m a k e s a blue pigment. T h e colony growth m e d i a contains ampicillin, s o only the cells which incorporated a vector with the antibiotic g e n e survive. T h e inserts are actually ligated right into the middle of the L a c - Z g e n e so the cells that incorporated a vector containing no insert survive, but a p p e a r blue, while the vectorplus-insert colonies have a non-functioning L a c - Z g e n e and are white. T h e white colonies, e a c h containing about 1 0 cells, c a n then be 6  picked from the growth media using a robot. T h o s e colonies are grown further in 384 well incubation plates so e n o u g h of e a c h colony exists that the insert c a n be extracted. T h e s e arrays of cell colonies in 384 well plates, e a c h well containing o n e vector and D N A fragment of interest are called clone libraries. T h e advantage of maintaining the library a s template in E .  coli cells is that cells from e a c h colony c a n be  stored, re-plated, grown and s e q u e n c e d as n e e d e d . T h e best c o m m o n a p p r o a c h to large scale s e q u e n c i n g today is to actually construct the libraries in two steps. A clone library of  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  random fragments of order 100kb are ligated into  bacterial artificial  chromosome ( B A C ) vectors and grown in a similar w a y to the shorter plasmid vectors. T h e s e B A C s , w h o s e locations with respect to e a c h other are found through a p r o c e s s called restriction fragment mapping, are then s h e a r e d into r a n d o m fragments, to m a k e s e q u e n c i n g clone libraries.  A.3 DNA Purification T h e next step in preparing s e q u e n c e fragments is taking s o m e of the clone libraries a n d extracting the template. A typical low-cost protocol, and o n e u s e d in the present experiments, is the alkaline-lysis a p p r o a c h [96].  First, s o m e 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 d i s c a r d e d and the cells r e s u s p e n d e d in buffer (usually Tris-HCI) a n d E D T A (ethylenediaminetetraacetic acid). E D T A chelates divalent metals ions, which inhibits D N A s e s ( e n z y m e s that cut D N A ) . T h e cells are then lysed with sodium hydroxide ( N a O H ) a n d s o d i u m dodecyl(lauryl)sulfate ( S D S , a c o m m o n detergent).  The S D S  m a k e s holes in the cell m e m b r a n e s and the N a O H denatures the cellular D N A , separating it into single stranded fragments ( s s D N A ) . T h e template D N A is circular however, s o is topologically constrained. P o t a s s i u m acetate (KAc) is then a d d e d , which d o e s three things: T h e circular D N A is allowed to renature but s h e a r e d cellular D N A remains denatured. T h e s s D N A is precipitated, since large s s D N A molecules are insoluble in high salt. A d d i n g K A c to the S D S also forms K D S , which is insoluble. T h i s allows for the e a s y removal of the S D S from the plasmid D N A . T h e s a m p l e is again centrifuged to remove cell debris, K D S and cellular s s D N A . T h e template, and potentially s o m e  128  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  g e n o m i c D N A , is in the supernatant, while all other unwanted material is in the pellet. T h e supernatant containing the D N A of interest must then be c l e a n e d of e x c e s s salts. Ethanol or isopropanol and a salt - usually a m m o n i u m acetate - are a d d e d 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 c a n be r e s u s p e n d e d in buffer, ready for cycle s e q u e n c i n g .  A.4 Cycle Sequencing T h e method of D N A s e q u e n c i n g by electrophoresis w a s d e v e l o p e d by S a n g e r [30] a n d independently by Gilbert a n d M a x a m [31], in 1977.  Although the original protocol is still in u s e in low  throughput settings, it involves radio-labelled nucleotides a n d a separate separation must be d o n e for e a c h of the four b a s e s . A significant a d v a n c e occurred in 1986 w h e n H o o d et al. [32] reported laser-induced fluorescence (LIF) detection methods for D N A . With four different flourophores, separation w a s now possible in o n e lane rather than four, with no radiation handling issues. T h i s s e q u e n c i n g protocol is in wide use, and is carried out in the following way: T e m p l a t e (the vector plus insert described above) D N A is mixed with deoxyneucleotides  ( d N T P s : , A , C , G , and T ) , dideoxyneucleotides  ( d d N T P s ) , D N A polymerase ( e n z y m e s which a d d complementary d N T P s and d d N T P s to a strand of D N A ) 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 c a n be copied regardless of s e q u e n c e . 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. T h i s prevents another nucleotide being a d d e d after a d d N T P is incorporated. T h e  129  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  d d N T P s are also fluorescently labeled, with a different colour for e a c h of the four nucleotides. T h e reaction o c c u r s at three temperatures. A b o v e 9 0 ° C , the D N A denatures, b e c o m i n g single stranded. T h e temperature is then lowered to 5 0 ° C , and primers bind to the template. T h e temperature is then raised to 6 0 ° C and the p o l y m e r a s e s begin extending the primer with the available d N T P s , making a complementary c o p y 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, s o m e fragments of e a c h size are p r o d u c e d , e a c h sharing a c o m m o n starting point but terminated at a different nucleotide. A s e a c h 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 c a n be identified by colour. C y c l e s e q u e n c i n g reactions typically u s e thirty thermal cycles to generate e n o u g h D N A for s e q u e n c i n g . After thermal cycling, s a m p l e s are again c l e a n e d up with ethanol precipitation, and then dried down in their reaction plates, ready for s e q u e n c i n g . Just before loading the plates onto the s e q u e n c e r s , the s a m p l e s are r e s u s p e n d e d in d H 0 . 2  T h e full protocol normally involves aliquoting the ethanol purified template into two new plates before cycle s e q u e n c i n g a n d then performing the cycle s e q u e n c i n g reactions using o n e primer specific to e a c h e n d of the template in e a c h plate. T h e two s e q u e n c e s that result are complementary to e a c h other, and m a y or m a y not overlap, d e p e n d i n g on the length of the insert. S e q u e n c i n g data is a s s e m b l e d into actual D N A s e q u e n c e by c o m p a r i n g different pieces of s e q u e n c e to find where they overlap. Overlapping p i e c e s c a n be a s s e m b l e d into  contigs of continuous  overlapping data. F o r a purely random g e n o m e , the a s s e m b l y error probability is  130  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  where N is the n u m b e r of reads, L is the a v e r a g e read length, a n d G is the total length of D N A to be r e a s s e m b l e d [8]. Clearly longer read lengths L a n d a greater n u m b e r of reads N are desirable. In fact for high quality g e n o m e s e q u e n c i n g , at least five times overlap is required. S e q u e n c i n g via B A C m a p s , where the location in the g e n o m e of e a c h 100-200 kb B A C is known, r e d u c e s the value of G from order 1 0 10 . 5  9  to  T h i s is in fact a principle s o u r c e of contention in the C e l e r a / H G P  debate a s it has b e e n argued that C e l e r a G e n o m i c ' s "whole g e n o m e shotgun" a p p r o a c h would never have worked had they not u s e d the H u m a n G e n o m e Project's framework to e n h a n c e their a c c u r a c y . Interestingly, the error probability for real g e n o m e s , which are up to 10% repeats, has not be b e e n formally studied. It is postulated that as m a n y key repeat intervals in g e n o m i c D N A are on the order of 1 kb, so read lengths of 1.5 kb would provide a significant advantage, but this h a s never b e e n quantified [97],[98].  A.5 Genome Sciences Center Sample Preparation T h e s a m p l e s prepared for experiments performed o n the M e g a B A C E were prepared in the following manner. T h i s protocol is reproduced from Watcher et al. [58] which details experiments in r e s u s p e n d i n g s a m p l e s in dilute a g a r o s e to prevent current decline. Further results stemming from this work are reported in section 4.1 a n d Appendix B.1. Bacteria containing a single clone from the M a m m a l i a n G e n e Collection ( M G C - 1 0 7 9 0 ) were inoculated into e a c h well of a 96-well culture block ( B e c k m a n Coulter) in 1.2 m L of 2 x Y T m e d i a (Becton Dickinson) s u p p l e m e n t e d with Chloramphenicol (Sigma) at 12.5 jug/mL.  T h e block w a s s e a l e d with a sheet of A i r P o r e ™ tape (Qiagen)  a n d incubated for 16 hours at 3 7 ° C with agitation at 290 rpm in a N e w  A p p e n d i x A Properties of D N A a n d D N A S e q u e n c e M e t h o d s  Brunswick Scientific shaking-incubator fitted with custom holders. Following growth, cell pellets were collected by centrifugation for 20 minutes at 1400 g a n d the media d e c a n t e d . T h e plasmid D N A w a s then isolated using the modified alkaline lysis procedure d e s c r i b e d above. C y c l e s e q u e n c i n g w a s performed using D Y E n a m i c energy transfer ( E T ) dye brew mix ( A m e r s h a m Biosciences).  T o increase the  s p e e d and efficiency of fluid transfers a n d d e c r e a s e well-to-well variability all fluid transfer steps were performed with Hydra 96-channel microdispensers (Robbins Scientific). All solutions a n d reactions were prepared with deionized 18 M Q c m water. 6 uL of the h o m o g e n i z e d template D N A (164 ug/mL) w a s s e q u e n c e d in e a c h 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, a n d 6 ul_ of D N A , the remaining volume w a s d H 0 . 2  C y c l e s e q u e n c i n g w a s performed in a  P T C - 2 2 5 D N A engine tetrad ( M J R e s e a r c h ) with a ramp s p e e d 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 a g a r o s e resuspension, the s e q u e n c i n g reactions from all plates were collected by centrifugation after thermal cycling, pooled and re-aliquoted into 28 fresh 96-well R o b b i n s plates. T o concentrate the s e q u e n c e d products and remove extra salts and dye-terminators, the reactions were ethanol precipitated. 60 uL of 95% ethanol a n d 2 uL of 7.5 mol/L a m m o n i u m acetate (pH 7.5) were a d d e d to e a c h well a n d , after mixing by repeated pipetting with a R o b b i n s Hydra, D N A precipitates were collected by centrifuging the cycle plate for 30 min at 2750 g at 4 ° C . T h e ethanol/salt mixture w a s d e c a n t e d immediately following centrifugation by inverting and vigorously shaking the plates to remove the liquid from the wells.  Following a  w a s h with 150 uL of 70% ethanol the plates were s p u n inverted at 700  132  A p p e n d i x A Properties of D N A and D N A S e q u e n c e M e t h o d s  g over p a p e r towelling for 1 min to remove any residual ethanol. T h e reaction pellets were dried in a S p e e d V a c with the rotor r e m o v e d , on high heat for 2 minutes. T h e plates were s e a l e d with foil tape a n d the precipitated s e q u e n c i n g reactions were stored at - 2 0 ° C in plastic bags. For the experiments in bubble growth a n d propagation reported in section 4.2 and A p p e n d i x C , 96 well plates with ethanol purified template dried down and stored at - 2 0 ° C were received at the Marziali lab, and cycle s e q u e n c i n g a n d ethanol precipitation were performed a s described a b o v e . T h e only difference w a s that reagents were a d d e d manually using a single channel Gilson Distriman manual pipettor and an eight channel electric pipettor instead of a R o b b i n s Hydra. T h e s a m p l e s were also not pooled a n d realiquoted after cycle s e q u e n c i g  133  134  A p p e n d i x B T h e Effect of S a m p l e R e s u s p e n s i o n in A g a r o s e  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 w a s to find methods to mitigate current decline with minimal a d d e d cost in s a m p l e preparation steps, reagents or hardware. R e d u c i n g the concentration of long fragments through restriction digests or filtration had b e e n reported [14, 42, 57] but none had been widely adopted by g e n o m e centers, presumably for cost reasons.  R e s u s p e n d i n g the s a m p l e in  a g a r o s e prior to electrokinetic injection w a s instead s u g g e s t e d as a low cost method to preferentially reduce the concentration of long fragments during electrokinetic injection. T h i s method w a s investigated at the Marziali lab and at the G e n o m e S c i e n c e s C e n t e r a n d ultimately adopted as standard procedure on the M e g a B A C E  1000  at the G S C . T h e G S C proved the a g a r o s e resupension technique by r e s u s p e n d i n g identical pooled and realiquoted s a m p l e s from a single clone from the m a m m a l i a n g e n o m e collection ( M G C - 1 0 7 9 0 ) in d H 0 2  a n d various concentrations of A g a r o s e [58].  S a m p l e preparation is  d e s c r i b e d in detail a b o v e in A p p e n d i x A . 5 Pairs of identical plates were r e s u s p e n d e d in 20 u l dO.02% to 0.6% ( S e a K e m G o l d A g a r o s e F M C Bioproducts). O n e plate from e a c h pair w a s s e q u e n c e d on e a c h of the two M e g a B A C E s at the G S C .  With a g a r o s e  resuspension,  a v e r a g e read lengths rose from 198 to 653 bp and "successful" runs,  135  A p p e n d i x B T h e Effect of S a m p l e R e s u s p e n s i o n in A g a r o s e  classified a s more than 50 Phred20 b a s e s , increased from 47% to 98.4% of reads.  800  700  600  500  400  300  200  (b) Agarose  100  20 40 Total Loaded Charge (mC)  60  20 40 Total Loaded Charge (mC)  60  Figure 35 Read length vs total loaded charge for (a) Samples resuspended in dH 0 as shown in Figure 8. (b) The same samples 2  resuspended in 0.06% agarose. Each "x" is one capillary.  T h e c a u s e of the improvement with a g a r o s e w a s m a d e clear by analyzing the raw current a n d signal data. Figure 35 c o m p a r e s total loaded charge after injection from water resuspension, (also s h o w n Figure 8), with T L C after a g a r o s e resuspension.  While in section 4.1 a  correlation between T L C and read length w a s shown, the a g a r o s e almost completely prevented current decline from occurring. A l m o s t all capillaries after a g a r o s e resuspension show a T L C over 40 m C .  A p p e n d i x B T h e Effect of S a m p l e R e s u s p e n s i o n in A g a r o s e  While the efficacy of loading from a g a r o s e w a s demonstrated, it w a s not known if the reduction in incidence of current decline w a s d u e to preferential suppression of large fragments or an overall s u p p r e s s i o n of fragments. T h i s w a s investigated in the Marziali lab using the single capillary instrument. S a m p l e s of 1 kb ladder (New E n g l a n d Biolabs N 3 2 3 2 S ) consisting of 0.5 to 10 kb double stranded fragments w a s u s e d as a s a m p l e with a representative size range, but with more a consistent injection behaviour then cycle s e q u e n c e products, which likewise led to the choice of X D N A for current decline experiments.  20 u.L of ladder w a s mixed into 20 u.L 5x S y b r G r e e n a n d  60 u,L d H 0 to m a k e 10 x 10 uJ_ aliquots. T h e s e were dried down a n d 2  r e s u s p e n d e d in either 10 uL d H 0 or 10 ul. of 0.08% A g a r o s e ( S e a k i m 2  G o l d , F M C Bioloabs) dissolved in d H 0 . 2  T h e s a m p l e s were then  injected for 15 s e c at 5 (j,A a n d run at 2 jaA. Representative electropherograms are shown in Figure 36. T h e ratio of the a r e a s of the 3-10 kb p e a k s to the 500/517 bp p e a k s for e a c h electropherogram w a s then found. T h e average ratio for three s a m p l e s r e s u s p e n d e d in d H 0 w a s 9.6 a n d the a v e r a g e for three s a m p l e s r e s u s p e n d e d in 2  A g a r o s e w a s 8.9, a difference of about 7%. T h e reduction in peak a r e a for the 500/517 bp p e a k s were about 12% from water to a g a r o s e , a n d 18% for the 3-10 kb p e a k s from water to a g a r o s e .  In other words,  the overall reduction in injected D N A w a s larger than the preferential reduction in longer fragments.  136  Figure 36 Electropherograms of 1kb ladder resuspended in Dl H 0 and 0.08% Agarose 2  Although long fragments could not be s e e n 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 w a s  a n a l y z e d in the following way. Capillaries with a total loaded c h a r g e over 3 0 m C , were isolated, as capillaries with lower T L C exhibited inconsistent florescence data. T h e flour c h a n n e l s of fluorescence data in the high T L C capillaries were s u m m e d and the first fifteen minutes of that data starting from the onset of p e a k s at the detector w a s integrated to get a signal strength value for e a c h capillary. T h e s e were then a v e r a g e d over all high T L C capillaries on that plate. T h e results, s h o w n in Table 3, indicate that, the quantity of small fragments w a s  138  A p p e n d i x B T h e Effect of S a m p l e R e s u s p e n s i o n in A g a r o s e  reduced by about 20% by the agarose.  T h e large variation in injected  fragment quantity c a n also be s e e n in the range of values obtained. Integrated F l u o r e s c e n c e  Machine  % Drop  A r b . Units dH 0  0.06% A g a r o s e  MB1  220±120  164±75  25%  MB2  115±35  98±21  15%  2  Table 3 Signal strength of the first -50 DNA bases in capillaries resuspended in Dl H 0 and Agarose. Machines refer to the two 2  MegaBACE sequencers at the GSC.  T a k e n together, the M e g a B A C E a n d single capillary data for the effect of A g a r o s e resuspension indicate that s o m e preferential reduction in injection of large fragments is a c c o m p a n i e d by a c o m p a r a b l e reduction in the quantity of all fragments injected.  This  would tend to militate against the u s e of a g a r o s e in current s a m p l e preparation protocols e v e n with a more sensitive but fault prone gel as dilutions have reduced the quantity of s a m p l e to near detection limits. (It w a s in fact found that the surface tension of liquid a g a r o s e m a d e pipetting into 384 well plates impractical). T h e curious a s p e c t of these results is that if a g a r o s e merely reduced the quantity of fragments a c r o s s the board, the s a m e result ought to be achievable by reducing injection time. T h i s has never been reported as a viable option and it is not known why. P e r h a p s the most plausible explanation is that the a g a r o s e works by preferentially retarding very long g e n o m i c fragments a n d that in fact these very long fragments are the primary culprit in current decline. T h e quantity of shorter (<10kb) fragments m a y not be so critical in this matrix formulation, despite published reports in the past  A p p e n d i x B T h e Effect of S a m p l e R e s u s p e n s i o n in A g a r o s e  showing current decline to o c c u r with template sized fragments. [14, 42].  Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour.  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  140  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d B u b b l e Behaviour.  not after injection of D N A below the threshold for depletion region formation a n d not after the formation of depletion regions with depleted buffers. W e tentatively call these "surface charge-induced depletion regions" ( S C I D R s ) a s the formation m e c h a n i s m survives matrix replacement so must be on the capillary surface, a n d it w a s s h o w n in chapter 5 that the p r e s e n c e of bound charges is likely to be the c a u s e of boundary m o v e m e n t of this type. A typical S C I D R is s h o w n in Figure  37 . 2  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!  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d B u b b l e Behaviour.  T h e driving m e c h a n i s m 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 a n d  its depletion region were allowed to propagate into the capillary about 10mm.  T h e matrix w a s then p u m p e d out and the cathode buffer  replaced. T h e s u b s e q u e n t S C I D R propagated right past the a r e a affected by the D N A a n d depletion region. Neither the quantity of injected D N A nor the D N A ' s run time w a s found to correlate with the s u b s e q u e n t d e g r e e 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).  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and B u b b l e Behaviour.  143  E v e n more direct evidence for c h a n g e s 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 w a s allowed to grow to about 10mm. T h e first millimeter of capillary w a s then clipped off. T h e S C I D R boundary traveled forward another two millimeters a n d then c a m e to a halt. W h e n the L P A w a s again p u m p e d out and electrophoresis restarted, no depletion region formed, which indicates that the part of the capillary c a u s i n g the S C I D R had been permanently removed. This s a m e experiment w a s repeated with D N A (not shown) where the IR image was u s e d to locate the cathode boundary which w a s clipped off after five minutes. T h e a n o d e boundary continued in another two millimeters and again c a m e to a halt.  2  4 Time (min)  6  8  2  4 Time (min)  6  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.  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d B u b b l e Behaviour.  144  T h e observations d e s c r i b e d a b o v e are intriguing a n d s h e d s o m e light o n how S C I D R s m a y form a s well as, more generally, how the a n o d e boundaries m a y propagate. A s this is a surface effect, it must involve interactions with the surface coating. T h e a n t i - E O F coating in these capillaries is m a d e 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 a n d p r e s u m a b l y interact with L P A as it is p u m p e d in to prevent it from moving under E O F [48]. Deterioration of the coating is believed to manifest itself through s o m e combination of shearing of the fixed acrylamide, hydrolysis of e x p o s e d  Si-0  groups and adsorbtion of c h a r g e d s p e c i e s onto the capillary wall. T h e fact that S C I D R s are driven by s o m e wall modification close to the entrance of the capillary s u g g e s t s either a localized p H 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 o c c u r only at the entrance of the capillary. T h e fact that the boundaries c o m e to a halt a n d the depletion regions remain fixed after the source of the depletion region is r e m o v e d is to be expected.  O n c e a c h a n g e in concentration is established a n d the ionic s p e c i e s  in e a c h region are restored to the s a m e proportions, the regulation function requires that the boundary remain stationary. T h a t this boundary remains fixed also lends strong weight to the notion that the boundary is definitely not driven by a c h a n g e in transference number as in equation (5-42). T h e 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 w a s c a u s i n g the boundary to move, it might be expected to keep moving a s further fixed charge would continue to be e x p o s e d .  If the fixed charge w a s induced by a  c h a n g e in p H on the capillary surface or in the acrylamide, the restoration of the p H would presumably neutralize this effect.  If the S C I D R boundary is driven by  a pure c h a n g e in p H , as described in section 5.4.5, the e x c e s s O H " ions in the depletion region will be swept out by T A P S " ions coming in from the newly clipped e n d of the capillary. If the depletion region is of length l , the remaining d  145  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and Bubble Behaviour.  O H " ions in the depletion region [OH"] c a n m o v e the boundary forward a d  distance l according to e  [OH-]  d  1=1  d  (C-1)  [TAPS ]" 0  where [ T A P S ° ] is the neutral T A P S concentration in the background region. T h e b  depletion region conductivity is a s s u m e d to be 160 u.S/cm a n d | T A P S ] 0  b  =  2 5 m m o l / L . Equation (5-52) then gives the correct propagation rate if the depletion region's p H is 9.3 of [OH"] = 0.02 mmol/L. T h i s , however, gives a residual propagation distance l of 7 urn, more than two orders of magnitude too e  small. W h i l e the nickel particle data s u g g e s t s the p H d o e s indeed rise, this datum s u g g e s t s the p H rise itself is not the only m e c h a n i s m moving the boundary. T h e s e conclusions are not necessarily contradictory: the actual rise in p H is not known a n d it m a y not take a large rise in p H to charge the nickel particles e n o u g h to c h a n g e direction. A small rise in p H , not e n o u g h to m o v e a boundary, m a y be e n o u g h to charge the relevant s p e c i e s e n o u g h to display the o b s e r v e d behaviour. Intuitively, the m e c h a n i s m that best fits the data is that s o m e p H c h a n g e d o e s o c c u r which has the effect of locally charging the matrix or capillary wall. H o w this charge-induced p H c h a n g e o c c u r s a n d how the inside of the capillary is affected are unknown. This clearly represents a n opportunity for significant future investigation.  Future work could involve thermal imaging a n d capillary  cutting as well a s online monitoring of p H with U V detectors a n d indicator solutions a s well a s the setting up of artifical p H gradients a n d possibly different matrix polymers. A s an aside, it e m e r g e d in the course of this analysis, that the depth of single-sided depletion regions could be calculated from the rate of current decline, a s s u m i n g a given background conductivity a n d consistent behaviour at the anode. This was d o n e by fitting the current to the rising resistance:  Appendix C Secondary Effects of Ionic Depletion and Bubble Behaviour.  1(f) where R  0  V *  (C-2)  ('-*»('))+  0  off  is the initial resistance/unit length, I is the capillary length a n d  x (t) is the m e a s u r e d boundary position. T h e depletion region b  resistance  Rd, a n d R ff, an offset for the part of the capillary s u b m e r g e d 0  in the buffer, are free parameters.  F o r Figure 38b this gives a depletion  depth of 160 u S / c m , similar to that o b s e r v e d for the cut capillary in Figure 37. T h i s method is only useful w h e n there is only o n e depletion region a n d the rest of the capillary is electrically stable.  In s u c h  circumstances it c a n be u s e d to nondestructively estimate the depletion region conductivity.  C.2 Matrix ion depletion from anode-side buffer. 10  4 0  2  4  6  8  10 12 Time (min)  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.  146  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d B u b b l e Behaviour.  A s d i s c u s s e d in section 3.1, it w a s o b s e r v e d that replacing the L P A at the a n o d e e n d with buffer would c a u s e the current to decline by about 50%, a n d then stabilize. A typical e x a m p l e of this highly repeatable current decline is shown in Figure 40. A s s u m i n g a sharp moving boundary between regions of different conductivity, a propagation rate w a s calculated from the time taken from the beginning of the run to w h e n the current stabilized. T h i s c o r r e s p o n d e d to a propagation rate of 75 m / C . A capillary w a s then cut up from the a n o d e e n d after four minutes run time and a boundary w a s indeed found at the location predicted by the propagation rate. T h e a n o d e side conductivity w a s typical for that of undepleted capillaries and the cathode-side conductivity w a s typical of that for completely depleted capillaries. 1200  1800 1600  I  1000 -+•  1400 1200 _ E  — 800  c  O  1000 E  I" 600  --  o<x>o O  400  800 Sin  'i  600 ^oOo° O  200  Resistance Conductivity  30  25  20  15  400 200  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.  K  147  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and B u b b l e Behaviour.  In ignorance of buffer and matrix c o m p o n e n t s , it is not possible to s a y exactly what p r o c e s s is occurring in the capillary. T h e moving boundary equations a n d regulation function, however, c a n give s o m e insight into the properties of the moving ions. T h i s self sharpening boundary must be propagating at the s p e e d of the leading ion. T h i s rate of 75 m / C in the 1200 u,S/cm background electrolyte c o r r e s p o n d s to 40x10" m / V s . T h i s is faster than Tris a n d more typical of small 9  2  positive ions like N a . T h i s suggests that a n 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 a n o d e entrance to the capillary defined by the regulating function, and a moving boundary with different ionic s p e c i e s on either side. T h i s explains the experimentally o b s e r v e d result that increasing the buffer concentrations at the a n o d e doesn't c h a n g e the capillary conductivity. A s noted, it is not known what ion is being r e m o v e d from the matrix, although it is possible that it is e x c e s s T E M E D [47]. T E M E D is basic, s o would produce a positively ionic species.  In fact, equations (5-35) and (5-39) c a n 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 a s s u m e d to be 25 +  m m o l / L on the depleted side, and given mobilities in Table 2, the dissociated [Tris ] = 5 mmol/L a n d [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  t h e s e concentrations of undissociated s p e c i e s could easily arise in an e x c e s s of a positively c h a r g e free ion and would give a p H of 8.7. In about 75% of c a s e s where matrix depletion w a s r e c o r d e d , 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 c a u s e , in Figure 42. T h e first point c o r r e s p o n d s with the matrix depletion boundary from the a n o d e crossing a S C I D R boundary from  148  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and B u b b l e Behaviour.  the cathode. T h e s e c o n d point c o r r e s p o n d s to the matrix depletion boundary exiting the cathode e n d of the capillary. T h e IR image s h o w s the S C I D R boundary s p e e d i n g up from 1.7 to 3.1 m / C a s the invisibleto-infrared matrix depletion boundary c o m e s past. T h i s is to be expected from equation (5-52) a s conductivity drop from (typical values of) 1100 to 600 u.S/cm would predict exactly s u c h a rise. T h e D N A induced depletion region adjusts its propagation rate in the s a m e way, s h o w n in Figure 42(b). T h e anode-side of its depletion region propagates a c r o s s 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 s h o w e d that c a s e s where these transitions were o b s e r v e d always c o r r e s p o n d e d to c a s e s where X D N A had been previously introduced. F r e s h capillaries did not show this behaviour.  149  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d B u b b l e Behaviour.  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 w a s found that although bubbles are not a primary s o u r c e of current decline, they do act to perturb current decline a n d affect depletion region growth. T h e relationship between bubble a n d  150  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and B u b b l e Behaviour.  depletion region growth w a s examined in detail with thermal a n d visible light imaging c o m b i n e d with capillary cutting. B u b b l e s were introduced by capillary cooling a n d then X D N A was injected. Figure 43 s h o w s a representative e x a m p l e . W h i l e bubble growth o c c u r s with the depletion region, the depletion region actually grows faster than the bubble, while the bubble a p p e a r s to be driven forward with the cathode boundary. T h i s w a s 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 (•)  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and B u b b l e Behaviour.  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 e v i d e n c e of the s a m e behaviour is s e e n in the MegaBACE.  Figure 44 s h o w s data from one plate where continuous  long bubbles were isolated and binned by cathode e n d location and length.  M o s t bubbles begin 25-30 m m into the capillary a n d are 25 to  30 m m long. T h e bubbles' cathode e n d s are approximately coincident with cathode side boundaries of ionic depletion regions o b s e r v e d with the single capillary instruments for runs of c o m p a r a b l e total loaded charge. T h e s e bubbles are, however, considerably shorter than the  152  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d B u b b l e Behaviour.  6 0 - 8 0 m m ionic depletion regions at 2-5% of the background conductivity required to p r o d u c e the o b s e r v e d current in the single capillary experiments.  T h e s e 20-30 m m long bubbles would have to  h a v e a surrounding conductivity of about 1% of the background electrolyte, lower than any m e a s u r e d depletion region. W e c o n c l u d e therefore that Figure 44 s h o w s the s a m e effect a s Figure 43, a n d the depletion region e x p a n d s faster than the bubbles a n d that the bubbles are definitely not the c a u s e of current decline e v e n where they are well developed. Although bubbles are clearly not the principle c a u s e of current decline, they d o manifest t h e m s e l v e s in the current data in the form of current variability. C o n s i d e r again the two plates shown in Figure 8, p a g e 44, a n d Figure 35(a), p a g e 135. T h e s e were called plate 4 1 0 5 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 w a s very repeatable, a s s h o w n in Figure 11 a n d Figure 12. If s u c h behaviour w a s o b s e r v e d in the M e g a B A C E , o n e 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 a n d T L C - 1 0 m C . Figure 45 bins the 41 Ox plates' T L C by frequency. T h e r e is biomodal behaviour, with p e a k s at 10 and 50 m C , but there are a substantial number of capillaries with intermediate c h a r g e a s well. T h e s e are capillaries where bubble growth is c a u s i n g s o m e d e g r e e of current decline without the existence of a depletion region.  153  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion a n d Bubble Behaviour.  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 d e g r e e s of current decline c a n be s e e n in Figure 46, which s h o w s current traces for the 4105 plate. menagerie of unusual behaviours is s e e n .  A  D07 a n d E 1 0 s h o w the  current declining for a time a n d then rising. A 0 6 a n d B 0 4 s h o w high frequency dips early on while in A 0 8 the dips persist. profile consistent with bubble-free decline.  D09 shows a  C o l u m n 06 s h o w s various  capillaries which experience about 25% decline.  High frequency (on  the order of minutes or sections) variations have b e e n reported e l s e w h e r e [42] and are consistent with our single capillary observations of artificially introduced bubbles.  It m a y be that local  heating temporarily pinches off the current, causing it to fall, which in  154  A p p e n d i x C S e c o n d a r y Effects of Ionic Depletion and B u b b l e Behaviour.  turn cools the capillary a n d shrinks the offending bubble. Capillaries s u c h a s C 0 2 which experience steady decline at a lower rate are consistent with "bubble trains" s e e n in the M e g a B A C E and single capillary instrument where one bubble propagates m a n y centimeters into the capillary, leaving a string of small bubbles behind it at regular intervals. T h e s e could generate e n o u g h resistance to c a u s e 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  -t—'  D  • P"™"»--v»,  IN--  T i m e 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.  156  A p p e n d i x D L P A and Buffer Properties  Appendix D LPA and Buffer Properties D. 1 Conductivity and pH of Tris/TAPS Buffer Under Dilution F o r various reasons, it w a s n e c e s s a r y to m e a s u r e the conductivity a n d p H of the buffer under different temperatures and dilutions.  First, no value of the mobility of the T A P S ion w a s to be  found in the literature. S e c o n d , the effect of buffer depletion o n moving boundaries (section 5.4) or c h a r g e d particles (section 5.4.4) would be mediated by a c h a n g e in molar conductivity (o7C) and/or p H . 1.2 g of Tris a n d 2.4 g of T A P S were dissolved in 200 m L d H 0 2  to give a 50 m m o l / L solution. T h e conductivity a n d p H were m e a s u r e d using a V W R M o d e l 8000 p H meter and a V W R B e n c h / P o r t a b l e conductivity meter. T h e solution w a s then diluted by factors of two. T h e concentration of the dissociated ions w a s then calculated using the chemical equilbrium algorithm described in section 5.2 a n d fit to the o b s e r v e d conductivity data to find the mobility for T A P S , found to be 25x10" m A / s . 9  2  UTAPS  was  157  A p p e n d i x D L P A and Buffer Properties  Figure 47 (a) (•) measured conductivity data fit with U T A P S  =  25x10" m /vs. (b) measured (•) and calculated (+) pH values. 9  2  T h e striking feature of the data in Figure 47 is the linearity of the conductivity over two orders of magnitude of concentration. T h i s is different from the behaviour of most strong electrolytes, w h o s e ions o b e y the O n s a g e r limiting law near 1 mmol/L [87]. /U = jU +Ay[C 0  (D-1)  158  A p p e n d i x D L P A and Buffer Properties  35 Temperature °C  20  25  30  35 Temperature °C  40  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 s h o w s the temperature variation of p H a n d conductivity of the T r i s / T A P S . T h e former s h o w s that the p H c h a n g e is relatively small over the range of temperatures s e e n in this work (up to 7 ° C a b o v e ambient). T h e relationship between conductivity a n d temperature s h o w s the aforementioned 2 % / ° C variation d i s c u s s e d in the text.  D.2 The Thermal Expansion Coefficient of LPA T h e thermal expansion coefficient of L P A w a s m e a s u r e d to test the hypothesis that matrix shrinkage d u e to cooling could c a u s e bubbles to form in capillaries. T h i s is d i s c u s s e d in section 4.2.2. L P A ,  159  A p p e n d i x D L P A and Buffer Properties  which is about 95% water, was, surprisingly, found to h a v e a thermal e x p a n s i o n coefficient almost twice that of water. Coefficients for water and L P A were m e a s u r e d by heating a filled capillary in the single capillary instrument, removing the a n o d e and cathode buffer wells, a n d then removing the capillary. T h e distance to the resulting menisci at e a c h e n d of the capillary w a s m e a s u r e d , and the coefficient of thermal e x p a n s i o n calculated from  AL  1  AT  L  (D-2)  a =  where L is the portion of capillary (200 mm) subject to temperature change.  In this c a s e the temperature c h a n g e d from 5 0 ° C to 1 8 ° C ,  resulting in the d H 0 shrinking 2 m m a n d the L P A shrinking 4 m m . 2  T h e thermal expansion coefficients were respectively: a = 2.7x10" °C" 4  for water a n d a = 5.2x10" °C" for L P A . In fact, a for water is irregular 4  1  and falls from 0 - 4 ° C , is 0 at 4 ° C , 2x10" at 2 0 ° C and 4x10" at 4 0 ° C . It 4  4  is probably r e a s o n a b l e to a s s u m e that L P A has twice the thermal e x p a n s i o n coefficient as water over the range of 2 0 - 4 0 ° C . T h e a v e r a g e value of a for L P A in the temperature range of interest is therefore taken to be 3.8x10" °C" 4  1  1  Appendix E Temperature Measurement  Appendix E Temperature Measurement It w a s 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 e n d , the temperature of the capillary w a s m e a s u r e d , first by thermal imaging with a reference temperature a n d then by direct m e a s u r e m e n t 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 t h e r m o c o u p l e methods c a n be c h e c k e d 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 s h o w s the capillary with hot region, m i c r o s c o p e 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 w a s glued down with a thermocouple ( O m e g a T y p e T ) b o n d e d in the center. Another thermocouple w a s glued to the end of the capillary a s s e e n at the top right of the image. T h e s e two data points were then m a p p e d to the apparent brightness of the reference capillary to create a brightness vs. temperature m a p . T h e temperature of the actual capillary a n d depletion region w a s then calculated from that map. T h i s had to be d o n e for e a c h image as the brightness adjustment of the thermal c a m e r a w a s automatic.  F o r direct measurement, a  0.002"  thermocouple ( O m e g a T y p e T copper-constantin) w a s b o n d e d to the capillary opposite the m i c r o s c o p e 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 a n d thermal c a m e r a s h o w a rise in temperature of about five d e g r e e s , although the peak temperature rise at the start of the run is about s e v e n d e g r e e s a b o v e ambient. T h i s is in line with literature values.  Burgi et al [99] found an empirical formula  for the internal temperature rise in a 7 5 | i m capillary a s T=11.5*Power/Length (W/m). T h e power loss a c r o s s the depletion region is l /arjA, where I is the current and a t h e depletion region 2  d  conductivity estimated to be 100 u.S/cm. T h e temperature rise c a n then be found from the experimental current.  Appendix E Temperature Measurement  Time (min)  Figure 51 The rise in temperature in the depletion region according to T= 11.5*l /o A,. Temperature declines as the current 2  d  declines.  T h i s 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 m a k e the capillary get m u c h c l o s e r to boiling the buffer. A s s u c h it is understandable that no s p o n t a n e o u s bubble nucleation takes place.  163  

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