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A syncronous coefficient of drag alteration (SCODA) based technique for sequence specific enrichment… Thompson, Jason Donald 2011

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A Synchronous Coefficient of Drag Alteration (SCODA) Based Technique for Sequence Specific Enrichment of Nucleic Acids  by Jason Donald Thompson BASc, The University of British Columbia, 2002  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 (Vancouver) March 2011 © Jason Donald Thompson 2011   ii Abstract Sequence based enrichment of nucleic acids is a critical enabling component of future nucleic acid detection methods in many fields including detection of nucleic acid tumor biomarkers in body fluids, non-invasive prenatal detection of fetal genetic abnormalities, and detection of pathogenic microorganisms.  In many cases the problem of detecting the nucleic acid biomarker of interest is confounded by the presence of a large excess of nucleic acid sequences that may differ from the sequence of interest by only a single base.  Consequently, existing methods are limited in sensitivity and amount of starting material to avoid overwhelming the detection methods with background nucleic acids. This limits their usefulness to a small number of applications. Techniques for enrichment of specific sequences rely on hybridization, and are generally not capable of enriching for low abundance sequences by more than 10 fold, a limit imposed by the thermodynamics of hybridization. In this dissertation I present a technique for sequence enrichment of nucleic acids based on synchronous coefficient of drag alteration (SCODA), which enables sequence specific enrichment of nucleic acids from sample volumes greater than 100 μL, with concurrent concentration of the nucleic acids to volumes appropriate for PCR detection (<10 μL).  We have demonstrated that this technique is capable of at least 10,000 fold enrichment of target sequences with respect to   iii contaminating sequences differing by a single base.  We have additionally shown that this technique is capable of at least 100 fold enrichment of a target sequence with a single methylated cytosine residue in a background of unmethylated targets of identical sequence by exploiting the small difference in binding energy of a methylated target to its complementary probe compared to an unmethylated target.  To our knowledge this is the most specific hybridization based sequence enrichment scheme in existence, and this is the first demonstration of hybridization based enrichment of unmodified methylated DNA.  Although some technical challenges must be overcome before this method will become a tool appropriate for routine laboratory use, we believe that the challenges are not insurmountable, and this method has the potential to enable routine analysis of low abundance nucleic acids.   iv Table of Contents Abstract.................................................................................................................. ii Table of Contents ................................................................................................. iv List of Tables ........................................................................................................ vi List of Figures...................................................................................................... vii Symbols, Nomenclature and Abbreviations ...................................................... ix Acknowledgments ................................................................................................ xi Dedication ........................................................................................................... xiii 1. Introduction................................................................................................... 1 2. Affinity SCODA .......................................................................................... 10 2.1. One Dimensional SCODA Concentration................................................................... 11 2.2. Two dimensional SCODA........................................................................................... 13 2.3. Generation of a Time Varying Mobility Field............................................................. 15 2.4. DNA Mobility in an Affinity Matrix........................................................................... 17 2.5. Thermally Driven ssSCODA....................................................................................... 22 2.6. Molecular Separation with Affinity SCODA .............................................................. 24 2.7. Generation of a Time Varying Temperature Gradient ................................................ 28 3. Implementation of Sequence Specific SCODA Concentration............... 33 3.1. Instrumentation Overview........................................................................................... 34 3.2. Imaging System........................................................................................................... 35 3.3. Gel Cassette Construction ........................................................................................... 38 3.4. Migration Through an Affinity Gel............................................................................. 39 3.5. Gel Thickness.............................................................................................................. 44 3.6. Predictions of Focusing and Separation ...................................................................... 47 4. ssSCODA Demonstration........................................................................... 55 5. Optimization of Operating Conditions ..................................................... 59 5.1. Buffer Salinity ............................................................................................................. 59   v 5.1.1. Equilibrium Calculation for an Electrophoretic Buffer .......................................... 60 5.1.2. Effect of Salt on Hybridization Rate ...................................................................... 62 5.1.3. Ion Depletion and Bound Charges.......................................................................... 66 5.1.4. Reduced Injection Times ........................................................................................ 69 5.2. Five channel Sample Chamber Geometry ................................................................... 74 5.3. dsDNA Denaturation................................................................................................... 85 5.4. Phase Lag Induced Rotation........................................................................................ 87 5.5. Effect of Secondary Structure ..................................................................................... 88 6. ssSCODA Performance .............................................................................. 91 6.1. Length Independence of Focusing............................................................................... 91 6.2. Single Base Mismatch Rejection Ratio ....................................................................... 97 6.3. Mutation Enrichment................................................................................................. 102 6.4. Methylation Enrichment............................................................................................ 106 6.5. ssSCODA Yield vs Purity ......................................................................................... 112 7. Future Work.............................................................................................. 115 7.1. Sample Extraction for Offline Detection................................................................... 115 7.2. Online Detection ....................................................................................................... 118 7.3. Multiplexed Enrichment............................................................................................ 121 7.4. Other Applications of Affinity SCODA.................................................................... 122 8. Conclusions................................................................................................ 123 Works Cited....................................................................................................... 125    vi List of Tables Table 1  Oligonucleotide used to measure temperature dependent mobility........ 41 Table 2 Hybridization energies and melting temperatures ................................... 42 Table 3 Voltage pattern for SCODA focusing with D/Q = 2. .............................. 48 Table 4 Applied voltages for focusing under bias.. .............................................. 53 Table 5 Focusing plus bias potentials ................................................................... 56 Table 6 List of targets run for measuring the rejection ratio. ............................... 99 Table 7 Binding energy and melting temperatures of EZH2 targets. ................. 103    vii List of Figures Figure 2.1  A plot of SCODA drift velocity in 1-D. ............................................. 13 Figure 2.2 Plot of mobility as a function of temperature...................................... 21 Figure 2.3 A plot of mobility versus temperature for two different molecules. ... 25 Figure 2.4 The effect of an applied DC bias on drift velocity in 1-D................... 27 Figure 2.5 Electric field pattern for SCODA based concentration.. ..................... 30 Figure 2.6  Stepwise rotation of the electric field leading to focusing. ................ 32 Figure 3.1 Schematic of ssSCODA instrumentation. ........................................... 35 Figure 3.2  Two colour epifluorescence imaging system.. ................................... 37 Figure 3.3 Gel cassette assembly.. ........................................................................ 39 Figure 3.5 Temperature dependence of DNA target velocity............................... 44 Figure 3.6  Gel geometry and properties used for eletrothermal modeling. ......... 49 Figure 3.7 Result of electro thermal model for a single SCODA step. ................ 50 Figure 3.8 SCODA velocity vector field. ............................................................. 52 Figure 3.9 Prediction of focusing under DC bias. ................................................ 54 Figure 4.1 Time series of ssSCODA focusing under bias.. .................................. 57 Figure 5.1 Effect of salinity on rates of hybridization. ......................................... 63 Figure 5.2 Top: Result of focusing with 200 mM NaCl added to the gel............. 66 Figure 5.3 Electrolyte depletion as a result of bound negative charges................ 68 Figure 5.4 Schematic of Sample Injection............................................................ 69 Figure 5.5 Schematic of 5 channel injection......................................................... 76   viii Figure 5.6 Sample chamber with a large height mismatch................................... 78 Figure 5.7 Injection out of free solution (top) and agarose (bottom).................... 80 Figure 5.8 Improved geometry for sample injection.. .......................................... 82 Figure 5.9 Injection from the sample chamber shown in Figure 5.8.. .................. 83 Figure 5.10 Example of phase lag induced rotations.. .......................................... 88 Figure 6.1 Focus location under bias for 250 bp and 1000 bp fragments............. 96 Figure 6.2 Rejection of 100 nt oligonucleotides differing by a single base. ...... 100 Figure 6.3 Enrichment of EZH2 Y641N mutation. ............................................ 105 Figure 6.4 Mobility vs. temperature for methylated and unmethylated targets.. 108 Figure 6.5 The difference between the two curve fits from Figure 6.4. ............. 109 Figure 6.6   Separation of methylated and unmethylated targets........................ 110 Figure 6.7 Washing of unmethylated DNA from the gel.................................... 111 Figure 7.1 A cross section of a SCODA gel illustrating diffusive extraction..... 116     ix Symbols, Nomenclature and Abbreviations   Term Definition 6-FAM 6-Carboxyfluorescein.  A common fluorophore with maximal excitation wavelength of 494 nm (blue) and maximal emission of 518 nm (green) agarose Hydrogel derived from seaweed commonly used as a separation matrix in electrophoresis. Characterized by the percentage (w/v) of agarose in solution. cDNA Complementary DNA.  DNA synthesized by performing a reverse transcriptase PCR reaction on messenger RNA. Contains DNA sequences complementary to messenger RNA Cy5 Cyanine-5.  A common fluorophore with a maximal excitation wavelength of 643 nm (red) and maximal emission of 667 nm (deep red) dsDNA Double stranded DNA EDTA Ethylenediaminetetraacetic Acid – a compound commonly used to stabilize DNA by sequestering divalent cations required by DNA-degrading enzymes. FWHM Full Width Half Maximum.  A common expression for quantifying the width of a peak defined as the width of the peak at half of its maximum value. metagenomics The study of microbial DNA extracted directly from environmental samples, without cultivation of the microorganisms in the laboratory. PCR Polymerase Chain Reaction.  A technique for sequence selective exponential amplification of DNA polyacrylamide A hydrogel created by the polymerization of acrylamide monomers in solution.  Polyacrylamide is characterized by the percentage of acrylamide monomers (w/v) in solution (%T) and the percentage of monomers that are crosslinkers (%C) pUC19 A plasmid (circular double stranded DNA molecule) approximately 3000 bases in length commonly used for cloning genes into bacteria. SCODA Synchronous Coefficient of Drag Alteration ssDNA Single stranded DNA   x ssSCODA Sequence Specific Synchronous Coefficient of Drag Alteration TBE Tris borate EDTA.  A buffer commonly used in electrophoresis.  1xTBE consists of 89 mM tris, 89 mM boric acid, and 2 mM Na2EDTA       xi Acknowledgments First and most importantly, I am indebted to my supervisor Dr. Andre Marziali who as provided me with the perfect balance of guidance and freedom as well as an unparalleled optimism without which this work would not have been possible. I would like to thank Drs. Eric Cytrnbaum, Carl Hansen and Ivan Sadowski for serving on my supervisory committee. I would like to thank Ryan Morin and Marco Marra of the Genome Sciences Centre for providing EZH2 cDNA that was used to generate Figure 6.3. I would also like to thank all of the members of the Marziali Lab, past and present, without which this experience would have been far less enjoyable. Specifically I would like to thank fellow graduate students Jon Nakane, Robin Coope, Matt Wiggin, Joel Pel and Nahid Jetha who have all at various times provided advice, fruitful discussions, and contributed to various antics that made the Marziali Lab an extremely enjoyable place to work.  I would also like to thank Dylan Gunn who helped me to explore some dead ends early on in this work, and David Broemeling who always made sure we got paid, and that there was enough money for science. Finally I would like to thank Boreal Genomics, for providing the space where the final portion of this work was performed.  In particular I would like to   xii acknowledge Gosuke Shibahara who performed the preliminary experiments on phase sensitive detection mentioned in Chapter 7.   xiii Dedication      For Janice (my favorite).  This would not have been possible without you.    1 1. Introduction The ability to interrogate biological samples for the presence or absence of rare sequence variants is of growing importance.  For example, non-invasive detection of nucleic acid mutations associated with tumors requires the ability to detect rare somatic mutations in a large background of wild-type sequences1-7.  Detection of pathogenic sequences in body fluids is hampered by the presence of excessive amounts of background DNA from both the host and related non-pathogenic species8.  Recent interest in metagenomics for the analysis of non-culturable microorganisms has elucidated the importance of rare microorganisms in environments such as soil and the gut9,10.  The presence or absence of these organisms in the gut has implications on human disease states and the ability to detect them may help to guide treatment decisions in the future. Methods for the analysis of nucleic acid sequences typically extract information about the sequence of an unknown nucleic acid target through either hybridization to a known nucleic acid sequence (eg DNA microarrays, primer annealing during PCR), or through the action of an sequence dependent enzyme (eg restriction enzymes, polymerases used in PCR and sequencing by synthesis).  Although traditional biochemical methods of sequence analysis have proved very capable of analyzing the most abundant nucleic acids present in a given sample, their ability to analyze low abundance variants is fundamentally limited by the specificity of   2 either the enzymatic or hybridization reactions on which they are based11,12. Consider PCR for example: since its invention in 1983 PCR has become the de facto method of nucleic acid detection due to its unique combination of sensitivity and specificity.  PCR is capable of sequence specifically amplifying a single copy of a template DNA molecule several million fold to easily detectable levels. However PCR as a detection technique is limited in its ability to detect rare sequence variants in a sample.  This is primarily a result of non specific amplification of the more abundant sequences that out compete rare sequences for primers and polymerases, a problem that is exacerbated if the rare target DNA is similar in sequence to the more abundant background DNA.  Investigators have employed various strategies to improve the ability of PCR to detect rare sequences, either by reducing the amplification efficiency of the high abundance sequence13-16 or selectively degrading the more abundant variant with restriction enzymes during the amplification process17.  Alternatively investigators have used digital PCR schemes to detect rare sequence variants18.  In these schemes a sample is split into a large number of small volumes such that each sub-sample contains either 0 or 1 copy of the target DNA per reaction volume.  Because there is only one template molecule per reaction, non specific amplification is no longer a problem, and rare sequences can be enumerated by simply counting the number of successful amplification reactions.  Collectively these techniques are capable of detecting rare sequence variants whose abundance is between 1,000 and 10,000   3 fold lower than the most abundant background sequence.  This specificity is limited by the fidelity of the polymerases used during amplification of the target sequences that typically introduce single base substitution errors at a rate of about 1 in 10,000 19, however this error rate depends on the reaction conditions, polymerase used, and sequence being amplified.  The sensitivity of PCR based techniques are further limited by sample volume limitations20,21.  If for example one wanted to interrogate a sample that contains a mutated oncogene but has a 10,000 fold excess of wild type copies of the gene then in order to overcome shot noise one must ensure that there are between 10 and 100 copies of the mutant in the sample, and therefore 105 to 106 copies of the wild type gene.  If the mutated gene is to be amplified from human genomic DNA then one must add between 1 μg and 10 μg of total template DNA to the PCR reaction.  This is typically beyond the acceptable input DNA limits of PCR reactions as it tends to both reduced amplification efficiency of the target sequence and increased non-specific amplification.  Many of the recent advances in nucleic acid analysis have focused on improving sensitivity of detection22, reduction of reaction volumes and massive parallelization23.  This has lead to an improved ability to analyze a large number of nucleic acid sequences with small amounts of starting material. However, since all analysis methods are still fundamentally based on the same biochemical reactions, be it hybridization or enzymatic, there has not been a dramatic improvement in the specificity of nucleic acid analysis.  For example   4 most contemporary high throughput sequencing schemes typically have error rates at around 1 in 100 bases with substantial sequence bias24.  Consequently, despite the fact that these schemes can generate billions of bases of sequence data in a few days, they are limited in their ability to target low abundance sequences which requires much higher specificity to overcome signals generated by excess background DNA. The detection of rare sequence variants can be achieved with any standard nucleic acid analysis method if one can first enrich a sample for the sequence of interest. If one could enrich for a low abundance sequence to the point where it is present at a molar concentration comparable to the most abundant sequence in the sample then it would be possible to detect even the rarest of sequence variants using a standard PCR reaction.  All existing methods of sequence enrichment currently rely on some form of sequence specific hybridization between synthetic probe DNA and a complementary strand of target DNA.  Hybridization based enrichment schemes generally fall into two categories: solution phase hybridization or solid phase hybridization, depending on whether hybridization of the capture probe to the target is performed in solution 25, or if the probes are first immobilized to a solid support 26.  In the case of solution phase hybridization probes are typically synthesized with an affinity tag such as biotin.  Target DNA and probe DNA are mixed together in solution and allowed to hybridize; probes   5 are then captured using the affinity tag, often with magnetic beads, or some type of solid support.  Unbound DNA is then washed from the solid supports and replaced with clean solution.  The probe-target duplexes are then denatured, releasing enriched targets.  Solid phase enrichment is performed in a similar manner except that the probes are immobilized to a solid support prior to hybridization with the target.  These techniques are generally quite good at enriching for target sequences when the contaminating background sequence has little or no homology to the target.  However hybridization enrichment schemes such at these that rely on a single hybridization event to enrich for a target sequence are generally not capable of much better than five fold enrichment of targets with single nucleotide resolution11,17.  This sensitivity is consistent with thermodynamic predictions of sensitivity of hybridization with respect to single base substitutions11, and is a result of the fact that when thermodynamic equilibrium is achieved between a perfectly matched target, a target with a single base mismatch, and a capture probe there will always be some mismatched target bound to the probes; the closer the binding energy of the perfect match-probe duplex to the mismatch-probe duplex the greater the fraction of probe sites that will be occupied by mismatch targets.  Increasing the stringency of hybridization conditions can reduce the amount of mismatch bound, but cannot eliminate it without dramatically reducing the amount of perfect match bound; higher purity comes at the expense of lower yield.  These techniques can be improved through   6 the use of hairpin probes or competing fragments that can shift the equilibrium of the hybridization reaction enough to achieve enrichment factors of 10 to 20 fold 27, however beyond this repeated hybridizations must be used to further purify the target.  In these schemes a target sample is washed past beads, through a column or over a solid surface, where it binds to immobilized complementary targets. Unbound molecules are washed away, the bound target is released and the process repeated 28.  Repeated hybridization-wash cycles can achieve arbitrarily high purification factors, limited only by the number of times one wishes to repeat the purification cycle, but in practice they are labor intensive and the losses scale geometrically with the iteration count.  These losses are particularly problematic when searching for rare sequence variants since by definition the samples will contain a limited number of target molecules. In this dissertation I will present a technique for sequence specific enrichment of nucleic acids that is capable of overcoming many of the problems associated with existing techniques for enrichment of rare sequence variants.  This technique is a modified version of Synchronous Coefficient Of Drag Alteration (SCODA) based purification.  SCODA based transport is achieved by synchronizing a periodic driving force, which would otherwise impart zero net motion, with a periodic drag alteration.   Provided the periodic driving force and periodic drag alteration are at the same frequency the result is net motion despite zero time averaged forcing.   7 With careful choice of both the temporal and spatial configuration of the forcing and drag altering fields one generate unique velocity fields, in particular one can generate a velocity field that has a non-zero divergence, such that this method of transport can be used for concentration and purification.  In the first demonstration of SCODA based purification, time varying electric fields provided both the periodic driving force and a means to alter the drag (or equivalently the mobility) of DNA molecules. This was possible because, while migrating through a sieving matrix such as agarose or polyacrylamide, the mobility of DNA depends on the magnitude of an applied electric field29.  By applying an appropriate periodic electric field pattern to an agarose or polyacrylamide gel a convergent velocity field can be generated for all molecules in the gel whose mobility depends on electric field.  The field dependant mobility is a result of the interaction between a reptating DNA molecule and the sieving matrix, and is a general feature of charged molecules with high conformational entropy and high charge to mass ratios moving through sieving matrices.  Since nucleic acids tend to be the only molecules present in most biological samples that have both a high conformational entropy and a high charge to mass ratio, SCODA based purification has been shown to be highly selective for nucleic acids 30.  In this dissertation it will be shown that with a modified SCODA matrix that contains immobilized single stranded oligonucleotides it is possible to find SCODA operating conditions where repeated transient interactions between target DNA   8 and immobilized probes result in a mobility that depends on the magnitude of the applied electric fields, which can be exploited to create a convergent velocity field only for target DNA that is complementary to the immobilized oligonucleotide probes.  With an appropriate choice of operating conditions complementary targets can be driven towards the central region of a gel where they can be detected directly or extracted for offline detection. With this purification technique each target must under go multiple hybridizations to the immobilized probes before reaching the centre of the gel, these repeated hybridizations impart this technique with a specificity, which to my knowledge exceeds all other hybridization based enrichment techniques.  Combining this selectivity with some of the other desirable features of SCODA based purification, including high yields and the ability to process large volumes, should result in a purification and enrichment technique that will enable application of PCR-based target detection of very low abundance markers.  This technique has the potential to revolutionize application of PCR-based diagnostics, and to enable a new and very powerful set of biomarker detection assays for highly sensitive pathogen and tumor detection. In this dissertation a general theory of SCODA based concentration will be presented followed by a discussion of how interactions between gel bound oligonucleotide probes and single stranded target DNA can lead to a temperature dependent mobility that can be exploited to achieve sequence specific SCODA   9 (ssSCODA) based concentration.  I will then review the important experimental parameters for successful demonstration of ssSCODA enrichment.  This will be followed by a discussion of optimization to enhance the performance of ssSCODA and improve its reliability.  The results of experiments that measure the ability of ssSCODA to enrich for low abundance sequence variants with single base specificity, and the ability of ssSCODA to enrich for methylated DNA targets that are identical in sequence but differ from the background DNA by a single methylated cytosine reside will be shown.  Finally, I present a discussion of work that is currently underway to both refine the method of ssSCODA and expand is applicability such that it can be routinely used as a preparatory method by non-experts.   10 2. Affinity SCODA SCODA based transport is a general technique for moving particles through a medium by first applying a forcing field to induce periodic motion of the particles; then superimposing on this forcing field a perturbing field that periodically alters the drag (or equivalently the mobility) of the particles such that the particles will move further during one part of the forcing cycle.  Specifically, the drift velocity v(t) of a particle driven by an external force F (t) with a time varying drag coefficient ³(t) is given by29:  v(t) = F (t) ³(t)  [2.1] If the external force and drag coefficient vary periodically such that  F (t) = F0 sin(!t) [2.2] and,  1 ³(t) = 1 ³0 + sin(!t + Á) ³1  [2.3] Then the drift velocity averaged over one complete cycle is given by:  ¹v(t) = F0 2³1 cos(Á) [2.4]   11 By varying the drag of the particle at the same frequency as the external applied force, one can induce a net drift with zero time-averaged forcing.  In the remainder of this chapter I will first show how one can use the result of equation [2.4] with an appropriate choice of driving force and drag coefficients that vary in time and space to generate a convergent velocity field in one and two dimensions. I will then show how one can realize a time varying drag coefficient and driving force in a real system to specifically concentrate only certain sequences of DNA. 2.1. One Dimensional SCODA Concentration By combining a spatially uniform driving force that varies periodically in time, with a drag coefficient that varies in time as well as in space it is possible to generate convergent velocity field in one dimension.  For this example we will consider the case of a charged particle with mobility ¹ moving under the influence of an applied electric field E; its velocity will be given by:  v(x; t) = ¹(x; t)E(x; t) [2.5] If we let the electric field vary periodically in time such that:  E(x; t) = E0 sin(!t) [2.6] and we set up a linear mobility gradient within the domain ¡L · x · L that varies at the same period:   12  ¹(x; t) = ¹0 + (kx) sin(!t + Á) [2.7] where k can be thought of as the amplitude of the mobility variation.  There are a number of ways in which one can establish a mobility gradient for charged molecules moving in solution under the influence of an applied external electric field, for example by establishing a temperature or pH gradient.  The details of how this is accomplished in the context of ssSCODA are discussed in Sections 2.4 and 2.5.  Assuming we can establish the mobility gradient of equation [2.7], then the velocity becomes:  v(x; t) = [¹0 + (kx) sin(!t + Á)][E0 sin(!t)] [2.8] If we then take the time average of this velocity over one complete cycle we are left with the following drift velocity:  ¹vd(x; t) = ! 2¼ Z 2¼ ! 0 v(x; t)dt [2.9]  ¹vd(x; t) = kx 2 E0 cos(Á) [2.10] This velocity field has an equilibrium point at x = 0 and can be made convergent or divergent depending on the sign of kE0cos(Á).  For positive values the velocity field is divergent and for negative values it is convergent.  Figure 2.1 below shows the velocity plotted as a function of x for the case where  kE0cos(Á) < 0.   13  Figure 2.1  A plot of equation [2.10] showing the SCODA drift velocity over the domain extending from –L to +L.  The arrows indicate the direction of drift.  All particles between –L and +L will drift towards the zero velocity point at x = 0.  Outside of the domain the time averaged velocity is zero as the mobility is only altered between –L and +L. Here the velocity takes on a positive value for negative values of x and vice versa for positive values of x resulting in all particles within the domain drifting towards x = 0 where the velocity is zero. 2.2. Two dimensional SCODA To extend the result of equation [2.10] to two dimensions we use a rotating electric field and a rotating mobility gradient:  ~E = E0 cos(!t)̂i¡E0 sin(!t)ĵ [2.11]  ¹ = ¹0 + k[x cos(!t + Á)¡ y sin(!t + Á)] [2.12]   14 As in the one dimensional case ~v = ¹~E , and we can perform the same integration as in equation [2.9] to find the time averaged drift velocity:  ¹vx = ! 2¼ Z 2¼ ! 0 E0 cos(!t)(¹0 + k(x cos(!t + Á)¡ y sin(!t + Á)))dt [2.13]  ¹vy = ! 2¼ Z 2¼ ! 0 ¡E0 sin(!t)(¹0 + k(x cos(!t + Á)¡ y sin(!t + Á)))dt [2.14] This results in the following expression for the drift velocity:  ~v = E0k 2 ³ (x cos(Á)¡ y sin(Á)) î + (x sin(Á) + y cos(Á)) ĵ  ́ [2.15] If we rewrite this in polar coordinates and simplify we get:  ~v = E0kr 2 ³ cos(Á)r̂ + sin(Á)μ̂  ́ [2.16] This result highlights a number of important aspects of SCODA in two dimensions.  First it shows that despite the zero time averaged forcing there will always be non-zero drift everywhere except at the centre of the gel where r = 0. Second, it shows that the nature of the drift depends on the relative phase, Á, of the two signals, with the strength of focusing (the radial, r̂, term) being proportional to the cosine of the phase lag between the electric field oscillations and the mobility oscillations.  For a 0° phase angle we have a purely focusing velocity field with net drift directed towards the centre of the domain.  For a 180°   15 phase angle the velocity field is pure de-focusing with net drift away from the centre of the gel.  And for phase angles of 90° and 270° the velocity field is purely rotational.  At intermediate angles the resultant velocity field will be a combination of both rotational and focusing components.  This suggests that to achieve efficient focusing one must ensure that the phase difference between the driving force and the mobility variation is as small as possible. 2.3. Generation of a Time Varying Mobility Field Now we turn our attention to how one might go about altering the mobility of a particle in time and space in order to generate a convergent velocity field.  In the first demonstration of SCODA based concentration Marziali et al.29 exploited the fact that the mobility of DNA in a sieving matrix such as agarose or polyacrylamide depends on the magnitude of the applied electric field 31,32.  In this example they used electric fields to both drive the periodic motion of DNA and to alter its mobility.  To achieve a convergent velocity field the authors superimposed over the dipole electric field described in equation [2.11] a quadrupole field that rotates at twice the frequency of the dipole field.  It can be shown 29 that this results in a radial velocity field as in equation [2.16] with a magnitude that is proportional to the strength of the dipole field and the quadrupole field.  This field dependent mobility is a property of molecules that have both a high conformational entropy, and a high charge to mass ratio, a   16 property of DNA and RNA but otherwise not common for other biomolecules. For complex biological solutions, such as cell lysates, blood, or soil often the only molecules with a large field dependent mobility are DNA and RNA.  Because of this, electrophoretic SCODA based concentration and purification has proven to be an extremely specific technique for the extraction and purification of nucleic acids from complex solutions30,33.  Although the specificity of electrophoretic SCODA for nucleic acids is quite remarkable, there are applications that require greater selectivity.  For example, one may be interested in molecules that have a mobility that does not normally depend strongly on electric field, such as short nucleic acids, less than 200 bases.  Or, one may be interested in purifying only a subset of all the nucleic acids in a sample, for example purifying out a single gene from a sample of genomic DNA.  This level of specificity can be made possible using a SCODA matrix that has an affinity to the molecule to be concentrated. Using such a matrix one can choose operating conditions where the target molecules transiently bind to the affinity matrix with the effect of reducing the overall mobility of the target molecule as it migrates through the affinity matrix. If one can then periodically alter the strength of these transient interactions this will have the effect of periodically altering the mobility and one can therefore generate SCODA drift as shown in sections 2.1 and 2.2.  This technique is called affinity SCODA, and is generally applicable to any target molecule that has an affinity to a matrix.  In the remainder of this dissertation I will discuss a specific   17 example of affinity SCODA: sequence specific SCODA (ssSCODA).  In this case the target molecule is DNA, and the affinity matrix contains immobilized oligonucleotides that are complementary to the target DNA.  Although the remainder of the dissertation will be based around sequence specific SCODA many of the principles discussed will be applicable to other forms of affinity SCODA. 2.4. DNA Mobility in an Affinity Matrix  In this section we will discuss the electrophoretic mobility of a target DNA molecule moving through an affinity matrix containing immobilized probe DNA molecules that are complementary to the target, and show how one can perturb the mobility of a DNA molecule moving through such a matrix. The interactions between the target and immobilized probes can be described by first order reaction kinetics:  [T] + [P] kf¡*)¡ kr [T¢¢¢P] [2.17] Here [T] is the target, [P] the immobilized probe, [T¢¢¢P] the probe-target duplex, kf  is the forward (hybridization) reaction rate, and kr the reverse (dissociation) reaction rate.  Since the mobility of the target is zero while it is bound to the   18 matrix, the effective mobility of the target will be reduced by the relative amount of target that is immobilized on the matrix:  ¹e®ective = ¹0 [T] [T] + [T¢¢¢P] [2.18] Where ¹0 is the mobility of the unbound target.  Using reasonable estimates for the forward reaction rate34 and a probe concentration on the order of 10 μM then one can assume that time constant for hybridization should be significantly less than one second.  So long as we keep the period of our perturbing field longer than this then we can assume that the binding kinetics are fast and can rewrite equation [2.18] in terms of reaction rates:  kf [T][P] = kr[T¢¢¢P] [2.19]  [T] = kr kf [T¢¢¢P] [P]  [2.20] Inserting [2.20] into equation [2.18] and simplifying we get:  ¹e®ective = ¹0 1 1 + kf kr [P ]  [2.21] From this result it can be seen that the mobility can be altered by modifying either the forward, or reverse reaction rates.  This can be achieved in a number of different ways, for example by adjusting the salinity, pH, concentration of   19 denaturants, concentration of catalysts, or by physically pulling duplexes apart with an external electric field 351.  While modifying these parameters may have application in other embodiments of affinity SCODA, the simplest approach to modifying the mobility of DNA targets moving through an affinity matrix is through control of the matrix temperature. To show how this is possible it is helpful to make some simplifying assumptions. First we assume that we have a large number of probes relative to target molecules, so long as this is true then even if a large fraction of the target molecules become bound to the probes the concentration of free probes, [P ], will not change much and we can assume that [P ] is constant.  Also, we assume that the forward reaction rate kf  does not depend on temperature.  This not strictly true, as the forward reaction rate does depend on temperature 36,37, and secondary structure in the probe or target sequence can result in a temperature dependant forward reaction rate 38.  However we will be operating in a regime near the duplex melting temperature where the reverse reaction rate has an exponential dependence on temperature and the forward reaction rate has a much weaker temperature dependence, varying by about 30% over a range of 30°C around the melting temperature 39, and additionally assume that the target sequence is free of any significant secondary structure.  Although this final assumption of no  1 See section 6.1 for a more detailed discussion of force based dissociation of nucleic acids   20 secondary structure would not always be correct, for now it simplifies the analysis and a more detailed discussion of the effects of secondary structure are given in Section 5.5.  To determine the temperature dependence of the reverse reaction rate we assume an Arrhenius model for unbinding kinetics, which is justified by recent work in nanopore force spectroscopy 35,40.  kr = Ae ¢G kbT  [2.22] Here A is an empirically derived constant, ¢G is the probe-target binding energy, kb is the Boltzmann constant, and T  the temperature.  Inserting this into [2.21], rewriting the free energy ¢G as ¢H ¡ T¢S , and collecting constant terms we can rewrite the mobility as:  ¹e®ective = ¹0 1 1 + ¯e ¡¢H+T¢S kbT  [2.23]    21 0.00 0.25 0.50 0.75 1.00 Tm-10°C Tm μ/μ0 Temperature Tm+10°C  Figure 2.2 Plot of equation 1.1.7 near the duplex melting temperature Tm illustrating the relative change in mobility as a function of temperature.  Equation [2.23] describes a sigmoidal mobility temperature dependence.  The shape of this curve is shown in Figure 2.2.  At low temperature the mobility is nearly zero.  This is the regime where thermal excitations are insufficient to drive target molecules off of the affinity matrix.  At high temperature target molecules move at the unbound mobility, where the thermal energy is greater than the binding energy.  Between these two extremes there exists a regime where a small   22 change in temperature results in a large change in mobility.  This is the operating regime for ssSCODA and tends to lie near the melting temperature of the probe target duplex.  Equations [2.10] and [2.16] state that the speed of concentration is proportional to k, which is a measure of how much the mobility changes during one SCODA cycle.  Operating near the probe target duplex melting temperature, where the slope of the mobility versus temperature curve is steepest, ensures that if one uses temperature to alter the mobility, then k is maximized for a given temperature swing during a SCODA cycle. 2.5. Thermally Driven ssSCODA It is possible to describe ssSCODA in one dimension by replacing the time dependent mobility of equation [2.7] with the temperature dependent mobility of equation [2.23] and a time dependent temperature:  T (x; t) = Tm + Ta( x L ) sin(!t + Á) [2.24] Here the temperature oscillates around Tm, the probe target melting temperature, and Ta is the maximum amplitude of the temperature oscillations at x = §L.  To get an analytical expression for the drift velocity, vd = ¹E, as a function of temperature we perform a Taylor expansion of equation [2.23] around Tm:   23  ¹e®ective = ¹(Tm)¡ ¹0¯¢He ¡¢H+T¢S kbTm kbT 2m ³ 1 + ¯e ¡¢H+T¢S kbTm ´2 (T ¡ Tm) + O((T ¡ Tm)2)[2.25] Which we can rewrite as:  ¹e®ective = ¹(Tm) + ®(T ¡ Tm) + O((T ¡ Tm)2) [2.26] Here we have simply collected the first term in the Taylor expansion into the constant ®.  Combining [2.24], and [2.26] into an expression for the mobility one obtains an expression similar to [2.7]:  ¹(t) = ¹(Tm) + μ ®Tax L ¶ sin(!t + Á) [2.27] We can use [2.27] to determine the time averaged drift velocity for both the one dimensional and two dimensional cases by simply replacing k with:  ® Ta L = ¹0¯¢He ¡¢H+T¢S kbTm kbT 2m ³ 1 + ¯e ¡¢H+T¢S kbTm ´2 μTaL ¶  [2.28] The drift velocity is then given by:  ¹vd(x; t) = ®Tax 2L E0 cos(Á) [2.29] in one dimension, and:   24  ~v = E0®Tar 2L ³ cos(Á)r̂ + sin(Á)μ̂  ́ [2.30] in two dimensions.  This result suggests that if one creates a two dimensional gel that is functionalized with immobilized probes, then by combining a rotating temperature gradient with a rotating dipole electric field we should be able to force all target molecules within the gel towards a central region in the gel, thus concentrating the target. 2.6. Molecular Separation with Affinity SCODA If we begin with two molecular species in our domain, each with a different binding energy to the bound probes it is possible to separate these two molecular species by superimposing a small DC bias over the applied time varying electric field.  In the one dimensional case the electric field becomes:  E(x; t) = E0 sin(!t) + Eb [2.31] And the final drift velocity has superimposed on the SCODA focusing velocity a constant velocity proportional to the strength of the bias field:  ¹vd(x; t) = ®Tax 2L E0 cos(Á) + ¹(Tm)Eb [2.32] This will tend to move the final focus location either to the left or right depending on the direction of bias.  The amount by which this bias moves a focus off centre   25 depends on the strength of the interaction between the target and probe molecules. The strength of the target-probe interaction can therefore serve as a “handle” for molecular separation. Consider the difference between a complementary target, and a mismatch target with reduced binding energy to the immobilized probe.  Reducing the probe-target binding energy, ¢G in equation [2.23], will serve to shift the mobility versus temperature curve to the left on the temperature scale as shown below in Figure 2.3.  Figure 2.3 A plot of mobility versus temperature for two different molecules with different binding energies to bound probe molecules.   26 If we operate at the optimal focusing temperature for the higher binding energy molecule, Tm in Figure 2.3, then the mobility of the lower binding energy molecule will be higher and have weaker temperature dependence.  In terms of equation [2.32] the molecule with lower binding energy will have a larger value of ¹(Tm) and a smaller value of ®.  This means that a lower binding energy molecule will have a lower SCODA drift velocity and a higher velocity under DC bias, resulting in a different final focus location than the high binding energy molecule as illustrated in Figure 2.4.   27 Drift Velocity X 0-L +L 0 Drift Velocty With Bias +L Final focus position for low binding energy molecule Final focus position for high binding energy molecule Figure 2.4 The effect of an applied DC bias on molecules with two different binding energies. The red curve represents the drift velocity of a target molecule with a lower binding energy to the bound probes than the molecules represented by the blue curve.  The final focus location is the point where the drift velocity is equal to zero. The molecules represented by the red curve have both a lower SCODA drift velocity and a higher DC velocity compared to the molecules represented by the blue curve.  When a SCODA focusing is combined with a DC bias the lower binding energy molecules will focus further away from the unbiased focus at x = 0, resulting in two separate foci, one for each molecular species. Additionally, if the separation in binding energies is large enough, and a high enough DC bias is applied it should be possible to completely wash low binding energy molecules off of the gel while still capturing molecules with higher binding energy.  The two dimensional case is the same as the one dimensional case, the superimposed velocity from the applied bias final focus off centre in the direction of the bias.   28 2.7. Generation of a Time Varying Temperature Gradient The model of thermally driven affinity SCODA presented in the previous sections requires a rotating temperature gradient in order to achieve a convergent velocity field.  One can generate a periodically varying temperature gradient in a number of ways, including the use of heaters or thermoelectric chillers to periodically heat and cool regions of the gel, or the use of radiative heating to similar effect. However, since we already need to apply an electric field to drive target molecule periodic motion in the gel, a convenient method for heating the gel is to use Joule heating.  In the two dimensional thermal model of SCODA presented in section 2.2 the applied electric field was constant everywhere in the gel, and the direction rotated in time.  This electric field configuration will not result in focusing as there is no spatial gradient in the electric field and the resultant Joule heating will not set up a temperature gradient.  It is possible to generate a spatial temperature gradient if one uses a geometry and electric field pattern typical of those used for electrophoretic SCODA 29,30,33,41.  This system employs a two dimension gel with four electrodes.  Voltages are applied to the four electrodes such that the electric field in the gel is non-uniform, containing regions of high electric field (and consequently high temperature) and low electric field.  The electric field is oriented such that the regions of high electric field tend to push negatively   29 charged DNA molecules towards the centre of the gel, while regions of low electric field tend to push DNA molecules away from the centre of the gel.  An example of such a field pattern is illustrated in Figure 2.5.   30 Step 1  Figure 2.5 Electric field pattern suitable for two dimensional SCODA based concentration. Voltages applied at electrodes A, B, C and D, are –V, 0, 0, and 0 respectively.  Arrows represent the velocity of a negatively charged analyte molecule such as DNA.  Colour represents electric field strength.  The high field regions near electrode A tend to push DNA molecules towards the centre of the gel, while the lower field regions near electrodes B, C, and D tend to push DNA molecules away from the centre of the gel. This electric field pattern is then rotated in a stepwise manner by rotating the voltage pattern around the four electrodes such that the time averaged electric   31 field is zero as shown in Figure 2.6.  This rotating field will result in net migration towards the centre of the gel for any molecule that has a mobility that increases with electric field.  It was shown earlier that the mobility of a DNA molecule moving through an affinity matrix depends on temperature, not electric field.  The applied electric field will tend to increase the temperature of the gel through Joule heating; the magnitude of the temperature rise at any given point in the gel being proportional to the square of the magnitude of the electric field.  This will be at the same period as the electric field oscillations and can therefore drive affinity SCODA based concentration in a two dimensional gel.   32  Figure 2.6  Stepwise rotation of the electric field leading to focusing of molecules whose mobility increases with electric fields.  A particle path is shown.  After four steps the particle’s net displacement is towards the centre of the gel.  Molecules that do not experience a change in mobility with changing temperature or field will experience zero net motion in a zero time averaged electric field.   33 3. Implementation of Sequence Specific SCODA Concentration In the previous chapter we outlined a theoretical framework for affinity based purification and enrichment.  This chapter will outline the requirements for successful implementation of ssSCODA based concentration and purification of nucleic acids.  Here the challenge is to apply an appropriate time varying electric field to an affinity matrix such that the resulting Joule heating drives bound molecules off the affinity matrix while the electric field simultaneously drives the unbound molecules towards a central focusing region in the matrix.  This requires a unique electrophoresis apparatus consisting of a region for containing the affinity matrix, buffer reservoirs, power supplies capable of delivering large enough voltages and currents to cause the desired effect, precise temperature control of the gel region, and a two colour fluorescence imaging system for the monitoring of two different target sequences in the gel.  The physical requirements of this electrophoresis apparatus are driven by both the theoretical framework outlined in Chapter 2 as well as empirical measurements of target DNA migration through an affinity gel.   34 3.1. Instrumentation Overview The instrument used for implementation of sequence specific SCODA based concentration and purification of nucleic acids is a modified version of instruments developed for electrophoretic SCODA 29,30,33,41.  The instrument was adapted to accommodate thin polyacrylamide gels, temperature control of the gel was added by placing the gel cassette onto a temperature controlled spreader plate, a two colour fluorescence imaging system was incorporated, and the voltage and current capabilities of the power supplies were increased.  The instrument consists of an Ultravolt 1/2C24-NP125 bipolar +/-500 V 125 W power supply (Ultravolt Ronkonkoma, NY) with four independently controllable output voltage channels.  Each output channel is based on an APEX PA94 high voltage, high current operational amplifier (Cirrus Logic Inc, Austin, TX) configured as an inverting amplifier with a gain of -40, allowing the output channels to be driven from a +/-10 V analog control signal.  This power supply drives current through a custom designed gel cassette system fabricated with alternating layers of pressure sensitive adhesive and acrylic.  The gel cassettes are in contact with a temperature controlled aluminum spreader plate.  The temperature of the spreader plate is measured with an RTD, and temperature is controlled with a high capacity thermoelectric chiller (HP-199-1.4-1.5, TE Tech, Traverse City, MI) mounted to a liquid cooled heat sink.  The gel is imaged from above through a purpose built   35 two colour epifluorescence imaging system capable of imaging fluorescein and Cy5 or similar dyes.  The power supply, temperature control system and imaging system are all controlled through a PC running LabView® (National Instruments, Austin, TX).  A schematic of this system is shown in Figure 3.1.  LabView PC Gel Cassette 4 Channel High Voltage Amplifier Camera and Imaging system Peltier controlled Spreader PlateLow Voltage Amp  Figure 3.1 Schematic of ssSCODA instrumentation. 3.2. Imaging System A purpose built two colour epifluorescence imaging system was used to image the gels during injection and concentration.   The system consists of two high intensity LED based excitation sources: a blue source centred at 450 nm (LXML- PR01-350, Phillips Lumileds, San Jose California) for the excitation of fluorescien and similar dyes, and a red source centred at 632 nm (LXML-PD01-   36 0030, Phillips Lumileds, San Jose California) for the excitation of Cy5 and similar dyes.  Light from the LED's are collected and collimated by condenser lenses, the beams cleaned up with excitation filters then combined with a short pass dichroic filter.  Excitation light then passes through a secondary lens, is reflected off of a dual band dichroic beam splitter and through the object lens as shown in Figure 3.2 such that a uniform collimated beam emerges from the object lens.  The emitted fluorescence is collected by the object lens then passes through the dual band dichroic beam splitter and is focused onto a CCD array by the image lens. Emission filters are mounted on a stepper motor driven filter wheel between the image lens and the CCD camera.  The filter wheel stepper motor is driven by a Parker Compumotor 6104  stepper driver (Parker Hannifin, Cleveland OH).   37  Figure 3.2  Two colour epifluorescence imaging system.  Top: Schematic optical layout.  Bottom: Image of actual system. CCD Camera Stepper Motor Driven Filter Wheel  Blue Excitation Filter Red Excitation Filter Short Pass Dichroic Beam CombinerDual Band Dichroic Beam Splitter Emission Filters Gel Red LED Blue LED Object Lens Image Lens   38 3.3. Gel Cassette Construction Affinity gels are cast within custom fabricated single use gel cassettes.  The cassettes are comprised of three layers: a glass microscope coverslip is used as the bottom layer that is in contact with the spreader plate, bonded to this is a 100 μm thick layer of double sided pressure sensitive adhesive that is laser cut to define the gel area.  Bonded to the top surface of the PSA is a 1.5 mm thick acrylic cover with access holes laser machined to enable electrical contact to the gel area.  The cassettes are mated to a reusable buffer reservoir and sealed with a silicone gasket.  Current is sourced through carbon electrodes placed in the buffer reservoirs.  The details of the gel cassette assembly are shown below in Figure 3.3.   39  Figure 3.3 Gel cassette assembly.  Top: schematic of the gel cassette and buffer reservoir assembly.  Middle: top view of the buffer reservoirs and an exploded view of a gel cassette.. Bottom Left: Image of assembled gel cassette and buffer reservoirs on the spreader plate.  Bottom Right: Gel cassette. 3.4. Migration Through an Affinity Gel In order to verify the predicted temperature dependent mobility expressed in equation [2.23] experiments were performed to measure the response of target DNA velocity to changes in temperature.  Initial experiments were done with 100   40 nt oligonucleotides as target DNA.  Oligonucleotides are single stranded so do not need to be denatured to interact with the affinity gel, and they are short enough that they have a negligible field dependent mobility.  This second point was important for initial attempts at ssSCODA based focusing as attempts with longer molecules were confounded by the tendency for long molecules to focus in a non- sequence specific manner from the electrophoretic SCODA effect. To perform these measurements a polyacrylamide gel (4%T, 2%C) in 1xTB (89 mM tris, 89 mM boric acid) with 0.2 M NaCl and 10 μM acrydite probe oligo was cast in a one dimensional version of the gel cassettes shown in Figure 3.3 containing only two access ports rather than four.  Polymerization was initiated through the addition of 2 μl of 10% w/v APS and 0.2 μl TEMED per ml of gel. Mobility measurements were performed on two different 100 nt oligonucleotides differing by a single base containing sequences with a perfect match (PM) to the probe and a single base mismatch (sbMM).  These target oligonucleotides were end labeled with either 6-FAM  or Cy5 (IDT DNA).  Probe and target sequences used for these experiments are shown in Table 1.  These initial measurements were performed with targets 100 nt in length, rather than longer targets, so that subsequent focusing attempts were not confounded by electrophoretic SCODA based focusing which does not efficiently focus targets much shorter that about 200nt long.   41  Sequence Probe 5'  ACT GGC CGT CGT TTT ACT  3' PM Target 5'  CGA TTA AGT TGA GTA ACG CCA CTA TTT TCA CAG TCA TAA CCA TGT AAA ACG ACG GCC AGT GAA TTA GCG ATG CAT ACC TTG GGA TCC TCT AGA ATG TAC C  3' sbMM Target 5'  CGA TTA AGT TGA GTA ACG CCA CTA TTT TCA CAG TCA TAA CCA TGT AAA ACT ACG GCC AGT GAA TTA GCG ATG CAT ACC TTG GGA TCC TCT AGA ATG TAC C  3'  Table 1  Oligonucleotide sequences used for measurement of mobility temperature dependence. Regions complementary to the probe are highlighted in the target sequences.  The mismatched base is underlined in the sbMM target. The probe sequence was chosen to be complementary to pUC19 for subsequent experiments with longer targets.  The 100 nt targets contain a sequence complementary to the probe (perfect match: PM) or with a single base mismatch (sbMM) to the probe with flanking sequences to make up the 100 nt length.  The flanking sequences were designed to minimize the effects of secondary structure and self hybridization.  Initial sequences for the regions flanking the probe binding site were chosen at random.  Folding and self hybridization energies were then calculated using Mfold 42 and the sequences were altered one base at a time to minimize these effects ensuring that the dominant interactions would be between target strands and the probe.   42 Table 2 shows the binding energies and melting temperatures for the sequences shown in Table 1.  The largest Tm for non probe-target hybridization is 23.9°C and the greatest secondary structure Tm is 38.1°C.  Both of these values are far enough below the sbMM target-probe Tm that they should not interfere target- probe interactions.  Probe PM Target sbMM Target Secondary Structure Probe -35.4+0.1012*T Tm = 12.2°C -145.3+0.4039*T Tm = 65.1°C -126.8+0.3598*T Tm = 55.8°C -20.3+0.07049*T Tm = 14.8°C PM Target -145.3+0.4039*T Tm = 65.1°C -40.2+0.1124*T Tm = 23.9°C -40.2+0.1111*T Tm = 20.9°C -24.3+0.07808*T Tm = 38.1°C sbMM Target -126.8+0.3598*T Tm = 55.8°C -40.2+0.1111*T Tm = 20.9°C -40.2+0.1124*T Tm = 23.9°C -24.3+0.07808*T Tm = 38.1°C  Table 2 Hybridization energies and melting temperatures calculated using mfold.  The binding energy, ¢G, is given as ¢H ¡ T¢S , Where ¢H  is the enthalpy and ¢S  the entropy in units of kcal/mol and kcal/mol K respectively.   The following parameter values were used for calculation: temperature = 50°C, [Na+] = 0.2 M, [Mg++] = 0 M, Strand concentration = 10 μM To measure the velocity response as a function of temperature the fluorescently labeled target was first injected into the gel at high temperature (70°C), and driven under a constant electric field into the imaging area of the gel. Once the injected band was visible the temperature of the spreader plate was dropped to 55°C.  An electric field of 25 V/cm was applied to the gel cassette while the temperature was ramped from 40°C to 70°C at a rate of 0.5°C/min.  Images of the gel were taken every 20 sec.  Image processing software written in LabView® (National   43 Instruments, Austin TX) was used to determine the location of the centre of the band in each image and this position data was then used to calculate velocity. Figure 3.4 shows a plot of target DNA mobility as a function of temperature. Using the values of ¢G for our probe and target sequences shown in Table 2 the velocity versus temperature curves were fit to equation [2.23] determine the two free parameters: the mobility ¹0, and ¯  a constant that depends on the kinetics of the hybridization reaction. A fit of the data shown in Figure 3.4 shows good agreement with the theory of migration presented in section 2.4.  The separation between the perfect match and single base mismatch targets suggest that it should be possible to find an operating temperature where the focusing speed of the perfect match target is significantly greater than that of the mismatched target enabling separation of the two species through application of a DC bias field as illustrated in Figure 2.4.   44  Figure 3.4 Measurement of temperature dependence of DNA target mobility through a gel containing immobilized complementary oligonucleotide probes.  R2 value for the PM fit and MM fits were 0.99551 and 0.99539 respectively. 3.5. Gel Thickness According to equation [2.16] SCODA velocity will be proportional to the cosine of the phase lag between the mobility oscillations and the field oscillations. This phase lag, which must be minimized in order to achieve efficient focusing manifests itself in two ways: the delay between changes in electric field strength and changes in temperature, and the delay between changes in temperature and   45 changes in mobility2.  The phase lag between changes in field and changes in temperature is determined by both the thermal mass of the gel and its surrounding material, and the rate at which heat flows into and out of the gel.  Minimizing the phase lag is equivalent to minimizing the thermal time constant of the gel.  The thermal time constant,¿ , is equal to the product of the thermal mass of the gel and thermal resistance to heat conduction out of the bottom of the gel and into the spreader plate:  ¿ = ½cV μ t kA ¶  [3.1] Here ½ is the density of the gel material, c the heat capacity, k the thermal conductivity and V , A, and t are the volume, surface area and thickness of the gel respectively.  In practice the gel does not sit directly on the spreader plate but is electrically insulated from the spreader plate with a layer of glass.  The effect of this layer of glass is to further increase the thermal time constant.  The composite time constant for a number of layers can be calculated by multiplying sum of the thermal masses and the sum of the thermal resistances.  ¿n = ÃX n ½iciVi !ÃX n ti kiAi !  [3.2]  2 The effect of slow mobility changes on phase lag will be discussed in detail in section 5.1.2   46 In this case however the areas are all equal and therefore cancel so equation [3.2] simplifies to:  ¿n = ÃX n ½iciti !ÃX n ti ki !  [3.3] To minimize the thermal time lag, one must minimize the gel thickness, the thickness of the bottom surface of the gel cassette, and maximize the thermal conductivity of the bottom surface of the gel cassette.  To this end gels were cast 100 μm thick and 100 μm thick glass coverslips were used for the bottoms of the gel cassettes resulting in a calculated value for the thermal time constant of 0.15 sec.  The period at which the rotating electric field pattern is applied to this gel must be much greater than this value to prevent a reduction in efficiency due to thermal phase lags. Alternative materials for the bottoms of the gel cassettes were explored and it was found that thin glass bottoms were the best compromise between cost, availability, dimensional stability and thermal conductivity.  Alternative materials that were explored include various thin plastic layers, and ceramic layers such as alumina and boron nitride.  Relative to most plastics, the thermal conductivity of glass is approximately 10 fold higher and the stiffness is approximately 20-50 fold higher (depending on the plastic and grade of glass).  Relative to ceramics, such as alumina or boron nitride, glass is both less thermally conductive and has a   47 lower Young’s modulus; however these materials tend to be both expensive and difficult to use in prototype fabrication. 3.6. Predictions of Focusing and Separation The electric field and subsequently the Joule heating within an ssSCODA gel are controlled by both the voltage applied to the source electrodes, and the shape of the gel.  Marziali et al.29 use superimposed rotating dipole and quadrupole fields to drive electrophoretic SCODA concentration.  The ratio of the strength of these two fields, the dipole to quadrupole ratio (D=Q), has an impact on the efficiency of SCODA focusing with a maximum at around D=Q = 4:5, however the optimum is relatively flat with the SCODA force staying relatively constant for values between 1.75 and 10 41.  One convenient choice of D=Q is 2.  With this particular choice, only two distinct potentials need to be applied to the source electrodes, which can be achieved by connecting one electrode to a common voltage rail, grounding the other three, and rotating this pattern in a stepwise manner through the four possible configurations as shown in Table 3.  Although analog amplifiers were used for all of the work in this study, using a D/Q ratio of 2 allows one to use discrete MOSFET switches, which greatly simplifies and reduces the required size and complexity of the power supplies.   48  Electrode A Electrode B Electrode C Electrode D Step 1 -V 0 0 0 Step 2 0 -V 0 0 Step 3 0 0 -V 0 Step 4 0 0 0 -V Table 3 Voltage pattern for SCODA focusing with D/Q = 2. A starting point for a sequence specific gel geometry was the geometry used for the initial demonstration of electrophoretic SCODA.  This geometry, pictured in Figure 3.5, can be defined by two numbers, the gel width and the corner radius. We started by using a geometry that had a width of 10 mm and a corner radius of 3 mm.  An electro-thermal model of this geometry was implemented in COMSOL Multiphysics® modeling software (COMSOL, Inc, Burlington MA, USA)  to determine the electric field and temperature profiles within the gel and establish whether or not those field and temperature profiles could drive concentration of a target with the temperature dependent mobility shown in Figure 3.4.  This model simultaneously solves Ohm’s Law and the heat equation within the domain, using the power density calculated from the solution of Ohms Law as the source term for the heat equation and using the temperature solution from the heat equation to determine the temperature dependent electrical conductivity of the electrolyte in the gel.  Boundary conditions and other model parameters are illustrated in Figure 3.5.   49  Figure 3.5  Gel geometry.  Boundary conditions and bulk gel properties used for eletrothermal modeling are shown. In order to get an accurate estimate of the temperature profile within the gel the heat conducted out of the top and bottom of the gel must be modeled.  The gel cassettes described in section 3.1.1 are placed on an aluminum spreader plate that acts as a constant temperature reservoir.  To model heat flow into the spreader plate the heat transfer coefficient of the glass bottom, given by k=t, was used. The temperature and electric field profiles solved by this model for a single step of the SCODA cycle are shown in Figure 3.6.  The voltage applied to the four electrodes was -120 V, 0 V, 0 V, 0 V, and the spreader plate temperature was set to 55°C (328 K)   50  Figure 3.6 Result of electro thermal model for a single step of the SCODA cycle.   Voltage applied to the four electrodes was -120 V, 0 V, 0 V, 0 V.  Spreader plate temperature was set to 55°C (328 K).  Colour map indicates gel temperature and the vector field shows the relative magnitude and direction of the electric field within the gel.  Note that as DNA is negatively charged its migration direction will be opposite to the direction of the electric field. With the thermal model described above and the mobility curve fit from Figure 3.4 it is possible to determine the SCODA velocity everywhere in the gel by   51 taking the time average of the instantaneous drift velocity integrated over one complete cycle:  ~vs = 1 ¿ Z ¿ 0 ¹(T (~r; t)) ~E(~r; t)dt [3.4] Where ¹ is the temperature dependent mobility, E the electric field and ¿  the period of the SCODA cycle.  The temperature and electric field were solved for four steps in the SCODA cycle and coupled with the mobility function in equation [2.23]. In this manner, we can calculate the SCODA velocity everywhere in the gel.  Since we are using discrete steps, if we assume that the period is long enough that we can neglect the phase lag between the electric field and temperature, then the integral in equation [3.4] becomes a sum:  ~vs = P ¹(Ti(~r)) ~Ei(~r)tiP ti  [3.5] where the velocity is summed over all four steps in the cycle.  Figure 3.7 shows a vector plot of the SCODA velocity using the mobility versus temperature curve for the perfect match target shown in Figure 3.4 and the temperature and electric field values calculated above.   52  Figure 3.7 SCODA velocity vector plots. The velocity field plotted above shows a zero velocity point at the geometric centre of the gel, with the velocity at all other points in the gel pointing towards the centre.  This predicts that one should be able to collect all target DNA within the gel at the centre of the electric field pattern. In order to predict the utility of this technique for separation of similar sequences, a DC bias is superimposed over the voltage pattern shown in Table 3 resulting in the voltage pattern shown below in Table 4.   53   Electrode A Electrode B Electrode C Electrode D Step 1 -120 5 10 5 Step 2 0 -115 10 5 Step 3 0 5 -110 5 Step 4 0 5 10 -115 Table 4 Applied voltages for focusing under bias.  Shown is a 120 V focusing potential superimposed over a 10 V DC bias. The resulting velocity plots of both the perfect match and single base mismatch targets are shown in Figure 3.8.  The zero velocity location of the perfect match target has been moved slightly off centre in the direction of the bias, however the mismatch target has no zero velocity point within the gel.  This suggests that it should be possible to completely wash a mismatch target from the gel area while capturing the perfect match, enabling selective focusing of a specific sequence.    54  Figure 3.8 Prediction of focusing under DC bias.  Top: Velocity field for perfect match target. Red dot indicates final focus location. Bottom: Velocity field for the  single base mismatch target. Electric field and temperature were calculated using COMSOL using a spreader plate temperature of 61°C.  Velocity was calculated using equation [3.5] and data fits shown in Figure 3.4   55  4. ssSCODA Demonstration In the previous chapter, measurements of the temperature dependence of target DNA mobility in an affinity gel, and calculations of the electric field and temperature within the gel geometry predicted that it should be possible to separate DNA molecules with single base specificity using the affinity SCODA technique.  To test this experimentally a gel cassette was fabricated with the geometry described in the previous chapter.  A 4% polyacrylamide gel containing 10 μM acrydite modified probe oligos (Integrated DNA Technologies, www.idtdna.com) was cast in the cassette as described in section 3.4. Equimolar amounts of the perfect match and single base mismatch targets were injected into the affinity gel at 30°C with an electric field of 100 V/cm applied across the gel such that both target molecules would be initially captured an immobilized at the gel buffer interface.  The temperature was then increased to 70°C and a constant electric field of 20 V/cm applied to the gel to move the target into the imaging area of the gel.  The temperature was then dropped to 62°C and a 108 V/cm focusing field superimposed over an 8 V/cm DC bias as shown in Table 4 was applied to the four source electrodes with a period of 5 seconds.   56   Electrode A Electrode B Electrode C Electrode D Step 1 -108 4 8 4 Step 2 0 -104 8 4 Step 3 0 4 -100 4 Step 4 0 4 8 -104 Table 5 Focusing plus bias potentials applied to the gel shown in Figure 4.1  Figure 4.1 shows images of concentration taken every 2 min.  The perfect match target was tagged with 6-FAM and shown in green, the mismatch target was tagged with Cy5 and is shown in red.    57  Figure 4.1 Time series of ssSCODA focusing under bias.  Perfect match DNA is tagged with 6- FAM (green) and single base mismatch DNA is tagged with Cy5 (red).  Images taken at 3 min intervals.  The first image was taken immediately following injection.  The camera gain was reduced on the green channel after the first image was taken.  DNA is injected into the right side of the gel and focusing plus bias fields are applied.  The perfect match target (green) experiences a drift velocity similar to that shown in the left panel of Figure 3.8 and moves towards a central focus location.  The more weakly focusing mismatch target (red) experiences a velocity field similar to that shown in the right panel of Figure 3.8 and is pushed off the edge of the gel by the bias field. This experiment verifies the predictions of Figure 3.8 demonstrating that it is possible to generate two different velocity profiles for two DNA targets differing by only a single base enabling purification of the target with the higher binding energy to the gel.  It is clear from the images shown above in Figure 4.1 that there are two distinct velocity profiles generated for the two different sequences of target DNA.  A dispersive velocity field is generated for the single base mismatch target (red) and a non dispersive velocity field is generated for the perfect match Bias Direction   58 target.  This suggests that it should be possible to efficiently enrich for targets with single base specificity even if there is a large excess of mismatch target in the sample.  Achieving a high level of enrichment at high efficiencies requires careful control of a number of experimental parameters that will be discussed in the next chapter.   59 5. Optimization of Operating Conditions Moving from the demonstration of sequence specific SCODA based purification of the previous chapter towards a practical purification tool, which can achieve both high yield and high sample purity, requires a more detailed understanding of some of the physical properties of this system.  In this chapter some details of the process that proved to be important for achieving good sample enrichment at reasonable yields will be reviewed.  A relatively high salinity running buffer proved to be important for ensuring both efficient and stable focusing, as well as minimizing the time required to electrokinetically inject target DNA from an adjacent sample chamber into the SCODA gel.  Both injection time and efficiency were further improved through optimization of the geometry of the sample chamber.  A method for the elimination of the phase lag induced rotation discussed in section 2.2 is presented and the chapter concludes with a brief discussion of the effects of secondary structure. 5.1. Buffer Salinity Early attempts of measuring the temperature dependent mobility in an affinity gel (e.g. Figure 3.4) as well as the first demonstrations of ssSCODA were performed in buffers used for electrophoretic SCODA.  These are typically standard electrophoresis buffers such as tris-borate EDTA (TBE), often diluted 4 to 6 fold   60 to reduce the gel conductivity, enabling the application of high electric fields within thermal limitations imposed by Joule heating, resulting in shorter concentration times 41.  Although it is possible to achieve ssSCODA based concentration in a 1xTBE buffer (89 mM tris, 89 mM boric acid, 2 mM disodium EDTA), this type of buffer proved to be far from optimal for sequence specific SCODA due to the relatively low concentration of dissociated ions at equilibrium. A low concentration of dissociated ions results in slow hybridization kinetics, exacerbates ionic depletion associated with immobilizing charges (oligonucleotide probes) in the gel, and increases the time required to electrokinetically inject target DNA into the gel. 5.1.1. Equilibrium Calculation for an Electrophoretic Buffer A typical electrophoresis buffer consists of a weak acid and a weak base in solution.  The acid will dissociate and create a free proton (H+), and the base will dissociate to create a free hydroxide ion (OH-).  The H+ and OH- then combine to form water.  To determine the total concentration of dissociated ions in a typical electrophoresis buffer we need to consider these three equilibrium reactions:   HA Ð A¡ + H+ [5.1]  BOH Ð B+ + OH¡ [5.2]  H2O Ð H+ + OH¡ [5.3]   61  Where HA is the undissociated acid, and BOH is the undissociated base.  For example in tris-borate buffer BOH is tris, and HA is boric acid.  There are a total of seven chemical species interacting in these three reactions and there are six unknown concentrations (we know the concentration of H2O since it is essentially constant during the reaction), so we’ll need six equations to find all the equilibrium concentrations. The first three are the equilibrium equations for the above three reactions:   [A¡][H+] [HA] = Ka(acid) [5.4]  [B+][OH¡] [BOH] = Ka(base) [5.5]  [H+][OH¡] = Kw [5.6] where:  Ka = 10¡pKa [5.7] We also know that the total concentration of acid or base (dissociated plus undissociated) must be equal to the amount we added to the solution:  [HA] + [A¡] = Cacid [5.8]   62  [BOH] + [B+] = Cbase [5.9] And finally there must be zero net charge:  [A¡] + [OH¡] = [B+] + [H+] [5.10] Using concentrations of 89 mM tris base and 89 mM boric acid a pKa of 9.24 for boric acid and 8.3 for tris, one can solve equations [5.4] through [5.10] for the concentration of all the species.  This results in a concentration of 1.49 mM each of dissociated tris and dissociated boric acid. 5.1.2. Effect of Salt on Hybridization Rate The presence of positive counter ions shields the electrostatic repulsion of negatively charged complementary strands of DNA resulting in increased rates of hybridization.  Figure 5.1, reprinted from Tsuruoka et al. 43 shows the effect of increasing the concentration of Na+ ions on the rate of DNA hybridization. The hybridization rate increases by about 10 fold when [NaCl] is increased from 10 mM to 1 M of [NaCl], with most of the gain achieved by the time one reaches about 200 mM.  At low concentrations of positive counter ions, below about 10 mM, the rate of hybridization is more strongly dependent on salt concentration, roughly proportional to the cube of the salt concentration 34.  The calculations of section 5.1.1 suggest that the total positive counter ion concentration of 1xTBE is around 5.5 mM (1.5 mM of dissociated tris, and 4 mM of Na+ from the disodium   63 EDTA).  At this ion concentration it was possible to achieve focusing however the slow hybridization rates resulted in weak focusing and large final focus spot sizes.  Figure 5.1 Effect of salinity on rates of hybridization.  Reprinted from Tsuruoka et al.43 A slow rate of hybridization can lead to weak focusing through an increase in the phase lag between the changes in electric field and changes in mobility.  Equation [2.16] describes the SCODA velocity as being proportional to cos(Á), where Á represents the phase lag between the mobility oscillations and the electric field oscillations.  In the case of ssSCODA a phase lag can result from both a slow thermal response as was discussed in section 3.5 as well as from slow hybridization kinetics.   64 This phase lag results in slower focusing times and larger spot sizes since the final spot size is a balance between the inward SCODA-driven drift, and outward diffusion-driven drift.  Faster focusing times are always desirable as this tends to reduce the overall time to enrich a target from a complex mixture.  A smaller spot size is also desirable as it improves one’s ability to discriminate between different molecular species.  As discussed in section 2.6, when focusing under bias the final focus spot will be shifted off center by an amount that depends on both the mobility of the target and the speed of focusing, both of which depend on the strength of the interaction between the target and the gel bound probes.  The amount of separation required to discriminate between two similar molecules when focusing under bias therefore depends on the final focus spot diameter. Smaller spot diameters should improve one’s ability to discriminate between two targets with similar affinity to the gel bound probes. At the low rates of hybridization achieved with 1xTBE buffer, reliable focusing was only achievable with probe concentrations near 100 μM.  Increasing the salt concentration from around 5 mM to 200 mM through the addition of NaCl, while keeping the probe concentration at 100 μM had the effect of reducing the final focus spot size as shown in Figure 5.2.  All images in Figure 5.2 were taken after a similar amount of focusing time (approximately 5 min), however the increased salinity resulted in increased Joule heating, which required a four fold reduction   65 of field strength to prevent boiling when focusing with 200 mM NaCl.  Equation [2.30] states that the focusing speed is proportional to the electric field strength, so that fact that comparable focusing times are achieved with a four fold reduction in electric field strength suggests that the field normalized focusing speed is considerably faster under high salinity conditions. Although the total time for focusing was not reduced by the addition of 200 mM NaCl, the ability to focus quickly at low electric field strengths is important for the suppression of non-specific electrophoretic SCODA.  All target DNA molecules will focus irrespective of their sequence in the polyacrylamide gels used for ssSCODA due to electrophoretic SCODA.  The speed of electrophoretic SCODA focusing increases with electric field 41, so decreasing the field strength will have the effect of reducing the non-specific SCODA focusing speed, allowing one to wash non-target DNA molecules from the gel more easily by applying a DC bias. The addition of 200 mM NaCl to the gel also allows one to reliably focus complementary targets at 100 fold lower probe concentrations.  This result suggests that it should be possible to include up to 100 different probe sequences in a single gel, allowing one to simultaneously enrich for more than one target.   66  Figure 5.2 Top: Result of focusing with 200 mM NaCl added to the gel.  Probe concentrations are (l to r) 100 uM, 10 uM and 1 uM.  Bottom: Focusing in 1xTBE with no added NaCl at 100 uM probe concentration.  Focusing was not reliable at 10 uM and 1 uM probe in 1xTBE.   Different amounts of target were injected in each of these experiments, and the camera gain was adjusted prevent saturation. 5.1.3. Ion Depletion and Bound Charges The 100 μM probe concentration required to achieve efficient concentration in 1xTBE results in 2 mM of bound negative charges within the gel when a 20 nt probe is used, which is comparable to the total amount of dissolved negative ions within the gel (around 5.5 mM).  This high proportion of bound charge can result in the formation of regions within the gel that become depleted of ions when a constant electric field is placed across the gel 44-48 as it is during injection and during focusing under bias.  This process can be illustrated by considering a one dimensional gel containing bound negative charges with buffer on either side as 100uM Probe 1xTB, 0.2M NaCl 100uM Probe 1xTBE 1uM Probe 1xTB, 0.2M NaCl 10uM Probe 1xTB, 0.2M NaCl   67 shown in Figure 5.3.  The total current in all three regions of Figure 5.3 must be equal and each region must maintain electroneutrality.  These two constraints will force a larger proportion of the current to be carried by the positive ions in the gel region than in the buffer regions.  As a result there will be a depletion of ions out of the anode end boundary between the gel and buffer, and an accumulation of ions into the cathode boundary.  The rate at which ions are depleted (or accumulated) at the gel buffer boundary increases with an increase in the immobile fraction of negative charges.   68  Figure 5.3 Electrolyte depletion as a result of bound negative charges in a gel in electrical contact with electrolyte solutions containing no bound charges.  In the above schematic ©+ represents the flux of positive ions, and ©¡ represents the flux of negative charges.  Because some of the negative charges in the gel are immobile, in order to maintain electroneutrality and ensure that the same amount of current flows in the gel and the upstream and downstream buffers and a larger proportion of the current through the gel must be carried by the positive charges.  This results in a net flux of ions into the cathode end boundary between the gel and buffer, and depletion of ions at the anode end boundary between the buffer and gel. The depletion region formed results in a drop in current during injection and while focusing under bias.  It was found that this leads to inefficient and incomplete injection of sample, and that focusing after long injections or during extended periods of focusing under bias (to wash mismatched targets from the gel) resulted in unstable focusing behavior.  Localized regions of reduced salinity have the dual effect of reducing hybridization rates, which changes optimal focusing temperatures, as well as locally increasing the temperature through   69 increased Joule heating.  This resulted in target DNA either focusing off centre or being washed off the gel entirely.  In extreme cases these depletion regions resulted in enough localized heating to boil the gel. The rate at which ions are depleted (or accumulated) at a boundary increases as the fraction of charges that are immobile increases; a high salinity running buffer can therefore help to minimize many of the ion depletion problems associated with immobilizing charges in an ssSCODA gel by enabling focusing at lower probe concentrations, as well as reducing the fraction of bound charges by adding additional free charges. 5.1.4. Reduced Injection Times In order to introduce target molecules into a focusing gel for purification they are first placed in a sample chamber adjacent to the gel.  An electric field is then applied across both the gel and sample to electrokinetically inject the sample into the gel. SampleGel +V Source Electrode  Figure 5.4 Schematic of Sample Injection   70 The conductivity of the gel affects the time required to inject all of a sample into a gel through two competing mechanisms.  For a fixed injection voltage, increasing gel conductivity results in a larger proportion of the voltage being established across the sample chamber, which increases the electric field in the sample chamber, decreasing injection times.  However, the increased heating of the sample will tend to put a lower limit on the maximum amount of current that can be run through the gel without boiling, which will tend to increase injection times. We can determine which effect is stronger by using Ohm's law to calculate injection time in terms of the maximum allowable current within the gel.  We will then solve the heat equation to determine how the maximum allowable current depends on the electrical conductivity of the gel.  The result will be an expression relating the injection time to the electrical properties, thermal properties and geometry of the gel and sample chamber. Starting with Ohm’s law, using ~J  for the current density, ¾ the electrical conductivity, and ~E  the electric field:  ~J = ¾ ~E  [5.11]  We write the maximum tolerable current in the gel Imax as:  Imax = ~Jgel maxAgel [5.12]   71 where Agel is the cross sectional area of the gel.  The following expression for the electric field in the injection chamber follows from noting that the current in the gel must be the same as the current in the injection chamber (the subscript inj denotes the injection chamber):  ~Jinj = Imax Ainj = ¾inj ~Einj [5.13]  ~Einj = Imax Ainj¾inj  [5.14] The velocity of a DNA molecule moving through the injection chamber, vinj will be:  vinj = ¹Einj [5.15]  vinj = ¹Imax Ainj¾inj  [5.16] where ¹ is the mobility of the DNA target in the sample chamber.  The time required for injection is simply:  t = linj vinj  [5.17] where linj is the length of the injection chamber.  Substituting [5.16] into [5.17] we have the following expression for the injection time:   72  t = linjAinj¾inj ¹Imax  [5.18]  t = Vinj¾inj ¹Imax  [5.19] where Vinj is the volume of the injection chamber. Equation [5.19] relates the injection time to the maximum current that can be run through the gel and injection chamber.  The maximum current is set by a maximum temperature rise one can tolerate in the gel.  To determine how the current relates to this maximum temperature, we need to consider the thermal profile in the vertical direction of the gel.  Consider the 1-D heat equation:  @u @t = k c @2u @z2 + q c  [5.20]  u(0; t) = Tc [5.21]  du dx ¯̄̄̄ x=h = 0 [5.22] Here u is temperature, k is the thermal conductivity, c is the volumetric heat capacity, q is the internal heat generated per unit volume.  At the bottom of the gel we enforce a constant temperature boundary condition where Tc is the temperature of the cold plate, and we assume no heat is lost through the top of the gel at z = h.  Since we are only interested in the steady state solution we set   73 ut = 0 and don’t need to worry about initial conditions.  This reduces [5.20] to an ordinary differential equation:  d2u dz2 = ¡ q k  [5.23] The solution to this equation with the above boundary conditions is:  u(z) = ¡qz 2 2k + qhz k + Tc [5.24] The maximum temperature will be at the top where z = h.  We can now write down the maximum temperature rise in the gel as  ¢Tmax = u(h)¡ Tc [5.25]  ¢Tmax = qh2 2k  [5.26] Rearranging to get the maximum power density we can tolerate in the gel we have:  qmax = h2¢Tmax 2k  [5.27] Equation [5.19] relates injection time to the maximum current we can tolerate in the gel.  We want to remove current from this equation to see how the injection   74 time scales with gel height, and gel conductivity.  Using Ohm’s law we can relate the power density in the gel to the current:  qmax = I2max ¾gelh2gw 2 g  [5.28] Here ¾gel is the electrical conductivity of the gel, hg is the gel height, and wg is the gel width.  Substituting this into equation [5.27] and solving for Imax we get:  Imax = wg p 2k¢Tmax¾g  [5.29] Inserting this into [5.19] we get:  t = Vinj¾inj ¹injwg p 2k¢Tmax¾g  [5.30] which states that increased gel conductivity will result in reduced injection times. 5.2. Five channel Sample Chamber Geometry Equation [5.30] for the injection time states that for a given sample volume, injection time can be minimized by keeping the sample salinity as low as possible. This leads to two practical problems when injecting a sample into a gel through one of the four arms of the gel as shown in Figure 5.4.  The first is the requirement for feedback electrodes.  With a low salinity sample the impedance across the sample chamber can be high (and potentially vary from sample to   75 sample) compared to the impedance across the gel.  In order to accurately control the electric field in the gel during focusing it is therefore necessary to measure the voltage at the gel buffer interface and use that measurement to adjust the voltage at the source electrode30,41.  The second problem is that salt will tend to diffuse out of the gel and into the sample chamber over the course of a run leading to non-uniform gel salinity, which can result in variable focus locations, focus instabilities, and in extreme cases, gel boiling.  One solution to this problem is to add a fifth channel to the gel to be used exclusively for injection.  An example of this geometry is shown in Figure 5.5; here a channel in one of the gel corners allows access to a sample chamber that is otherwise isolated from the other four buffer reservoirs containing the source electrodes.   76 Gel +V Source Electrode Sample  Figure 5.5 Schematic of 5 channel injection.  Current is sourced from an electrode behind the sample and two electrodes grounded at the opposite end of the gel.  The other two gel electrodes are left floating. Because the space between the gel and source electrodes used for focusing will always have the same buffer composition, this geometry enables focusing without electrical feedback to control the electric field across the gel while still allowing for low conductivity samples to keep injection times short.   In addition the injection arm is partially filled with gel that provides a diffusion barrier between   77 the gel and the sample reducing the amount of ions that diffuse out of the gel and into the sample chamber during the course of a run. Equation [5.19] states that the injection time is independent of the shape of the sample chamber and depends only on the volume; however this equation assumes that the sample is not mixed during injection.  In practice, the vertical dimensions of the sample chamber proved to have a dramatic effect on injection times.  As discussed in section 3.5 the need for fast thermal response times constrains the gel thickness to around 100 μm.  It is desirable to be able to process sample volumes of up to 1 ml, which requires that there be a height mismatch between the gel and sample to prevent the area of the sample reservoir becoming unreasonably large. When this is the case there will be a difference in current density between the gel and the sample chamber, which can lead to excessive heating of the sample near the gel buffer interface.  A first naive attempt at designing an injection system for thin gels, shown in Figure 5.6, resulted in poor injection efficiencies and long injection times.  In this system the large height mismatch between the gel and sample chamber led to excessive heating near the interface between the gel and sample, which results in the formation of convection currents in the sample chamber.  This had the effect of mixing the sample chamber before injection was complete, which increased the injection time.   78  Figure 5.6 Sample chamber with a large height mismatch between sample and gel.  Colour represents the amount of Joule heating – blue is less heating and red is more heating.   The black lines are electric field lines.  With this geometry there is excessive heating at the gel buffer interface, which leads to the formation of convection currents resulting in increased injection times and reduced injection efficiency.  The injection time for an unmixed sample chamber is simply the transit time of a target molecule across the length of a sample chamber and is given by equation [5.19].  When the sample chamber is mixed during injection, the amount of target remaining in the sample chamber, T  will decay exponentially with time:  T = T0 exp μ ¡V ¾ ¹I t ¶  [5.31] where T0 is the amount of target initially in the sample chamber, V  is the volume and ¾ the electrical conductivity of the sample chamber; the mobility of the target   79 is given by ¹ and I  is the injection current.   To compare this to un-mixed injection consider the time required to deplete a fraction of the target from the sample chamber f = T=T0.  For the un-mixed sample chamber we have:  t = f V ¾ ¹I  [5.32] and for the mixed sample chamber we have:  t = ¡ ln(1¡ f)V ¾ ¹I  [5.33] which is always greater than equation [5.32] for all values of f . The effect of mixing a sample chamber during injection is shown in Figure 5.7. Here fluorescently tagged target DNA was injected out of a sample chamber with the geometry of Figure 5.6 having a volume of 250 μl and a conductivity of 200 μS/cm at a current of 2 mA.  The top row of Figure 5.7 shows injection out of free solution, while the bottom row the sample was injected out of a 0.5% agarose gel to suppress convection currents.  Equation [5.19] predicts that injection out of free solution should be complete after 55 seconds, however after 20 min target DNA is still moving into the gel from the sample chamber.  Despite the 10 fold decreased mobility of the target in agarose compared to free solution 49-54 the bottom series shows complete injection within 20 min.  This result suggests that without   80 agarose in the sample chamber the sample is being mixed, most likely by natural convection as a result of uneven heating of the sample.  Although adding agarose or a similar hydrogel to the sample to will suppress convection currents during injection, the result is a similar total injection time due to the fact that the mobility of DNA in agarose is much lower than it is in free solution. It would therefore be desirable to suppress convection currents without reducing the mobility of the target DNA in the sample chamber.  Figure 5.7  Comparison of injection out of free solution (top) and agarose (bottom) with sample chamber from Figure 5.6.  100 nt DNA tagged with 6-FAM with no homology to gel probes was injected at 2 mA injection current.  Images taken at 1, 5, 10, 15, and 20 min.  Top: target was injected out of free solution.  In the final image there is still DNA moving into the gel from the injection chamber visible as faint fluorescence signal above background.  Bottom: target is injected out of agarose to suppress convection. After 20 min injection is complete.  The onset of natural convection occurs when the Rayleigh number reaches some critical value.  The Rayleigh number is the product of the Prandtl number, which describes the ratio of momentum diffusivity (viscosity) and thermal diffusivity, Free solution 0.5% agarose   81 and the Grashof number, which describes the ratio of buoyant forces to viscous forces.  Ra ´ GrPr = g®¢Th 3 º·  [5.34] Above, g is the acceleration due to gravity, ® is the thermal expansion coefficient of the fluid, ¢T  the temperature rise of the fluid, h the characteristic length scale (usually the vertical height of the fluid column), º the kinematic viscosity, and · the thermal diffusivity.  Calculation of the critical Rayleigh number for all but the simplest systems is a non trivial matter; however equation [5.34] does provide a clue as to how to minimize the likelihood of convection currents forming.  Since our sample must be in an aqueous solution, the fluid properties cannot be changed.  It is possible to increase the viscosity of the solution, however this change is undesirable as it will result in longer injection times as the mobility of DNA, ¹, will be reduced in proportion with any increase in viscosity according to the Einstein relation:  ¹ = 1 6¼´r  [5.35] where ´ is the viscosity and r the radius of the DNA molecule.  To reduce the likelihood of convection the only remaining options are to reduce the temperature rise, through a reduction in current density at the gel buffer interface; and reduce   82 of the height of the sample chamber.  Both of these parameters were changed with the design of the 250 μl sample chamber shown in Figure 5.8.  Figure 5.8 Improved geometry for sample injection.  Top: A rendering and image of a gel cassette with an integrated sample chamber.  Bottom: Cross section of gel and sample chamber.  Red lines are electric field lines, and colour represents heating – red is more heating while blue is less heating.  Sample chamber height is reduced to 1.5 mm and integrated into gel cassette.  The reduced height and reduced heating at the gel buffer interface compared to the sample bulk effectively prevents the formation of convection currents. The height of the sample chamber was reduced to 1.5 mm, and the injection channel width was increased from 2 mm to 4 mm where the channel interfaces with the sample.  With these changes, the injection time decreased from greater than 20 min as shown in the top panel of Figure 5.7 to around 2 min, for the same 250 ul sample with a conductivity of 2 mS/cm, which is close to the predicted 1.5mm sample height 0.1mm gel height Gnd +V Sample Chamber Gel   83 injection time of 1 min using equation [5.19].  Injection of 100 nt and 500 nt DNA fragments from the sample chamber of Figure 5.8 is shown in Figure 5.9.  The images were taken after 2 min and 5 min of injection and show a much tighter injection band with a sharp trailing edge suggesting that convective mixing has been effectively suppressed.   Figure 5.9 Injection from the sample chamber shown in Figure 5.8.  Sample volume: 250 μl, sample conductivity: 200 μS/cm, injection current: 2 mA.   Left 100 nt fragments, right 500 nt fragments.  The top row was taken after 2 min of injection and the bottom row taken after 5 min. The images in the top row of Figure 5.9 show that injection is complete within two minutes.  In this experiment the injection current was approximately 2 mA for 2 min 100nt 2 min 500nt 5 min 100nt 5 min 500nt   84 the duration of the injection.  At this injection current equation [5.19] predicts that injection should be complete within 75 sec, which is in good agreement with the measured injection time for this system.  This result suggests that so long as convective mixing can be suppressed, then injection out of large volumes should be possible in a reasonable amount of time.  Injecting out of a  5 ml sample volume with a conductivity of 200 μS/cm (equivalent to about 2 mM of NaCl) should be achievable with 20 min of injection. The ability to sample large volumes has important consequences for interrogation of samples containing rare sequences as one’s ability to measure the presence of rare sequences is often limited by the volume one can sample.  Consider for example the problem of interrogating a human blood sample for rare sequences such as somatic mutations or pathogen sequences.  A typical extraction kit such as a Qiagen PAXgene blood extraction kit is capable of recovering between 150-500 μg of DNA from 8.5 ml of blood.  If one then uses a PCR based method to detect a rare sequence variant in the extracted DNA one will be limited to only sampling around 1 ug of the extracted DNA to prevent saturating the PCR reaction with non-specific template sequences.  This effectively limits the total volume of blood one can sample to between 20 μl and 50 μl.  If one is interested in interrogating the blood sample for rare sequences, to overcome shot noise one must have at least 10 copies in the PCR reaction to reliably detect the sequence.  In this   85 example one will not be able to detect a rare sequence in a blood sample if the sequence is present at levels lower than around 200-500 copies per ml of blood. With sequence based enrichment only the sequence of interest is purified, so by processing the DNA from 5 ml of blood with ssSCODA and extracting only the sequence of interest, one will no longer run into template limits of PCR and can effectively use PCR to sample the entire 5 ml sample.  This should improve the detection limits from a few hundred copies per ml, to a few copies per ml. 5.3. dsDNA Denaturation Target DNA will not interact with the gel immobilized probes unless it is single stranded.  The simplest method for generating single stranded DNA from double stranded DNA is to boil samples prior to injection.  One potential problem with this method is that samples can re-anneal prior to injection reducing the yield of the process, as the re-annealed double stranded targets will not interact with the probes and can be washed off of the gel by the bias field.  Provided target concentration and sample salinity are both kept low, renaturation of the sample can be minimized.  DNA renaturation is governed by first order reaction kinetics 34 and can be described by the following chemical reaction:  [S1] + [S2] kf¡*)¡ kr [S1¢¢¢S2] [5.36]   86 Where S1 and S2 are the two complementary strands and S1¢¢¢S2 is the renatured double stranded DNA.  By keeping the temperature of the sample near room temperature after boiling the rate of denaturation can effectively be reduced to zero and therefore be ignored.  The rate of renaturation will therefore be proportional to the concentration of the denatured single stranded DNA:  d[S1¢¢¢S2] dt = kf [S1][S2] [5.37] To measure the effect of target concentration on renaturation and overall efficiency, fluorescently labeled double stranded PCR amplicons complementary to gel bound probes were diluted into a 250 μl volume containing about 2 mM NaCl and denatured by boiling for 5 min followed by cooling in an ice bath for 5 min.  The sample was then placed in the sample chamber of a gel cassette, injected into the focusing gel and concentrated to the centre of the gel.  After concentration was complete the fluorescence of the final focus spot was measured, and compared to the fluorescence of the same quantity of target that was manually pipetted into the centre of an empty gel cassette.  This experiment was performed with 100 ng (2£ 1011 copies) and 10 ng (2£ 1010 copies) of double stranded PCR amplicons.  The 100 ng sample resulted in a yield of 40% and the 10 ng sample resulted in a yield of 80%.  This confirms the prediction that lower DNA concentration will result in higher yields.   87 5.4. Phase Lag Induced Rotation To separate target DNA that differs by a single base a DC bias is superimposed over the focusing fields.  If the separation in binding energy is great enough then the mismatched target can be washed entirely off of the gel.  The ability to wash weakly focusing contaminating fragments from the gel can be affected by the phase lag induced rotation discussed in section 2.2, where the SCODA velocity of a two dimensional system was given by:  ~vSCODA = jvSCODAj(cos(Á)r̂ + sin(Á)μ̂) [5.38] Where Á is the phase lag between the electric field oscillations and the mobility oscillations.  Aside from reducing the proportion of the SCODA velocity that contributes to concentration this result has additional implications when washing weakly focusing contaminants out of the gel.  The rotational component will add to the DC bias and can result in zero or low velocity points in the gel that can significantly increase the time required to wash mismatched targets from the gel. An example of this problem is shown below.  The targets shown in Figure 5.10 focus weakly under SCODA fields and when a small bias is applied to wash them from the gel, the wash field and the rotational velocity induced by the SCODA fields sum to zero near the bottom left corner of the gel.  This results in long wash times, and in extreme cases weak trapping of the contaminant fragments.  To   88 overcome this problem one can alter the direction of the field rotation every period.  This results in much cleaner washing and focusing with minimal dead zones.  This scheme was applied during focus and wash demonstration shown in Figure 4.1; the mismatched target is cleanly washed from the gel without rotation. With this scheme we still have reduced focusing velocity due to the phase lag, but there is not an additional rotational component of the SCODA velocity.  Figure 5.10 Example of phase lag induced rotations.  The field rotation is counterclockwise, that induces a clockwise rotation of the targets in the gel.  Images were taken at 5 min intervals. 5.5. Effect of Secondary Structure Secondary structure in the target DNA will decrease the rate of hybridization of the target to the immobilized probes.   This will have the effect of reducing the Rotation Direction DC bias direction   89 focusing speed by increasing the phase lag described in equation [2.16].  The amount by which secondary structure decreases the hybridization rate depends on the details of the secondary structure.  With a simple hairpin for example, both the length of the stem and the loop affect the hybridization rate 38.  For most practical applications of ssSCODA, where one desires to enrich for a target molecule differing by a single base from contaminating background DNA, both target and background will have similar secondary structure.  In this case the ability to discriminate between target and background will not be affected, only the overall process time.  By increasing the immobilized probe concentration and the electric field rotation period one can compensate for the reduced hybridization rate. There are potentially cases where secondary structure can have an impact on ones ability to discriminate target from background.  It is possible for a single base difference between target and background to affect the secondary structure in such a way that background DNA has reduced secondary structure and increased hybridization rates compared to the target, and is the basis for single stranded conformation polymorphism (SSCP) mutation analysis. This effect has the potential to both reduce or enhance ones ability to successfully enrich for target DNA, and care must be taken when designing target and probe sequences to minimize the effects of secondary structure.  Once a target molecule has been chosen one has the freedom to move the probe position around the mutation site,   90 as well as adjusting the length of the probe molecule.  In extreme cases one can also hybridize oligonucleotides to sequences flanking the region where the probe anneals to further suppress secondary structure.   91 6. ssSCODA Performance In the following chapter some measurements of the performance of the system will be discussed.  The length dependence of the final focus location while focusing under DC bias was measured and shown to be independent of length for fragments ranging from 200 nt to 1000 nt in length; an important result, which implies that ssSCODA is capable of distinguishing nucleic acid targets by sequence alone without the need for ensuring that all targets are of a similar length.  Measurements of the ability to enrich for target sequences while rejecting contaminating sequences differing from the target by only a single base will be presented, followed by a demonstration of ssSCODA's ability to enrich for target DNA differs only by a single methylated cytosine residue with respect to contaminating background DNA molecules. 6.1. Length Independence of Focusing The ability to purify nucleic acids based on sequence alone, irrespective of fragment length, is a desirable feature of any sequence enrichment strategy as it eliminates the need to ensure that all target fragments are of similar length prior to enrichment.  The theory of ssSCODA presented in Chapter 2 predicts that ssSCODA enrichment should be independent of target length. However, effects   92 not modeled in Chapter 2 may lead to length dependence, and experiments were therefore performed to confirm the length independence of ssSCODA. When a SCODA electric field pattern is applied to an affinity gel, all target molecules, even those that interact weakly with probe molecules, will drift towards the same focus location at the centre of the gel.  Separation of different molecular species is achieved through the application of a constant electric field, superimposed over the time varying focusing field, which moves the focus location off centre.  The amount by which the final focus is displaced from the gel centre is determined by a balance between the focus velocity and the DC velocity, both of which depend on the strength of the interaction between the target molecule and the immobilized probes.  A weaker interaction results in a lower focus velocity and a higher DC velocity, which causes weakly interacting targets to be pushed further off center for a given bias field than strongly interacting targets, thus enabling separation based on the strength of the interaction between targets and probes.  According to the theory of thermally driven ssSCODA developed in Chapter 2 the final focus location under bias should not depend on the length of the target strands.  In section 2.6 the SCODA drift velocity and DC bias velocities were calculated for a one dimensional model of affinity SCODA. The final focus location under bias is the point of zero velocity, where the   93 SCODA velocity and bias velocity exactly cancel.  In the one dimensional case this point can be found by setting equation [2.32] to zero:  ¹(Tm)Eb = 1 2 ®Ta x L E0 cos(Á) [6.1] Length dependence of the final focus location enters into this expression through the length dependence of the unimpeded mobility of the target ¹0. However, since both ¹(Tm) and ® are proportional to ¹0 , the length dependence will cancel from this expression.   The final focus location of a target concentrated with thermally driven ssSCODA should therefore not depend on the length of the target, even if a bias is present. There are two potential sources of length dependence in the final focus location, not modeled in Chapter 2, which must also be considered: electrophoretic SCODA, and force based dissociation of probe target duplexes.  DNA targets of sufficient length (>200 nt) have a field dependent mobility in the polyacrylamide gels used for ssSCODA, and will therefore experience a sequence independent focusing force when focusing fields are applied to the gel.  The total focusing force experienced by a target molecule will therefore be the sum of the contributions from electrophoretic SCODA and ssSCODA.  Under electrophoretic SCODA, the focusing velocity tends to increase for longer molecules 41, while the DC velocity tends to decrease so that under bias the final focus location depends   94 on length.  The second potential source of length dependence in the final focus location is force based dissociation.  The theory of ssSCODA presented in Chapter 2 assumed that probe-target dissociation was driven exclusively by thermal excitations.  However it is possible to dissociate double stranded DNA with an applied force.  Specifically, an external electric field pulling on the charged backbone of the target strand can be used to dissociate the probe-target duplex.  The applied electric field will tend to reduce the free energy term ¢G in equation [2.22] by an amount equal to the energy gained by the charged molecule moving through the electric field 40.  This force will be proportional to the length of the target DNA as there will be more charges present for the electric field to pull on for longer target molecules, so for a given electric field strength the rate of dissociation should increase with the length of the target. To measure whether or not these two effects contribute significantly to the length dependence of the final focus location, two different lengths of target DNA, each containing a sequence complementary to gel immobilized probes, were focused under bias and the final focus location measured and compared.  The target DNA was created by PCR amplification of a region of pUC19 that contains a sequence complementary to the probe sequence in Table 1.  Two reactions were performed with a common forward primer, and reverse primers were chosen to generate a 250 bp amplicon and a 1000 bp amplicon.  The forward primers were   95 fluorescently labeled with 6-FAM and Cy5 for the 250 bp and 1000 bp fragments respectively.  The targets were injected into an ssSCODA gel and focused to the centre before applying a bias field.  A bias field of 10 V/cm was superimposed over 120 V/cm focusing fields for 10 min at which point the bias was increased to 20 V/cm for an additional 7 min.  Images of the gel were taken every 20  sec, with a 1 sec delay between the 6-FAM channel and the Cy5 channel.  The field rotation period was 5 sec.  Images were post processed to determine the focus location of each fragment.  Figure 6.1 shows the focus location versus time for the 250 bp (green) and 1000 bp (red) fragments.  The left panel is an image of final focus of the two fragments at the end of the experiment.   96  Figure 6.1 Top: Focus location under bias for 250 bp (green) and 1000 bp (red) fragments. Bottom: Image of the gel at the end of the run.  Green and red channels have been superimposed. 15 20 25 30 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 H or iz on ta l f oc us  p os iti on  (m m ) Time (min)  250bp 10V bias  1000bp 10V bias  250bp 20V bias  1000bp 20V bias Length Dependence of Focus Postion under DC bias   97 There is a small difference in final location that can be attributed to the fact that the two images were not taken at the same phase in the SCODA cycle.  This result shows that the final focus position does not depend on length, implying that under these operating conditions electrophoretic SCODA focusing is much weaker than ssSCODA focusing, and that ssSCODA is driven largely by thermal dissociation rather than force-based dissociation.  This result has important practical implications as it suggests that ssSCODA is capable of distinguishing nucleic acid targets by sequence alone without the need for ensuring that all targets are of a similar length. 6.2. Single Base Mismatch Rejection Ratio To determine the specificity of ssSCODA with respect to rejection of sequences differing by a single base, different ratios of synthetic 100 nt target DNA containing either a perfect match (PM) or single base mismatch (sbMM) to a gel bound probe, were injected into a gel and focused under wash fields to remove the excess sbMM DNA.  The PM target sequence was labeled with 6-FAM and the sbMM with Cy5; after washing the sbMM target from the gel the amount of fluorescence at the focus location was quantified for each dye and compared to a calibration run.  For the calibration run, equimolar amounts of 6-FAM labeled PM and Cy5 labeled PM target DNA were focused to the centre of the gel and the fluorescence signal at the focus location was quantified on each channel.  The   98 ratio of the signal Cy5 channel to the signal on the 6-FAM channel measured during this calibration is therefore the signal ratio when the two dye molecules are present in equimolar concentrations.  By comparing the fluorescence ratios after washing excess sbMM from the gel to the calibration run it was possible to determine the amount of sbMM DNA rejected from the gel. These experiments were performed with a sample injection configuration shown in Figure 5.4.  Samples containing target sequences shown in Table 1 were added to the sample chamber and an electric field of 50 V/cm was applied across the sample chamber at 45°C to inject the sample into a gel containing 10 μM of immobilized probe.  Once the sample was injected into the gel, the liquid in the sample chamber was replaced with clean buffer and focusing was performed with a superimposed wash field.  A focusing field of 60 V/cm was combined with a DC wash field of 7 V/cm, the latter applied in the direction opposite to the injection field.  It was found that this direction for the wash field led to complete rejection of the mismatched target DNA in the shortest amount of time.  Table 6 below shows the amount of DNA injected into the gel for each experiment.   99 Run Description: Cy5 Labeled Target 6-FAM Labeled Target 1:1 Calibration 10 fmol PM 10 fmol PM 100:1 1 pmol sbMM 10 fmol PM 1,000:1 10 pmol sbMM 10 fmol PM 10,000:1 100 pmol sbMM 10 fmol PM 100,000:1 1 nmol sbMM 10 fmol PM Table 6 List of targets run for measuring the rejection ratio of ssSCODA with respect to single base differences.  The PM and sbMM targets are as described in Table 1. After the mismatched target had been washed from the gel, the focusing fields were turned off and the temperature of the gel was reduced to 25°C prior to taking an image of the gel for quantification.  It was important to ensure that all images used for quantification were taken at the same temperature, since Cy5 fluorescence is highly temperature dependent, with the fluorescence decreasing at higher temperatures.  The ratio of fluorescence on the Cy5 and 6-FAM channels were compared to the 1:1 calibration run to determine the rejection ratio for each run.  Figure 6.2 shows the results of these experiments.   100  Figure 6.2 Rejection ratio of sbMM DNA .Four different ratios of sbMM:PM were injected into a gel and focused under bias to remove excess sbMM.  The PM DNA was tagged with 6-FAM and the sbMM DNA was tagged with Cy5.  Top: fluorescence signal from the final focus spot after excess sbMM DNA had been washed from the gel.  The fluorescence signals are normalized to the fluorescence measured on an initial calibration run where a 1:1 ratio of PM-FAM:PMCy5 DNA was injected and focused to the centre of the gel.  Bottom: rejection ratios calculated by dividing the initial ratio of sbMM:PM by the final ratio after washing. MM Rejection Ratio 1 10 100 1000 10000 100000 100 1000 10000 100000 Excess MM Loaded R ej ec tio n R at io Normalized Fluorescence Signal from Focused DNA 0.001 0.01 0.1 1 10 100 100 1000 10000 100000 Excess MM Loaded Fl uo re sc en ce  S ig na l ( A U ) PM Signal MM Signal   101 It was found that rejection ratios of about 10,000 fold are achievable.  However it should be noted that images taken during focusing and wash at high sbMM:PM ratios suggest that there were sbMM molecules with two distinct velocity profiles. Most of the mismatch target washed cleanly off of the gel while a small amount was captured at the focus.  These final focus spots visible on the Cy5 channel likely consisted of Cy5 labeled targets that were incorrectly synthesized with the single base substitution error that gave them the PM sequence.  The 10,000:1 rejection ratio measured here corresponds to estimates of oligonucleotide synthesis error rates with respect to single base substitutions 55, meaning that the mismatch molecule synthesized by IDT likely contains approximately 1 part in 10,000 perfect match molecules.  This implies that the residual fluorescence detected on the Cy5 channel, which I attribute to unresolved mismatch may in fact be Cy5 labeled perfect match that has been enriched from the mismatch sample. Consequently the rejection ratio of ssSCODA may actually be substantially higher than 10,000:1. Performing measurements to confirm this requires a source of target DNA that has been synthesized with greater fidelity than the rejection ratio we are attempting to measure.  One possible source of high fidelity DNA is to use DNA that has been synthesized by cloning into bacteria and then sequenced for verification of the clones.  The DNA synthesis fidelity of E. coli with respect to   102 single base substitutions is approximately one error per 107 nucleotides 12.  By limiting the E. coli to growth to around 30 generations after sequence verification one should be able to obtain targets where only about 1 in 106 have an error that turns a single base mismatch target into a perfect match. Performing these measurements additionally requires either a more sensitive detection system, or the ability to efficiently extract purified targets from the centre of the gel so that targets can be PCR amplified and detected offline.  More sensitive detection is necessary for measuring high rejection ratios to avoid loading into to the gel excessive amounts of target DNA, which can lead to problems related to those discussed in section 5.1.3 where excessive amounts of bound or slow moving charges can lead to the formation of ion depletion regions within the gel 48.  The total amount of DNA that must be loaded to measure a given rejection ratio is equal the detection limit (amount of perfect match DNA) multiplied by the rejection ratio (amount of mismatch DNA). 6.3. Mutation Enrichment In the previous section 10,000 fold enrichment of a target differing by a single base from background DNA was demonstrated with synthetic oligonucleotides. These synthetic oligonucleotides were purposely designed to maximize the difference in binding energy between the perfect match-probe duplex and the mismatch-probe duplex.  The ability of ssSCODA to enrich for real, biologically   103 relevant sequences has also been explored.  In these experiments cDNA was isolated from cell lines that contained either a wild type version of the EZH2 gene or a Y641N mutant, which has previously been shown to be implicated in B-cell non-Hodgkin Lymphoma56.  460 bp regions of the EZH2 cDNA that contained the mutation site were PCR amplified using fluorescent primers in order to generate fluorescently tagged target molecules that could be visualized during concentration and washing.  The difference in binding energy between the mutant-probe duplex and the wild type-probe duplex at 60°C was 2.6 kcal/mol compared to 3.8 kcal/mol for the synthetic oligonucleotides used in the previous experiments. This corresponds to a melting temperature difference of 5.2°C for the mutant compared to the wild type.  Table 7 below shows the free energy of hybridization and melting temperature for the wild type and mutants to the probe sequence. Target Binding Energy Wild Type -161.9+0.4646T Tm = 57.1°C Y641N Mutant -175.2+0.4966T Tm=62.3°C Table 7 Binding energy and melting temperatures of EZH2 targets to the gel bound probe. A 1:1 mixture of the two alleles were mixed together and separated with ssSCODA.  30 ng of each target amplicon was added to 300 μl of 0.01x   104 ssSCODA running buffer.  The target solution was immersed in a boiling water bath for 5 min then placed in an ice bath for 5 min prior to loading onto the gel cassette in order to denature the double stranded targets.  Sample was injected with an injection current of 4 mA for 7 min at 55°C.  Once injected, a focusing field of 150 V/cm with a 10 V/cm DC bias was applied at 55°C for 20 min. The result of this experiment is shown in Figure 6.3.  The behavior of these sequences is qualitatively similar to the higher Tm difference sequences shown in Figure 4.1 and in section 6.2.  The wild type (mismatch) target is completely washed from the gel while the mutant (perfect match) is driven towards the centre of the gel.  In this case the efficiency of focusing is reduced as some of the target re-annealed forming double stranded DNA that did not interact with the gel bound probes. However, as was discussed in section 5.3 this efficiency improves as the amount of loaded target is reduced.   105  Figure 6.3 Enrichment of EZH2 Y641N mutation from a mixture of wild type and mutant amplicons. Repeating the experiments of the previous section, which demonstrated 10,000 fold enrichment of target DNA from a background containing an excess of DNA differing by a single base from the target sequence was not possible as this required more sensitive detection than was available in this system.  The lower limit of detection with the optical system used was around 10 ng of singly labeled 460 bp DNA.  To measure a 10,000 fold enrichment ratio with this system would 0 min 10 min 20 min   106 require loading 100 μg of mismatched target, which is not practical to generate with PCR.  Improving the detection sensitivity would reduce the requirements on the total amount of mismatched target that needs to be loaded to measure high rejection ratios.  To this end, work is ongoing towards a method for the extraction of purified targets from the centre of the gel, which will enable the use of PCR as a detection scheme. 6.4. Methylation Enrichment The ability of ssSCODA based purification to selectively enrich for molecules with similar binding energies was demonstrated by enriching for methylated DNA in a mixed population of methylated and unmethylated targets with identical sequence.  DNA Methylation involves the addition of a methyl group to the 5’ position on the pyrmidine ring in cytosine57.  Methylation of cytosine in CpG islands is commonly used in eukaryotes for long term regulation of gene expression57, and aberrant methylation patterns have been implicated in many human diseases including cancer.  It has been shown previously that methylation of cytosine residues increases the binding energy of hybridization relative to unmethylated duplexes 58-60.  The effect is small. However, previous studies report an increase in duplex melting temperature of around 0.7°C per methylation site in a 16 nt sequence 59 when comparing duplexes with both strands unmethylated to duplexes with both strands methylated.  To my knowledge this difference has not   107 previously been exploited for the enrichment of methylated DNA as all affinity techniques that rely on single binding events would provide little to no enrichment. Fluorescently tagged PM oligonucleotides described in Table 1 were synthesized by IDT with a single methylated cytosine residue within the capture probe region (residue 50 in the PM sequence of Table 1).  DC mobility measurements of the two strands were performed to generate the velocity versus temperature curves as described in section 3.4; this curve is shown in Figure 6.4.   108  Figure 6.4 Measurement of mobility versus temperature for methylated and unmethylated targets. Data points were fit to equation Error! Reference source not found.. Fitting of these curves to equation Error! Reference source not found. suggest that the difference in binding energy is around 0.19 kcal/mol at 69°C, which is about a third of the thermal energy3.  The curve further suggests that separation of the two targets will be most effective at an operating temperature of around 69°C, where the two fragments have the greatest difference in mobility as shown below in Figure 6.5.  3 At 69°C  = 0.65kcal/mol   109  Figure 6.5 The difference between the two mobility versus temperature curves which were fit to the data from Figure 6.4.  The maximum value of this difference is at 69.5°C, which is the temperature for maximum separation while focusing under bias.  The dashed line represents extrapolation beyond the data points taken in Figure 6.4. This temperature is slightly higher than was run in previous experiments and although it should result in better discrimination, focus times are longer as the higher temperature limits the maximum electric field strength one can operate at without boiling the gel. Initial focusing tests showed that it is possible to separate of the two targets by focusing with a superimposed DC bias.  Figure 6.6 shows the result of an experiment where equimolar ratios of methylated and unmethylated targets were   110 injected into a gel, focused with a period of 5 sec at a focusing field strength of 75 V/cm and a bias of 14 V/cm at 69°C.  Figure 6.6   Separation of methylated (6-FAM, green) and unmethylated (Cy5, red) targets by focusing under bias.  The experiment was repeated with dyes swapped with identical results. Achieving enrichment by completely washing the unmethylated target from the gel proved to be difficult with the current geometry as the gel buffer interface was obscured by the buffer wells preventing the use of visual feedback to control bias fields while attempting to wash the unmethylated target from the gel.  To overcome this problem gels were cast in two steps: first a gel without probe oligos was cast in one of the arms of the gel and once the first gel had polymerized the remainder of the gel area was filled with gel containing probe oligos.  The gels were cast such that the interface between the two was visible with the fluorescence imaging system.  This system allowed one to adjust in real time the bias voltage so that the unmethylated target would enter the gel without oligos   111 and be quickly washed from the gel, while the methylated target could be retained in the focusing gel.  Figure 6.7 shows the result of this experiment.  Figure 6.7 Washing of unmethylated DNA from the gel.  Top two images were taken after an intial focus but before attempts to wash.  The bottom two images were taken after washing the unmethylated target from the gel.  All images were taken with the same gain and shutter settings. In this experiment a 100 fold excess of unmethylated target was injected into the gel, focused to the centre without any wash fields applied.  The targets were then focused with a bias field to remove the unmethylated target, and finally focused to the centre of the gel again for fluorescence quantification.  Fluorescence quantification of these images indicates that the enrichment factor was 102 fold Unmethylated Methylated Initial focus prior to wash: 10pmol unmethylated, 0.1pmol  methylated  Final focus post wash   112 with losses of the methylated target during washing of 20%.  This experiment was repeated with the dye molecules swapped (methylated Cy5 and unmethylated 6- FAM) with similar results. Here I have demonstrated for the first time enrichment of methylated DNA using the difference in binding energy between a methylated versus unmethylated target strand and its complementary probe.  Existing methods for detection and enrichment of methylated DNA include: antibody based enrichment, which selects for methylated DNA based on methylation density and is sequence independent; restriction digestion of unmethylated DNA, which is specific only to regions for which there exists a methylation site; and bisulfite conversion where methylated cytosine residues are converted to uracil – a method that has problems with efficiency as the bisulfite treatment tends to degrade nucleic acids.  The technique presented here has unique properties in that it is sequence selective, can interrogate any sequence, and is capable of enriching for a single methylated cytosine residue without modification of the target. 6.5. ssSCODA Yield vs Purity Existing hybridization based enrichment techniques that rely on a single hybridization event, such as bead based or solid phase capture techniques cannot perform much better than a five fold enrichment11,22.  This is a result of the fact   113 that when thermodynamic equilibrium is achieved between the perfect match target, mismatched target, and probe, there will always be some mismatched target bound to the probes. The closer the binding energy of the perfect match, the greater will be the fraction of probe sites occupied by mismatch targets. Increasing the stringency of hybridization conditions can reduce the amount of mismatch bound, but cannot eliminate it without dramatically reducing the amount of perfect match bound; higher purity comes at the expense of lower yield.  Because ssSCODA relies on repeated interactions between target and probe to generate a non-dispersive velocity field for target molecules, while generating a dispersive field for contaminants (so long as a bias is applied) we are able to achieve high specificity without sacrificing yield.  If one assumes that the final focus spot is Gaussian, which is justified by calculating the spot size for a radial velocity field balanced against diffusion41, then the spot will extend all the way out to the edge of the gel.  Here diffusion can drive targets off the gel where there is no restoring focusing force and an applied DC bias will sweep targets away from the gel where they will be lost.  In this manner the losses for ssSCODA can scale with the amount of time one applies a wash field; however the images used to generate Figure 5.2  indicate that the spot has a FWHM of 300 um and under bias it sits at approximately 1.0 mm from the gel centre.  If we assume that there is 10 fmol of target in the focus spot, then the concentration at the edge of the gel where a bias is applied is 1e-352 M; there are essentially zero   114 target molecules present at the edges of the gel where they can be lost under DC bias.  This implies that the rate at which losses accumulate due to an applied bias is essentially zero.  The system is not lossless however.  Target can adsorb to the sample well prior to injection or it can be run off the edge of the gel during injection.  Double stranded targets can re-anneal before or during focusing, which prevents them from focusing and allows them to be washed off with the contaminating molecules.  If the target is to be extracted from the gel for subsequent analysis there may be losses associated with the extraction process.  A key feature of ssSCODA is that all of these losses are decoupled from the purity, which is not true of other hybridization based purification schemes.   115 7. Future Work The demonstrations of ssSCODA-based enrichment presented in the previous chapter show great promise for this platform as a tool for highly specific enrichment of nucleic acids.  Moving forward from these demonstrations towards a tool suitable for routine laboratory use requires the development of reliable methods of extracting purified targets from ssSCODA gels.  Furthermore the combination of high specificity and small volume of the final focus spot (10 nl in Figure 5.2) presents a unique opportunity to optically detect small numbers of target molecules without the need for PCR amplification.  The utility of ssSCODA would be further enhanced by the ability to enrich for multiple sequences simultaneously.  Finally, it should be possible to use the more general technique of affinity SCODA (of which ssSCODA is a subset) to purify any charged molecule for which an affinity matrix can be fabricated. 7.1. Sample Extraction for Offline Detection The development of a reliable and efficient method for extracting purified target DNA from a gel would enable the use of routine PCR for detection of purified targets with sensitivity down to a single copy of the target.  In electrophoretic SCODA diffusive extraction is used to extract target molecules from the centre of a SCODA gel.  Here the gel is cast with a hole at the central focus location and   116 filled with the running buffer solution as shown in Figure 7.1 below (reprinted from  41).  This configuration allows one to focus under bias to wash contaminants out of the gel then focus the target DNA into the central buffer well by turning off the bias fields.  Figure 7.1 A cross section of a SCODA gel illustrating diffusive extraction.  A gel (grey) is cast with a small hole at the centre and filled with buffer (blue).  DNA molecules will focus into the central buffer region where they can be extracted.  Reprinted from 41. This has proved to be an efficient method of extracting targets from electrophoretic SCODA gels that are typically between 1 mm and 5 mm thick.  As discussed in section 3.5 ssSCODA requires the use of gels that are 0.1 mm thick or less in order to achieve adequate thermal performance.  Simply adding 0.1 mm of liquid to the well is not possible as capillary forces will result in the liquid being drawn up the sides of the well.  Adding a larger volume of liquid results in poor wash performance as contaminant molecules can become trapped in the extraction well above the plane of the gel where the electric fields are low requiring a long time to wash from the gel.  Initial attempts at diffusive extraction   117 have been done without liquid in the well and the well sealed to prevent the gel from drying out during sample injection and washing.  Liquid is then added after contaminants have been washed from the gel for the final focusing step. Preliminary results with this configuration suggest that this method of extraction should be feasible, extraction efficiencies of 80% have been measured and as few as 1000 copies of target have successfully been PCR amplified; there has however been poor run to run repeatability.  The source of run to run variations in extraction efficiency and purity is thought to be a result of a combination of variations in the thickness and flatness gel cassettes, which ultimately leads to variations in focus locations under bias resulting in variable wash efficiency and extraction efficiency. Variable gel cassette geometry can lead to differences in gel temperatures from run to run.  In the current system gel temperature is controlled by placing the gel cassette in thermal contact with a temperature controlled spreader plate as illustrated in Figure 3.3.  During ssSCODA purification the gel temperature will be determined by a balance between the rate of Joule heating in the gel and heat extraction to the spreader plate.  The gel temperature is therefore sensitive to the thermal interface resistance between the gel cassette and the spreader plate, which is in turn dependent on the flatness of the gel cassette: the flatter the gel cassette the lower the thermal interface resistance due to more intimate contact with the   118 spreader plate.  Because the strength of focusing is highly temperature dependent, a property that is normally exploited to achieve separation of similar targets, unwanted variations in temperature can lead to variable wash and extraction efficiencies. There are three approaches currently being explored to improve the repeatability of wash and extraction efficiency.  The first is the use of fluorescent surrogate molecules that focus similarly to targets but will not amplify in subsequent PCR reactions allowing one to use optical feedback to control focusing conditions in real time.  The second is the development of gel cassettes that can be fabricated with tighter flatness tolerances for more consistent thermal contact with the spreader plate.  And finally methods of directly measuring gel temperature during focusing are being explored, including infrared imaging, the use of temperature sensitive dyes, and measuring the impedance of the gel, which depends on temperature. 7.2. Online Detection An alternative to extraction followed by off line amplification and detection is to perform online detection of the target in the gel cassette without the need for extraction.    Because of the extreme specificity achieved with ssSCODA, it is not necessary to rely on the specificity of PCR based amplification to detect specific sequences provided one can detect the targets at the final focus location. The final   119 focus spots shown in Figure 5.2, Figure 6.1, and Figure 6.7 are approximately 10 nl in volume (300 μm FWHM in a 100 μm thick gel).  Sensitivities of laser induced fluorescence systems with low cost optics and detectors typically fall in the range of 10-11 M, 61,62 which results in detection limit of approximately 105 flurophores in a 10 nl volume.  Using multiple dye labels per target molecule (for example: SYBR, YOYO, or multiply labeled oligonucleotide probes) and choosing a high copy number RNA target one could potentially use ssSCODA for sequence based detection of 10's of cells without the need for further amplification.  This would require integration of a laser induced fluorescence detection system along with careful choice of gel cassette and surrounding materials to minimized background fluorescence. An alternate strategy for further improving the signal to noise ratio of fluorescence detection with a SCODA based concentration system is to employ a lock-in detection technique 63,64.  In these techniques the unknown signal is modulated at a known frequency, and when detected the unknown signal is multiplied by the modulating signal and integrated to generate the output signal:  O = 1 T Z T 0 f(t) ¤ g(t)dt [7.1] Where O is the output signal, f(t) the unknown signal, g(t) the known reference signal and T  the total integration time.  If f(t) and g(t) vary periodically they can   120 be rewritten as a Fourier series, then due to the orthogonality of sine functions when we integrate their product, only the components of f(t) and g(t) that have the same frequency will result in a non-zero integral.  This technique is in effect a method of generating an extremely narrow band pass filter centered around the frequency of the modulating signal with a bandwidth that is inversely proportional to the length of time over which one integrates for.  With SCODA based concentration the focus spot will orbit around the centre of the gel at the period of the applied electric field oscillations.  It is possible to use the applied electric field as the reference signal, g(t), and use it to detect the oscillating fluorescence signal from the moving focus spot.  Because SCODA generates a non-dispersive velocity field, it is possible to integrate for very long times without the focus spot diffusing away and reducing the intensity of the detected fluorescence signal.  We have performed early proof of concept work of this technique and shown a 100 fold signal to noise ratio improvement.  This early work was done without taking care to reduce initial background levels prior to applying the lock in detection technique.  Future work will involve testing the ultimate detection limits with this scheme with careful engineering of the system to minimize background fluorescence. To further improve the sensitivity of fluorescence based techniques it should also be possible to perform signal amplification of the concentrated targets at the   121 center of the gel.  It should be possible to integrate microfluidic flow channels into an ssSCODA cassette that could be used to introduce PCR reagents to the central focus location where amplification of the target could be performed. Alternatively, one could also use an enzymatic based fluorescence amplification system.  In these schemes a non-fluorescent substrate is converted to a fluorescent molecule by enzymes coupled to the target molecules 65.  This type of amplification has much lower specificity than PCR based amplification, however given the specificity demonstrated for ssSCODA, additional specificity from the signal amplification step should not be necessary. 7.3. Multiplexed Enrichment All of the experiments presented in this dissertation were performed on a single channel system to purify a single target sequence.  The utility of ssSCODA would be improved if it were possible to enrich for more than one sequence per sample. The images in Figure 5.2 show that it is possible to concentrate target DNA at probe concentrations as low as 1 uM, as well as with probe concentrations as high as 100 uM.  This suggests the possibility of performing multiplexed concentration by simply polymerizing gels with multiple probe sequences.  This would allow one to simultaneously enrich for up to 100 different sequences using a single gel. Additionally it is possible to run multiple gels in parallel from the same power   122 supply.  This requires careful control of gel impedances, and gel temperatures to ensure that each gel will focus its targets similarly. 7.4. Other Applications of Affinity SCODA Beyond the immediate work required to move from the initial demonstrations presented here towards a robust tool for general laboratory there are also interesting research questions worth pursuing are related to other applications of affinity SCODA.  All of the experimental work presented in this thesis is related to sequence specific SCODA, which is one embodiment of the broader technique of affinity SCODA.  There are potentially an unlimited number of applications for affinity SCODA as any charged molecule that has an affinity to the SCODA matrix can be purified in this manner.    123 8. Conclusions This work has demonstrated the ability to perform at least 10,000 fold enrichment of a target sequence in the presence of excess contaminating sequences differing by a single base.  Additionally, the target sequence is concentrated 25,000 fold from an input volume of 250 μl to an output volume of 10 nl.  It should be noted that there is no fundamental limit to the input volume, as larger input volumes simply require more time to electrokinetically inject target DNA into the ssSCODA gel.  Performing this level of enrichment and concentration prior to PCR based detection has the effect of both reducing the sequence complexity of the template DNA, which relaxes the specificity requirements of the PCR reaction, and increasing the effective volume that the PCR reaction can sample, which is equivalent to increasing the sensitivity of the PCR reaction. In addition to the exceptional sequence enrichment performance, ssSCODA has proved to have a unique capability of enriching for target sequences based on methylation status.  It is possible to exploit the small increase in binding energy imparted to a target-probe duplex by a single methylated cytosine residue to enrich for a methylated target.  It was demonstrated that ssSCODA is capable of 100 fold enrichment of a methylated target out of a background containing a 100 fold excess of unmethylated targets that are identical in sequence.  This is the first demonstration of hybridization based enrichment of unmodified methylated DNA   124 and differs fundamentally from the three leading methods for analysis of methylated DNA in that it is capable of enriching for any sequence containing a methylated cytosine residue without the need for chemical modification of the target DNA. The affinity SCODA based method of sequence and methylation enrichment presented in this dissertation promises to be an enabling technology for the detection of nucleic acids in applications where the sequence of interest is present in low abundances and overwhelmed by a large excess of similar sequences. Some application areas include the non-invasive detection of nucleic acid tumor biomarkers from body fluids where mutated tumor DNA is typically overwhelmed by wild type DNA; non-invasive pre-natal diagnoses of fetal genetic abnormalities using maternal blood, where fetal DNA is overwhelmed by maternal DNA; and detection and monitoring of pathogenic microorganisms where DNA from pathogenic species can be overwhelmed by DNA from related non-pathogenic species and the host.  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