Activation energy of single-stranded DNA moving through cross-linked polyacrylamide gels at 300 V/cm effect of temperature on sequencing rate in high-electric-field capillary gel electrophoresis

In DNA sequencing, single-stranded DNA fragments are separated by gel electrophoresis. This separation is based on a sieving mechanism where DNA fragments are retarded as they pass through pores in the gel. In this paper, we present the mobility of DNA sequencing fragments as a function of temperature; mobility is determined in 4% T LongRanger gels at an electric field of 300 V/cm. The temperature dependence is compared with the predictions of the biased reptation model. The model predicts that the fragment length for the onset of biased reptation with stretching increases with the square of temperature; the data show that the onset of biased reptation with stretching decreases with temperature. Biased reptation fails to model accurately the temperature dependence of mobility. We analyzed the data and extracted the activation energy for passage of sequencing fragments through the gel. For fragments containing less than ca. 200 bases, the activation energy increases linearly with the number of bases at a rate of 25 J/mol per base; for longer fragments, the activation energy increases at a rate of 6.5 J/mol per base. This transition in the activation energy presumably reflects a change in conformation of the DNA fragments; small fragments exist in a random coil configuration and larger fragments migrate in an elongated configuration.     

Reptation-breathing theory of pulsed electrophoresis: dynamic regimes, antiresonance and symmetry breakdown effects

We apply the concepts of tube and reptation to the pulsed electrophoresis of DNA, considering both biased reptation and "breathing" modes (internal modes of the chain). Using suitable preaveraging approximations, analytical expressions are derived which relate displacement in crossed field electrophoresis to molecular weight, field strength, field period, pore size of the gel, and the angle between the field. These expressions provide scaling laws for the change of mobility when one (or more) of the parameters is varied as well as "universal" velocity versus molecular weight versus pulse time curves. These results are quantitatively compared with experiments. At some point which depends on field angle, field strength and chain length, however, we predict a failure of this model due to symmetry breakdown and loss of ergodicity. Qualitatively, this should lead to considerable band spreading and/or splitting of the highest DNA bands into two bands migrating sideways from the diagonal. The case of field inversion is also investigated. It is shown that only breathing modes can explain the strong differences in mobility experienced by chains of different length when opposite fields of equal amplitude are applied: the "trapping" of chains in conformations of low mobility is associated with an antiresonance-like coupling between the external field and the internal modes.     

Universal interpolating function for the dispersion coefficient of DNA fragments in sieving matrices

The separation of DNA fragments by (slab or capillary) gel electrophoresis has been studied extensively. To characterize the separation achieved by such systems, one needs to understand the impact (and their dependency upon the experimental quantities) of two physical parameters: the electrophoretic mobility mu and the diffusion coefficient D. Three different regimes have been shown to exist for both mu and D: the Ogston regime, the reptation regime and the reptation with orientation regime (note that separation is only possible for the first two regimes). In the small electric field limit, both mu and D are apparently well described by theories for all three regimes. Unfortunately this results in disjointed scaling laws and no theory-based general equations can apply to all regimes. Recently, an empirical interpolating formula has been proposed that adequately fits the low electric field mobility mu of dsDNA fragments across all three regimes and is compatible with accepted theories. In this article we review and clarify the current state of knowledge regarding the size dependence of the mobility and the diffusion coefficient and propose an interpolating formula for molecular size dependence of the low field diffusion coefficient D. With formulas for both the mobility and the diffusion coefficient as a function of the experimental conditions one could, in principle, optimize any gel/polymer matrix-based electrophoresis system for a wide range of DNA molecular sizes.     

Modeling ssDNA electrophoretic migration with band broadening in an entangled or cross-linked network

We use a coarse-grained model proposed by Graham and Larson based on the temporary network model by Schieber et al.. [1] to simulate the electrophoretic motion of ssDNA and corresponding band broadening due to dispersion. With dimensionless numbers reflecting the experimental physical properties, we are able to simulate ssDNA behavior under weak to moderate electric field strengths for chains with 8-50 entanglements per chain ( approximately 1000-8500 base pairs), and model smoothly the transition from reptation to oriented reptation. These results are fitted with an interpolation equation, which allows the user to calculate dimensionless mobilities easily from input parameters characterizing the gel matrix, DNA molecules, and field strengths. Dimensionless peak widths are predicted from mobility fluctuations using the central limit theorem and the assumption that the mobility fluctuations are Gaussian. Using results from previous studies of ssDNA physical properties (effective charge xiq and Kuhn step length b(K)) and sieving matrix properties (pore size or tube diameter a), we give scaling factors to convert the dimensionless values to "real" experimental values, including the mobility, migration distance, and time. We find that the interpolation equation fits well the experimental data of ssDNA mobilities and peak widths, supporting the validity of the coarse-grained model. The model does not account for constraint release and hernia formation, and assumes that the sieving network is a homogeneous microstructure with no temperature gradients and no peak width due to injection. These assumptions can be relaxed in future work for more accurate prediction.     

Mobility, diffusion and dispersion of single-stranded DNA in sequencing gels

Electrophoresis of single-stranded DNA in denaturing polyacrylamide gels is presently a standard procedure for the sequencing of DNA fragments. A thorough understanding of the factors that determine the resolution of DNA fractionated in polyacrylamide gels is necessary to optimize the performance of DNA sequencers. Significant research on the mobility of double-stranded (ds)DNA molecules in agarose and polyacrylamide gels has been performed, and the phenomenon of band broadening of single-stranded (ss)DNA fragments in DNA sequencing gels has received attention only recently. In this paper, we present a detailed study of mobility, diffusion and dispersion of ssDNA in sequencing gels as a function of molecular size, gel concentration and electric field strength. DNA mobility is shown to be essentially independent of electric field in the range of 0-60 V/cm. The band broadening is greatly enhanced in the presence of an electric field and the dispersion coefficient (DE) can be an order of magnitude higher than the field-free diffusion coefficient. The measured migration parameters approximately follow the predictions of the biased reptation including fluctuations (BRF) theory. However, deviations due to nonidealities of the separation conditions are observed. The measured migration parameters can be used to optimize the performance of separation systems.     

Conformation dependence of DNA electrophoretic mobility in a converging channel

The electrophoresis of λ‐DNA is observed in a microscale converging channel where the center‐of‐masses trajectories of DNA molecules are tracked to measure instantaneous electrophoretic (EP) mobilities of DNA molecules of various stretch lengths and conformations. Contrary to the usual assumption that DNA mobility is a constant, independent of field and DNA length in free solution, we find DNA EP mobility varies along the axis in the contracting geometry. We correlate this mobility variation with the local stretch and conformational changes of the DNA, which are induced by the electric field gradient produced by the contraction. A “shish‐kebab” model of a rigid polymer segment is developed, which consists of aligned spheres acting as charge and drag centers. The EP mobility of the shish‐kebab is obtained by determining the electrohydrodynamic interactions of aligned spheres driven by the electric field. Multiple shish‐kebabs are then connected end‐to‐end to form a freely jointed chain model for a flexible DNA chain. DNA EP mobility is finally obtained as an ensemble average over the shish‐kebab orientations that are biased to match the overall stretch of the DNA chain. Using physically reasonable parameters, the model agrees well with experimental results for the dependence of EP mobility on stretch and conformation. We find that the magnitude of the EP mobility increases with DNA stretch, and that this increase is more pronounced for folded conformations.     

Anomalously fast migration of triplet-repeat DNA in capillary electrophoresis with linear polymer solution

We investigated the capillary electrophoretic behavior of single-stranded DNA fragments in methylcellulose solution, and found that triplet-repeat DNA showed anomalously faster mobilities than DNA markers with random sequence. Through the further study on the electrophoretic data, reptation model is proven appropriate to describe the migration of DNA under our experimental conditions. Accordingly, with the equations based on reptation theory, we could obtain the persistence length of DNA fragments and find that these values of triplet-repeat DNAs are larger than that of DNA markers with random sequence, which means the former DNAs are less flexible than the latter ones when they migrate in the electric field. This phenomenon is supposed to result from the characteristic higher-order structure formed by GC base pairs within triplet-repeat DNA, which is further proven by the resumed migration order in accordance with DNA size when the denaturant is added into the sieving matrix.     

Capillary electrophoresis in sieving matrices: selectivity per base, mobility slope, and inflection slope

We compare the migration behavior of DNA sequencing fragments in hydroxyethyl cellulose (HEC) to the theoretical model of migration in the reptation mode. Good agreement was found for the mobility curve. We derived empirical equations for the relationship between selectivity per base and sieving matrix concentration and between the mobility slope and matrix concentration. We propose the inflection slope, i.e., the slope of the log-log mobility curve at its inflection point, as the quantitative parameter of sieving performance.     

DNA electrophoresis in confined, periodic geometries: a new lakes-straits model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimm's approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.     

Effect of nonparallel alternating fields on the mobility of DNA in the biased reptation model of gel electrophoresis

Chromosome-size DNA molecules can now be separated using a variety of pulsed field gel electrophoresis techniques. In this article, we study the predictions of the biased reptation model concerning the effect of two pulsed fields, making an arbitrary angle, on the power of separation of gel electrophoresis. Separation is predicted to be largely enhanced for obtuse angles, in agreement with experiments. Interestingly, very large molecules, which are not separated by pulsed fields, are predicted not to migrate along the gel diagonal for fairly long periods of time. Finally, we discuss the optimization of these techniques using the results of the theory, and the limitations of the latter when fluctuations and intramolecular modes probably dominate the system.     

Confinement effects on electromigration of long DNA molecules in an ordered cavity array

Confinement effects on the electromigration of long dsDNA molecules in an array of well-ordered, molecular sized cavities interconnected by nanopores are described. The array was prepared by replicating the structure of a colloidal crystal of microspheres in a polymer matrix. Both conformation and mobility studies show that the electrophoretic behavior of large DNA molecules is distinct from that in gels and other microfabricated sieves, showing a peak in mobility versus electric field, and an inversion in the separation order with field strength. A simple model was proposed to interpret this unexpected observation qualitatively. We conclude that the molecular behavior of DNA can be modified by the combination of entropic effect and electric trapping as a consequence of both unique geometry and conductivity of this cavity array material. This approach provides insights for design and optimization of on-chip molecular sieving structures for rapid separation of long DNA molecules. It may lead to a promising material for manipulation and size fractionation of other biological macromolecules.     

Comparison of RNA, single-stranded DNA and double-stranded DNA behavior during capillary electrophoresis in semidilute polymer solutions

We present a study of the separation of RNA, single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) in semidilute linear hydroxyethylcellulose (HEC) solution. Our results strive to provide a better understanding of the mechanisms of nucleic acid migration during electrophoresis in polymer solutions under native and denaturing conditions. From a study of the dependence of mobility on chain length and applied electric field, we found that RNA and ssDNA show better separation and higher resolution over a larger range of sizes compared to dsDNA. In addition, RNA reptation without orientation extends to longer chain lengths in comparison to ssDNA, possibly as a result of different type of short-lived secondary structure formations. Such a comparative study between nucleic acid capillary electrophoresis helps to optimize RNA separation and provides better understanding of RNA migration mechanisms in semidilute polymer solutions under denaturing conditions.     

Computer simulation of DNA gel electrophoresis: influence of solid friction on linear and circular chains

The effect of solid friction between DNA molecules and gel fibres during gel electrophoresis has been studied using Brownian dynamics simulations. To investigate the effect of the topology of the polyelectrolyte chains, we have studied both linear and circular molecules. The results show that the migration properties of linear molecules seem to be almost uneffected by solid friction. There is, however, a significant effect on the mobility of circular molecules of the same size. Increasing the electric field strength increases the mobility of the linear molecules while for the circular chains, the mobility goes through a maximum when friction is included.     

Characteristics of migration patterns of DNA oligomers in gels and the relationship to the question of intrinsic DNA bending

We have developed a methodology that is capable of quantitatively describing the electrophoretic mobility patterns of oligomeric B-DNA through polyacrylamide gels (PAG) in the presence of varying concentration of the organic solvent 2-methyl-2,4-pentanediol (MPD), used routinely to induce DNA crystallization. The model includes the ion atmosphere and its polarization, electrostatic excluded volume, hydrodynamic interactions, and fluctuation effects that characterize the overall size of the migrating polyion. Using this model, and by critically examining the mobility patterns of linear random-sequence B-DNA molecules in PAG as a function of MPD, we address the question of the discrepancy between current models used to explain the molecular origins of A-tract-induced DNA bending. Direct analysis of the mobility of B-DNA oligomers on PAG, and comparison to the mobility of A-tract-containing oligomers, shows a significant apparent effect of MPD on the mobility of generic B-DNA sequences, which is larger than the effect on A-tract-containing oligomers. The effect is chain-length dependent, especially at lower MPD concentration. Thus, the apparent reduction in gel mobility, as a function of MPD, is not unique to A-tract regions or A-tract-containing molecules. However, our analysis suggests that MPD molecules are probably excluded from the surface of both B-DNA and A-tract molecules. This is supported by circular dichroism studies on A-tract and B-DNA molecules in solutions containing various MPD concentrations.     

DNA electrophoresis in agarose gels: effects of field and gel concentration on the exponential dependence of reciprocal mobility on DNA length

Electrophoretic mobilities of DNA molecules ranging in length from 200 to 48 502 base pairs (bp) were measured in agarose gels with concentrations T = 0.5% to 1.3% at electric fields from E = 0.71 to 5.0 V/cm. This broad data set determines a range of conditions over which the new interpolation equation nu(L) = (beta+alpha(1+exp(-L/gamma))(-1) can be used to relate mobility to length with high accuracy. Mobility data were fit with chi(2) > 0.999 for all gel concentrations and fields ranging from 2.5 to 5 V/cm, and for lower fields at low gel concentrations. Analyses using so-called reptation plots (Rousseau, J., Drouin, G., Slater, G. W., Phys. Rev. Lett. 1997, 79, 1945-1948) indicate that this simple exponential relation is obeyed well when there is a smooth transition from the Ogston sieving regime to the reptation regime with increasing DNA length. Deviations from this equation occur when DNA migration is hindered, apparently by entropic-trapping, which is favored at low fields and high gel concentrations in the ranges examined.     

Simultaneous measurements of the electrophoretic mobility,diffusion coefficient and orientation of dsDNA during electrophoresis in polymer solutions

We determined simultaneously the electrophoretic mobility, diffusion coefficient D and molecular orientation during electrophoresis of dsDNAs in polymer solutions ranging from the dilute to the semidilute regime. We established, for the first time, master scaling laws for the diffusion coefficient showing a universal behavior. A model found in the literature designed for the dilute regime allows, surprisingly, to describe the mobility data over the whole range of concentrations studied and at the same time the biased reptation with fluctuations (BRF) failed for the semidilute regime, even when constraint release of the network was taken into account. These quantitative determinations of D are of practical interest to evaluate band broadening during capillary electrophoresis and provide data for stimulating investigation of the physics of DNA electrophoretic motion.     

Two tube models of rubber elasticity

Polymer entanglements lead to complicated topological constraints and interactions between neighboring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they effectively confine each individual chain in a tube-like geometry. In polymer networks, due to crosslinks preventing the global reptation and constraint release, entanglements acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. In this article we discuss two different models of rubber elasticity, both utilizing the reptation ideas. First, we apply the classical ideas of reptation statistics to calculate the effective rubber-elastic free energy of an entangled rubbery network. In the second approach, we examine the classical Rouse dynamics of chains with quenched constraints at their ends by crosslinks, and along the primitive path by entanglements. We then proceed to average a microscopic stress tensor for the network system and present it in a manageable form in the equilibrium t → ∞ limit. Particular attention is paid to the treatment of compressibility and hydrostatic pressure in a sample with open boundaries. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2679–2697, 2006     

Orientation of DNA and the agarose gel matrix in pulsed electric fields

Transient electric birefringence has been used as an analytical tool to study the orientation of DNA in agarose gels, and to study the orientation of the matrix alone. The sign of the birefringence of DNA oriented in an agarose gel is negative, as observed in free solution, indicating that the DNA molecules orient parallel to the direction of the electric field. If the median pore diameter of the gel is larger than the contour length of the DNA molecule, the DNA effectively does not see the matrix and the birefringence relaxation time is the same as observed in free solution. However, if the median pore diameter of the gel is smaller than the contour length of the DNA, the DNA molecule becomes stretched as well as oriented. For DNA molecules of moderate size (less than or equal to 4 kb), stretching in the gel causes the birefringence relaxation times to increase to the values expected for fully stretched molecules. Complete stretching is not observed for larger DNA molecules. The orientation and stretching of DNA molecules in the gel matrix indicates that end-on migration, or reptation, is a likely mechanism for DNA electrophoresis in agarose gels. When the electric field is rapidly reversed in polarity, very little change in the orientation of the DNA is observed if the DNA molecules were completely stretched and had reached their equilibrium orientation before the field was reversed in direction. Hence completely stretched, oriented DNA molecules are able to reverse their direction of migration in the electric field with little or no loss of orientation. However, if the DNA molecules were not completely stretched or if the equilibrium orientation had not been reached, substantial disorientation of the DNA molecules is observed at field reversal. The forced rate of disorientation in the reversing field is faster than the field-free rate of disorientation. Complicated patterns of reorientation can be observed after field reversal, depending on the degree of orientation in the original field direction. The effect of pulsed electric fields on the orientation of the agarose gel matrix itself was also investigated.(ABSTRACT TRUNCATED AT 400 WORDS)     

Do orientation effects contribute to the molecular weight dependence of the free solution mobility of DNA?

The free solution mobility of DNA increases with increasing molecular weight and then levels off and becomes constant at molecular weights above approximately 400 bp (Stellwagen, N. C., Gelfi, C., Righetti, P. G., Biopolymers 1997,42, 687-703). To investigate whether the increase in mobility could be attributed to an increased orientation of the larger DNA molecules in the electric field, the free solution mobility of DNA was measured by capillary electrophoresis as a function of electric field strength. Mixtures containing 20-, 118- and 422-bp DNA molecules, and 20-, 422- and 2116-bp DNAs, were studied. If the larger DNA molecules in each mixture were oriented by the electric field, their mobilities should increase with electric field strength faster than the mobility of the 20-bp oligomer, which is too small to be oriented by the electric fields used in this study. Instead, the ratios of the mobilities of the 118-, 422- and 2116-bp fragments to the mobility of the 20-bp oligomer were independent of electric field strength. Hence, orientation effects are not important for DNA molecules up to 2 kbp in size, in electric fields up to 500 V/cm in amplitude. An explanation is suggested.     

Theory for the capillary electrophoretic separation of DNA in polymer solutions

We present a mathematical model based on the models of Hubert et al. [Macromolecules 29 (1996) 1006] and Sunada and Blanch [Electrophoresis, 19 (1998) 3128] to describe the electrophoretic mobility of DNA by a transient entanglement coupling mechanism. The proposed model takes into account the interactions between molecules in the capillary and the cross-section of collision between DNA and polymer molecules. The results show that the calculated values agree remarkably well with our electrophoretic mobility data.