Gel electrophoretic mobility of single-stranded DNA: the two reptation field-dependent factors

The reptation model is the dominant theory in understanding the electrophoretic separation of single-stranded DNA molecules in gels or entangled polymer solutions. Recently, we showed that the Ogston and reptation regimes are separated by an entropic trapping regime at low field intensities. Here, we report the first comparison of the field-dependent part of the DNA mobility for both small and long reptating molecules. We show that both mobilities increase linearly with field intensity, with the mobility of the longer (comigrating) fragments increasing faster than that of the smaller ones. We compare our results to the predictions of the biased reptation model.     

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.     

Analysis of limiting factors of DNA band separation by a DNA sequencer using fluorescence detection.

The factors affecting the electrophoretic separation of DNA bands in DNA base sequencing using fluorescence detection are analyzed. All the factors contributing to DNA band spacing and band width are evaluated; DNA diffusion and thermal effects on gels are the main considerations. The dependence of the gel's electrical resistivity on gel temperature and the variation of temperature over gel thickness are associated with a broadening of DNA band width. As a result of the analyses the maximum separable base number is represented as a function of various electrophoretic variables. The best separations are possible with an electric field strength corresponding to gel thickness. The maximum separable base number increases as the gel thickness decreases. It also increases as the migration distance increases, but it becomes saturated and has an upper limit when the migration distance is long. This upper limit increases as gel thickness decreases. DNA fragments with 600 and 601 bases can be completely separated from each other under optimum conditions for a 0.2 mm thick gel plate. Furthermore, using the band spacing information, under the same conditions, 750 bases could be assigned separately.     

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.     

Separation performance of single-stranded DNA electrophoresis in photopolymerized cross-linked polyacrylamide gels

Considerable effort has been directed toward optimizing performance and maximizing throughput in ssDNA electrophoresis because it is a critical analytical step in a variety of genomic assays. Ultimately, it would be desirable to quantitatively determine the achievable level of separation resolution directly from measurements of fundamental physical properties associated with the gel matrix rather than by the trial and error process often employed. Unfortunately, this predictive capability is currently lacking, due in large part to the need for a more detailed understanding of the fundamental parameters governing separation performance (mobility, diffusion, and dispersion). We seek to address this issue by systematically characterizing electrophoretic mobility, diffusion, and dispersion behavior of ssDNA fragments in the 70-1,000 base range in a photopolymerized cross-linked polyacrylamide matrix using a slab gel DNA sequencer. Data are collected for gel concentrations of 6, 9, and 12%T at electric fields ranging from 15 to 40 V/cm, and resolution predictions are compared with corresponding experimentally measured values. The data exhibit a transition from behavior consistent with the Ogston model for small fragments to behavior in agreement with the biased reptation model at larger fragment sizes. Mobility data are also used to estimate the mean gel pore size and compare the predictions of several models.     

Physical interpretation of the L(r) parameter in the theory for the gel electrophoresis of partially denatured DNA

Partial strand melting of dsDNA during gel electrophoresis typically results in an abrupt reduction of mobility. Several DNA analysis technologies are based on this phenomenon. Inspired by the de Gennes' theory for the reptation of branched polymers in gels, Lerman et al. (Ann. Rev. Biophys. Bioeng. 1984, 13, 399-423) proposed a mathematical expression to predict this reduced mobility. The latter contains only two parameters: the average number of denatured bases p (which can be obtained using a theory for DNA melting) and a constant L(r). However, there is confusion in the literature regarding the physical interpretation of L(r) and little is known about its dependence upon experimental parameters. The purpose of this short communication is to derive an explicit equation for the parameter L(r) from the de Gennes theory of reptation. Our derivation shines light on the meaning of L(r), clarifies the scope of the underlying approximations, and makes predictions about the dependence of L(r) upon the gel pore size and the persistence length of ssDNA.     

Mobility and activation energy of single-stranded DNA in denaturing cross-linked polyacrylamide slab gels

An original apparatus based on laser-induced fluorescence detection is presented. One lane migration combined to four equidistant detection points allows the study of the dynamics of DNA bands during electrophoresis. We focus this article on the study of the mobility of DNA sequencing fragments as a function of temperature; mobility is determined in 4% T, 5% C and 4.3% T, 5% C cross-linked polyacrylamide gels at an electric field of 45 V/cm [T=(g acrylamide+g N,N'-methylenebisacrylamide)/100 ml solution; C=g N,N'-methylenebisacrylamide/% T]. Activation energy has been investigated under these experimental conditions with a temperature varying from 25 to 50 degrees C. The activation energy for migration through the cross-linked polyacrylamide gel decreases with fragment length under our experimental conditions and it varies along the migration.     

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.     

Low-cost, high-sensitivity laser-induced fluorescence detection for DNA sequencing by capillary gel electrophoresis.

A low cost, 0.75-mW helium neon laser, operating in the green region at 534.5 nm, is used to excite fluorescence from tetramethylrhodamine isothiocyanate-labelled DNA fragments that have been separated by capillary gel electrophoresis. The detection limit (3 sigma) for the dye is 500 ymol [1 yoctomole (1 ymol) = 10(-24) mol] or 300 analyte molecules in capillary zone electrophoresis; the detection limit for labeled primer separated by capillary gel electrophoresis is 2 zmol [1 zeptomole (1 zmol) = 10(-21) mol]. The Richardson-Tabor peak-height encoded sequencing technique is used to prepare DNA sequencing samples. In 6% T, 5% C acrylamide, 7 M urea gels, sequencing rates of 300 bases/hour are produced at an electric field strength of 200 V/cm; unfortunately, the data are plagued by compressions. These compressions are eliminated with addition of 20% formamide to the sequencing gel; the gel runs slowly and sequencing data are generated at a rate of about 70 bases/hour.     

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.     

A computer simulation of trapping electrophoresis

The gel electrophoretic migration of streptavidin-DNA complexes is severely altered by the phenomenon known as “trapping electrophoresis.” We present a first computer simulation study of this process. Our simulations use the very efficient biased reptation algorithm. The steady state is characterized by a large increase in band broadening and interband separation. However, we also find that for a narrow range of molecular sizes, the separation power of gel electrophoresis is greatly increased. We discuss the implications of our findings for the possible improvement of DNA sequencing technologies. © 1992 John Wiley & Sons, Inc.     

A theoretical study of an empirical function for the mobility of DNA fragments in sieving matrices

The separation of DNA fragments by gel electrophoresis has been studied extensively over the last two decades. More recently, similar studies have been carried out to characterize the separation achieved by the current capillary array electrophoresis systems and their sieving polymer solutions. In all cases, at least three different mobility regimes have been shown to exist: the Ogston regime when the radius of gyration of the DNA fragment is smaller than the pore size, the reptation regime when the DNA is larger than the pore size but remains in a random coil conformation, and finally the reptation-with-orientation regime where the DNA orients in the field direction and essentially all resolution is lost. Unfortunately, although theory helps us understand the different regimes and how to properly exploit them, we still have no theory-based general equations that would apply to all regimes. Such equations would be especially useful to analyze data, optimize separation systems and interpolate mobilities to estimate unknown molecular sizes. Recently, van Winkle, Beheshti and Rill (Electrophoresis 2002, 23, 15-19) proposed an intriguing empirical formula that seems to adequately fit the mobility of dsDNA fragments across all three regimes. In this paper, I investigate the relation between this empirical formula and the known theories of gel electrophoresis, and I study the dependence of its fitting parameters upon the experimental conditions. Finally, I examine how this equation may need to be modified to capture the more subtle details predicted by fundamental theories of DNA gel electrophoresis.     

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.     

Pulsed field sequencing gel electrophoresis.

The effect of pulsed fields on sequencing gel electrophoresis is investigated, using DNA fragment markers ranging in size from 20 to 6557 bases. For high continuous electric fields (5000 V/55 cm) band inversion is observed in which fragments larger than 4000 bases migrate faster than those of 800-1000 bases. The use of one-dimensional pulsed field gel electrophoresis (ODPFGE) eliminates band inversion and extends the monotonic size-mobility relationship of the DNA markers up to about 4000 bases. The relevance of these results, obtained using a manual sequencing process with autoradiographic detection, to automated sequences is discussed.     

Relaxations in chitin: Evidence for a glass transition

Relaxations in chitin have been investigated in the temperature range 298–523 K using impedance spectroscopy in the frequency range 10⁻¹–10⁸ Hz. The objective was to detect a glass‐transition temperature for this naturally occurring, semicrystalline polysaccharide. The impedance study was complemented with X‐ray diffraction, thermogravimetric, and differential scanning calorimetry measurements. Preliminary impedance data treatment includes the subtraction of the dc conductivity contribution, the exclusion of contact and interfacial polarization effects, and obtaining a condition of minimum moisture content for further analysis. When all these aspects are taken into account, two relaxations are clearly revealed in the impedance data. For the first time, evidence is presented for a relaxation process, which exhibits a non‐Arrhenius temperature dependence, in dry α‐chitin (∼0.1% moisture content), and likely represents the primary α‐relaxation. This evidence suggests a glass transition temperature for chitin of 335 ± 10 K estimated on the basis of the temperature dependence of the conductivity and of the relaxation time. A second relaxation in dry α‐chitin, not previously reported in the literature, is observed from 353 K to the onset of thermal degradation (∼483 K) and is identified as the σ‐relaxation often associated with proton mobility. It exhibits a normal Arrhenius‐type temperature dependence with activation energy of 113 ± 3 kJ/mol. The latter has not been previously reported in the literature. A high frequency secondary β‐relaxation is also observed with Arrhenius activation energy of 45 ± 1 kJ/mol. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 932–943, 2009     

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.     

Temperature-dependence of preconditioning for lengthened capillary DNA sequencing

A previous study shows that electrophoretic preconditioning of a commercial polymer solution increases the spacing and resolution of DNA fragments fractionated in this solution by CE at 50 degrees C (Griess, G. A. et al., Electrophoresis 2005, 26, 102). The present study shows that this preconditioning effect on peak spacing progressively increases when the temperature of preconditioning increases to 70 degrees C, though fractionation is still performed at 50 degrees C. An increase in peak sharpness accompanies the increase in peak separation for DNA fragments longer than 200 bases. Changing the preconditioning temperature from 50 to 70 degrees C optimally improves resolution of fragment analysis in the range of 600-2000 nucleotides. When DNA sequencing is performed with automated base calling and 70 degrees C preconditioning at 319 V/cm (47 cm long capillary, Applied Biosystems 310 apparatus), the range of high-quality base calls is increased by 25% to 750; the range of low-quality base calls is increased by about 100% to 1200 in comparison to DNA sequencing without preconditioning.     

Modeling the stability and the motion of DNA nucleobases on the gold surface

We simulate the structure and dynamics of the four DNA bases on the most stable gold surface. The experimental adsorption energies are reproduced to about 1 kcal mol(-1), and the existence of anchor points in the molecules is evidenced. The simulations also show that the bases drift on the gold surface with a degree of mobility that is not inversely proportional to the experimental (and calculated) desorption energies. When the same type of calculations is applied to pairs of bases it is seen that for at least two of them, namely GG and TT, there is a cooperative effect that increases their adsorption energy with respect to those of the single molecules. The molecular mobility on the surface is still present when a pair of interacting bases is considered.     

Optimization of DNA electrophoretic behavior in poly(vinyl pyrrolidone) sieving matrix for DNA sequencing

Poly(vinyl pyrrolidone) solution was used as a separation matrix in capillary electrophoresis for DNA sequencing. Four-label four-color detection was performed for base calling. Dye-labeled DNA showed large mobility shifts at normal conditions for DNA separation. Temporal correction of mobility shifts was achieved by normalizing with respect to pure peaks that are without spectral interference or temporal overlap at each color channel. To achieve even better performance, a DNA separation condition that does not require corrections for mobility shifts was found. Dichlororhodamine-labeled DNA fragments showed ideal electrophoretic behaviors according to DNA size in the presence of 10 M urea. The base-calling accuracy of dichlororhodamine-labeled M13mp18 and PGEM/U DNA were 99.3% for 333 bases and 99% for 315 bases, respectively. Base calling of unknown DNA samples obtained in the presence of 10 M urea showed 99.1% accuracy.     

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.