Motion of megabase deoxyribonucleic acid during field‐inversion gel electrophoresis: Investigation by nonlocal Monte Carlo

Advances in the separation of bacteriophages and related particles

Nondenaturing gel electrophoresis is used to both characterize multimolecular particles and determine the assembly pathways of these particles. Characterization of bacteriophage-related particles has yielded strategies for characterizing multimolecular particles in general. Previous studies have revealed means for using nondenaturing gel electrophoresis to determine both the effective radius and the average electrical surface charge density of any particle. The response of electrophoretic mobility to increasing the magnitude of the electrical field is used to detect rod-shaped particles. To increase the capacity of nondenaturing gel electrophoresis to characterize comparatively large particles, some current research is directed towards either determining the structure of gels used for electrophoresis or inducing steric trapping of particles in dead-end regions within the fibrous network that forms a gel. A trapping-dependent technique of pulsed-field gel electrophoresis is presented with which a DNA-protein complex can be made to electrophoretically migrate in a direction opposite to the direction of migration of protein-free DNA.

High-frequency alternating-crossed-field gel electrophoresis with neutral or slightly charged interpenetrating networks to improve DNA separation

Toward improving DNA separations, this work reports the effects of high-frequency square-wave AC fields superimposed perpendicular to the direct current (DC) separation field on DNA migration in both polyacrylamide-based interpenetrating networks (IPNs) and in agarose networks. Compared to standard polyacrylamide gels, IPNs allow the separation of larger DNA (9000 bp vs. 5000 bp at 5 V/cm). In novel polyacrylamide-based IPNs, an alternating current (AC) field of 5 Hz increased the maximum DNA size separable. This effect was extended to larger DNA sizes with increasing electric-field strength up to and apparently beyond the power supply-limited maximum electric-field strength of 48 V/cm. The orthogonal AC field also increased mobility. These two results combine to yield a reduction in separation time of up to a factor of 20 in novel polyacrylamide-based IPNs. When negatively charged acrylic-acid groups were incorporated into the IPNs, the use of the AC field changed the DNA-network interaction, which altered the size dependence of DNA mobility. In agarose gels, an AC field of 50 Hz increased the size range separable; however, there was no increase in DNA mobility. There was no change in size dependence of mobility in an AC field when the number of charged groups in the agarose network was increased. Based on results in the literature, possible mechanisms were examined for the effects of the AC field on DNA separation.

Reptation theories of electrophoresis

In this review, we present the main aspects of the reptation theory, which has provided an essential insight into the processes at work during DNA electrophoretic separation in gels. We avoid mathematical developments, and rely as much as possible on an intuitive description. We first present the original biased reptation model, which assumes that the DNA threads its way as a "worm" of fixed length among the fibers of the gel. We then introduce a more recent version, the model of Biased Reptation with Fluctuations (BRF), which allows for longitudinal flexibility along the DNA. We then propose a quantitative comparison with experiments performed in constant field, and discuss the application of reptation theories to pulsed field techniques either with crossed fields or with field inversion. We also discuss at some length the different experiments that led to a criticism of reptation ideas, such as orientation measurements and videomicroscopy. Finally, we use these experiments together with various computer simulations developed recently for gel electrophoresis, to propose a more realistic qualitative description of DNA motion in gels, and we discuss what elements in this motion are relevant to reptation and what processes are not included in present analytical models.

Deterministic model of DNA gel electrophoresis in strong electric fields

We present a new model for the motion of a megabase-long DNA molecule undergoing gel electrophoresis. We assume that the dynamics of large segments of DNA is almost deterministic and can be described by a set of simple mechanical equations. This allows the numerical study of gel electrophoresis of ultra-high molecular weight DNA. A strong electric field forces DNA in a gel into a tree-like structure with branches-loops of different sizes. We determined the loop-size distribution function. This distribution has a power law form, confirming the hypothesis of the statistical self-similarity of a moving polymer. We find periodic configuration changes in the motion of a circular polymer, with the average period proportional to the molecular weight. During the period, a polymer goes through three distinct phases: a simple V-shape configuration, a growing tree, and a decaying tree. For a linear polymer this periodicity is much less pronounced because of additional perturbations to the dynamics caused by free ends. A circular polymer stays in a simple V-shaped configuration about 30% of the time, independent of molecular weight (10% for a linear polymer).

Real-time velocity of DNA bands during field-inversion gel electrophoresis

The velocity v of bands of double-stranded, linear DNAs containing 48.5-5700 kbp was determined with 0.3 s resolution during field-inversion agarose gel electrophoresis (FIGE) for a broad range of the forward pulse period T+, keeping the duration of the backward pulse T- = T+/3. Within 0.6 s or less after the field changed sign from-to +, the velocity showed a sharp positive peak; a similar spike, but with negative velocity, occurred immediately after the field changed from + to -. For long pulses, the magnitude of this spike increased with M0.36, reaching ten times the steady-state velocity for M = 5.7 kbp. After this spike, the velocity dipped to 55-75% of its value in a steady field, then increased to a small secondary peak before reaching a steady-state plateau. The duration of the velocity trough, and the time of the small peak, increased as M1. For standard FIGE conditions (ratio of forward:reverse pulse duration, T+:T- = 3:1; equal forward and reverse field amplitudes, E+ = E-), the mobility mu = integral of vdt over a complete cycle was a minimum when E+ terminated at the end of the velocity trough. The minimum occurred because the velocity during E+ sampled primarily the trough, and because the backward velocity during E- was exceptionally large; the negative velocity spike was maximized when T+ terminated at the end of the velocity trough. Computer simulations of FIGE by Zimm (J. Chem. Phys. 1991, 94, 2187-2206) and by Duke and Viovy (J. Chem. Phys. 1992, 96, 8552-8563) generate real-time velocities that are in excellent agreement with our experimental data.

Conformational dynamics of DNA during biased sinusoidal field gel electrophoresis

DNA motion during biased sinusoidal field gel electrophoresis around the antiresonance condition was investigated by direct observation using fluorescent microscopy and Brownian dynamics simulation. Time development of the center of mass velocity, vx, and the principal value of the gyration tensor, R1, was measured at this antiresonance condition. The typical stretch-contract motion, which is observed in steady field and at high frequency field, is severely suppressed, and there are two or more dominant kinks that compete with each other. Analysis of the kink motion from the simulation results supports this picture.

Cyclic migration of DNA in gels: DNA stretching and electrophoretic mobility

Available data from spectroscopic and microscopy studies of electrophoretic orientation of long DNA (above 40 kbp) in agarose gels is analyzed on the basis of the fact that the migration in constant fields is cyclic in nature. Defining a cycle period as the time between two consecutive compact states, a simple model is used to obtain data on the average time period (< T >) and the step length (< L >) of the migration cycle from spectroscopic measurements of the dynamics of helix orientation and center-of-mass velocity. Furthermore, the degree of orientation is used to analyze tube-orientation and DNA stretching contributions to < L > and < T >. Finally, the average electrophoretic velocity v = < L >/< T > is analyzed in terms of < L > and < T > for different DNA sizes (Lc), field strengths (E), and gel concentrations (A). The main results of the analysis are: (i) the increase and saturation of the electrophoretic mobility with increasing E is mainly governed by < L > via the degree of DNA stretching, (ii) DNA molecules of different sizes migrate with the same velocity because < L > and < T > both increase approximately linearly with Lc, and (iii) migration in a denser gel is slower mainly because < T > increases, while the step length is approximately constant. Assuming the charge Q of DNA is the same as in free solution, these results suggest that the reason the fundamental reptation equation for the electrophoretic mobility mu = (Q/zeta) < (hx/Lt)2 > also applies in the presence of strong fluctuations in the tube length Lt, and end-to-end distance hx, is that the friction coefficient zeta for motion along the tube is lower the more stretched the DNA is.

Statistical features in the lakes-straits model and the influence of hernias

We evaluate numerically the mobility of DNA chains under field-inversion gel electrophoresis (FIGE) conditions in the framework of the lakes-straits model introduced by Zimm (Phys. Rev. Lett. 1988, 61, 2965-2968; J. Phys. Chem. 1991, 94, 2197-2206). We extend the model by allowing both simple and also multiple-branched hernias; this is achieved by arranging the data structure used in the algorithm so that each fragment in a lake can be treated separately. We show that the existence of hernias allows the probe to migrate faster and that with hernias the mobility minimum in FIGE shifts to smaller field periods. These effects occur only if the electric field is strong enough. We also discuss the influence of the model's parameters on the mobility.

DNA separation with field inversion capillary electrophoresis

We have built an automated pulsed field capillary electrophoresis system on the basis of a commercially available device. Using entangled polymer solutions as separating matrix, we demonstrate a considerable improvement of separation of double-stranded DNA in the range of 1-50 kbp under pulsed field conditions. The influence of the main parameters, i.e. pulse frequency and electric field, is studied and the results are compared to existing electrophoresis theories.

Effects of DNA charge and length on the electrophoretic mobility of intercalated DNA

DNA molecules ranging in size from 1 to 630 kilobase pair and intercalated with either ethidium bromide (EtBr) or propidium iodide (PI) were electrophoresed in 1% agarose at four different electric field strengths. The extent of intercalation of EtBr under the conditions of our electrophoresis experiments was determined by a spectroscopic technique, whereas the extent of intercalation of PI was inferred from previous studies. The effects of the increase in DNA contour length and the concomitant decrease of linear charge density were separated based on our analysis of the mobility data. We conclude that the main factor responsible for the reduced electrophoretic mobility of intercalated DNA is the diminished linear charge density and not the increased contour length.

Two-dimensional motion of DNA bands during 120 degrees pulsed-field gel electrophoresis

The position and velocity of a band of double-stranded, linear DNA from bacteriophage G were measured during 120 degrees pulsed-field gel electrophoresis, using a video micrometer. Both the x and y coordinates were determined simultaneously in the plane of a 1% agarose gel; x is the mean drift direction. For pulse durations T greater than the tube renewal time T*, the path traced by the band of 670 kb DNA in the xy plane was in remarkably good accord with that predicted by Southern's ratchet model. However, the measured instantaneous velocity vx showed a sharp backward spike each time the field changed direction, with amplitude about twice the mean drift velocity. This spike is not consistent with models which assume a constant curvilinear velocity of DNA in a tube, nor with the biased reptation model without fluctuations. The corresponding measurements of vy showed a sharp positive spike with amplitude more than 3 times the plateau velocity in the y direction; neither model predicted this. The sharp velocity spikes are consistent with the idea that, for T > T*, a large fraction of the DNA chains are stretched into U-shaped or herniated configurations. When the field changes direction, the arms of the U's and the hernias recoil rapidly in response to intramolecular DNA chain tension. Because the base of a U or hernia is fixed by gel fibers, the center of mass of the chain recoils backward every time the field changes direction.