Solid friction and polymer relaxation in gel electrophoresis

Noise-Activated Fast Locomotion of DNA through the Frictional Landscape of Nanoporous Gels

It is hypothesized that nonlinear solid friction between the gel matrix and DNA molecules inhibits the motion of DNA through the nanopores of the gel during electrophoresis. In this article, it is demonstrated that external noise can alleviate the effect of solid friction, thus enhancing the mobility of DNA in an electrophoretic setting. In the presence of noise, the mobility of DNA increases by more than ∼113% compared to conventional electrophoresis. Although at a high power of noise, DNA exhibits Arrhenius kinetics, at a low power of noise, super-Arrhenius kinetics suggests the collective behavior of the activated motion of DNA molecules. A stochastic simulation following modified Langevin dynamics with the asymmetric pore size distribution of the agarose gel successfully predicts the mobility of DNA molecules and reveals the salient features of the overall dynamics. This "noise lubricity" may have a broader applicability from molecular to macroscopic locomotion.

Mechanism of DNA trapping in nanoporous structures during asymmetric pulsed-field electrophoresis

We investigate the trapping mechanism of individual DNA molecules in ordered nanoporous structures generated by crystalline particle arrays. Two requisites for trapping are revealed by the dynamics of single trapped DNA, fully-stretched U/J shapes and hernia formation. The experimental results show there is a stronger possibility for hernias to lead the reorientation upon switching directions of the voltage at high field strengths, where trapping occurs. Fully stretched DNA has longer unhooking times than expected by a classic rope-on-pulley model. We propose a dielectrophoretic (DEP) force reduces the mobility of segments at the apex of the U or J, where field gradients are highest, based on simulations and observations of the trapping force dependence on field strength. A modified model for unhooking time is obtained after the DEP force is introduced. The new model explains the unhooking time data by predicting an infinite trapping time when the ratio of arm length differences (of the U or J) to molecule length Δx/L < β, where β is a DEP parameter that is found to strongly increase with electric field. The DNA polarizability calculated with the DEP model and experimental value of β is of the same magnitude of reported value. The results indicate the tension at the apex of U/J shape DNA is the primary reason for DNA trapping during pulsed field separation, instead of hernias.

Driven polymer translocation through a narrow pore

Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions. We show that there is a range of polymer lengths in which the system is approximately translationally invariant, and we develop a coarse-grained description of this regime. From this description, general features of the distribution of times for the polymer to pass through the pore may be deduced. We also introduce a more microscopic model. This model provides a physically reasonable scenario in which, as in experiments, the polymer's speed depends sensitively on its chemical composition, and even on its orientation in the channel. Finally, we point out that the experimental distribution of times for the polymer to pass through the pore is much broader than expected from simple estimates, and speculate on why this might be.

Trapping of megabase-sized DNA molecules during agarose gel electrophoresis

Megabase DNA molecules become trapped in agarose gels during electrophoresis if the electric field exceeds a few volts per cm. Fluorescence microscopy reveals that these molecules invariably arrest in U-shaped conformations. The field-vs.-size dependence for trapping indicates that a critical molecular tension is required for trapping. The size of unligated lambda-ladders, sheared during gel electrophoresis at a given field, coincides with the size of molecules trapped at that field, suggesting that both processes occur through nick melting near the vertex of the U-shape. Consistently, molecules nicked by exposure to UV radiation trap more readily than unexposed ones. The critical trapping tension at the vertex is estimated to be 15 pN, a force sufficient to melt nicks bent around gel fibers, and, according to our model, trap a molecule. Strategies to reduce molecular tension and avoid trapping are discussed.

Forces on chromosomal DNA during anaphase

In the course of anaphase, the chromosomal DNA is submitted to the traction of the spindle. Several physical problems are associated with this action. In particular, the sister chromatids are generally topologically intertwined at the onset of anaphase, and the removal of the intertwinings results from a coupling between the enzymatic action of type II DNA topoisomerases and the force exerted by the spindle. We propose a physical analysis of some of these problems: 1) We compare the maximum force the spindle can produce with the force required to break a DNA molecule, and define the conditions compatible with biological safety during anaphase. 2) We show that the behavior of the sister chromatids in the absence of type II DNA topoisomerases can be described by two distinct models: a chain pullout model accounts for the experimental observations made in the budding yeast, and a model of the mechanical rupture of rubbers accounts for the nondisjunction in standard cases. 3) Using the fluctuation-dissipation theorem, we introduce an effective protein friction associated with the strand-passing activity of type II DNA topoisomerases. We show that this friction can be used to describe the situation in which one chromosome passes entirely through another one. Possible experiments that could test these theoretical analyses are discussed.

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.