Gary W. Slater

Diffusion coefficient of DNA molecules during free solution electrophoresis.

The free‐draining properties of DNA normally make it impossible to separate nucleic acids by free‐flow electrophoresis. However, little is known, either theoretically or experimentally, about the diffusion coefficient of DNA molecules during free‐flow electrophoresis. In fact, many authors simply assume that the Nernst‐Einstein relation between the mobility and the diffusion coefficient still holds under such conditions. In this paper, we present an experimental study of the diffusion coefficient of both ssDNA and dsDNA molecules during free‐flow electrophoresis. Our results unequivocally show that a simplistic use of Nernst‐Einsteins relation fails, and that the electric field actually has no effect on the thermal diffusion process. Finally, we compare the dependence of the diffusion coefficient upon DNA molecular size to results obtained previously by other groups and to Zimms theory.

Modeling the separation of macromolecules: a review of current computer simulation methods.

Theory and numerical simulations play a major role in the development of improved and novel separation methods. In some cases, computer simulations predict counterintuitive effects that must be taken into account in order to properly optimize a device. In other cases, simulations allow the scientist to focus on a subset of important system parameters. Occasionally, simulations even generate entirely new separation ideas! In this article, we review the main simulation methods that are currently being used to model separation techniques of interest to the readers of Electrophoresis. In the first part of the article, we provide a brief description of the numerical models themselves, starting with molecular methods and then moving towards more efficient coarse‐grained approaches. In the second part, we briefly examine nine separation problems and some of the methods used to model them. We conclude with a short discussion of some notoriously hard‐to‐model separation problems and a description of some of the available simulation software packages.

Theory of DNA electrophoresis: a look at some current challenges.

Although electrophoresis is one of the basic methods of the modern molecular biology laboratory, new ideas are being suggested at an accelerated rate, in large part because of the pressing demands of the biomedical community. Although we now have, at least for some methods, a fairly good theoretical understanding of the physical mechanisms that lead to the observed peak spacings, widths and shapes, this knowledge is often too qualitative to be used to guide further technical developments and improvements. In this article, we review some selected elements of the current state of our theoretical ignorance, focusing mostly on DNA electrophoresis, and we offer several suggestions for further theoretical investigations.

Free-solution electrophoresis of DNA

We report the first experimental evidence that double-stranded DNA fragments can be electrophoretically separated in free-solution (i.e., in the absence of a sieving matrix) when either a single or two streptavidin molecules are attached to the end(s) using biotinylated nucleotides. As previously predicted, higher resolution is obtained at higher electric fields or when two streptavidin molecules are attached to each DNA fragment. The resolution is also affected by the diameter and coating of the capillaries.

Diffusing diffusivity: a model for anomalous, yet Brownian, diffusion.

Wang et al. [Proc. Natl. Acad. Sci. U.S.A. 106, 15160 (2009)] have found that in several systems the linear time dependence of the mean-square displacement (MSD) of diffusing colloidal particles, typical of normal diffusion, is accompanied by a non-Gaussian displacement distribution G(x,t), with roughly exponential tails at short times, a situation they termed “anomalous yet Brownian” diffusion. The diversity of systems in which this is observed calls for a generic model. We present such a model where there is diffusivity memory but no direction memory in the particle trajectory, and we show that it leads to both a linear MSD and a non-Gaussian G(x,t) at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression “diffusing diffusivity”. G(x,t) is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.

Separating DNA sequencing fragments without a sieving matrix

The possibility of separating appropriately labeled DNA fragments using free‐flow capillary electrophoresis was predicted a few years ago based on simple theoretical arguments. Free‐flow separation of double‒stranded DNA (dsDNA) fragments in the 100—1000 base range was later demonstrated using a streptavidin label. In this article, we now report that end‒labeled free‒flow electrophoresis (ELFSE) can also be used to sequence single‒stranded DNA (ssDNA). The first 100 bases of a DNA sequencing reaction were read without any sieving matrix when fractionated streptavidin was added to the 5′‒end of the ssDNA fragments. These separations required only 18 min and did not require coated capillaries. An analysis of the results indicates that sample injection, analyte‒wall interactions and thermal diffusion are the limiting factors at this time. Extrapolating from our data, we predict that several hundred bases could be sequenced in less than 30 min with the proper conditions. ELFSE thus offers an attractive potential alternative to polymer solutions for DNA sequencing in capillaries and microchips.

A Monte Carlo algorithm to study polymer translocation through nanopores. I. Theory and numerical approach

The process during which a polymer translocates through a nanopore depends on many physical parameters and fundamental mechanisms. We propose a new one-dimensional lattice Monte Carlo algorithm that integrates various effects such as the entropic forces acting on the subchains that are outside the channel, the external forces that are pulling the polymer through the pore, and the frictional effects that involve the chain and its environment. Our novel approach allows us to study the polymer as a single Brownian particle diffusing while subjected to a position-dependent force that includes both the external driving forces and the internal entropic bias. Frictional effects outside and inside the pore are also considered. This Monte Carlo method is much more efficient than other simulation methods, and it can be used to obtain scaling laws for various polymer translocation regimes. In this first part, we derive the model and describe a subtle numerical approach that gives exact results for both the escape probability and the mean translocation time (and higher moments of its distribution). The scaling laws obtained from this model will be presented and discussed in the second part of this series.

The theory of DNA separation by capillary electrophoresis

The Human Genome has been sequenced in large part owing to the invention of capillary electrophoresis. Although this technology has matured enough to allow such amazing achievements, the physical mechanisms at play during separation have yet to be completely understood and optimized. Recently, new separation regimes and new physical mechanisms have been investigated. The use of free-flow electrophoresis and new modes of pulsed-field electrophoresis have been suggested, while we have observed a shift towards single nucleotide polymorphism analysis and microchip technologies. A strong theoretical basis remains essential for the efficient development of new methods.

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.

A model of the DNA transient orientation overshoot during gel electrophoresis

Linear dichroism and electric birefringence measurements show that when an electric field is applied to a DNA molecule at equilibrium in an agarose gel, the isotropic molecular conformation quickly orients in the field direction, reaching first a maximum ‘‘overshoot’’ orientation before it relaxes towards a somewhat less oriented but still anisotropic steady‐state conformation. We present here a simple analytical model of this overshoot effect together with numerical results from a computer simulation of gel electrophoresis. The predicted dependence of the overshoot time and orientation upon field intensity and molecular size are in good agreement with experimental results. The dynamics of the overshoot involves U‐shape conformations that disappear only after the internal elastic forces completely dominate the electric forces. It is also predicted that a different overshoot regime takes place for low electric fields and small molecular sizes, and that a primary and a secondary overshoot may appear for ver...