Wang et al. [PNAS 106 (2009) 15160] 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 (DisD), 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 DisD at short times. In our model, the diffusivity is undergoing a (perhaps biased) random walk, hence the expression "diffusing diffusivity". The DisD is predicted to be exactly exponential at short times if the distribution of diffusivities is itself exponential, but an exponential remains a good fit to the DisD for a variety of diffusivity distributions. Moreover, our generic model can be modified to produce subdiffusion.In a microscopically homogeneous and rheologically simple (Newtonian) fluid like water, the diffusion of microscopic particles obeys simple laws of Brownian motion known since Einstein [1]. For instance, the mean-square displacement (MSD) x 2 of a particle along a particular direction, x, is linear in time t,where D is the diffusion constant, or the diffusivity, while the distribution of displacements is Gaussian [2]. In "crowded" fluids containing colloidal particles, macromolecules, filaments, etc., the situation can be more complicated and Eq. (1) is generally not valid at all times. In many such cases (see, e.g., Refs. [3-13]), experimental data are consistent withwhere ν < 1, over a significant time range. Processes described by Eq. (2) with ν = 1 are called anomalous diffusion, more specifically, subdiffusion for ν < 1. While much experimental work has concentrated on the MSD, the full displacement distribution (DisD) can be measured using single-particle tracking techniques (SPT) [3-6, 11, 12, 14, 15]. In the continuous-time random walk (CTRW) model of anomalous diffusion [16,17] the DisD is significantly non-Gaussian with a characteristic cusp at x = 0 [18]. However, the fractional Brownian motion (fBm) model [19][20][21] demonstrates that the combination of anomalous MSD with the normal, Gaussian shape of the DisD is possible.On the other hand, it is often tacitly assumed that if the DisD is non-Gaussian, then the factors that cause it to deviate from Gaussian should also make the MSD nonlinear. Recent SPT experiments by Granick's group [22,23] show that this is not always the case. Several systems were considered: submicroscopic polystyrene beads on the surface of a lipid bilayer tube [22], beads in an entangled solution of actin filaments [22], and liposomes in a nematic solution of aligned actin filaments [23]. In all three systems, the MSD is essentially precisely linear over the whole experimental time range, from ∼ 0.1 s to a few seconds. Yet, coexisting w...

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-Einstein's 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 Zimm's theory.

DNA is a free-draining polymer. This subtle but "unfortunate" property of highly charged polyelectrolytes makes it impossible to separate nucleic acids by free-flow electrophoresis. This is why one must typically use a sieving matrix, such as a gel or an entangled polymer solution, in order to obtain some electrophoretic size separation. An alternative approach consists of breaking the charge to friction balance of free-draining DNA molecules. This can be achieved by labeling the DNA with a large, uncharged molecule (essentially a hydrodynamic parachute, which we also call a drag-tag) prior to electrophoresis; the resulting methodology is called end-labeled free-solution electrophoresis (ELFSE). In this article, we review the development of ELFSE over the last decade. In particular, we examine the theoretical concepts used to predict the ultimate performance of ELFSE for single-stranded (ssDNA) sequencing, the experimental results showing that ELFSE can indeed overcome the free-draining issue raised above, and the technological advances that are needed to speed the development of competitive ELFSE-based sequencing and separation technologies. Finally, we also review the reverse process, called free-solution conjugate electrophoresis (FSCE), wherein uncharged polymers of different sizes can be analyzed using a short DNA molecule as an electrophoretic engine.

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.

We present a model of DNA electrophoresis in unentangled polymer solutions based on a new separation mechanism in which the DNA drags along polymer molecules it encounters during migration. Taking into account the deformation and the hydrodynamic resistance of the polymers in the flow, the mutual disengagement time of the DNA and the polymer, and the average number of polymers dragged by one DNA, we build a self-consistent theory leading to predictions for the DNA velocity as a function of the experimental conditions. Our results agree with the data of Barron et al. (1994), and important separation regimes are also identified.