Pulsed-field acceleration: the electrophoretic behavior of large spherical particles in agarose gels

Biased random walks on a lattice: exact numerical method to study the effect of alternating fields in disordered and asymmetric systems of obstacles

The migration of a particle in a system of obstacles under the action of an external field is often modeled using lattice Monte Carlo algorithms. For example, such simulation methods have been used to study the electrophoresis of charged molecules in sieving gels and the separation of particles using ratchet systems. In the case of constant fields or low-frequency alternating fields, the Monte Carlo simulation method can be mapped onto a numerical or algebraic matrix problem that can be solved exactly. In this Rapid Communication, we generalize this matrix approach to treat periodic time-dependent fields. The evolution of the spatial distribution function during a period is computed using a sequence of transfer matrices, and a steady-state closure relation allows us to calculate the exact mean velocity of the particle during a complete cycle. As an example, we examine the properties of a simple spatially asymmetric ratchet system in the presence of periodic alternating fields (symmetric and asymmetric) as well as random telegraph signals.

Application of the concept of an electrophoretic ratchet

Fractionation via a gel electrophoretic ratchet has previously succeeded for comparatively large (radius R > or = 95 nm) spheres (Serwer, P, Griess, G.A., Anal. Chim. Acta 1998, 372, 299-306). The electrical oscillations are the following electrical field pulses: high field --> low field --> high field, etc. The field is inverted after each pulse; the time-integral of the field can be zero. Response to the ratchet is caused by steric trapping in the high field-direction, but not in the low field-direction. Trapping and, therefore, response to the ratchet decrease as R decreases. The smaller spheres do not respond to the ratchet. In the present study, spheres with R values smaller than 95 nm are made, for the first time, to respond to a similar gel electrophoretic ratchet. To achieve this objective, the heterogeneity of pore size is increased for the gel used. The heterogeneity of pore size is increased by (i) forming the gel with degraded hydroxyethyl agarose, and (ii) gelling at comparatively high temperature. If a particle still does not respond to the ratchet (because the particle is too small), this particle has a net migration in the high field-direction, when the above-described pulsed field is biased in the high field-direction. If a particle does respond to the improved ratchet, the particle has a net migration in the low field-direction. Here, the R of ratchet-responding spheres is reduced to 30-50 nm. These ratchet-responding spheres include both intact bacteriophage particles (R = 30 nm) and latex spheres. The smaller ratchet-responding spheres have an electrophoretic mobility that decreases in magnitude as the electrical field increases in magnitude. A ratchet-based procedure is developed here to achieve continuous preparative gel electrophoresis.

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.

Trapping electrophoresis and ratchets: a theoretical study for DNA-protein complexes

Recently, Griess and Serwer (1998. Biophys. J. 74:A71) showed that it was possible to use trapping electrophoresis and unbiased but asymmetrical electric field pulses to build a correlation ratchet that would allow the efficient separation of naked DNAs from identical DNAs that form a complex with a bulky object such as a protein. Here we present a theoretical investigation of this novel macromolecular separation process. We start by looking at the general features of this electrophoretic ratchet mechanism in the zero-frequency limit. We then examine the effects of finite frequencies on velocity and diffusion. Finally, we use the biased reptation model and computer simulations to understand the band-broadening processes. Our study establishes the main experimental regimes that can provide good resolution for specific applications.

Improved resolution in the gel electrophoresis of proteins by a periodically interrupted electric field

The capability of the commercial gel electrophoresis apparatus with intermittent scanning of fluorescence (HPGE-1000, LabIntelligence) to provide time-dependent zone dispersion allows one to quantitate resolution. Using a model protein separation, that between phycoerythrin and fluorescein-labeled conalbumin, resolution was compared between separations conducted at a constant field strength of 80 V/cm and one conducted in 10-s pulses of the same field strength, interrupted periodically by 120 s in the absence of an electric field. Resolution was improved by a factor of two in the discontinuous application of the electric field compared to that obtained in its continuous application. Similarly, the intermittent application of 80 V/cm for 10 s, followed by 120-s pauses, gave rise to twice the resolution obtained from a continuous application of 7 V/cm.

An exactly solvable Ogston model of gel electrophoresis. II. Sieving through periodic gels

Recently, we developed a lattice model to study the dynamics of particles being electrophoresed in gels (G. W. Slater, H. L. Guo, Electrophoresis 1995, 16, 11-15). In Part I of this series (G. W. Slater, H. L. Guo, Electrophoresis 1996, 17,977-988), we showed how to calculate the exact electrophoretic mobility of one-site particles in the limit where the electric field intensity E is vanishingly small. Since we can solve the model for arbitrary gel structures in two or more dimensions, we compared our results with those of the Ogston-Morris-Rodbard-Chrambach model (OMRCM) of gel electrophoresis, which assumes that the mobility (mu) of charged particles is directly proportional to the fractional gel volume (f) that is available to them. Our results and theoretical analysis indicated that the OMRCM is a mean-field approximation that can be useful as a rough guide; however, it generally misses the subtle sieving effects related to the correlations between the position of the obstacles in a given gel structure. In this paper (Part II) we study, for two-dimensional periodic gels, the exact relationships between the zero-field mobility mu and the gel concentration C for larger particle sizes. The fact that mu is a strong function of the particle size suggests that we can separate large particles using two-dimensional periodic gels (similar to those fabricated by W.D. Volkmuth and R.H. Austin, Nature 1992, 358, 600-602). We analyze our data using Ferguson-like plots and we show that one can indeed use a generalized retardation coefficient, K, to estimate the effective pore size aK and effective fiber size rK for these model gels. We conclude that the retardation coefficient is a useful concept to characterize a sieving structure even though it does not permit the inference of the exact gel structure.

An exactly solvable Ogston model of gel electrophoresis: I. The role of the symmetry and randomness of the gel structure

The Ogston-Morris-Rodbard-Chrambach model (OMRCM) of gel electrophoresis assumes that the mobility (mu) of charged particles is directly proportional to the fractional volume (f) of the gel that is available to them. Many authors have studied the fractional volume f in detail for various particle shapes, but the original assumption, that mu sf, has not been scrutinized seriously. In fact, this geometrical model of electrophoresis does not take into account the connectivity of the gel pores or the precise gel architecture. Recently (G. W. Slater and H. L. Guo, Electrophoresis 1995, 16, 11-15) we developed a Monte Carlo computer simulation algorithm to study the electrophoretic motion of simple particles in gels in the presence of fields of arbitrary strength. Our preliminary results indicated that the mobility and the fractional volume were not generally proportional to one another. In this article, we show how to calculate, in the limit where the field intensity is vanishingly small, the exact electrophoretic mobility of particles in any type of gel in two or more dimensions. Our results, presented here for some simple two-dimensional systems, indicate that a particle can have different electrophoretic mobilities in gels in which it has access to the same fractional available volume f. The curvature of the Ferguson plot is shown to be related to the symmetry and the degree of randomness that characterize the gel. We also demonstrate that the OMRCM is, in fact, a mean field approximation that corresponds to a uniform, annealed gel. We thus conclude that the relation between the electrophoretic mobility and the gel concentration (C) is a delicate function of the gel architecture, and that one needs more than the fractional volume f to fully characterize the transport properties of migrating particles in separation media. Exact relationships between the mobility mu and the gel concentration C are given for our model gels.