Trapping gel electrophoresis of end-labeled DNA: an analytical model for mobility and diffusion

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.

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.

Recent developments in DNA electrophoretic separations

DNA electrophoresis is now a fairly mature technology. Nevertheless, as we approach the 21st century, new ideas are frequently suggested that could lead to a revolution for DNA sequencing and mapping. Here, we review some of the novel concepts that have been studied since ca. 1990. Our review focuses on new separation mechanisms, new sieving matrices and recent conceptual advances.

Mechanisms of retardation of rigid spherical particles with 3 to 1,085 nm radius in capillary electrophoresis, using buffered polyacrylamide (molecular weight 5 x 10(6)) solutions

Subjecting particles in the size range of 3 to 1085 nm radius (R) to capillary electrophoresis in buffered solution of entangled uncrosslinked polyacrylamide (M(r) 5 x 10(6)), it was found that particle size-dependent retardation ("molecular sieving") becomes electric field- and particle size range-dependent once the particle size exceeds 15-20 nm in radius. The field strength dependence of the retardation coefficient [KR = d(log mobility)/ d(polymer concentration] and the positive or negative sign of dKR/dR suggest the existence of two different mechanisms of molecular sieving depending on the particle size range: particles with diameters less than the screening length (or blob size) of the polymer network are thought to penetrate into the available spaces within a discontinuous polymer network; particles with diameters larger than the screening length (or blob size) of the polymer network are thought to undergo size-dependent retardation by exerting shear stress against polymer chains, and displacing them, so as to cause local deformations in a continuous polymer network. A limit in the separating capacity of molecular sieving, due to a sharp increase in the rate of band widening with polymer concentration, was found when the value of the retardation coefficient exceeded 60 (mL/g).

Theory of solitary waves in electrophoresis

A theoretical study about the generation of solitary waves (SW) in electrophoresis and capillary electrophoresis is performed. Two models that use velocity terms in Fick's first law and absorption and decaying terms in Fick's second law are presented. These models give the time evolution of the band or zone shape in electrophoresis and capillary electrophoresis in the presence of electromagnetic radiation. In particular, the effect of electrophoretic mobility changes of the analytes due to radiation excitation is included in the present models. The analytes are represented either by three-level or four-level systems. It is shown that the resulting system of coupled nonlinear partial differential equations governing the spatial motion of these bands over time exhibits SW solutions for some values of the equation parameters. We analyze the conditions in which these SWs, which propagate with constant velocity, constant area, constant standard deviation, and without change of form, are generated. The results of the present models are compared with those from a previous two-level model (Phys. Rev. Lett. 1995, 75, 1210-1213). The velocities of these SWs are calculated analytically. The time evolution of their standard deviations is shown. The numerical integration of a two-component electrophoresis run shows higher resolutions under some conditions. The expected practical difficulties which may be encountered when observing this phenomenon are discussed. Some practical difficulties that are likely to limit its useful application in electrophoresis and capillary electrophoresis are mentioned.

Pulsed-field-trapping electrophoresis: a computer simulation study

Experimental investigations have shown that adding a large, globular and neutral protein (such as streptavidin) at one end of the DNA fragments to be separated by gel electrophoresis strongly affects the dynamics of these molecules, leading to what is known as trapping electrophoresis (TE). In TE, the velocity decreases much more rapidly with DNA molecular size than under normal gel electrophoresis conditions, suggesting that TE may be used to increase the power of separation of polyacrylamide gel electrophoresis. Unfortunately, the bands are broader and fewer readable bands can fit on a single gel slab. Our previous theoretical study of TE also predicted the existence of long-lasting anomalous regimes where one cannot define a velocity or a diffusion constant. These secondary effects of trapping are related to the very broad distribution of detrapping times (the time needed to exit a trap). In order to increase the usefulness of TE, it has been suggested that pulsed fields may help the molecules exit traps more rapidly. In this article, we present a detailed numerical study of pulsed field TE. We conclude that simple pulsed fields alone may not be enough to increase the sequencing power of polyacrylamide TE because the rate of band broadening cannot be controlled. We also report the existence of anomalous regimes in the presence of pulsed fields, a factor that has been previously neglected in analytical models. Other approaches are also proposed.