Capillary electrophoretic separation of uncharged polymers using polyelectrolyte engines. Theoretical model.

We recently demonstrated that the molecular mass distribution of an uncharged polymer sample can be analyzed using free-solution capillary electrophoresis of DNA-polymer conjugates. In these conjugates, the DNA is providing the electromotive force while the uncharged polydisperse polymer chains of the sample retard the DNA engine with different amounts of hydrodynamic drag. Here we present a theoretical model of this new analytical method. We show that for the most favourable, diffusion-limited electrophoresis conditions, there is actually an optimal DNA size to achieve the separation of a given polymer sample. Moreover, we demonstrate that the effective friction coefficient of the polymer chains is related to the stiffness of the two polymers of the conjugate, thus offering a method to estimate the persistence length of the uncharged polymer through mobility measurements. Finally, we compare some of our predictions with available experimental results.

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-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.

Molar mass profiling of synthetic polymers by free-solution capillary electrophoresis of DNA-polymer conjugates.

The molar mass distribution of a polymer sample is a critical determinant of its material properties and is generally analyzed by gel permeation chromatography or more recently, by MALDI-TOF mass spectrometry. We describe here a novel method for the determination of the degree of polymerization of polydisperse, uncharged, water-soluble polymers (e.g., poly(ethylene glycol) (PEG)), based upon single-monomer resolution of DNA-polymer conjugates by free-solution capillary electrophoresis. This is accomplished by end-on covalent conjugation of a polydisperse, uncharged polymer sample (PEG) to a monodisperse, fluorescently labeled DNA oligomer, followed by electrophoretic analysis. The monodisperse, charged DNA "engine" confers to each conjugate an equal amount of electromotive force, while the varying contour lengths of the uncharged, polydisperse polymers engender different amounts of hydrodynamic drag. The balance of electromotive and hydrodynamic forces enables rapid, high-resolution separation of the DNA-polymer conjugates as a function of the size of the uncharged PEG tail. This provides a profile of the molar mass distribution of the original polymer sample that can be detected by laser-induced fluorescence through excitation of the dye-labeled DNA. We call this method free solution conjugate electrophoresis (FSCE). Theory-based analysis of the resulting electrophoresis data allows precise calculation of the degree of polymerization of the PEG portion of each conjugate molecule. Knowledge of the molecular mass of the uncharged polymer's repeat unit allows for direct calculation of the molar mass averages as well as sample polydispersity index. The results of these analyses are strikingly reminiscent of MALDI-TOF spectra taken of the same PEG samples. PEG samples of 3.4-, 5-, and 20-kDa nominal average molar mass were analyzed by FSCE and MALDI-TOF; the values of the molar mass averages, Mw and Mn, typically agree to within 5%. Measurements and molar mass calculations are performed without any internal standards or calibration. Moreover, when DNA-polymer conjugate analysis is performed in a chip-based electrophoresis system, separation is complete in less than 13 min. FSCE offers an alternative to MALDI-TOF for the characterization of uncharged, water-soluble polymers that can be uniquely conjugated to DNA.

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.

The gel edge electric field gradients in denaturing polyacrylamide gel electrophoresis.

It has previously been shown that zones of higher electric field form close to the loading end of the gel during denaturing polyacrylamide gel electrophoresis. Here we show that the field can reach up to three times its normal mean value a few cm in front of the loading wells when 44.5 mM Tris-44.5 mM boric acid-1 mM EDTA is used as the gel buffer. We also demonstrate that this electric field gradient is mostly due to the difference in ion transference numbers at the gel/buffer interface caused by the high viscosity of the urea solution contained in the gel. This field gradient leads to increased band widths and forces us to redefine both the electrophoretic mobility and the mean field intensity. We discuss some methods that can be used to minimize the effects of this gradient.

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.

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

As shown by Ulanovsky, Drouin and Gilbert (Nature 1990, 343, 190-192), the gel electrophoretic migration of DNA is severely reduced by steric trapping when streptavidin is attached to one end of the polyelectrolyte. We present a model that allows us to calculate both the mobility and the diffusion coefficient, hence the resolution factor of the resulting separation. We compare our results to those of Défontaines and Viovy (Electrophoresis 1993, 14, 8-17) and we show that the averages over the molecular conformations must be done carefully. We also show that trapping increases diffusion substantially and that this makes constant-field trapping electrophoresis incapable of increasing the number of bases read per sequencing run. Finally, we conclude that severe trapping may lead to highly anomalous transport behavior where one cannot define a velocity or a diffusion constant.