Monitoring Polyelectrolyte Mobility by Gel ... - ACS Publications

Chapter 12

Downloaded by UNIV MASSACHUSETTS AMHERST on September 4, 2012 | http://pubs.acs.org Publication Date: December 4, 1992 | doi: 10.1021/bk-1992-0480.ch012

Monitoring Polyelectrolyte Mobility by Gel Electrophoresis Evangelia Arvanitidou, David Hoagland, and David Smisek Department of Polymer Science and Engineering, University of Massachusetts, Amherst, MA 01003

Electrophoretic methods are applied to studies of probe chain motion in gels, exploiting free solution measurements of the same motion to isolate gel matrix effects. Trends observed for gels, particularly in relationships between mobility and chain length and between mobility and chain topology, support a three state entanglement depiction, each state characterized by its own chain transport mechanism. These include excluded volume (unentangled regime), entropie barriers (weakly entangled regime), and reptation (strongly entangled regime). Intermediate entanglement provides the best fractionation, and evidence is presented that spatial variations in chain entropy control motion whenever the probe size approximately matches the gel mesh spacing. The backbone charge density, potentially an uncontrolled variable for synthetic samples, is shown to exert negligible influence on the mobility of highly charged probe molecules. Gel electrophoresis has long been recognized as the method of choice for fractionating and analyzing mixtures of high molecular weight biological molecules (7). Despite the method's widespread acceptance, until recently only minor efforts had been made to develop a comprehensive understanding of electrophoretic transport mechanisms at the molecular level. Fundamental research was finally spurred in the early 80's with the discovery that pulsed field gel electrophoresis can fractionate enormous, chromosome-sized DNA chains (2). Fully exploiting pulsed field methods requires a sophisticated understanding of molecular transport in gel media, and the conspicuous lack of such understanding initiated a wave of research activity that continues unabated. Recognizing the richness and universality of electrophoretic transport mechanisms, and realizing that applications in the synthetic polymer field were notably lacking, we began a systematic study of the electrophoresis of model polymers about 5 years ago; these polymers serve as model materials in the sense that we select chemical structures that are well-suited for the testing of proposed transport mechanisms. In the absence of a basic molecular description for even the simplest electrophoretic techniques, we have focused our attentions on the least complicated cases: electrophoresis in homogeneous gels and solvents under steady, low applied fields. The present contribution will summarize our most recent findings in this area. 0097-^156/92y0480-0190$06.25/0 © 1992 American Chemical Society

In Polyelectrolyte Gels; Harland, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1992.

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The term electrophoresis is used to describe the migration of a charged solute under the action of an electric field. At steady state, the driving force due to die electric field balances the drag exerted on the solute by the surrounding medium. The resulting steady motion is characterized by the electrophoretic mobility μ, defined as the ratio of the velocity u to the field strength E:


μ=ιι/Ε

(D

In the low field limit, μ is independent of E. At higher fields, μ may vary with E, reflecting the potential of strong applied fields to alter solute friction. As a random coil polymer stretches and orients in thefielddirection with increasing E, for example, μ willrisesince these processes reduce drag. Pulsed field electrophoretic methods rely entirely on the nonlinear nature of μ(Ε), with the nonlinearity greatly accentuated by the presence of a strongly confining gel. Operation in the nonlinear μ(Ε) range with steady fields, however, significantly reduces the sensitivity of mobility to solute structure. Our research program has thus been directed almost entirely toward experiments performed at very low applied fields (5 2 V/cm), incapable of perturbing equilibrium polymer structure and verified in each case to produce mobilities independent of E. The penalty for following this strategy is a lengthy runtime(~ 2 days) for high molecular weight samples (i.e., those with molecular weights above 106). If a system is diluted in charged solute and Ε is small, μ can be related to the solute diffusion coefficient in the same environment, μ ~ DQ ~ DN

(2)

where D is the tracer diffusion coefficient, Q is the total solute charge, and Ν is the degree of polymerization; a prefactor involving the ionic strength and the density of ionic groups along the backbone has been neglected. Essentially the classical Einstein relationship for ion mobility, equation 2 is derived under the implicit assumption that long range intramolecular hydrodynamic interactions are the same for both diffusion and electrophoresis; in fact, long range hydrodynamic interactions are absent during electrophoresis of flexible macromolecules (reasons to be discussed later), so the proper diffusion coefficient for equation 2 is the one evaluated in the absence of hydrodynamic interactions (i.e., using the Rouse model). The information contained in μ is analogous, within a factor involving the charge density and ionic strength, to the information contained in D. Most importantly, this equation provides a means of relating the molecular weight dependences of μ and D. Therefore, electrophoresis provides a convenient means to study diffusion phenomena in a variety of environments ranging from gels to polymer solutions to porous media. Support media (gels) were originally introduced in electrophoretic methods to suppress convection currents arising from Joule heating. Investigators later recognized that the same media might also be responsible for electrophoretic separations based on molecular size. Agarose and poly(acrylamide) gels are the most common separation media, mainly because of their simple preparations and high mechanical strengths. Properly prepared gels contain few, if any, bound ionic groups; if such groups are present, solvent flow created by the electrical forces on mobile counterions can produce solute convection (i.e., electro-osmosis) greatiy in excess of solute motion by electrophoresis. Agarose possesses large pores (~10-100 nm) (3,4) and is consequendy employed to study larger macromolecules such as DNA restriction fragments. Poly(acrylamide) gels, with smaller pores (5), are used for separating proteins and sequencing short DNA fragments. Agarose is a natural polysaccharide, isolated from red algae, with a low percentage of bound, negatively charged functional groups. Gelation occurs as aqueous solutions are cooled to room



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temperature; the mean pore size, as well as the highly distributed pore size distribution, depends strongly on agarose concentration. Poly(acryiamide) gels are the product of polymerization of acryiamide in the presence of a multifunctional crosslinker such as Ν,Ν'-methylene-bis-acrylamide. The gel network is formed at room temperature in the presence of the buffer solution selected for the electrophoresis experiment. Poly(acrylamide) gels are normally prepared at higher gel concentrations (3.0-20.0 wt. %) than agarose gels (0.1-4.0 wt. %). Many polymers routinely analyzed by gel electrophoresis can also be studied by aqueous size exclusion chromatography (SEC). Electrostatic exclusion from the pores of the support, coil expansion due to intramolecular electrostatic repulsion, and adsorption on support walls are a few of the difficulties that can make aqueous SEC less attractive than gel electrophoresis (6). Moreover, velocity gradients in the chromatography experiment create band-broadening effects not present in electrophoresis. The resolution of an electrophoretic separation can thus be much higher than one produced chromatographically; for example, 500 basepair DNA chains are routinely baseline resolved from 499 basepair DNA chains by electrophoresis in sequencing gels. Even under the most ideal circumstances, chromatographic methods for high molecular weight polymers are restricted to much lower resolutions (6,7). In fact, with synthetic polymers of molecular weight less than 10^, gel electrophoresis can theoretically provide discrete molecular weight distributions, i.e., with each degree of polymerization resolved into a separate band. Efforts to attain this unprecedented separation quality are currently being pursued for anionically polymerized poly(styrene) samples. The final advantage of electrophoresis is its molecular weight range; separations are obtained for molecules ranging in size from dimers to whole chromosomes with 10? repeat units. The negative features of the electrophoretic approach, as opposed to SEC, are the need for solute charge and solubility in a high dielectric constant solvent such as water. In some cases an inappropriate solute, such as the poly(styrene) just mentioned, can be readily modified to provide a charged analog with the original backbone structure and length. Numerous biopolymer applications of gel electrophoresis have been developed, with new methods reported regularly in journals such as Electrophoresis. The most common and perhaps most important applications are the molecular weight fractionation of proteins in poly(acrylamide) gels (8-10) and DNA fragments in agarose gels (11-13). Determination of the molecular weight distributions of synthetic polyelectrolytes by gel electrophoresis was first attempted by Chen and Morawetz (14). They described poly(acrylamide) gel electrophoresis of low molecular weight p o l y s t y r e n e sulfonate) [PSS], adapting conventional protein sizing techniques. Recently, Smisek and Hoagland (75) discussed methods to measure PSS molecular weight in agarose gels, a procedure more akin to fractionation of large DNA fragments. In their initial studies with synthetic polymers, both groups demonstrated that by using monodisperse polyelectrolyte standards, a calibration curve could be developed between molecular weight and mobility. This curve, in conjunction with the measurement of the mobility of an unknown of the same chemical type, permitted determination of molecular weight and its distribution by comparison. This approach sidesteps the need for a molecular level understanding of the mechanism of molecular weight fractionation. Without a fuller understanding, however, further quantitative applications in the synthetic polymer field will remain problematical since only a handful of charged polymers with monodisperse standards are available. Although electrophoresis is simple to perform, many parameters are known to affect the mobility (gel concentration and type, ionic strength, electric field strength, chain stiffness). Our goal is to understand, at a molecular and pore size level, the influence of each parameter. The most novel feature of this work is the use of model synthetic polymers as the probe species. By using model solutes and gels, we attempt to focus directly on the mechanisms of electrophoresis. Efforts to develop satisfactory


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model gels, however, have not been entirely successful; we believe that access to model gels (or alternative media) will eventually become a major research issue in the electrophoresis field.


Experimental Electrophoresis in poly(acrylamide) gels is performed in a vertical apparatus using an Ephortec 500-V power supply operating at constant voltage. After each run, the gel is stained with a pH 4.0, 0.01 wt. % methylene blue solution for 15 minutes and destained with distilled water for several hours; stained bands are then scanned using an ISCO Model 1312 densitometer operated at 580 nm. Poly(acrylamide) gels are prepared from a 40% stock solution of acrylamide/bis-acrylamide (29:1 ratio) mixed with 25 ml TEMED, 600 μΐ of 10 wt % ammonium persulfate, 10 ml 0.01 M sodium phosphate dibasic buffer (1=0.03 M), and water. The volumes of water and of the aciylarmde/bis-acrylamide stock solution are varied to control gel concentration. Since polymerization of acrylamide is inhibited by oxygen, gels are poured between two 19.5 cm χ 21.5 cm glass plates. The gel thickness is dictated by rigid spacers inserted between the plates and is typically about 1.0 cm. Polymerized gels are allowed to solidify for 30 minutes at room temperature before use. Gel concentrations range from 3.0 to 7.0 wt. %. Agarose gels are prepared by dissolving FMC SeaKem agarose in a 0.01 M sodium phosphate dibasic buffer solution at a high temperature (95 C). After cooling, the solution is cast in a 15 cm χ 15 cm tray, and electrophoresis is performed in the horizontal mode (submarine cellfromBioRad). Agarose concentrations vary from 0.3 to 0.9 wt. %. The staining procedure is the same as for poly(acrylamide) gels; in a few cases, with DNA as the probe species, ethidium bromide is exchanged for methylene blue in the staining step, and DNA bands are recorded photographically over a UV transilluminator. Further experimental details on run procedures were presented in an earlier publication (75). Electrophoresis of PSS in the absence of gel, termed free solution electrophoresis, is performed with a Coulter Electronics DELSA electrophoretic light scattering apparatus. Samples are prepared at a series of concentrations spanning the dilute and semidilute regimes, and the true dilute solution mobility is obtained by extrapolating mobility data to zero polymer concentration. The DELSA instrument permits redundant scattering measurement at four angles using two crossed incident beams to create an optical grating at the scattering volume. The scattering volume is located at the stationary plane of the electrophoresis chamber to eliminate extraneous solute convection arising from electro-osmosis. The rate of motion of the charged solute is determinedfromthe frequency spectrum of the fluctuating scattered light intensity; the fluctuation occurs as charged solute moves through the grating. Unless the same velocity is measured at all angles, the data are not reported here. At low molecular weight and/or at low ionic strength, the scattering contrast decreases and the mobility becomes unobtainable by this method. In a few cases, the free solution mobility has been verified by direct measurement on a dilute solution in a capillary electrophoresis apparatus (ISCO). A range of narrow molecular weight distribution PSS samples are available (4,000

Monitoring Polyelectrolyte Mobility by Gel ... - ACS Publications

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