Biophysics
Theoretical comparison of the self diffusion and mutual diffusion of interacting membrane proteins
(lateral diffusion/fluorescence photobleaching/in situ electrophoresis)
BETHE A. SCALETTAR, JAMES R. ABNE, AND JOHN C. OWICK
Self diffusion and mutual diffusion in twodimensional membrane systems are analyzed. It is shown that interprotein interactions can produce markedly different density- dependent changes in the diffusion coefficients describing these two processes; the qualitative differences are illustrated by using a theoretical formalism valid for dilute solutions. Results are obtained for three analytical potentials: hard-core repulsions, soft repulsions, and soft repulsions with weak attractions. Self diffusion Aais inhibited by all three interactions. In contrast, mutual diffusion is inhibited by attractions but is enhanced by repulsions. It is shown that such interaction-dependent differences in self diffusion and mutual diffusion could underlie, among other things, the disparity in protein diffusion coefficients extracted from fluorescence recovery after photobleaching and postelectrophoresis relaxation data.
Abbreviations: FRAP, fluorescence recovery after photobleaching; PER, postelectrophoresis relaxation. fIn previous work (27) we determined the potential that characterizes the interactions between proteins in mouse liver gap junction at high (native) lateral densities. Since it is possible that the gapjunction force varies with density (29), we defer analysis of diffusion in the presence of the gap-junction potential.
Proc. Natl. Acad. Sci. USA Vol. 85, pp. 6726-6730, September 1988
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The lateral diffusion of membrane proteins has been extensively studied (1-8). A considerable body of experimental data has established rates of protein diffusion in both natural membranes and well-characterized Mhodel bilayer systems. The experimental work has hdlped to identify the physical variables (e.g., membrane viscosity, temperature, protein geometry, and protein concentration) that influence diffusion and has amply demonstrated the biological importance of protein mobility. Theoretical descriptions of two-dimensional diffusion (9, 10) have qlso served to define those properties of the bilayer that most profoundly affect the diffusion of proteins. Similarly, recent computer simulation studies have shown that interprotein interactions modulate membrane protein mobility (11-13).
In this paper we analyze the interaction dependence of two important types of diffusional phenomena in bidmembranes: self diffusion and mutual diffusion. We focus on these two processes because each it manifest experimentally and each underlies fundamental biological phenomena. Self diffusion is perhaps most easily explained in the context of a thought experiment. Imagine a uniform system in which a single solute molecule is labeled. Brownian forces will cause this molecule to undergo some mean-squared displacement (r2) in a time t. In two dimensions, the self-diffusion coefficient, DS, is then defined by the relationship (r2) = 4Dst. Self diffusion is monitored by fluorescence recovery after photobleaching (FRAP; refs. 14-17). Moreover, certain biological processes [e.g., visual transduction (18) and mitochondrial bioenergetics (19)] rely on self-diffusive motion to bring about the requisite intermolecular contacts. Mutual diffusion, on the other hand, refers to the relaxation of fluctuations or gradients in protein concentration. A mutual diffusion coefficient, Dm, can be defined, for example, by Fick's laws. An understanding of mutual diffusion will help us to appreciate protein movement toward coated pits (theoretical discussions include ref. 20 and references therein) and the disassembly of structures such as gap junctions (21). Tfie mutual diffusion coefficient can be experimentally determined by monitoring postelectrophoresis relaxation (PER; refs. 22 and 23).
At infinite dilution, the self- and mutual-diffusion coefficients have the same value, Do. This "bare" diffusion coefficient is given, within the confines of one model, by the Saffman- Delbruck equation (9). However, at nonzero lateral protein densities, membrane proteins interact through mutual excluded volume and sometimes through longer-ranged potentials (24-27). These interactions can produce markedly different density-dependent changes in DS and Dm. Here the aim is to understand the qualitative effects that interactions can have on protein diffusion; hence, we present a relatively simple theory and numerical data that describe dilute systems containing a single protein species. For the sake of clarity, we will temporarily neglect hydrodynamic interactions between protein molecules; the interested reader is referred to the three-dimensional literature (28). We study three analytical potentialsL-hard-core repulsions, soft repulsions, and soft repulsions with weak superimposed attractions-that illustrate the richness of possible interaction- modified diffusive behavior. All three potentials inhibit self diffusion. In contrast, mutual diffusion is slowed by attractions and enhanced by repulsions. We conclude by showing that interaction-induced differences in self diffusion and mutual diffusion could underlie the observed disparity (23) in diffusion coefficients determined by FRAP and PER.
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