The present proposal is to explore, by means of numerical and theoretical investigations, the feasibility of the hypothesis that biomembranes define spaces that have a random fractal geometry, and to design experimental tests of the hypothesis. Numerical methods will be developed for the study of molecular mobility in two-dimensional hard sphere fluids, so that the time/distance scale dependence of lipid/lipid and lipid/protein obstruction can be more fully elucidated. Experimental measurements of anomalous transport properties will be developed in order to find evidence of (1) dependence of the diffusion coefficient on the measurement length scale and (2) time- dependence of the second order rate coefficient in homogeneous solutions and in biomembranes. The goal of these research planning activities is to design experimental and theoretical protocols that will form the basis of a proposal to the NSF for a Research in Undergraduate Institutions grant, to support a three year program of research carried out be undergraduate students at Lawrence University, under the direction of the present PI. %%% Molecular mobility may be an important determinant of metabolic rates in biomembranes, particularly for enzymes and substrates that are spatially restricted, as in portions of the photosynthetic and respiratory electron transport chains. Biomembranes are heterogeneous, disordered media that may possess fractal geometry. Recent theoretical investigations have suggested that transport properties, such as diffusion and conduction, may well be anomalous in heterogeneous spaces. The diffusion constant has been shown to depend on the length scale of measurement in random fractals, and the rate coefficient of bimolecular reactions, a constant in homogeneous reaction spaces, has been shown to be time dependent. The research planning activities proposed here are motivated by the idea that these recent theoretical developments may provide fundamental new insights into the nature of molecular mobility in biomembranes. If membranes are fractal objects, then they may display anomalous transport properties experimentally, and this may not only resolve some longstanding issues in biophysics, such as the disagreement between diffusion constants measured on different length scales, but also have profound metabolic implications.
