Diffusion influenced binary reactive processes in membranes involving identical particles: a Monte Carlo study.

Simple random walk simulations on triangular lattices were performed in order to obtain a basic quantitative understanding of the kinetics of diffusion influenced binary reactive processes of membrane associated peptides or proteins within the two dimensionality of lipid bilayers. The results of the Monte Carlo simulations are compared with various formal approximate steady-state approaches, such as presented by Keizer [Acc. Chem. Res., 18 (1985) 235-241] in the context of statistical nonequilibrium thermodynamics or by Hardt [Biophys. Chem., 10 (1979) 239-243], based on the well known work of Delbrück and Adam. For diffusion controlled binary reactions of identical particles, nice agreement with the numerically simulated values is found in the low concentration limit for both Hardt's and Keizer's approach. For the latter a fluctuating steady-state particle source has to be considered. The dependence of the steady-state rate coefficient on system size is investigated, and the results are compared to the work of Swartz and Peacock-López [J. Chem. Phys., 95 (4) (1991) 2727-2731]. In order to elucidate the results, a practical application is considered. An application to a dimerization reaction on vesicles of typical experimental dimensions is given.