An idealized dynamical model of simple diffusional interactions between macromolecules and between macromolecules and surfaces

Abstract

A model for hard-sphere, nonelectrostatic diffusional interactions between macromolecules and between macromolecules and surfaces is presented. Quantities such as average free path and impact frequency are derived, being validated by full three-dimensional simulations of large numbers of random flights. A method for obtaining the total collision rate is developed based on absorption boundary conditions applied to the time-independent diffusion equation, multiplied by the probable number of subsequent encounters. A distribution function is obtained that describes both the spatial and temporal impact profiles of diffusing molecules with surfaces as well as the detailed nature of individual encounters. Conclusions are that the interaction of diffusing macromolecules with surfaces is an extremely efficient process; trajectories are typified by clusters of relatively closely spaced encounters separated by relatively long excursions prior to reimpact. Results should be applicable to the development of kinetic models for describing such complex phenomena as ligand binding to receptors on cell surfaces.