Monte Carlo simulation of particle adsorption rates at high cell concentration

A practical method of simulating Brownian diffusion of small particles and their adsorption by randomly placed cells is used to estimate the adsorption process rate constant. The ratio of the rate constant to its classical value, 4 pi RD for dilute perfectly adsorbing spheres, is found to be determined by cellular excluded volume. This ratio varies from 1 for dilute solutions of spheres to approximately 40 for spheres in the maximum possible concentration. A function that usefully estimates the rate constant for all possible values of cell concentration, cell radius, and particle diffusion constant is given for random fields of identical spherical cells. The method is also applied to primitive cubic, body centered, and face centered lattices of spheres. At any given excluded volume and concentration the face and body centered lattices have about the same adsorption rate constant whereas the primitive cubic lattices has a smaller one which is, in turn, greater than that for randomly placed spheres. The results will be useful in determining diffusion limited reaction rates under high excluded volume conditions. These include adsorption by red blood cells at normal concentration, the adsorption of molecules by beads in a column, and adsorption of bacteriophage at very high bacterial concentrations.