Kinetic analysis of the attachment of a biological particle to a surface by macromolecular binding

Motivated by the problem of microbial deposition, a dynamic model is developed for the attachment of a Brownian particle to a surface mediated by colloidal forces as well as macromolecular bridging. The model predicts the attachment probability of the particle to the surface based upon the free energy as a function of fluctuating bond number and separation distance from the surface. From this model, the mean first-passage time approach is used to predict the mean time required for the particle moving from the unattached state to the attached state based on the properties of the binding macromolecules. This approach provides an analytical approximation for mean transition time from the secondary energy minimum as well as the attachment rate constant for the general case where neither binding nor particle diffusion are necessarily rate-limiting.