Diffusion and multistage kinetics of macromolecular and viral adsorption

We derive the equations that describe adsorption of diffusing particles onto a surface followed by additional surface kinetic steps before being transported across the interface. Multistage surface kinetics occurs during membrane protein insertion, cell signaling, and the infection of cells by virus particles. For example, after nonspecific binding, additional kinetic steps, such as binding of receptors and coreceptors, must occur before virus particle fusion can occur. We couple the diffusion of particles in the bulk phase with the surface kinetics and derive an effective, integro-differential boundary condition that contains a memory kernel describing the delay induced by the surface reactions. This boundary condition takes the form of a singular perturbation problem in the limit where particle-surface interactions are short-ranged. Moreover, depending on the surface kinetics, the delay kernel induces a nonmonotonic, transient replenishment of the bulk particle concentration near the interface. Our approach generalizes that of Ward and Tordai [1] and Diamant and Andelman [2] to include surface kinetics, giving rise to qualitatively new behaviors.