Diffusion-controlled reaction between polymers and receptors on membranes

We propose a physical model for the diffusion-controlled reaction between polymers and receptors on a membrane surface. By using the superposition approximation, we solve the hierarchical reaction-diffusion equation and determine the reaction rate for a variety of situations. The functional group attached to a polymer behaves as a Brownian particle on a long time scale. On a time scale shorter than the relaxation time of the polymer conformation, dynamics of the functional group constrained within the polymer size enhance the reaction rate. If the receptor is allowed to diffuse on the membrane surface, the reaction rate is further enhanced, due to the spanning effect of the receptor over multiple polymer molecules.