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We propose a physical model for the di usion-controlled reaction between polymers and receptors on a membrane surface. By using the superposition approximation, we solve the hierarchical reaction-di usion 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 di use on the membrane surface, the reaction rate is further enhanced, due to the spanning e ect of the receptor over multiple polymer molecules.


We propose a physical model for the di usion-controlled reaction between polymers and receptors on a membrane surface. By using the superposition approximation, we solve the hierarchical reaction-di usion 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 di use on the membrane surface, the reaction rate is further enhanced, due to the spanning e ect of the receptor over multiple polymer molecules.