Reaction rate enhancement by surface diffusion of adsorbates

Ligands can be captured by a surface target through either direct bulk diffusion or surface diffusion following reversible adsorption to the surface. We have solved a steady state boundary value problem for a perfect sink disk target in the surface, taking into account bulk and surface diffusion coefficients D and Ds and adsorption/desorption kinetic rate constants ka and kd at non-target regions. Solutions have been successfully found by numerical computation. The results show that the rate of capture from the surface depends non-linearly on Ds, D, ka, kd and geometrical dimensions. In particular, we demonstrate that not only is the non-target region equilibrium constant Keq (= ka/kd) important in determining the rate of capture from the surface, but so are the kinetic rate constants ka and kd separately. In all cases, the surface adsorption/diffusion combination enhances the total rate of capture. The results should be useful for predicting reaction rates of biological membrane bound receptor clusters and substrate-immobilized enzymes.