Receptor-ligand diffusion-limited reaction rates on curved membranes

We provide an expression for the diffusion-limited reaction rate on a curved surface, or membrane, in perturbative deformation regime. This result is applied to specific case of calculating receptor-ligand association at membrane deforming, transmembrane receptor proteins, inclusions. The dynamics mechanochemical coupling between chemical activity and local curvature further investigated, effect thermal fluctuations also discussed. It found inclusions, that their concomitant rates can be typically reduced by as much 20% due locally induced geometry.