We introduce a reaction-diffusion system capable of modeling ligand migration inside of proteins as well as conformational fluctuations of proteins, and present a detailed analytical and numerical analysis of this system in general dimension. The main observable, the probability of finding the system in the starting state, exhibits dimension-dependent as well as dimension-independent properties, allowing for sharp experimental tests of the effective dimension of the process in question. We discuss the application of this theory to ligand migration in myoglobin and to the description of gating fluctuations of ion channel proteins.