The subdiffusive targeting problem.

Recent experiments in living cells have observed subdiffusive motion, where the mean squared displacement of a molecule grows sublinearly with time as [x (2)] approximately t(alpha). Motivated by these experiments, we develop a theory for subdiffusion-limited bimolecular enzyme kinetics. As in normal diffusion, the statistics of the reaction times depend on the ratio between the distance to the target and the reaction rate in a scale invariant manner. Contrary to some studies, we find no critical value of alpha and therefore no evidence to suggest that it has been a target of evolutionary optimization.