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 〈x²〉∼ t^α. 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 α and therefore no evidence to suggest that it has been a target of evolutionary optimization.

Eaves, J. D. and Reichman, D. R. The subdiffusive targeting problem. J. Phys. Chem. B. 112, 4283 (2008)