Barkai, Garini, and Metzler reply: We thank Bob Eisenberg for his comment. Indeed, the role of electrostatic effects in the complex dynamics measured in macromolecularly crowded systems is an open question. Typically, biopolymers, and many artificial crowding agents, do carry surface charges. In physiological salt conditions, counterions screen electrostatic fields over nanometer length scales and are highly mobile, yet one perhaps cannot exclude force mediation between the macromolecules in solution due to electrostatic effects. An immediate consequence should be an increased effective size of biomacromolecules due to coordinated counterion layers.
The data from numerous single-particle tracking experiments in living cells and artificially crowded environments clearly show anomalous diffusion, including observations of weak ergodicity breaking and aging. Our analysis in terms of stochastic processes remains valid, independent of the specific—and likely complex—physical description based on first principles. That validity is due to the probabilistic nature of the stochastic approach: Although it captures the detailed dynamics of a system, it is not limited to specific kinds of interactions. Future studies of the effects of temperature and charges in crowded cells should prove interesting. For example, the influence of charges on the anomalous diffusion exponent α and the anomalous diffusion constant Kα in the mean squared displacement 〈r2(t)〉 ≃ Kαtα remains an open challenge for both theory and experiment.
