Stochastic nanoswimmer: a multistate model for enzyme self-propulsion and enhanced diffusion

Several enzymes show enhanced diffusion in the presence of substrate a feature that is explained by postulating that the enzyme in the bound state has a higher diffusion constant than in the unbound state. In a recent experiment [Jee et al. PNAS, 115, E10812 (2018)], it was observed that some of these enzymes perform a run-and-tumble motion, where the self-propulsion velocities can be of the order of mm/s. Theoretical models of nanoscale swimmers have not been able to explain the high self-propulsion speeds measured in experiments. Here we model the enzyme as a dimer with fluctuating mobility. We show that even a dimer can perform a run-and-tumble motion when the dimer switches between states of different mobility in the enzymatic cycle. Within a three-state enzymatic cycle, we investigate the conditions under which self-propulsion speeds consistent with experiments can be obtained.