Switching Statistics of a Flagellar Motor: First-Passage Time and Dynamic Binding

Bacterial chemotaxis relies on the clockwise-to-counterclockwise switching (and the reverse CCW-to-CW switching) of the flagellar motor’s rotational direction. Yet, despite its central role, the switch mechanism remains poorly understood. Here we study the switch statistics of the flagellar motor using computer simulations that combine first-passage time ideas and the property of dynamic binding of CheY-P to FliM. The simulated clockwise bias and switching frequency as a function of CheY-P concentration agree with the experimental results for E. coli. Moreover, the simulation results show a robust peak, which is present in some experimental reports, in the distribution of the time intervals of both clockwise and counterclockwise rotation.     

Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.