Exit times of totally asymmetric simple exclusion processes.

We address the question of the time needed by N particles, initially located on the first sites of a finite one-dimensional lattice of size L, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when N≪L, the mean exit time of the particles is asymptotically given by T_{N}(L)∼L+ß_{N}sqrt[L] for large lattices. Building upon exact results obtained for two particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients ß_{N}. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of N particles in the regime where N is finite while the lattice size L→∞. This complements previous asymptotic results obtained by Johansson [Commun. Math. Phys. 209, 437 (2000)0010-361610.1007/s002200050027] in the limit where both N and L tend to infinity while keeping the particle density N/L finite.

Relaxation time asymmetry in stator dynamics of the bacterial flagellar motor.

The bacterial flagellar motor is the membrane-embedded rotary motor, which turns the flagellum that provides thrust to many bacteria. This large multimeric complex, composed of a few dozen constituent proteins, is a hallmark of dynamic subunit exchange. The stator units are inner-membrane ion channels that dynamically bind to the peptidoglycan at the rotor periphery and apply torque. Their dynamic exchange is a function of the viscous load on the flagellum, allowing the bacterium to adapt to its local environment, although the molecular mechanisms of mechanosensitivity remain unknown. Here, by actively perturbing the steady-state stator stoichiometry of individual motors, we reveal a stoichiometry-dependent asymmetry in stator remodeling kinetics. We interrogate the potential effect of next-neighbor interactions and local stator unit depletion and find that neither can explain the observed asymmetry. We then simulate and fit two mechanistically diverse models that recapitulate the asymmetry, finding assembly dynamics to be particularly well described by a two-state catch-bond mechanism.