Active Brownian motion with directional reversals

Abstract

Active Brownian motion with intermittent direction reversals is common in bacteria like Myxococcus xanthus and Pseudomonas putida. We show that, for such a motion in two dimensions, the presence of the two timescales set by the rotational diffusion constant D-R and the reversal rate gamma gives rise to four distinct dynamical regimes: (I) t << min(gamma(-1), D-R(-1)), (II) gamma(-1) << t << D-R(-1), (III) D-R(-1) << t << gamma(-1), and (IV) t >> max(gamma(-1), D-R(-1)), showing distinct behaviors. We characterize these behaviors by analytically computing the position distribution and persistence exponents. The position distribution shows a crossover from a strongly nondiffusive and anisotropic behavior at short times to a diffusive isotropic behavior via an intermediate regime, II or III. In regime II, we show that, the position distribution along the direction orthogonal to the initial orientation is a function of the scaled variable z alpha x(perpendicular to)/t with a nontrivial scaling function, f (z) = (2 pi(3))(-1/2)Gamma(1/4 + iz)Gamma(1/4 - iz). Furthermore, by computing the exact first-passage time distribution, we show that a persistence exponent alpha = 1 emerges due to the direction reversal in this regime.