Run-and-tumble particles with preferred reorientation

Abstract

Run-and-tumble particles (RTPs) are canonically modeled with uniform reorientation probabilities, an assumption that breaks down for many biological microswimmers. In this work, we investigate the dynamics of RTPs with arbitrary non-uniform tumble distributions. By deriving an exact Doi-Peliti field theory, we explicitly calculate a wide array of spatial and orientational observables. Notably, we demonstrate that the spatial dynamics exhibit an effective persistence and chirality governed entirely by the first Fourier modes of the tumble distribution, establishing a formal mapping to the dynamics of chiral active Brownian particles. Furthermore, our field-theoretic framework provides a systematic method to compute spatial moments to arbitrary order, allowing for the complete characterization and identification of complex tumbling dynamics. We illustrate the framework with wrapped Gaussian and bimodal Gaussian distributions, demonstrating explicit control over persistence and chirality. We further extend the field theory to $d$ dimensions, recovering the mean squared displacement in terms of a single effective tumble rate. Our results establish a direct link between the shape of the tumble distribution and the emergent dynamics, and provide a foundation for the study of interacting RTPs with non-uniform reorientation.

21 pages, 7 figures