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Run-and-tumble processes successfully model several living systems. Whilestudies have typically focused on particles with isotropic tumbles, recentexamples exhibit "tumble-turns", in which particles undergo 90{\deg} tumblesand so possess explicitly anisotropic dynamics. We study the consequences ofsuch tumble-turn anisotropicity at both short and long-time scales. We modelrun-and-tumble-turn particles as self-propelled particles subjected to anangular potential. Using agent-based simulations, we study the interplay ofnoise and potential on the particles' trajectories, demonstrating that thelong-time effect is to alter the tumble-turn time, which governs the long-timedynamics. In particular, when normalized by this timescale, trajectories becomeindependent of the underlying details of the potential. As such, we develop asimplified continuum theory, which quantitatively agrees with agentsimulations. The hydrodynamic limit reveals that the transition to diffusivedynamics precedes the transition to isotropic dynamics as the hydrodynamiclimit, while purely diffusive, can drive anisotropicity at intermediate times.

Anisotropic run-and-tumble-turn dynamics