Effective dynamics of microorganisms that interact with their own trail

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the timescale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.