Trail-mediated self-interaction

A number of microorganisms leave persistent trails while moving along surfaces. For single-cell organisms, the trail-mediated self-interaction will influence the dynamics. It has been discussed recently [Kranz et al., Phys. Rev. Lett. 117, 038101 (2016)] that the self-interaction may localize the organism above a critical coupling (c) to the trail. Here, we will derive a generalized active particle model capturing the key features of the self-interaction and analyze its behavior for smaller couplings < (c). We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.