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A number of microorganisms leave persistent trails while moving alongsurfaces. For single-cell organisms, the trail-mediated self-interaction willinfluence its dynamics. It has been discussed recently [Kranz \textit{et al.}Phys. Rev. Lett. \textbf{117}, 8101 (2016)] that the self-interaction maylocalize the organism above a critical coupling $\chi_c$ to the trail. Here wewill derive a generalized active particle model capturing the key features ofthe self-interaction and analyze its behavior for smaller couplings $\chi <\chi_c$. We find that fluctuations in propulsion speed shift the localizationtransition to stronger couplings.

Trail-Mediated Self-Interaction