  A number of microorganisms leave persistent trails while moving along
surfaces. For single-cell organisms, the trail-mediated self-interaction will
influence its dynamics. It has been discussed recently [Kranz \textit{et al.}
Phys. Rev. Lett. \textbf{117}, 8101 (2016)] that the self-interaction may
localize the organism above a critical coupling $\chi_c$ 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 $\chi <
\chi_c$. We find that fluctuations in propulsion speed shift the localization
transition to stronger couplings.
