Invariance properties of bacterial random walks inside domains with variable geometry and structural disorder

Motile cells often explore natural environments characterized by a high degree of structural complexity. Moreover cell motility is also intrinsically noisy due to spontaneous random reorientation and speed fluctuations. The interplay of different noise sources gives rise to complex dynamical behavior that can be strongly sensitive to details and hard to model quantitatively. In striking contrast to this general picture we show that the mean residence time of swimming bacteria inside artificial complex microstructures
can be quantitatively predicted by a generalization to active matter of a recently discovered invariance property of random walks. By systematically varying geometry and structural disorder we produce systems that exhibit strongly different distributions of path length and dwell time but whose mean values is invariant and can be predicted with precision by the sole free volume to surface ratio.
Biological implications include the possibility of predicting and controlling the colonization of complex natural environments using only geometric informations.