  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. This
interplay of internal and external noise sources gives rise to a 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 of a
recently discovered invariance property of random walks. We find that
variations in geometry and structural disorder have a dramatic effect on the
distributions of path length while mean values are strictly constrained 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.
