Abstract
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 reorientations 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 is quantitatively predicted by a generic invariance property of random walks. We find that while external shape and internal disorder have dramatic effects on the distributions of path lengths and residence times, the corresponding mean values are constrained by the sole free surface to perimeter ratio. As a counterintuitive consequence, bacteria escape faster from structures with higher density of obstacles due to the lower accessible surface.
Highlights
Motile cells often explore natural environments characterized by a high degree of structural complexity
A recently rediscovered invariance property of random walks implies that the average path length inside a closed domain of arbitrary shape is only proportional to the volume to surface ratio with a numerical prefactor that solely depends on the spatial dimensions[15,16]
The pillars play the role of obstacles and by varying their number we can tune the degree of internal complexity of the structures
Summary
Motile cells often explore natural environments characterized by a high degree of structural complexity. Cell motility is intrinsically noisy due to spontaneous random reorientations 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 is quantitatively predicted by a generic invariance property of random walks. Arrays of scattering obstacles have been used to demonstrate the possibility of rectification and sorting in self-propelled systems[9–11] In these applications it is often found that small details in dynamical behavior can have significant quantitative consequences. For all obstacle densities, the mean residence time is only determined by the microstructure surface to perimeter ratio and the mean inverse speed
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