Non-Gauss Athermal Fluctuations in Bacterial Bath

Abstract

Many active materials and biological systems are driven far from equilibrium by inclusions that spontaneously generate forces and give rise to flows/distortions in the surrounding material. Probing and characterizing these athermal fluctuations are essential to understand the properties and behaviors of such systems. Bacterial bath, where microscopic force generators (swimming E-coli) are randomly distributed in fluids, is a simple model system to study non-equilibrium fluctuation. We observe the trajectory of passive tracers dispersed in bacterial bath with video microscopy and analyze the lag-time dependent distribution of the displacements (van-Hove correlation function). It is found that for long lag times, the distributions are highly non-Gauss with broad tail, similar to those found in active cytoskeletal networks (actin gel actively actuated with myosin motor proteins). It has been found that the van Hove distribution in active cytoskeletal networks follows truncated Levy statistics; since the fluctuation driven by single force generator presents power-law distribution with diverging variance, sum action of multiple motor proteins converges to Levy distribution rather than Gauss by generalized central limit theorem. However, the origin of non-Gauss fluctuations is still elusive in bacterial bath suspension.Here we discuss an analogy between fluctuations in bacterial bath and those in active cytoskeletal networks, based on the fact that the impact of single force generator in these systems (velocity field around a bacteria and displacement field around a motor protein) both exhibit 1/r2 spatial decay.