Run-and-tumble bacteria slowly approaching the diffusive regime

Physical Review. E
Andrea Villa-TorrealbaRodrigo Soto

Abstract

The run-and-tumble (RT) dynamics followed by bacterial swimmers gives rise first to a ballistic motion due to their persistence and later, through consecutive tumbles, to a diffusive process. Here we investigate how long it takes for a dilute swimmer suspension to reach the diffusive regime as well as what is the amplitude of the deviations from the diffusive dynamics. A linear time dependence of the mean-squared displacement (MSD) is insufficient to characterize diffusion and thus we also focus on the excess kurtosis of the displacement distribution. Four swimming strategies are considered: (i) the conventional RT model with complete reorientation after tumbling; (ii) the case of partial reorientation, characterized by a distribution of tumbling angles; (iii) a run-and-reverse model with rotational diffusion; and (iv) a RT particle where the tumbling rate depends on the stochastic concentration of an internal protein. By analyzing the associated kinetic equations for the probability density function and simulating the models, we find that for models (ii), (iii), and (iv) the relaxation to diffusion can take much longer than the mean time between tumble events, evidencing the existence of large tails in the particle displacemen...Continue Reading

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Jan 22, 2021·Soft Matter·Pablo de CastroPeter Sollich

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