Abstract
The bacterium Escherichia coli in suspension in a liquid medium swims by a succession of runs and tumbles, effectively describing a random walk. The tumbles randomize incompletely, i.e. with a directional persistence, the orientation taken by the bacterium. Here, we model these tumbles by an active rotational diffusion process characterized by a diffusion coefficient and a diffusion time. In homogeneous media, this description accounts well for the experimental reorientations. In shallow gradients of nutrients, tumbles are still described by a unique rotational diffusion coefficient. Together with an increase in the run length, these tumbles significantly contribute to the net chemotactic drift via a modulation of their duration as a function of the direction of the preceding run. Finally, we discuss the limits of this model in propagating concentration waves characterized by steep gradients. In that case, the effective rotational diffusion coefficient itself varies with the direction of the preceding run. We propose that this effect is related to the number of flagella involved in the reorientation process.
Highlights
Micro-organisms living in liquids have developed several strategies to explore their environment and colonize new niches more favorable for their development [1,2,3]
One of the most studied organisms, in this respect, is probably the petrichously flagellated bacterium Escherichia coli whose motion is classically described by a succession of runs and tumbles [4]
The authors have shown that the active translational diffusion coefficient of a bacteria is affected by its mean reorientation angle following, Dt~
Summary
Micro-organisms living in liquids have developed several strategies to explore their environment and colonize new niches more favorable (nutrients, temperature, oxygen...) for their development [1,2,3]. One of the most studied organisms, in this respect, is probably the petrichously flagellated bacterium Escherichia coli whose motion is classically described by a succession of runs and tumbles [4]. Run and tumble durations are exponentially distributed with mean durations that are respectively ,trun., s and ,ttumble.,0.1 s [6]. It has been noticed in [7] that the reorientations during tumbles were not fully random and that it was necessary to introduce a directional persistence (or a memory in the orientation between two successive runs) to describe the 3D trajectory of the bacterium. The trajectory can be described by a persistent random walk characterized by an active translational diffusion coefficient Dt,Vrun2,trun.,100 mm2/s [8,9] comparable to the one of a small molecule experiencing Brownian motion [10]
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