Optimal search in E.coli chemotaxis

TL;DR

This paper investigates the optimal width of a Gaussian nutrient concentration profile that minimizes the search time of E.coli bacteria in chemotaxis, considering both deterministic and stochastic initial conditions and time-varying fields.

Contribution

It identifies the existence of an optimal Gaussian width for efficient bacterial search and validates findings through analytical and numerical methods in various scenarios.

Findings

Optimal Gaussian width minimizes search time.

Existence of optimal width confirmed for different initial conditions.

Numerical simulations agree with analytical predictions.

Abstract

We study chemotaxis of a single {\sl E.coli} bacterium in a medium where the nutrient chemical is also undergoing diffusion and its concentration has the form of a Gaussian whose width increases with time. We measure the average first passage time of the bacterium at a region of high nutrient concentration. In the limit of very slow nutrient diffusion, the bacterium effectively experiences a Gaussian concentration profile with a fixed width. In this case we find that there exists an optimum width of the Gaussian when the average first passage time is minimum, {\sl i.e.}, the search process is most efficient. We verify the existence of the optimum width for the deterministic initial position of the bacterium and also for the stochastic initial position, drawn from uniform and steady state distributions. Our numerical simulation in a model of a non-Markovian random walker agrees well with our analytical calculations in a related coarse-grained model. We also present our simulation results for the case when the nutrient diffusion and bacterial motion occur over comparable time-scales and the bacterium senses a time-varying concentration field.