title: Optimal search in E. coli chemotaxis.
abstract: We study chemotaxis of a single 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, 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.
authors.affiliation: Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India.
authors.forename: Subrata
authors.initials: S
authors.lastname: Dev
authors.affiliation: Department of Theoretical Sciences, S. N. Bose National Centre for Basic Sciences, Block JD, Sector III, Salt Lake, Kolkata 700098, India.
authors.forename: Sakuntala
authors.initials: S
authors.lastname: Chatterjee
mesh_terms: D002633:Chemotaxis; D003198:Computer Simulation; D004058:Diffusion; D004926:Escherichia coli / Q000502:physiology*; D005502:Food; D008954:Models, Biological; D009010:Monte Carlo Method; D009068:Movement; D013269:Stochastic Processes