A Discrete Biased Random Walk Model Based on Bacterial Chemotaxis

Abstract eng:
A bacterial cell moves in a ballistic manner for a certain time period (run), and then changes its direction randomly (tumble). When a cell senses that it has moved to higher attractant chemical concentration, it reduces the frequency of the direction change. Collectively, this modulation produces bacterial chemotactic response, in which the cells accumulate around the chemoattractant source. In this study, a discrete biased random walk model based on bacterial chemotaxis was investigated. A steady distribution of cells was analytically obtained in one dimensional model. In this model, the cells move along a uniformly spaced number line at the rate of one interval per time step. A chemical attractant source is placed at the origin. The probability mass function of cells decays with the distance from the source as a geometric sequence. We confirmed the distribution by Monte Carlo simulations.

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