Persistence of direction increases the drift velocity of run and tumble chemotaxis

TL;DR

This paper analytically investigates how persistence of direction, temporal gradient sensing, and Brownian motion influence the drift velocity in E. coli chemotaxis, revealing a synergy that enhances movement efficiency.

Contribution

It provides an analytic model incorporating persistence, temporal sensing, and Brownian motion, which was previously neglected in chemotaxis models.

Findings

Persistence of direction enhances drift velocity.

Temporal comparisons synergize with persistence to improve chemotaxis.

Rotational Brownian motion reduces drift velocity.

Abstract

Escherichia coli is a motile bacterium that moves up a chemoattractant gradient by performing a biased random walk composed of alternating runs and tumbles. Previous models of run and tumble chemotaxis neglect one or more features of the motion, namely (i) a cell cannot directly detect a chemoattractant gradient but rather makes temporal comparisons of chemoattractant concentration, (ii) rather than being entirely random, tumbles exhibit persistence of direction, meaning that the new direction after a tumble is more likely to be in the forward hemisphere, and (iii) rotational Brownian motion makes it impossible for an E. coli cell to swim in a straight line during a run. This paper presents an analytic calculation of the chemotactic drift velocity taking account of (i), (ii) and (iii), for weak chemotaxis. The analytic results are verified by Monte Carlo simulation. The results reveal a synergy between temporal comparisons and persistence that enhances the drift velocity, while rotational Brownian motion reduces the drift velocity.