Chemotactic drift speed for bacterial motility pattern with two alternating turning events

TL;DR

This paper extends the linear theory of bacterial chemotaxis to calculate drift speed for bacteria with two alternating turning angles, relating chemotactic efficiency to cell size using experimental data.

Contribution

It generalizes the linear chemotaxis theory to include bacteria with two alternating turning angles, providing a framework to analyze more complex motility patterns.

Findings

Derived formulas for drift speed with two turning angles.

Linked chemotactic efficiency to bacterial cell size.

Applicable to various motility patterns with alternating angles.

Abstract

Bacterial chemotaxis is one of the most extensively studied adaptive responses in cells. Many bacteria are able to bias their apparently random motion to produce a drift in the direction of the increasing chemoattractant concentration. It has been recognized that the particular motility pattern employed by moving bacteria has a direct impact on the efficiency of chemotaxis. The linear theory of chemotaxis pioneered by de Gennes allows for calculation of the drift velocity in small gradients for bacteria with basic motility patterns. However, recent experimental data on several bacterial species highlighted the motility pattern where the almost straight runs of cells are interspersed with turning events leading to the reorientation of the cell swimming directions with two distinct angles following in strictly alternating order. In this manuscript we generalize the linear theory of chemotaxis to calculate the chemotactic drift speed for the motility pattern of bacteria with two turning angles. By using the experimental data on motility parameters of {\em V. alginolyticus } bacteria we can use our theory to relate the efficiency of chemotaxis and the size of bacterial cell body. The results of this work can have a straightforward extension to address most general motility patterns with alternating angles, speeds and durations of runs.