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Bacterial chemotaxis is one of the most extensively studied adaptiveresponses in cells. Many bacteria are able to bias their apparently randommotion to produce a drift in the direction of the increasing chemoattractantconcentration. It has been recognized that the particular motility patternemployed by moving bacteria has a direct impact on the efficiency ofchemotaxis. The linear theory of chemotaxis pioneered by de Gennes allows forcalculation of the drift velocity in small gradients for bacteria with basicmotility patterns. However, recent experimental data on several bacterialspecies highlighted the motility pattern where the almost straight runs ofcells are interspersed with turning events leading to the reorientation of thecell swimming directions with two distinct angles following in strictlyalternating order. In this manuscript we generalize the linear theory ofchemotaxis to calculate the chemotactic drift speed for the motility pattern ofbacteria with two turning angles. By using the experimental data on motilityparameters of {\em V. alginolyticus } bacteria we can use our theory to relatethe efficiency of chemotaxis and the size of bacterial cell body. The resultsof this work can have a straightforward extension to address most generalmotility patterns with alternating angles, speeds and durations of runs.

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