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

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 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.

细菌趋化性（bacterial chemotaxis）是细胞领域被广泛研究的适应性应答之一。诸多细菌可调控其看似随机的运动，使其朝着趋化剂浓度升高的方向产生定向漂移。学界已达成共识：运动细菌所采用的特定运动模式，会直接影响趋化作用的效率。由德热纳（de Gennes）开创的趋化性线性理论，可用于计算具有基础运动模式的细菌在弱浓度梯度下的漂移速度。然而，近期针对多种细菌的实验数据揭示了一种特殊运动模式：细菌近乎直线的游动段会穿插转向事件，转向后细胞的游动方向会以严格交替的顺序切换为两种截然不同的角度。本文将趋化性线性理论进行推广，以计算具有两种转向角度的细菌运动模式下的趋化漂移速度。通过利用溶藻弧菌（V. alginolyticus）运动参数的实验数据，我们可借助本理论关联趋化效率与细菌菌体的尺寸。本研究的结论可直接推广至绝大多数具备交替转向角度、运动速度及游动段持续时间的通用运动模式场景。