Instituto de Investigaciones Físicas de Mar del Plata, UNMdP and CONICET, Argentina.
Soft Matter. 2017 May 11;13(18):3385-3394. doi: 10.1039/c6sm02771g.
In this work we introduce a stochastic model to describe directional changes in the movement of swimming bacteria. We use the probability density function (PDF) of turn angles, measured on tumbling wild-type E. coli, to build a Langevin equation for the deflection of the bacterial body swimming in isotropic media. We have solved this equation analytically by means of the Green function method and shown that three parameters are sufficient to describe the movement: the characteristic time, the steady-state solution and the control parameter. We conclude that the tumble motion, which is manifested as abrupt turns, is primarily caused by the rotational boost generated by the flagellar motor and complementarily by the rotational diffusion introduced by noise. We show that in the tumble motion the deflection is a non-stationary stochastic process during times at which the tumbling occurs. By tuning the control parameter our model is able to explain small turns of the bacteria around their centres of mass along the run. We show that the deflection during the run is an Ornstein-Uhlenbeck process, which for typical run times is stationary. We conclude that, along the run, the rotational boosts do not exist and that only the rotational diffusion remains. Thus we have a single model to explain the turns of the bacterium during the run or tumble movements, through a control parameter that can be tuned through a critical value that can explain the transition between the two turn behaviours. This model is also able to explain in a very satisfactory way all available statistical experimental data, such as PDFs and average values of turning angles times, of both run and tumble motions.
在这项工作中，我们引入了一个随机模型来描述游泳细菌运动方向的变化。我们使用翻滚野生型大肠杆菌的转角概率密度函数（PDF）来构建各向同性介质中细菌体偏折的朗之万方程。我们通过格林函数方法对该方程进行了分析求解，并表明有三个参数足以描述细菌的运动：特征时间、稳态解和控制参数。我们得出结论，翻滚运动（表现为突然转弯）主要是由鞭毛马达产生的旋转加速引起的，而旋转扩散则是由噪声引起的。我们表明，在翻滚运动期间，当翻滚发生时，偏折是一个非稳态随机过程。通过调整控制参数，我们的模型能够解释细菌围绕质心的小转弯。我们表明，在奔跑过程中，偏折是一个 Ornstein-Uhlenbeck 过程，对于典型的奔跑时间是稳定的。我们得出结论，在奔跑过程中，旋转加速并不存在，只有旋转扩散仍然存在。因此，我们有一个单一的模型来解释细菌在奔跑或翻滚过程中的转弯，通过一个可以通过一个临界值来调整的控制参数，这个临界值可以解释两种转弯行为之间的转变。该模型还能够非常满意地解释所有可用的统计实验数据，如 PDF 和转弯角度的平均值，无论是奔跑还是翻滚运动。
