多定子细菌鞭毛马达的动力学研究
Dynamics of the bacterial flagellar motor with multiple stators
摘要：
细菌鞭毛马达驱动鞭毛丝的旋转，并使许多种类的细菌能够游动。扭矩是由固定在肽聚糖细胞壁上的定子单元与转子相互作用产生的。最近的实验[Yuan，J. & Berg，H. C.（2008）PNAS 105，1182-1185]表明，在零负载附近，电动机的速度与定子的数量无关。在这里，我们介绍了一个数学模型的电动机动力学，解释这种行为的基础上的一般假设，定子的步进率取决于由定子施加在转子上的转矩。我们发现，电机动力学可以用两个时间尺度来表征：转子的机械旋转的移动时间间隔和定子的化学转变所确定的等待时间间隔。我们发现，这两个时间尺度依赖于不同的负载，并且它们的交叉提供了微观解释实验观察到的扭矩-速度曲线中存在的两个制度。我们还分析了速度波动的单个电机使用我们的模型。我们表明，运动是平滑的，有更多的定子单元。然而，用于这种波动减小的机制取决于负载而不同。我们预测，速度波动是由每转的步数仅在低负载和高负载的外部噪声控制。我们的模型可以推广到研究其他分子马达系统的多个发电单元。
英文摘要：
The bacterial flagellar motor drives the rotation of flagellar filaments and enables many species of bacteria to swim. Torque is generated by interaction of stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent experiments [Yuan, J. & Berg, H. C. (2008) PNAS 105, 1182-1185] show that near zero load the speed of the motor is independent of the number of stators. Here, we introduce a mathematical model of the motor dynamics that explains this behavior based on a general assumption that the stepping rate of a stator depends on the torque exerted by the stator on the rotor. We find that the motor dynamics can be characterized by two time scales: the moving-time interval for the mechanical rotation of the rotor and the waiting-time interval determined by the chemical transitions of the stators. We show that these two time scales depend differently on the load, and that their crossover provides the microscopic explanation for the existence of two regimes in the torque-speed curves observed experimentally. We also analyze the speed fluctuation for a single motor using our model. We show that the motion is smoothed by having more stator units. However, the mechanism for such fluctuation reduction is different depending on the load. We predict that the speed fluctuation is determined by the number of steps per revolution only at low load and is controlled by external noise for high load. Our model can be generalized to study other molecular motor systems with multiple power-generating units.
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