Mathematical models for rotary protein motors driven by membrane potential

描述（由申请人提供）：细菌鞭毛马达（BFM）和ATP合酶的Fo马达（FoM）是唯一已知的由跨膜离子电位驱动的旋转蛋白马达。鞭毛马达是许多细菌物种中的运动细胞器，而鞭毛马达是细菌中的运动细胞器。 FoM驱动ATP的合成，ATP是通用的细胞燃料。这两种蛋白质在细胞生命中起着重要作用。到目前为止开发的数学模型从现象学上描述了电机的功能。也就是说，定子和转子之间的相互作用是通过构建驱动电位来处理的，这些驱动电位被人工调整以适应测量的行为。在缺乏详细的分子结构的情况下，这已经足够好了。然而，最近的实验已经阐明了这些马达的许多组件结构，我们可以直接解决分子间力如何合谋产生旋转扭矩的问题。一个基于结构的模型将提供一个解释如何跨膜离子电位转换成旋转扭矩，以及如何绑定的CheYP的转子反转扭矩。这一过程控制着细菌的“奔跑”和“翻滚”， 是其趋化性的基础。在目标1中，我们将使用定子和转子蛋白质的可用结构信息来解决由BFM的定子产生扭矩的物理机制。本工作基于D.布莱尔作为动力冲程驱动鞭毛马达的旋转。这种机制是基于脯氨酸残基诱导的构成定子的β-螺旋的弯曲。因此，当阳离子跳跃到定子的离子结合位点上时，该位点附近的氢键重新排列，从而诱导β-螺旋围绕脯氨酸残基的“扭结和旋转”运动。现有的分子动力学模拟，支持我们的能量为基础的计算，表明这是一个积极的合理机制。在这项工作中，我们将开发描述动力冲程机制的数学模型，并专注于解释以下实验：（i）由于定子和转子上的重要电荷突变而导致的电机效率下降，（ii）扭矩-速度曲线，（iii）步长分布，以及（iv）电机反转。我们的研究鞭毛电机说服我们重新审视我们以前发表的模型的Fo电机。在目标2中，我们表明，我们以前提出的静电功率冲程机制应该被替换为构象功率冲程，其在结构上类似于鞭毛马达中的脯氨酸铰链机制。使用这种新的机制，我们将解决一些悬而未决的问题，在供电旋转的FoM。这些研究将提出一个统一的机械化学机制的旋转电机，并可能有助于了解它们是如何从它们的进化的角度相关。

DESCRIPTION (provided by applicant): The bacterial flagellar motor (BFM) and the Fo motor (FoM) of ATP synthase are the only known rotary protein motors driven by transmembrane ion potentials. The flagellar motor is the organelle of locomotion in many bacterial species, while the FoM drives the synthesis of ATP, the universal cell fuel. Both proteins play a fundamental role in the lives of cells. The mathematical models developed until now describe the functioning of the motors phenomenologically. That is, the interactions between the stators and the rotor are treated by constructing driving potentials that are artificially tuned to fit the measured behavior This is good enough in the absence of a detailed molecular structure. However, recent experiments have elucidated many of the component structures of these motors to the point where we can address directly how intermolecular forces conspire to generate the rotary torques. A structure-based model will provide an explanation for how transmembrane ion potentials are converted into rotary torque, and how the binding of CheYP to the rotor reverses the torque. This process controls the alter- nation of 'runs' and 'tumbles' of the bacterium, which is the basis of its chemotaxis. In Aim 1, we will address the physical mechanism by which torque is generated by the stator of the BFM using the available structural information of the stator and rotor proteins. This work is based on the 'proline hinge' mechanism proposed by D. Blair as the power-stroke driving the rotation of the flagellar motor. This mechanism is based on the bending of the �-helices constituting the stator induced by a proline residue. Thus, when a cation hops onto the ion-binding site of the stator, the hydrogen bonds in the vicinity of the site rearrange thereby inducing a 'kink and swivel' movement of the �-helix about the proline residue. Existing molecular dynamics simulations, supported by our energy-based calculations, show that this is an energetically plausible mechanism. In this work we will develop mathematical models describing the power-stroke mechanism and focus on explaining the following experiments: (i) degradation of motor efficiency due to mutation of important charges on the stator and the rotor, (ii) torque-speed curves, (iii) step-size distributions, and (iv) motor reversals. Our studies of te flagellar motor have convinced us to revisit our previously published models of the Fo motor. In Aim 2, we show that the electrostatic power stroke mechanism we proposed previously should be re- placed by a conformation power stroke that is structurally similar to the proline hinge mechanism in the flagellar motor. Using this new mechanism we will address a number of unresolved issues in powering rotation of the FoM. These studies will present a unified mechanochemical mechanism for both the rotary motors and may help in understanding how they are related from the viewpoint of their evolution.