Mathematical models for rotary protein motors driven by membrane potential

描述(申请人提供)：细菌鞭毛马达(BFM)和三磷酸腺苷合成酶的Fo马达(FOM)是已知的唯一由跨膜离子势驱动的旋转蛋白质马达。鞭毛马达在许多细菌物种中是运动的细胞器，而 FOM推动了通用电池燃料三磷酸腺苷的合成。这两种蛋白质在细胞的生命中都扮演着基本的角色。到目前为止发展起来的数学模型从现象学的角度描述了马达的功能。也就是说，定子和转子之间的相互作用是通过构造驱动电势来处理的，这些驱动电势经过人工调整以适应测量的行为这在没有详细分子结构的情况下已经足够好了。然而，最近的实验已经阐明了这些马达的许多组件结构，以至于我们可以直接解决分子间力如何协同产生旋转力矩的问题。一个基于结构的模型将为跨膜离子势如何转换为旋转扭矩，以及CheYP与转子的结合如何逆转扭矩提供解释。这个过程控制细菌的“奔跑”和“翻滚”的变化，这是 是其趋化性的基础。在目标1中，我们将使用可用的定子和转子蛋白质的结构信息来解决BFM的定子产生扭矩的物理机制。这项工作是基于D.Blair提出的作为驱动鞭毛马达旋转的动力冲程的‘Proline铰链’机制。这一机制是基于构成定子的�-螺旋被脯氨酸残基诱导的弯曲。因此，当阳离子跃升到定子的离子结合部位时，该部位附近的氢键重新排列，从而导致�-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，由我们基于能量的计算支持，表明这是一个能量上可信的机制。在这项工作中，我们将建立描述功率冲程机制的数学模型，并重点解释以下实验：(I)由于定子和转子上重要电荷的突变而导致的电机效率下降，(Ii)转矩-速度曲线，(Iii)步长分布，以及(Iv)电机换向。我们对鞭毛马达的研究说服了我们重新审视之前发表的Fo马达模型。在目标2中，我们证明了我们先前提出的静电功率行程机制应该被结构上类似于鞭毛电机中的Pro铰链机制的构象功率行程所取代。利用这一新机制，我们将解决为FOM的轮换提供动力方面的一些悬而未决的问题。这些研究将为这两种旋转电机提供一个统一的机械力化学机制，并可能有助于从它们的进化角度理解它们是如何相关的。

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.