Mathematical Models of Molecular Motors

研究人员Oster 9626104和他的同事构建了数学模型来描述三类重要的蛋白质分子马达。(1)由核苷酸水解驱动的线性马达，包括(I)运动蛋白和肌球蛋白超家族，它们分别沿微管和肌动蛋白细丝移动；(Ii)HSP70，驱动蛋白质跨细胞内膜的转运；(Ii)RNA和DNA聚合酶，沿DNA双螺旋移动。(2)由电化学梯度驱动的旋转马达，包括(I)三磷酸腺苷合酶，合成三磷酸腺苷的机械力化学引擎，和(Ii)细菌鞭毛马达，驱动许多原核生物的运动。(3)由聚合自由能驱动的马达，包括在有丝分裂后期移动染色体的微管解聚过程，以及驱动某些致病细菌和病毒运动的聚合马达，如李斯特菌和痘苗杆菌。在每种情况下，方法都是通过建立由朗之万力学方程或福克-普朗克扩散方程组成的解析随机模型来开始的，这些方程描述了分子机械的机械力、化学和统计行为。然后，在可能的情况下，对这些模型进行数学分析，并在所有情况下进行数值模拟。推导了这些蛋白质马达的平均力学性质，如力-速度曲线，以及它们的随机性质，如轨迹变化。结果以可视化的形式呈现，便于生物学家理解并与实验数据进行比较。生物细胞最显著的特征，甚至是生命本身的标志，就是它们不断地运动。这些运动有两种：一种是将细胞从一个地方移动到另一个地方，另一种是将细胞内的重要物质从一个地方移动到另一个地方。这两种运动都是由特殊的蛋白质分子驱动的，这些蛋白质分子起着机器人马达的作用，由化学能量提供动力。这些蛋白质机器运行的世界被布朗运动所主导，这赋予了它们运动的统计特征。虽然这些分子机器在纳米的长度尺度和皮牛顿的力尺度上运行，但它们对细胞的生命绝对必要。仪器的最新进展使测量单个蛋白质马达的机械性能成为可能，而高性能计算的最新进展使它们能够进行真实的细节模拟，包括热波动的影响。总而言之，这些进展提供了一个前所未有的机会来推断生物分子马达是如何工作的。这是通过建立数学模型，通过仔细比较模型预测和实验数据来实现的。

Oster 9626104 The investigator and his colleague construct mathematical models to describe three important classes of protein molecular motors. (1) 'Linear' motors driven by nucleotide hydrolysis, including (i) the kinesin and myosin superfamily which move along microtubules and actin filaments, respectively, and (ii) HSP70, which drives the translocation of proteins across intracellular membranes; (ii) RNA and DNA polymerase, which move along the DNA double helix. (2) 'Rotary' motors driven by electrochemical gradients, including (i) ATP synthase, the mechanochemical engine that synthesizes ATP, and (ii) the bacterial flagellar motor, which drives the motion of many prokaryotic organisms. (3) Motors driven by polymerization free energy, including the microtubule depolymerization process that moves chromosomes during anaphase mitosis, and the polymerization motors which drive the motion of certain pathogenic bacteria and viruses, such as Listeria and Vaccinia. The approach in each case is to begin by formulating analytical stochastic models consisting of Langevin mechanical equations or Fokker-Planck diffusion equations that describe the mechanochemical and statistical behavior of the molecular machinery. These models then are analyzed mathematically where possible and by numerical simulation in all cases. The mean mechanical properties of these protein motors are derived, such as force-velocity curves, along with their stochastic properties such as trajectory variances. Results are presented in a visual format that facilitates comprehension by biologists and comparison with experimental data. The most striking feature of biological cells, and indeed the hallmark of life itself, is their constant motion. These motions are of two kinds: those that move the cell from one place to another, and those that move vital material from one place to another within the cell. Both kinds of motions are driven by specialized protein molecules that function as ti ny robotic motors, powered by chemical energy. The world in which these protein machines operate is dominated by Brownian motion, which gives their movements a statistical character. Although these molecular machines operate on a length scale of nanometers and a force scale of piconewtons, they are absolutely essential to the life of the cell. Recent advances in instrumentation have made it possible to measure the mechanical properties of individual protein motors, and recent advances in high-performance computing have enabled their simulation in realistic detail, including the effects of thermal fluctuations. Taken together, these advances provide an unprecedented opportunity to deduce how biomolecular motors work. This is done through the formulation of mathematical models, and through the careful comparison of model predictions with experimental data.