Mathematical Models of Molecular Motors

研究者和他的同事建立了数学模型来描述三种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)分别沿着微管和肌动蛋白丝移动的激酶和肌球蛋白超家族，以及（ii）驱动蛋白质跨细胞膜易位的HSP70；（ii） RNA和DNA聚合酶，它们沿着DNA双螺旋运动。(2)由电化学梯度驱动的“旋转”马达，包括：(i) ATP合成酶，合成ATP的机械化学引擎，（ii）细菌鞭毛马达，驱动许多原核生物的运动。(3)聚合自由能驱动的马达，包括有丝分裂后期染色体运动的微管解聚过程，以及驱动某些致病菌和病毒运动的聚合马达，如李斯特菌和牛苗。在每种情况下，方法都是从制定由朗格万力学方程或福克-普朗克扩散方程组成的分析随机模型开始的，这些模型描述了分子机械的机械化学和统计行为。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特性，如力-速度曲线，以及它们的随机特性，如轨迹方差。结果以视觉形式呈现，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，实际上也是生命本身的标志，就是它们的不断运动。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，这些蛋白质分子就像微型机器人马达一样，由化学能驱动。这些蛋白质机器运行的世界是由布朗运动主导的，这使它们的运动具有统计特征。尽管这些分子机器在纳米的长度尺度和皮牛顿的力尺度上运作，但它们对细胞的生命是绝对必要的。仪器仪表的最新进展使测量单个蛋白质马达的机械特性成为可能，高性能计算的最新进展使其能够进行逼真的细节模拟，包括热波动的影响。综合起来，这些进步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。这是通过制定数学模型，并通过模型预测与实验数据的仔细比较来完成的。

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.