THEORETICAL STUDIES ON THE DYNAMIC ASPECTS OF MACROMOLECULAR FUNCTION

在本报告所述期间，取得了重大进展，导致 在以下广泛领域出版了出版物：(1)传播 影响反应(2)自由能差的计算 (3)核磁共振弛豫谱的分析 数据。下面简要介绍两个项目。 不可逆扩散影响反应的动力学 研究了蛋白质和配基之间的反应活性是 由于其中一个分子的构象涨落而被随机选通 物种。如果门控是由配体引起的，我们证明 Smoluchowski速率方程可以简单地使用 随机选通的随时间变化的速率系数。但是，如果 门控是由蛋白质引起的，这不再是真的，除非当 门控动力学足够快，或者配体浓度 非常低。蛋白质周围的所有配体的动力学变成 即使当它们独立扩散时也是相互关联的。一个近似值 精确的蛋白质门控反应动力学理论 开发了快门限值和慢门限值。为了测试 该理论是一种基于路径的布朗动力学仿真算法。 采用积分公式计算了不同温度下的时间依赖性 蛋白质浓度。说明性模拟使用简单的 模型是针对不同的选通率进行的。结果是 与近似理论很好地吻合。 一类提高自由方程精度的简单公式 基于数值解推导出了两种状态之间的能量差 热力学积分。这些公式的实现 需要模拟初始和最终(可能还会有几个 中级)状态。它们涉及更高的自由能导数 这些状态与概率矩有关 扰动的分布。在给定特定数量的此类 导数，这些积分公式在以下意义上是最优的 它们精确到自由能的最高阶。 微扰理论。此方法的实用性如下所示 水的水合自由能。这个问题提供了一个疑问 严格的测试，因为自由能是一个高度非线性的函数 所以即使是四阶微扰理论也给出了一个 对自由能变化的估计非常差。我们的结果应该是 事实证明，对于复杂的、计算要求很高的问题最有用 自由能差异主要是由于自由能变化引起的 静电相互作用(例如，电子转移，离子带电， 蛋白质中氨基酸的质子化)。

In this reporting period significant progress that lead to seven publications was made in the following broad areas: (1) diffusion influenced reactions (2) the calculation of free energy differences from computer simulations, and (3) the analysis of NMR relaxation data. Two projects are briefly described below. The kinetics of the irreversible diffusion-influenced reactions between a protein and a ligand is studied when the reactivity is stochasitically gated due to conformations fluctuations of one of the species. If gating is due to the ligand, we show that the Smoluchowski rate equations can be generalized by simply using a stochastically-gated time-dependent rate coefficient,. However, if gating is due to the protein, this is no longer true, except when the gating dynamics is sufficiently fast or the ligand concentration is very low. The dynamics of all the ligands around a protein become correlated even when they diffuse independently. An approximate theory for the kinetics of protein-gated reactions that is exact in both the fast and slow gating limits is developed. In order to test this theory, a Brownian dynamics simulation algorithm based on a path- integral formulation is introduced to calculate the time dependence of the protein concentration. Illustrative simulations using a simple model are carried out for a variety of gating rates. The results are in good agreement with the approximate theory. A class of simple expressions of increasing accuracy for the free- energy difference between two states is derived based on numerical thermodynamic integration. The implementation of these formulas requires simulations of the initial and final (and possibly a few intermediate) states. They involve higher free-energy derivatives at these states which are related to the moments of the probability distribution of the perturbations. Given a specified number of such derivatives, these integrations formulas are optimal in the sense that they are exact to the highest possible order of free-energy perturbation theory. The utility of this approach is illustrated for the hydration free energy of water. This problem provides a quire stringent test because the free energy is a highly nonlinear function of the charge so that even fourth order perturbation theory gives a very poor estimate of the free-energy change. Our results should prove most useful for complex, computationally demanding problems where free-energy differences arise primarily from changes in the electrostatic interactions (e.g., electron transfer, charging of ions, protonation of amino acids in proteins).