THEORETICAL STUDIES ON THE DYNAMIC ASPECTS OF MACROMOLECULAR FUNCTION

在本报告所述期间，取得了重大进展， 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 从计算机模拟，和（3）NMR弛豫分析 数据 下文简要介绍两个项目。 不可逆扩散反应动力学 蛋白质和配体之间的反应性研究时， 随机门控由于构象波动之一， 物种 如果门控是由于配体，我们表明， Smoluchowski速率方程可以通过简单地使用 随机门控时间相关速率系数。 但如果 门控是由于蛋白质，这不再是真的，除非当 门控动力学足够快或配体浓度足够高， 很低 蛋白质周围所有配体的动力学 即使它们是独立扩散的也是相关的。 的近似 蛋白质门控反应的动力学理论， 开发了快速和慢速选通限制。 为了测试 这一理论，布朗动力学模拟算法的基础上的路径- 积分公式被引入到计算的时间依赖性 蛋白质浓度。 使用简单的 模型进行了各种浇口比。 结果 与近似理论一致。 一类简单的表达式的增加精度的自由- 基于数值计算， 热力学积分 这些公式的实施 需要模拟初始和最终（可能还有几个 中间状态）。 它们涉及更高的自由能衍生物， 这些状态与概率的矩有关 扰动的分布。 给定指定数量的此类 衍生物，这些积分公式在这个意义上是最佳的， 它们精确到自由能的最高阶 微扰理论 这种方法的效用是说明为 水的水合自由能。 这个问题提供了一个问题 严格的测试，因为自由能是高度非线性函数 所以即使是四阶微扰理论也能给出 对自由能变化的估计很差。 我们的结果应该 证明对复杂的计算要求高的问题最有用 其中自由能的差异主要来自于 静电相互作用（例如，电子转移，离子充电， 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).