Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom.
van't Hoff Institute for Molecular Sciences, University of Amsterdam, 1090 GD Amsterdam, The Netherlands
Proc Natl Acad Sci U S A. 2021 Jan 12;118(2). doi: 10.1073/pnas.2012423118.
From the point of view of statistical mechanics, a full characterization of a molecular system requires an accurate determination of its possible states, their populations, and the respective interconversion rates. Toward this goal, well-established methods increase the accuracy of molecular dynamics simulations by incorporating experimental information about states using structural restraints and about populations using thermodynamics restraints. However, it is still unclear how to include experimental knowledge about interconversion rates. Here, we introduce a method of imposing known rate constants as constraints in molecular dynamics simulations, which is based on a combination of the maximum-entropy and maximum-caliber principles. Starting from an existing ensemble of trajectories, obtained from either molecular dynamics or enhanced trajectory sampling, this method provides a minimally perturbed path distribution consistent with the kinetic constraints, as well as modified free energy and committor landscapes. We illustrate the application of the method to a series of model systems, including all-atom molecular simulations of protein folding. Our results show that by combining experimental rate constants and molecular dynamics simulations, this approach enables the determination of transition states, reaction mechanisms, and free energies. We anticipate that this method will extend the applicability of molecular simulations to kinetic studies in structural biology and that it will assist the development of force fields to reproduce kinetic and thermodynamic observables. Furthermore, this approach is generally applicable to a wide range of systems in biology, physics, chemistry, and material science.
从统计力学的角度来看，要全面描述一个分子系统，需要准确确定其可能的状态、它们的丰度以及它们之间的转换速率。为此，成熟的方法通过使用结构约束来增加关于状态的实验信息，以及通过热力学约束来增加关于丰度的实验信息，从而提高分子动力学模拟的准确性。然而，如何纳入关于转换速率的实验知识仍然不清楚。在这里，我们引入了一种将已知速率常数作为约束施加到分子动力学模拟中的方法，该方法基于最大熵和最大口径原理的结合。从现有的轨迹集合开始，该集合可以通过分子动力学或增强轨迹采样获得，该方法提供了一种与动力学约束一致的最小受扰路径分布，以及修改后的自由能和介面分布。我们说明了该方法在一系列模型系统中的应用，包括蛋白质折叠的全原子分子模拟。我们的结果表明，通过结合实验速率常数和分子动力学模拟，该方法能够确定过渡态、反应机制和自由能。我们预计，这种方法将扩展分子模拟在结构生物学中动力学研究的适用性，并有助于开发力场来重现动力学和热力学观测值。此外，该方法通常适用于生物学、物理学、化学和材料科学中的广泛的系统。
