Department of Chemistry, The Hong Kong University of Science and Technology, Kowloon, Hong Kong.
Department of Chemistry, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2020 Jul 7;153(1):014105. doi: 10.1063/5.0010787.
Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called "lag time"). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5-10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.
生物分子动力学在许多生物过程中起着重要作用。马尔可夫状态模型（MSM）提供了一种强大的方法来研究这些动态过程，通过基于许多短分子动力学（MD）模拟来预测长时间尺度的动力学。在 MSM 中，蛋白质动力学被建模为一个动力学过程，由离散时间间隔（称为“滞后时间”）在不同构象状态之间的一系列马尔可夫跃迁组成。为了实现这一点，必须构建一个主方程，该方程具有足够长的滞后时间，以使状态间跃迁真正成为马尔可夫过程。这对蛋白质的 MSM 研究提出了重大挑战，因为滞后时间受到可用的相对较短的 MD 模拟的长度限制，这些模拟可用于估计跃迁的频率。在这里，我们展示了如何使用广义主方程形式来获得蛋白质构象动力学的精确描述，而不受 MSM 滞后时间施加的时间分辨率限制。使用简单的动力学模型丙氨酸二肽和 WW 结构域，我们证明可以使用比 MSM 所需的 MD 模拟短 5-10 倍的 MD 模拟来构建这些准马尔可夫状态模型（qMSM）。这些 qMSM 仅包含少数亚稳态，因此可以极大地促进与蛋白质动力学相关的机制的解释。qMSM 为研究复杂生物分子的构象变化打开了大门，由于可用 MD 模拟的长度有限，具有少数状态的马尔可夫模型通常难以构建。
