Department of Chemistry, Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
Biophysics Graduate Program, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
J Chem Phys. 2023 Oct 7;159(13). doi: 10.1063/5.0167287.
The generalized master equation (GME) provides a powerful approach to study biomolecular dynamics via non-Markovian dynamic models built from molecular dynamics (MD) simulations. Previously, we have implemented the GME, namely the quasi Markov State Model (qMSM), where we explicitly calculate the memory kernel and propagate dynamics using a discretized GME. qMSM can be constructed with much shorter MD trajectories than the MSM. However, since qMSM needs to explicitly compute the time-dependent memory kernels, it is heavily affected by the numerical fluctuations of simulation data when applied to study biomolecular conformational changes. This can lead to numerical instability of predicted long-time dynamics, greatly limiting the applicability of qMSM in complicated biomolecules. We present a new method, the Integrative GME (IGME), in which we analytically solve the GME under the condition when the memory kernels have decayed to zero. Our IGME overcomes the challenges of the qMSM by using the time integrations of memory kernels, thereby avoiding the numerical instability caused by explicit computation of time-dependent memory kernels. Using our solutions of the GME, we have developed a new approach to compute long-time dynamics based on MD simulations in a numerically stable, accurate and efficient way. To demonstrate its effectiveness, we have applied the IGME in three biomolecules: the alanine dipeptide, FIP35 WW-domain, and Taq RNA polymerase. In each system, the IGME achieves significantly smaller fluctuations for both memory kernels and long-time dynamics compared to the qMSM. We anticipate that the IGME can be widely applied to investigate biomolecular conformational changes.
广义主方程 (GME) 提供了一种强大的方法，可通过基于分子动力学 (MD) 模拟构建的非马尔可夫动力学模型来研究生物分子动力学。在此之前，我们已经实现了 GME，即准马尔可夫态模型 (qMSM)，其中我们通过离散化 GME 来显式计算记忆核并传播动力学。qMSM 可以用比 MSM 短得多的 MD 轨迹来构建。然而，由于 qMSM 需要显式计算时变记忆核，因此当应用于研究生物分子构象变化时，它会受到模拟数据数值波动的严重影响。这可能导致预测的长时间动力学的数值不稳定性，极大地限制了 qMSM 在复杂生物分子中的适用性。我们提出了一种新方法，即积分 GME (IGME)，其中我们在记忆核衰减到零时解析地求解 GME。我们的 IGME 通过使用记忆核的时间积分克服了 qMSM 的挑战，从而避免了显式计算时变记忆核引起的数值不稳定性。使用我们对 GME 的解，我们开发了一种新的方法，基于 MD 模拟以一种数值稳定、准确和高效的方式计算长时间动力学。为了证明其有效性，我们将 IGME 应用于三种生物分子：丙氨酸二肽、FIP35 WW 结构域和 Taq RNA 聚合酶。在每个系统中，与 qMSM 相比，IGME 使记忆核和长时间动力学的波动都显著减小。我们预计 IGME 可以广泛应用于研究生物分子构象变化。
