Hinrichs Nina Singhal, Pande Vijay S
Department of Computer Science, Stanford University, Stanford, California 94305, USA.
J Chem Phys. 2007 Jun 28;126(24):244101. doi: 10.1063/1.2740261.
Markovian state models (MSMs) are a convenient and efficient means to compactly describe the kinetics of a molecular system as well as a formalism for using many short simulations to predict long time scale behavior. Building a MSM consists of grouping the conformations into states and estimating the transition probabilities between these states. In a previous paper, we described an efficient method for calculating the uncertainty due to finite sampling in the mean first passage time between two states. In this paper, we extend the uncertainty analysis to derive similar closed-form solutions for the distributions of the eigenvalues and eigenvectors of the transition matrix, quantities that have numerous applications when using the model. We demonstrate the accuracy of the distributions on a six-state model of the terminally blocked alanine peptide. We also show how to significantly reduce the total number of simulations necessary to build a model with a given precision using these uncertainty estimates for the blocked alanine system and for a 2454-state MSM for the dynamics of the villin headpiece.
马尔可夫状态模型（MSMs）是一种方便且高效的方法，可紧凑地描述分子系统的动力学，也是一种利用许多短模拟来预测长时间尺度行为的形式体系。构建一个MSM包括将构象分组为状态，并估计这些状态之间的转移概率。在之前的一篇论文中，我们描述了一种计算由于两个状态之间平均首次通过时间的有限采样而导致的不确定性的有效方法。在本文中，我们扩展了不确定性分析，以推导转移矩阵的特征值和特征向量分布的类似封闭形式解，这些量在使用该模型时有许多应用。我们在末端封闭的丙氨酸肽的六态模型上证明了这些分布的准确性。我们还展示了如何使用这些针对封闭丙氨酸系统和用于维林头piece动力学的2454态MSM的不确定性估计，显著减少构建具有给定精度模型所需的模拟总数。
