Department of Computational and Applied Mathematics, Rice University, Houston, Texas 77005-1892, United States.
J Chem Theory Comput. 2011 Feb 8;7(2):280-90. doi: 10.1021/ct1004966. Epub 2011 Jan 7.
The 1-D diffusion coefficient associated with a charged atom fluctuating in an ion-channel binding pocket is statistically analyzed. More specifically, unconstrained and constrained molecular dynamics simulations of potassium in gramicidin A are studied. Time domain transition density based inference methods are used to fit simple stochastic differential equations and also to carry out frequentist goodness of fit tests. Particular attention is paid to varying the time between adjacent time series observations due to the well-known "non-Markovian noise" that can appear in this system due to inertia and other unresolved coordinates influencing the dynamics. Different types of non-Markovian noise are shown by the goodness of fit tests to be statistically significant on vastly different time scales. On intermediate scales, a Markovian model is not rejected by the tests; models calibrated at these intermediate scales demonstrate a predictive capability for some physical quantities. However, in this intermediate regime, ergodic sampling does not occur over the length of a time series, but a local diffusion coefficient is deemed statistically acceptable for the observed raw data. It is demonstrated that a linear mixed effects model can be used to summarize the variation induced by slow unresolved degrees of freedom acting as a non-Markovian noise source. The utility of quantitative criteria for assessing low-dimensional stochastic models calibrated from time series generated by high-dimensional biomolecular systems is briefly discussed. Less coarse-grained data summaries of this type show promise for better understanding the kinetic signature of unresolved degrees of freedom in time series coming from simulations and single-molecule experiments.
统计分析了在离子通道结合口袋中波动的带电原子的 1-D 扩散系数。更具体地说，研究了革兰氏菌素 A 中钾的无约束和约束分子动力学模拟。使用时域转移密度推断方法拟合简单的随机微分方程，并进行频率主义拟合优度检验。特别注意由于惯性和其他未解析坐标对动力学的影响，在这个系统中可能出现的众所周知的“非马尔可夫噪声”，相邻时间序列观测之间的时间变化。拟合优度检验表明，不同类型的非马尔可夫噪声在非常不同的时间尺度上具有统计学意义。在中间尺度上，测试不拒绝马尔可夫模型；在这些中间尺度上校准的模型表现出对某些物理量的预测能力。然而，在这个中间范围内，遍历采样不会在时间序列的长度上发生，而是认为观察到的原始数据的局部扩散系数在统计学上是可以接受的。结果表明，可以使用线性混合效应模型来总结由充当非马尔可夫噪声源的缓慢未解析自由度引起的变化。简要讨论了从高维生物分子系统生成的时间序列校准的低维随机模型的定量标准的实用性。这种类型的粒度较小的数据汇总有望更好地理解来自模拟和单分子实验的时间序列中未解析自由度的动力学特征。
