Hnizdo Vladimir, Tan Jun, Killian Benjamin J, Gilson Michael K
Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, West Virginia 26505, USA.
J Comput Chem. 2008 Jul 30;29(10):1605-14. doi: 10.1002/jcc.20919.
Changes in the configurational entropies of molecules make important contributions to the free energies of reaction for processes such as protein-folding, noncovalent association, and conformational change. However, obtaining entropy from molecular simulations represents a long-standing computational challenge. Here, two recently introduced approaches, the nearest-neighbor (NN) method and the mutual-information expansion (MIE), are combined to furnish an efficient and accurate method of extracting the configurational entropy from a molecular simulation to a given order of correlations among the internal degrees of freedom. The resulting method takes advantage of the strengths of each approach. The NN method is entirely nonparametric (i.e., it makes no assumptions about the underlying probability distribution), its estimates are asymptotically unbiased and consistent, and it makes optimum use of a limited number of available data samples. The MIE, a systematic expansion of entropy in mutual information terms of increasing order, provides a well-characterized approximation for lowering the dimensionality of the numerical problem of calculating the entropy of a high-dimensional system. The combination of these two methods enables obtaining well-converged estimations of the configurational entropy that capture many-body correlations of higher order than is possible with the simple histogramming that was used in the MIE method originally. The combined method is tested here on two simple systems: an idealized system represented by an analytical distribution of six circular variables, where the full joint entropy and all the MIE terms are exactly known, and the R,S stereoisomer of tartaric acid, a molecule with seven internal-rotation degrees of freedom for which the full entropy of internal rotation has been already estimated by the NN method. For these two systems, all the expansion terms of the full MIE of the entropy are estimated by the NN method and, for comparison, the MIE approximations up to third order are also estimated by simple histogramming. The results indicate that the truncation of the MIE at the two-body level can be an accurate, computationally nondemanding approximation to the configurational entropy of anharmonic internal degrees of freedom. If needed, higher-order correlations can be estimated reliably by the NN method without excessive demands on the molecular-simulation sample size and computing time.
分子构型熵的变化对蛋白质折叠、非共价缔合和构象变化等过程的反应自由能有重要贡献。然而，从分子模拟中获取熵是一个长期存在的计算挑战。在这里，将最近引入的两种方法，最近邻（NN）方法和互信息展开（MIE）相结合，提供了一种有效且准确的方法，可从分子模拟中提取构型熵，达到内部自由度之间给定阶数的相关性。所得方法利用了每种方法的优势。NN方法完全是非参数的（即，它不对潜在概率分布做任何假设），其估计是渐近无偏且一致的，并且它能最佳地利用有限数量的可用数据样本。MIE是熵在互信息项中按递增阶数的系统展开，为降低计算高维系统熵的数值问题的维度提供了一个特征明确的近似。这两种方法的结合能够获得构型熵的良好收敛估计，捕捉到比最初MIE方法中使用的简单直方图法所能达到的更高阶的多体相关性。在此，将组合方法应用于两个简单系统进行测试：一个由六个圆形变量的解析分布表示的理想化系统，其完全联合熵和所有MIE项是确切已知的；以及酒石酸的R,S立体异构体，该分子有七个内旋转自由度，其内部旋转的全熵已通过NN方法估计。对于这两个系统，熵的全MIE的所有展开项都通过NN方法估计，并且为了比较，还通过简单直方图法估计了直至三阶的MIE近似值。结果表明，在两体水平截断MIE可以是对非谐内部自由度构型熵的一种准确且计算要求不高的近似。如果需要，可以通过NN方法可靠地估计高阶相关性，而对分子模拟样本大小和计算时间没有过高要求。
