Zhang Bin W, Deng Nanjie, Tan Zhiqiang, Levy Ronald M
Center for Biophysics and Computational Biology, Department of Chemistry and Institute for Computational Molecular Science, Temple University , Philadelphia, Pennsylvania 19122, United States.
Department of Chemistry and Physical Sciences, Pace University , New York, New York 10038, United States.
J Chem Theory Comput. 2017 Oct 10;13(10):4660-4674. doi: 10.1021/acs.jctc.7b00651. Epub 2017 Sep 28.
We describe a new analysis tool called Stratified unbinned Weighted Histogram Analysis Method (Stratified-UWHAM), which can be used to compute free energies and expectations from a multicanonical ensemble when a subset of the parallel simulations is far from being equilibrated because of barriers between free energy basins which are only rarely (or never) crossed at some states. The Stratified-UWHAM equations can be obtained in the form of UWHAM equations but with an expanded set of states. We also provide a stochastic solver, Stratified RE-SWHAM, for Stratified-UWHAM to remove its computational bottleneck. Stratified-UWHAM and Stratified RE-SWHAM are applied to study three test topics: the free energy landscape of alanine dipeptide, the binding affinity of a host-guest binding complex, and path sampling for a two-dimensional double well potential. The examples show that when some of the parallel simulations are only locally equilibrated, the estimates of free energies and equilibrium distributions provided by the conventional UWHAM (or MBAR) solutions exhibit considerable biases, but the estimates provided by Stratified-UWHAM and Stratified RE-SWHAM agree with the benchmark very well. Lastly, we discuss features of the Stratified-UWHAM approach which is based on coarse-graining in relation to two other maximum likelihood-based methods which were proposed recently, that also coarse-grain the multicanonical data.
我们描述了一种名为分层无箱加权直方图分析方法（Stratified-UWHAM）的新分析工具，当并行模拟的一个子集由于自由能盆地之间的势垒而远未达到平衡时（在某些状态下这些势垒很少被跨越或从未被跨越），该方法可用于从多正则系综计算自由能和期望值。分层UWHAM方程可以以UWHAM方程的形式获得，但状态集有所扩展。我们还为分层UWHAM提供了一种随机求解器Stratified RE-SWHAM，以消除其计算瓶颈。分层UWHAM和Stratified RE-SWHAM被应用于研究三个测试主题：丙氨酸二肽的自由能景观、主客体结合复合物的结合亲和力以及二维双阱势的路径采样。这些例子表明，当一些并行模拟仅局部平衡时，传统UWHAM（或MBAR）解提供的自由能和平衡分布估计存在相当大的偏差，但分层UWHAM和Stratified RE-SWHAM提供的估计与基准非常吻合。最后，我们讨论了基于粗粒化的分层UWHAM方法相对于最近提出的另外两种基于最大似然的方法的特点，这两种方法也对多正则数据进行粗粒化。
