Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix
Ligand Binding Thermodynamic Cycles: Hysteresis, the Locally Weighted Histogram Analysis Method, and the Overlapping States Matrix
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DOI：
10.1021/acs.jctc.9b00740
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发表时间：
2020-01-01
影响因子：
5.5
通讯作者：
Levy, Ronald M.
中科院分区：
文献类型：
--
作者：
Cui, Di;Zhang, Bin W.;Levy, Ronald M.
自由能微扰(FEP)模拟已被广泛应用于获得一系列与同一受体结合的同族配体的相对结合自由能的预测，这是计算机辅助药物发现中先导优化过程的重要组成部分。在多个同族配体组成一个涉及闭合热力学循环的微扰图的情况下，使用Bennett Accept Ratio(BAR)估计循环中每一条边的自由能变化之和通常会由于系统和随机误差而偏离零，这是循环闭合的滞后。在这项工作中，应用先进的重加权技术--无二进制加权直方图分析方法(UWHAM)和局部加权直方图分析方法(LWHAM)--来提供各边自由能变化的统计估计器，以消除滞后效应。作为一个例子，我们分析了一个封闭的热力学循环，其中包括四个与HIV-1整合酶结合的同种配体，这是一个很有希望的抗病毒治疗的靶点。我们证明，与FEP和BAR相比，通过使用UWHAM根据循环中的所有数据找到状态密度的单一估计，可以获得更准确和无滞后的自由能差估计。此外，通过将包含不同数目的邻态的LWHAM结果与包含所有态的UWHAM估计结果进行比较，我们展示了如何在LWHAM分析中确定最佳邻域大小，以平衡计算成本和自由能预测的精度。即使具有最小的邻域，LWHAM也可以使用与BAR相同的输入数据来改进BAR自由能估计。介绍了利用LWHAM的整体跳跃公式构造的重叠态矩阵，并绘制了其热图。热图提供了炼金术/热力学状态对之间重叠的定量测量。我们解释了如何利用重叠态矩阵的热图以及比较自由能变化的BAR和UWHAM估计，沿最有可能引起较大系统误差的边缘识别和改进FEP计算。
Free energy perturbation (FEP) simulations have been widely applied to obtain predictions of the relative binding free energy for a series of congeneric ligands binding to the same receptor, which is an essential component for the lead optimization process in computer-aided drug discovery. In the case of several congeneric ligands forming a perturbation map involving a closed thermodynamic cycle, the summation of the estimated free energy change along each edge in the cycle using Bennett acceptance ratio (BAR) usually will deviate from zero due to systematic and random errors, which is the hysteresis of cycle closure. In this work, the advanced reweighting techniques binless weighted histogram analysis method (UWHAM) and locally weighted histogram analysis method (LWHAM) are applied to provide statistical estimators of the free energy change along each edge in order to eliminate the hysteresis effect. As an example, we analyze a closed thermodynamic cycle involving four congeneric ligands which bind to HIV-1 integrase, a promising target which has emerged for antiviral therapy. We demonstrate that, compared with FEP and BAR, more accurate and hysteresis-free estimates of free energy differences can be achieved by using UWHAM to find a single estimate of the density of states based on all of the data in the cycle. Furthermore, by comparison of LWHAM results obtained from the inclusion of different numbers of neighboring states with UWHAM estimation involving all the states, we show how to determine the optimal neighborhood size in the LWHAM analysis to balance the trade-offs between computational cost and accuracy of the free energy prediction. Even with the smallest neighborhood, LWHAM can improve the BAR free energy estimates using the same input data as BAR. We introduce an overlapping states matrix that is constructed by using the global jump formula of LWHAM and plot its heat map. The heat map provides a quantitative measure of the overlap between pairs of alchemical/thermodynamic states. We explain how to identify and improve the FEP calculations along the edges that most likely cause large systematic errors by using the heat map of the overlapping states matrix and by comparing the BAR and UWHAM estimates of the free energy change.