Theory of binless multi-state free energy estimation with applications to protein-ligand binding
Theory of binless multi-state free energy estimation with applications to protein-ligand binding
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DOI：
10.1063/1.3701175
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发表时间：
2012-04-14
影响因子：
4.4
通讯作者：
Levy, Ronald M.
中科院分区：
文献类型：
--
作者：
Tan, Zhiqiang;Gallicchio, Emilio;Levy, Ronald M.
加权直方图分析方法（WHAM）通常用于计算自由能和期望从多个合奏。现有的衍生物的WHAM需要观察离散成有限数量的箱。然而，WHAM公式似乎持有，即使箱的大小是任意小。本文的目的是证明多状态Bennet接受比（MBAR）方法的有效性和价值，该方法被视为WHAM的无箱扩展。我们讨论了两个统计参数，以获得MBAR方程，在平行的自我一致性和最大似然推导已经知道的WHAM。我们表明，无箱的方法，像WHAM，不仅可以用来估计自由能和平衡的期望值，但也估计平衡分布。我们还提供了一些有用的结果，从统计文献中，包括MBAR估计的凸函数的最小化的决心。这导致了一种方法的MBAR自由能的计算优化算法，这可以是更有效的比现有的算法。MBAR的优点是数值计算的绝对蛋白质配体结合自由能的炼金术转换与软核势和没有。我们表明，无仓统计分析可以准确地处理稀疏分布的相互作用能样本，从未经修改的相互作用势，不能正确地使用标准的分仓方法进行分析。这表明，结合自由能模拟与未修改的潜力的无仓多状态分析提供了一个简单的替代使用软核潜力，这些炼金术的转变。(C)2012年美国物理学会。[http：//dx.doi.org/10.1063/1.3701175]
The weighted histogram analysis method (WHAM) is routinely used for computing free energies and expectations from multiple ensembles. Existing derivations of WHAM require observations to be discretized into a finite number of bins. Yet, WHAM formulas seem to hold even if the bin sizes are made arbitrarily small. The purpose of this article is to demonstrate both the validity and value of the multi-state Bennet acceptance ratio (MBAR) method seen as a binless extension of WHAM. We discuss two statistical arguments to derive the MBAR equations, in parallel to the self-consistency and maximum likelihood derivations already known for WHAM. We show that the binless method, like WHAM, can be used not only to estimate free energies and equilibrium expectations, but also to estimate equilibrium distributions. We also provide a number of useful results from the statistical literature, including the determination of MBAR estimators by minimization of a convex function. This leads to an approach to the computation of MBAR free energies by optimization algorithms, which can be more effective than existing algorithms. The advantages of MBAR are illustrated numerically for the calculation of absolute protein-ligand binding free energies by alchemical transformations with and without soft-core potentials. We show that binless statistical analysis can accurately treat sparsely distributed interaction energy samples as obtained from unmodified interaction potentials that cannot be properly analyzed using standard binning methods. This suggests that binless multi-state analysis of binding free energy simulations with unmodified potentials offers a straightforward alternative to the use of soft-core potentials for these alchemical transformations. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3701175]