Phase-space overlap measures. I. Fail-safe bias detection in free energies calculated by molecular simulation.
Phase-space overlap measures. I. Fail-safe bias detection in free energies calculated by molecular simulation.
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DOI：
10.1063/1.1992483
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发表时间：
2005-08
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影响因子：
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通讯作者：
Di Wu;D. Kofke
中科院分区：
文献类型：
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作者：
Di Wu;D. Kofke
我们考虑的方法来量化的重叠部分相空间的重要两个系统，标记为A和B。感兴趣的是A重要相空间中有多少对B重要，而B中有多少对A重要。建议采取两项措施。第一个考虑四个总能量分布，由所有组合形成，当对A或B系统进行采样时，将A系统或B系统的能量制成表格。A在B中的测度和B在A中的测度由定义在这些分布对上的两个重叠积分给出。第二个措施是基于信息论，并定义了两个相对熵，这是方便地表示在自由能微扰（FEP）的计算在A-->B和B-->A方向，分别耗散的工作。相空间重叠是自由能计算性能中的重要考虑因素。为了证明这一点，我们检查FEP计算中的偏见适用于一个系统的独立粒子的谐波势。系统被选择来表示一系列重叠情况，包括极端子集、子集、部分重叠和非重叠。偏置的幅度和对称性（A-->B vs B-->A）被示出与重叠很好地相关，并且因此与重叠测量很好地相关。相对熵用于缩放采样量以获得通用的偏差曲线。这个结果导致开发一个简单的启发式，可以应用于确定是否基于工作的自由能测量是免费的偏见。启发式是部分基于测量的自由能，但我们认为，它是故障安全的，因为任何偏见的测量不会促进错误的准确性。
We consider ways to quantify the overlap of the parts of phase space important to two systems, labeled A and B. Of interest is how much of the A-important phase space lies in that important to B, and how much of B lies in A. Two measures are proposed. The first considers four total-energy distributions, formed from all combinations made by tabulating either the A-system or the B-system energy when sampling either the A or B system. Measures for A in B and B in A are given by two overlap integrals defined on pairs of these distributions. The second measure is based on information theory, and defines two relative entropies which are conveniently expressed in terms of the dissipated work for free-energy perturbation (FEP) calculations in the A-->B and B-->A directions, respectively. Phase-space overlap is an important consideration in the performance of free-energy calculations. To demonstrate this connection, we examine bias in FEP calculations applied to a system of independent particles in a harmonic potential. Systems are selected to represent a range of overlap situations, including extreme subset, subset, partial overlap, and nonoverlap. The magnitude and symmetry of the bias (A-->B vs B-->A) are shown to correlate well with the overlap, and consequently with the overlap measures. The relative entropies are used to scale the amount of sampling to obtain a universal bias curve. This result leads to develop a simple heuristic that can be applied to determine whether a work-based free-energy measurement is free of bias. The heuristic is based in part on the measured free energy, but we argue that it is fail-safe inasmuch as any bias in the measurement will not promote a false indication of accuracy.