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Abstract：
Thermodynamic integration (TI), a powerful formalism for computing Gibbs free energy, has been implemented for many biophysical processes with alchemical schemes that require delicate human efforts to choose/design biasing potentials for sampling the desired biophysical events and to remove their artifactitious consequences afterwards. Theoretically, an alchemical scheme is exact but practically, an unsophisticated implementation of this exact formula can cause error amplifications. Small relative errors in the input parameters can be amplified many times in their propagation into the computed free energy [due to subtraction of similar numbers such as (105 ± 5)‒(100 ± 5) = 5 ± 7]. In this paper, we present an unsophisticated implementation of TI in 3n dimensions (3nD) (n=1,2,3…) for the potential of mean force along a 3nD path connecting one state in the bound state ensemble to one state in the unbound state ensemble. Fluctuations in these 3nD are integrated in the bound and unbound state ensembles but not along the 3nD path. Using TI3nD, we computed the standard binding free energies of three protein complexes: trometamol in Salmonella effector SpvD (n=1), biotin-avidin (n=2), and Colicin E9 endonuclease with cognate immunity protein Im9 (n=3). We employed three different protocols in three independent computations of E9-Im9 to show TI3nD\'s robustness. We also computed the hydration energies of ten biologically relevant compounds (n=1 for water, acetamide, urea, glycerol, trometamol, ammonium and n=2 for erythritol, 1,3-propanediol, xylitol, biotin). Each of the 15 computations is accomplishable within one (for hydration) to ten (for E9-Im9) days on an inexpensive GPU workstation. The computed results all agree with the available experimental data.
摘要：
热力学积分(TI)，计算吉布斯自由能的强大形式主义，已在许多生物物理过程中使用炼金术方案实施，这些方案需要精细的人力来选择/设计偏置潜力，以对所需的生物物理事件进行采样，并随后消除其人为后果。理论上,炼金术方案是精确但实用的，这个精确公式的简单实现可能会导致错误放大。输入参数中的小相对误差在传播到计算的自由能中可以放大很多倍[由于减去类似的数字，例如（105±5）〜（100±5）=5±7]。在本文中,我们提出了TI在3n维（3nD）（n=1,2,3...）中的简单实现，用于沿3nD路径的平均力的潜力，该路径将束缚状态集合中的一个状态连接到未束缚状态集合中的一个状态。这些3nD中的波动被整合在绑定和未绑定状态集合中，但不沿着3nD路径。使用TI3nD，我们计算了三种蛋白质复合物的标准结合自由能：沙门氏菌效应子SpvD（n=1）中的氨丁三醇，生物素-抗生物素蛋白（n=2），和具有同源免疫蛋白Im9的大肠杆菌素E9核酸内切酶(n=3)。我们在E9-Im9的三个独立计算中采用了三种不同的协议，以显示TI3nD的鲁棒性。我们还计算了10种生物相关化合物的水合能（对于水，n=1，乙酰胺,尿素,甘油，氨丁三醇,赤藓糖醇的铵和n=2，1,3-丙二醇,木糖醇,生物素）。15个计算中的每一个都可以在廉价的GPU工作站上在1天（对于水合）到10天（对于E9-Im9）内完成。计算结果与现有实验数据一致。
