Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods
Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods
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DOI：
10.1021/acs.jctc.9b00401
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发表时间：
2019-10-01
影响因子：
5.5
通讯作者：
York, Darrin M.
中科院分区：
文献类型：
--
作者：
Giese, Timothy J.;York, Darrin M.
采用PBEO/6-31G*密度泛函数方法，采用环境势复合Ewald方法，在严格静电的周期性边界条件下进行从头算量子力学/分子力学（QM/MM）分子动力学（MD）模拟，以检验MM -> QM/MM自由能修正对T4溶菌酶的17个小分子溶剂化自由能和8个配体结合自由能的收敛性。计算自由能的“间接”热力学循环被用来探讨一系列参考势是否能提高预测的统计质量。具体来说，我们构建了一系列参考势，优化了分子力学力场的参数，从分子力学/分子力学模拟中重现了从头计算的分子力学/分子力学力。优化形成了连续扩展参数的系统进展，包括键、角、二面体和电荷参数。对于每个参考电位，我们计算了MM -> QM/MM校正的基准质量参考值，通过在11个中间状态下执行混合MM和QM/MM哈密顿量，每个状态为200 ps。然后，我们比较了Zwanzig关系、热力学积分（TI）和Bennett接受比（BAR）方法作为参考电位、模拟时间和模拟中间状态数量的函数的正向和反向应用。我们发现，除非明确地模拟大量的中间状态，否则Zwanzig方程是不充分的。即使只考虑最终状态模拟，TI和BAR的平均符号误差也非常小，并且通过选择优化键和角度参数的参考电位可以减小TI和BAR误差的标准差。我们发现，对于这里考虑的相当刚性分子的数据集，一种可靠的方法是使用键+角参考势和仅限最终状态的BAR分析。这需要执行QM/MM模拟，以便生成参考数据，以参数化键+角度参考势，然后这个相同的模拟作为完整的QM/MM最终状态具有双重目的。结果在时间方面的收敛表明，运行不超过50ps的多个模拟，而不是运行一个长时间的模拟，可以更有效地利用计算资源。
We use the PBEO/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM -> QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM -> QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.