Ivanov Maxim V, Talipov Marat R, Timerghazin Qadir K
Department of Chemistry, Marquette University , P.O. Box 1881, Milwaukee, Wisconsin 53201-1881, United States.
J Phys Chem A. 2015 Feb 26;119(8):1422-34. doi: 10.1021/acs.jpca.5b00218. Epub 2015 Feb 16.
Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields.
进化方法，如遗传算法（GAs），为优化力场参数提供了强大的工具，特别是在将力场项与大量参考数据同时拟合的情况下。然而，文献中尚未探讨包括点电荷在内的非键相互作用参数的遗传算法拟合，这可能是由于即使是将原子点电荷与参考分子静电势（MEP）进行最小二乘拟合这个更简单的问题也存在诸多困难，而对于埋藏原子，拟合电荷往往表现出异常高的变化。在这里我们研究了遗传算法用于最小二乘MEP点电荷拟合的性能，并表明遗传算法优化受到经典埋藏原子效应的放大版本的影响，产生高度分散但相关的解。这种效应可以根据由最小二乘和海森矩阵的特征向量定义的MEP拟合问题的线性独立自然坐标来理解，这些坐标也等同于为分散的遗传算法解评估的协方差矩阵的特征向量。遗传算法对于由与多极展开的主导项相关的特征向量定义的高曲率坐标收敛很快，但对于主要依赖于埋藏原子电荷的低曲率坐标收敛困难。当使用海森矩阵或协方差矩阵特征向量进行点电荷优化时，进化技术的性能会显著提高，这种方法对于固定电荷生物分子力场的进化优化具有很大潜力。
