Generation of Pairwise Potentials Using Multidimensional Data Mining

The rapid development of molecular structural databases provides the chemistry community access to an enormous array of experimental data that can be used to build and validate computational models. Using radial distribution functions collected from experimentally available X-ray and NMR structures, a number of so-called statistical potentials have been developed over the years using the structural data mining strategy. These potentials have been developed within the context of the two-particle Kirkwood equation by extending its original use for isotropic monatomic systems to anisotropic biomolecular systems. However, the accuracy and the unclear physical meaning of statistical potentials have long formed the central arguments against such methods. In this work, we present a new approach to generate molecular energy functions using structural data mining. Instead of employing the Kirkwood equation and introducing the “reference state” approximation, we model the multidimensional probability distributions of the molecular system using graphical models and generate the target pairwise Boltzmann probabilities using the Bayesian field theory. Different from the current statistical potentials that mimic the “knowledge-based” PMF based on the 2-particle Kirkwood equation, the graphical-model-based structure-derived potential developed in this study focuses on the generation of lower-dimensional Boltzmann distributions of atoms through reduction of dimensionality. We have named this new scoring function GARF, and in this work we focus on the mathematical derivation of our novel approach followed by validation studies on its ability to predict protein–ligand interactions.分子结构数据库的快速发展，为化学界提供了海量可用的实验数据，可用于构建并验证计算模型。研究人员借助从实验获得的X射线（X-ray）与核磁共振（Nuclear Magnetic Resonance, NMR）结构中采集的径向分布函数（radial distribution functions），多年来依托结构数据挖掘策略开发了诸多所谓的统计势（statistical potentials）。此类势函数的构建以双粒子柯赫伍德方程（two-particle Kirkwood equation）为基础，将其原本适用于各向同性单原子系统的应用场景拓展至各向异性生物分子系统。然而，统计势的准确性不足且物理意义模糊，长期以来一直是该类方法备受争议的核心缘由。本研究提出了一种全新的基于结构数据挖掘的分子能量函数生成方法：我们并未采用柯赫伍德方程并引入“参考态（reference state）”近似，而是通过图模型（graphical models）对分子系统的多维概率分布进行建模，并借助贝叶斯场论（Bayesian field theory）生成目标成对玻尔兹曼概率。与当前基于双粒子柯赫伍德方程、模仿“基于知识的平均力势（potential of mean force, PMF）”的统计势不同，本研究开发的基于图模型的结构衍生势函数，通过维度约简聚焦于原子低维玻尔兹曼分布的生成。我们将这一新型打分函数命名为GARF，本文将首先阐述该新方法的数学推导过程，随后通过验证实验评估其预测蛋白质-配体相互作用（protein–ligand interactions）的能力。