Department of Applied Mathematics and Physics, Kyoto University, 606-8501 Kyoto, Japan.
Graduate School of Advanced Integrated Studies in Human Survavibility (Shishu-Kan), Kyoto University, 606-8306 Kyoto, Japan.
Front Biosci (Landmark Ed). 2022 Jun 10;27(6):188. doi: 10.31083/j.fbl2706188.
Drug design is one of the important applications of biological science. Extensive studies have been done on computer-aided drug design based on inverse quantitative structure activity relationship (inverse QSAR), which is to infer chemical compounds from given chemical activities and constraints. However, exact or optimal solutions are not guaranteed in most of the existing methods.
Recently a novel framework based on artificial neural networks (ANNs) and mixed integer linear programming (MILP) has been proposed for designing chemical structures. This framework consists of two phases: an ANN is used to construct a prediction function, and then an MILP formulated on the trained ANN and a graph search algorithm are used to infer desired chemical structures. In this paper, we use linear regression instead of ANNs to construct a prediction function. For this, we derive a novel MILP formulation that simulates the computation process of a prediction function by linear regression.
For the first phase, we performed computational experiments using 18 chemical properties, and the proposed method achieved good prediction accuracy for a relatively large number of properties, in comparison with ANNs in our previous work. For the second phase, we performed computational experiments on five chemical properties, and the method could infer chemical structures with around up to 50 non-hydrogen atoms.
Combination of linear regression and integer programming is a potentially useful approach to computational molecular design.
药物设计是生物科学的重要应用之一。基于逆定量构效关系（Inverse QSAR）的计算机辅助药物设计已经进行了广泛的研究，旨在从给定的化学活性和约束条件中推断化学化合物。然而，大多数现有方法并不能保证得到精确或最优的解决方案。
最近，提出了一种基于人工神经网络（ANNs）和混合整数线性规划（MILP）的新框架，用于设计化学结构。该框架由两个阶段组成：ANN 用于构建预测函数，然后基于训练的 ANN 和图搜索算法的 MILP 用于推断所需的化学结构。在本文中，我们使用线性回归代替 ANNs 来构建预测函数。为此，我们推导出了一种新的 MILP 公式，通过线性回归模拟预测函数的计算过程。
对于第一阶段，我们使用 18 种化学性质进行了计算实验，与我们之前的工作中的 ANNs 相比，该方法对于相对较多的性质具有良好的预测准确性。对于第二阶段，我们对五种化学性质进行了计算实验，该方法可以推断出大约有 50 个非氢原子的化学结构。
线性回归和整数规划的组合是计算分子设计的一种潜在有用的方法。
