A novel method for inference of chemical compounds with prescribed topological substructures based on integer programming

Abstract

Analysis of chemical graphs is becoming a major research topic in computational molecular biology due to its potential applications to drug design. One of the major approaches in such a study is inverse quantitative structure activity/property relationships (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a novel framework has been proposed for inverse QSAR/QSPR using both artificial neural networks (ANN) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, a feature vector $f(G)$ of a chemical graph $G$ is introduced and a prediction function ${\psi }_{\mathcal{N}}$ on a chemical property $\pi$ is constructed with an ANN $\mathcal{N}$. In the second phase, given a target value $y^{\ast }$ of the chemical property $\pi$, a feature vector $x^{\ast }$ is inferred by solving an MILP formulated from the trained ANN $\mathcal{N}$ so that ${\psi }_{\mathcal{N}}(x^{\ast })$ is equal to $y^{\ast }$ and then a set of chemical structures $G^{\ast }$ such that $f(G^{\ast })=x^{\ast }$ is enumerated by a graph enumeration algorithm. The framework has been applied to chemical compounds with a rather abstract topological structure such as acyclic or monocyclic graphs and graphs with a specified polymer topology with cycle index up to 2. In this paper, we propose a new flexible modeling method to the framework so that we can specify a topological substructure of graphs and a partial assignment of chemical elements and bond-multiplicity to a target graph.

arXiv admin note: text overlap with arXiv:2009.09646