Geometric Graph Learning with Extended Atom-Types Features for Protein-Ligand Binding Affinity Prediction

In recent years, graph theories have been widely used in chemical, biological, physical, social, and computer sciences. This is because graphs are useful for representing and analyzing a wide range of practical problems. In molecular modeling, graph representation is widely used since it is a natural way to model their structures, in which graph vertices represent atoms and graph edges represent possible interactions between them. In general, graph theories can be divided into three categories: geometric graph theory, algebraic graph theory, and topological graph theory. Geometric graph theory studies a graph's geometric connectivity, which refers to the pairwise relations among graph nodes or vertices [1]. Algebraic graph theory concerns the algebraic connectivity via the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as the adjacency matrix or the Laplacian matrix [2, 3]. In topological graph theory, embedding and immersion of graphs are studied along with their association with topological spaces, such as abstract simplicial complexes [4, 5]. There are numerous applications of graphs in chemical analysis and biomolecular modeling [6, 7, 8, 9], such as normal-mode analysis (NMA) [10, 11, 12, 13] and elastic network model (ENM) [14, 15, 16, 17, 18, 19] used to study protein B-factor prediction. Algebraic graph theory has been utilized in some of the most popular elastic network models (ENMs) such as the Gaussian network model (GNM) and the anisotropic network model (ANM).