Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening

This work introduces a number of algebraic topology approaches, such as multicomponent persistent homology, multi-level persistent homology and electrostatic persistence for the representation, characterization, and description of small molecules and biomolecular complexes. Multicomponent persistent homology retains critical chemical and biological information during the topological simplification of biomolecular geometric complexity. Multi-level persistent homology enables a tailored topological description of inter- and/or intra-molecular interactions of interest. Electrostatic persistence incorporates partial charge information into topological invariants. These topological methods are paired with Wasserstein distance to characterize similarities between molecules and are further integrated with a variety of machine learning algorithms, including k-nearest neighbors, ensemble of trees, and deep convolutional neural networks, to manifest their descriptive and predictive powers for chemical and biological problems. Extensive numerical experiments involving more than 4,000 protein-ligand complexes from the PDBBind database and near 100,000 ligands and decoys in the DUD database are performed to test respectively the scoring power and the virtual screening power of the proposed topological approaches. It is demonstrated that the present approaches outperform the modern machine learning based methods in protein-ligand binding affinity predictions and ligand-decoy discrimination

Static Analysis of Functional Programs

In this paper, the static analysis of programs in the functional programming language Miranda* is described based on two graph models. A new control-flow graph model of Miranda definitions is presented, and a model with four classes of callgraphs. Standard software metrics are applicable to these models. A Miranda front end for Prometrix, ¿, a tool for the automated analysis of flowgraphs and callgraphs, has been developed. This front end produces the flowgraph and callgraph representations of Miranda programs. Some features of the metric analyser are illustrated with an example program. The tool provides a promising access to standard metrics on functional programs