Exact Maximum Clique Algorithm for Different Graph Types Using Machine Learning

Toward mitigating the impact of non-bulk defects on describing water structure in salt aqueous solutions: Characterizing solution density with a network-based structural indicator

Structural indicators, also known as structural descriptors, including order parameters, have been proposed to quantify the structural properties of water to account for its anomalous behaviors. However, these indicators, mainly designed for bulk water, are not naturally transferrable to the vicinity of ions due to disruptions in the immediate neighboring space and a resulting loss of feature completeness. To address these non-bulk defects, we introduced a structural indicator that draws on the concept of clique number from graph theory and the criterion in agglomerative clustering, denoted as the average cluster number. This structural indicator aims to discern intrinsic structural characteristics within the water molecules regardless of the ions occupying the neighboring space, without requiring additional corrections. From molecular dynamics simulation results for neat water and salt aqueous solutions utilizing the TIP4P/2005 water model and the Madrid-2019 force field, we characterized the variations in densities with temperature using this network-based indicator, thereby demonstrating its practical utility. The findings suggest that at lower temperatures, the addition of ions disrupts the intrinsic structure of water molecules, with this effect diminishing as the temperature rises. Cations with larger charge density tend to induce stronger disruptions. This study highlights the importance of mitigating the impact of non-bulk defects before applying the indicators to analyze water's intrinsic structural properties in solutions. By doing so, the relationship between changes in water structure and solution behaviors can be more accurately assessed.

Protein binding sites for drug design

Drug development is a lengthy and challenging process that can be accelerated at early stages by new mathematical approaches and modern computers. To address this important issue, we are developing new mathematical solutions for the detection and characterization of protein binding sites that are important for new drug development. In this review, we present algorithms based on graph theory combined with molecular dynamics simulations that we have developed for studying biological target proteins to provide important data for optimizing the early stages of new drug development. A particular focus is the development of new protein binding site prediction algorithms (ProBiS) and new web tools for modeling pharmaceutically interesting molecules-ProBiS Tools (algorithm, database, web server), which have evolved into a full-fledged graphical tool for studying proteins in the proteome. ProBiS differs from other structural algorithms in that it can align proteins with different folds without prior knowledge of the binding sites. It allows detection of similar binding sites and can predict molecular ligands of various types of pharmaceutical interest that could be advanced to drugs to treat a disease, based on the entire Protein Data Bank (PDB) and AlphaFold database, including proteins not yet in the PDB. All ProBiS Tools are freely available to the academic community at http://insilab.org and https://probis.nih.gov.

ProBiS-Fold Approach for Annotation of Human Structures from the AlphaFold Database with No Corresponding Structure in the PDB to Discover New Druggable Binding Sites

ProBiS (Protein Binding Sites), a local structure-based comparison algorithm, is used in the new ProBiS-Fold web server to annotate human structures from the AlphaFold database without a corresponding structure in the Protein Data Bank (PDB) to discover new druggable binding sites. The ProBiS algorithm is used to compare each query protein structure predicted by the AlphaFold approach with the protein structures from the PDB to identify similarities between known binding sites found in the PDB and yet unknown binding sites in the AlphaFold database. Ligands bound in these identified similar PDB sites are then transferred to each query protein from the AlphaFold database, and binding sites are identified as ligand clusters on an AlphaFold protein. Small molecule binding sites are assigned druggability scores based on the similarity of their ligands to known drugs, allowing them to be ranked according to their perceived and actual potential for drug development. ProBiS-Fold provides interactive and downloadable binding sites for the entire human structural proteome, including more than 3000 new druggable binding sites that have no corresponding structure in the PDB, taking into account AlphaFold's model quality, to enable protein structure-function relationship studies and pharmaceutical drug discovery research. The web server is freely accessible to academic users at http://probis-fold.insilab.org.

A Review: Machine Learning for Combinatorial Optimization Problems in Energy Areas

Combinatorial optimization problems (COPs) are a class of NP-hard problems with great practical significance. Traditional approaches for COPs suffer from high computational time and reliance on expert knowledge, and machine learning (ML) methods, as powerful tools have been used to overcome these problems. In this review, the COPs in energy areas with a series of modern ML approaches, i.e., the interdisciplinary areas of COPs, ML and energy areas, are mainly investigated. Recent works on solving COPs using ML are sorted out firstly by methods which include supervised learning (SL), deep learning (DL), reinforcement learning (RL) and recently proposed game theoretic methods, and then problems where the timeline of the improvements for some fundamental COPs is the layout. Practical applications of ML methods in the energy areas, including the petroleum supply chain, steel-making, electric power system and wind power, are summarized for the first time, and challenges in this field are analyzed.