On combinatorial optimisation in analysis of protein-protein interaction and protein folding networks

Abstract: Protein-protein interaction networks and protein folding networks represent prominent research topics at the intersection of bioinformatics and network science. In this paper, we present a study of these networks from combinatorial optimisation point of view. Using a combination of classical heuristics and stochastic optimisation techniques, we were able to identify several interesting combinatorial properties of biological networks of the COSIN project. We obtained optimal or near-optimal solutions to maximum clique and chromatic number problems for these networks. We also explore patterns of both non-overlapping and overlapping cliques in these networks. Optimal or near-optimal solutions to partitioning of these networks into non-overlapping cliques and to maximum independent set problem were discovered. Maximal cliques are explored by enumerative techniques. Domination in these networks is briefly studied, too. Applications and extensions of our findings are discussed

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

Toward real-world automated antibody design with combinatorial Bayesian optimization

Antibodies are multimeric proteins capable of highly specific molecular recognition. The complementarity determining region 3 of the antibody variable heavy chain (CDRH3) often dominates antigen-binding specificity. Hence, it is a priority to design optimal antigen-specific CDRH3 to develop therapeutic antibodies. The combinatorial structure of CDRH3 sequences makes it impossible to query binding-affinity oracles exhaustively. Moreover, antibodies are expected to have high target specificity and developability. Here, we present AntBO, a combinatorial Bayesian optimization framework utilizing a CDRH3 trust region for an in silico design of antibodies with favorable developability scores. The in silico experiments on 159 antigens demonstrate that AntBO is a step toward practically viable in vitro antibody design. In under 200 calls to the oracle, AntBO suggests antibodies outperforming the best binding sequence from 6.9 million experimentally obtained CDRH3s. Additionally, AntBO finds very-high-affinity CDRH3 in only 38 protein designs while requiring no domain knowledge

Polynomial unconstrained binary optimisation inspired by optical simulation

We propose an algorithm inspired by optical coherent Ising machines to solve the problem of polynomial unconstrained binary optimisation (PUBO). We benchmark the proposed algorithm against existing PUBO algorithms on the extended Sherrington-Kirkpatrick model and random third-degree polynomial pseudo-Boolean functions, and observe its superior performance. We also address instances of practically relevant computational problems such as protein folding and electronic structure calculations with problem sizes not accessible to existing quantum annealing devices. In particular, we successfully find the lowest-energy conformation of lattice protein molecules containing up to eleven amino-acids. The application of our algorithm to quantum chemistry sheds light on the shortcomings of approximating the electronic structure problem by a PUBO problem, which, in turn, puts into question the applicability of quantum annealers in this context.Comment: 10 pages, 6 figure

Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction

Despite the recognized importance of the multi-scale spatio-temporal organization of proteins, most computational tools can only access a limited spectrum of time and spatial scales, thereby ignoring the effects on protein behavior of the intricate coupling between the different scales. Starting from a physico-chemical atomistic network of interactions that encodes the structure of the protein, we introduce a methodology based on multi-scale graph partitioning that can uncover partitions and levels of organization of proteins that span the whole range of scales, revealing biological features occurring at different levels of organization and tracking their effect across scales. Additionally, we introduce a measure of robustness to quantify the relevance of the partitions through the generation of biochemically-motivated surrogate random graph models. We apply the method to four distinct conformations of myosin tail interacting protein, a protein from the molecular motor of the malaria parasite, and study properties that have been experimentally addressed such as the closing mechanism, the presence of conserved clusters, and the identification through computational mutational analysis of key residues for binding.Comment: 13 pages, 7 Postscript figure

Computational methodologies applied to Protein-Protein Interactions for molecular insights in Medicinal Chemistry

In living systems, proteins usually team up into \u201cmolecular machinery\u201d implementing several protein-to-protein physical contacts \u2013 or protein-protein interactions (PPIs) \u2013 to exert biological effects at both cellular and systems levels. Deregulations of protein-protein contacts have been associated with a huge number of diseases in a wide range of medical areas, such as oncology, cancer immunotherapy, infectious diseases, neurological disorders, heart failure, inflammation and oxidative stress. PPIs are very complex and usually characterised by specific shape, size and complementarity. The protein interfaces are generally large, broad and shallow, and frequently protein-protein contacts are established between non-continuous epitopes, that conversely are dislocated across the protein interfaces. For this reason, in the past two decades, PPIs were thought to be \u201cundruggable\u201d targets by the scientific research community with scarce or no chance of success. However, in recent years the Medicinal Chemistry frontiers have been changing and PPIs have gained popularity amongst the research groups due to their key roles in such a huge number of diseases. Until recently, PPIs were determined by experimental evidence through techniques specifically developed to target a small group of interactions. However, these methods present several limitations in terms of high costs and labour- and time-wasting. Nowadays, a large number of computational methods have been successfully applied to evaluate, validate, and deeply analyse the experimentally determined protein interactomes. In this context, a high number of computational tools and techniques have been developed, such as methods designed to construct interaction databases, quantum mechanics and molecular mechanics (QM/MM) to study the electronic properties, simulate chemical reactions, and calculate spectra, and all-atom molecular dynamics simulations to simulate temporal and spatial scales of inter- and intramolecular interactions. These techniques have allowed to explore PPI networks and predict the related functional features. In this PhD work, an extensive use of computational techniques has been reported as valuable tool to explore protein-protein interfaces, identify their hot spot residues, select small molecules and design peptides with the aim of inhibiting six different studied PPIs. Indeed, in this thesis, a success story of in silico approaches to PPI study has been described, where MD simulations, docking and pharmacophore screenings led to the identification of a set of PPI modulators. Among these, two molecules, RIM430 and RIM442, registered good inhibitory activity with IC50 values even within the nanomolar range against the interaction between MUC1 and CIN85 proteins in cancer disease. Furthermore, computational alanine scanning, all-atom molecular dynamics simulations, docking and pharmacophore screening were exploited to (1) rationally predict three potential interaction models of NLRP3PYD-ASCPYD complex involved in inflammatory and autoimmune diseases; (2) identify a potentially druggable region on the surface of SARS-CoV-2 Spike protein interface and select putative inhibitors of the interaction between Spike protein and the host ACE2 receptor against COVID-19 (CoronaVIrus Disease 2019); (3) investigate intramolecular modifications as a consequence of a point mutation on C3b protein (R102G) associated with the age-related macular degeneration (AMD) disease; (4) design non-standard peptides to inhibit transcriptional events associated with HOX-PBX complex involved in cancer diseases; and (5) to optimise a patented peptide sequence by designing helix-shaped peptides embedded with the hydrogen bond surrogate approach to tackle cocaine abuse relapses associated with Ras-RasGRF1 interaction. Although all the herein exploited techniques are based on predictive calculations and need experimental evidence to confirm the findings, the results and molecular insights retrieved and collected show the potential of the computer-aided drug design applied to the Medicinal Chemistry, guaranteeing labour- and time-saving to the research groups. On the other hand, computing ability, improved algorithms and fast-growing data sets are rapidly fostering advances in multiscale molecular modelling, providing a powerful emerging paradigm for drug discovery. It means that more and more research efforts will be done to invest in novel and more precise computational techniques and fine-tune the currently employed methodologies

All-scale structural analysis of biomolecules through dynamical graph partitioning

From femtosecond bond vibrations to millisecond domain motions, the dynamics of biomolecules spans a wide range of time and length scales. This hierarchy of overlapping scales links the molecular and biophysical details to key aspects of their functionality. However, the span of scales combined with their intricate coupling rapidly drives atomic simulation methods to their limits, thereby often resulting in the need for coarse-graining techniques which cannot take full account of the biochemical details. To overcome this tradeoff, a graph-theoretical framework inspired by multiscale community detection methods and stochastic processes is here introduced for the analysis of protein and DNA structures. Using biophysical force fields, we propose a general mapping of the 3D atomic coordinates onto an energy-weighted network that includes the physico-chemical details of interatomic bonds and interactions.Making use of a dynamics-based approach for community detection on networks, optimal partitionings of the structure are identified which are biochemically relevant over different scales. The structural organisation of the biomolecule is shown to be recovered bottom-up over the entire range of chemical, biochemical and biologically meaningful scales, directly from the atomic information of the structure, and without any reparameterisation. This methodology is applied and discussed in five proteins and an ensemble of DNA quadruplexes. In each case, multiple conformations associated with different states of the biomolecule or stages of the underlying catalytic reaction are analysed. Experimental observations are shown to be correctly captured, including the functional domains, regions of the protein with coherent dynamics such as rigid clusters, and the spontaneous closure of some enzymes in the absence of substrate. A computational mutational analysis tool is also derived which identifies both known and new residues with a significant impact on ligand binding. In large multimeric structures, the methodology highlights patterns of long range communication taking place between subunits. In the highly dynamic and polymorphic DNA quadruplexes, key structural features for their physical stability and signatures of their unfolding pathway are identified in the static structure.Open Acces