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

A computer system to perform structure comparison using TOPS representations of protein structure

We describe the design and implementation of a fast topology–based method for protein structure comparison. The approach uses the TOPS topological representation of protein structure, aligning two structures using a common discovered pattern and generating measure of distance derived from an insert score. Heavy use is made of a constraint-based pattern matching algorithm for TOPS diagrams that we have designed and described elsewhere Gilbert et al. (1999). The comparison system is maintained at the European Bioinformatics Institute and is available over the Web via the at tops.ebi.ac.uk/tops. Users submit a structure description in Protein Data Bank (PDB) format and can compare it with structures in the entire PDB or a representative subset of protein domains, receiving the results by email

Quantitative surface field analysis: learning causal models to predict ligand binding affinity and pose.

We introduce the QuanSA method for inducing physically meaningful field-based models of ligand binding pockets based on structure-activity data alone. The method is closely related to the QMOD approach, substituting a learned scoring field for a pocket constructed of molecular fragments. The problem of mutual ligand alignment is addressed in a general way, and optimal model parameters and ligand poses are identified through multiple-instance machine learning. We provide algorithmic details along with performance results on sixteen structure-activity data sets covering many pharmaceutically relevant targets. In particular, we show how models initially induced from small data sets can extrapolatively identify potent new ligands with novel underlying scaffolds with very high specificity. Further, we show that combining predictions from QuanSA models with those from physics-based simulation approaches is synergistic. QuanSA predictions yield binding affinities, explicit estimates of ligand strain, associated ligand pose families, and estimates of structural novelty and confidence. The method is applicable for fine-grained lead optimization as well as potent new lead identification

Parallel Maximum Clique Algorithms with Applications to Network Analysis and Storage

We propose a fast, parallel maximum clique algorithm for large sparse graphs that is designed to exploit characteristics of social and information networks. The method exhibits a roughly linear runtime scaling over real-world networks ranging from 1000 to 100 million nodes. In a test on a social network with 1.8 billion edges, the algorithm finds the largest clique in about 20 minutes. Our method employs a branch and bound strategy with novel and aggressive pruning techniques. For instance, we use the core number of a vertex in combination with a good heuristic clique finder to efficiently remove the vast majority of the search space. In addition, we parallelize the exploration of the search tree. During the search, processes immediately communicate changes to upper and lower bounds on the size of maximum clique, which occasionally results in a super-linear speedup because vertices with large search spaces can be pruned by other processes. We apply the algorithm to two problems: to compute temporal strong components and to compress graphs.Comment: 11 page

Algorithm engineering for optimal alignment of protein structure distance matrices

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal Dali alignments for the very first time

Geometric, Feature-based and Graph-based Approaches for the Structural Analysis of Protein Binding Sites : Novel Methods and Computational Analysis

In this thesis, protein binding sites are considered. To enable the extraction of information from the space of protein binding sites, these binding sites must be mapped onto a mathematical space. This can be done by mapping binding sites onto vectors, graphs or point clouds. To finally enable a structure on the mathematical space, a distance measure is required, which is introduced in this thesis. This distance measure eventually can be used to extract information by means of data mining techniques