Efficient Algorithms for Finding Maximum and Maximal Cliques and Their Applications

The problem of finding a maximum clique or enumerating all maximal cliques is very important and has been explored in several excellent survey papers. Here, we focus our attention on the step-by-step examination of a series of branch-and-bound depth-first search algorithms: Basics, MCQ, MCR, MCS, and MCT. Subsequently, as with the depth-first search as above, we present our algorithm, CLIQUES, for enumerating all maximal cliques. Finally, we describe some of the applications of the algorithms and their variants in bioinformatics, data mining, and other fields

Binding site matching in rational drug design: Algorithms and applications

© 2018 The Author(s) 2018. Published by Oxford University Press. All rights reserved. Interactions between proteins and small molecules are critical for biological functions. These interactions often occur in small cavities within protein structures, known as ligand-binding pockets. Understanding the physicochemical qualities of binding pockets is essential to improve not only our basic knowledge of biological systems, but also drug development procedures. In order to quantify similarities among pockets in terms of their geometries and chemical properties, either bound ligands can be compared to one another or binding sites can be matched directly. Both perspectives routinely take advantage of computational methods including various techniques to represent and compare small molecules as well as local protein structures. In this review, we survey 12 tools widely used to match pockets. These methods are divided into five categories based on the algorithm implemented to construct binding-site alignments. In addition to the comprehensive analysis of their algorithms, test sets and the performance of each method are described. We also discuss general pharmacological applications of computational pocket matching in drug repurposing, polypharmacology and side effects. Reflecting on the importance of these techniques in drug discovery, in the end, we elaborate on the development of more accurate meta-predictors, the incorporation of protein flexibility and the integration of powerful artificial intelligence technologies such as deep learning

A novel method to compare protein structures using local descriptors

<p>Abstract</p> <p>Background</p> <p>Protein structure comparison is one of the most widely performed tasks in bioinformatics. However, currently used methods have problems with the so-called "difficult similarities", including considerable shifts and distortions of structure, sequential swaps and circular permutations. There is a demand for efficient and automated systems capable of overcoming these difficulties, which may lead to the discovery of previously unknown structural relationships.</p> <p>Results</p> <p>We present a novel method for protein structure comparison based on the formalism of local descriptors of protein structure - DEscriptor Defined Alignment (DEDAL). Local similarities identified by pairs of similar descriptors are extended into global structural alignments. We demonstrate the method's capability by aligning structures in difficult benchmark sets: curated alignments in the SISYPHUS database, as well as SISY and RIPC sets, including non-sequential and non-rigid-body alignments. On the most difficult RIPC set of sequence alignment pairs the method achieves an accuracy of 77% (the second best method tested achieves 60% accuracy).</p> <p>Conclusions</p> <p>DEDAL is fast enough to be used in whole proteome applications, and by lowering the threshold of detectable structure similarity it may shed additional light on molecular evolution processes. It is well suited to improving automatic classification of structure domains, helping analyze protein fold space, or to improving protein classification schemes. DEDAL is available online at <url>http://bioexploratorium.pl/EP/DEDAL</url>.</p

Formulation of Hybrid Knowledge-Based/Molecular Mechanics Potentials for Protein Structure Refinement and a Novel Graph Theoretical Protein Structure Comparison and Analysis Technique

Proteins are the fundamental machinery that enables the functions of life. It is critical to understand them not just for basic biology, but also to enable medical advances. The field of protein structure prediction is concerned with developing computational techniques to predict protein structure and function from a protein’s amino acid sequence, encoded for directly in DNA, alone. Despite much progress since the first computational models in the late 1960’s, techniques for the prediction of protein structure still cannot reliably produce structures of high enough accuracy to enable desired applications such as rational drug design. Protein structure refinement is the process of modifying a predicted model of a protein to bring it closer to its native state. In this dissertation a protein structure refinement technique, that of potential energy minimization using hybrid molecular mechanics/knowledge based potential energy functions is examined in detail. The generation of the knowledge-based component is critically analyzed, and in the end, a potential that is a modest improvement over the original is presented. This dissertation also examines the task of protein structure comparison. In evaluating various protein structure prediction techniques, it is crucial to be able to compare produced models against known structures to understand how well the technique performs. A novel technique is proposed that allows an in-depth yet intuitive evaluation of the local similarities between protein structures. Based on a graph analysis of pairwise atomic distance similarities, multiple regions of structural similarity can be identified between structures independently of relative orientation. Multidomain structures can be evaluated and this technique can be combined with global measures of similarity such as the global distance test. This method of comparison is expected to have broad applications in rational drug design, the evolutionary study of protein structures, and in the analysis of the protein structure prediction effort

Graph algorithms for NMR resonance assignment and cross-link experiment planning

The study of three-dimensional protein structures produces insights into protein function at the molecular level. Graphs provide a natural representation of protein structures and associated experimental data, and enable the development of graph algorithms to analyze the structures and data. This thesis develops such graph representations and algorithms for two novel applications: structure-based NMR resonance assignment and disulfide cross-link experiment planning for protein fold determination. The first application seeks to identify correspondences between spectral peaks in NMR data and backbone atoms in a structure (from x-ray crystallography or homology modeling), by computing correspondences between a contact graph representing the structure and an analogous but very noisy and ambiguous graph representing the data. The assignment then supports further NMR studies of protein dynamics and protein-ligand interactions. A hierarchical grow-and-match algorithm was developed for smaller assignment problems, ensuring completeness of assignment, while a random graph approach was developed for larger problems, provably determining unique matches in polynomial time with high probability. Test results show that our algorithms are robust to typical levels of structural variation, noise, and missings, and achieve very good overall assignment accuracy. The second application aims to rapidly determine the overall organization of secondary structure elements of a target protein by probing it with a set of planned disulfide cross-links. A set of informative pairs of secondary structure elements is selected from graphs representing topologies of predicted structure models. For each pair in this ``fingerprint\u27\u27, a set of informative disulfide probes is selected from graphs representing residue proximity in the models. Information-theoretic planning algorithms were developed to maximize information gain while minimizing experimental complexity, and Bayes error plan assessment frameworks were developed to characterize the probability of making correct decisions given experimental data. Evaluation of the approach on a number of structure prediction case studies shows that the optimized plans have low risk of error while testing only a very small portion of the quadratic number of possible cross-link candidates

New Approaches to Protein Structure Prediction

Protein structure prediction is concerned with the prediction of a protein's three dimensional structure from its amino acid sequence. Such predictions are commonly performed by searching the possible structures and evaluating each structure by using some scoring function. If it is assumed that the target protein structure resembles the structure of a known protein, the search space can be significantly reduced. Such an approach is referred to as comparative structure prediction. When such an assumption is not made, the approach is known as ab initio structure prediction. There are several difficulties in devising efficient searches or in computing the scoring function. Many of these problems have ready solutions from known mathematical methods. However, the problems that are yet unsolved have hindered structure prediction methods from more ideal predictions. The objective of this study is to present a complete framework for ab initio protein structure prediction. To achieve this, a new search strategy is proposed, and better techniques are devised for computing the known scoring functions. Some of the remaining problems in protein structure prediction are revisited. Several of them are shown to be intractable. In many of these cases, approximation methods are suggested as alternative solutions. The primary issues addressed in this thesis are concerned with local structures prediction, structure assembly or sampling, side chain packing, model comparison, and structural alignment. For brevity, we do not elaborate on these problems here; a concise introduction is given in the first section of this thesis. Results from these studies prompted the development of several programs, forming a utility suite for ab initio protein structure prediction. Due to the general usefulness of these programs, some of them are released with open source licenses to benefit the community

Graph-Based Approaches to Protein StructureComparison - From Local to Global Similarity

The comparative analysis of protein structure data is a central aspect of structural bioinformatics. Drawing upon structural information allows the inference of function for unknown proteins even in cases where no apparent homology can be found on the sequence level. Regarding the function of an enzyme, the overall fold topology might less important than the specific structural conformation of the catalytic site or the surface region of a protein, where the interaction with other molecules, such as binding partners, substrates and ligands occurs. Thus, a comparison of these regions is especially interesting for functional inference, since structural constraints imposed by the demands of the catalyzed biochemical function make them more likely to exhibit structural similarity. Moreover, the comparative analysis of protein binding sites is of special interest in pharmaceutical chemistry, in order to predict cross-reactivities and gain a deeper understanding of the catalysis mechanism. From an algorithmic point of view, the comparison of structured data, or, more generally, complex objects, can be attempted based on different methodological principles. Global methods aim at comparing structures as a whole, while local methods transfer the problem to multiple comparisons of local substructures. In the context of protein structure analysis, it is not a priori clear, which strategy is more suitable. In this thesis, several conceptually different algorithmic approaches have been developed, based on local, global and semi-global strategies, for the task of comparing protein structure data, more specifically protein binding pockets. The use of graphs for the modeling of protein structure data has a long standing tradition in structural bioinformatics. Recently, graphs have been used to model the geometric constraints of protein binding sites. The algorithms developed in this thesis are based on this modeling concept, hence, from a computer scientist's point of view, they can also be regarded as global, local and semi-global approaches to graph comparison. The developed algorithms were mainly designed on the premise to allow for a more approximate comparison of protein binding sites, in order to account for the molecular flexibility of the protein structures. A main motivation was to allow for the detection of more remote similarities, which are not apparent by using more rigid methods. Subsequently, the developed approaches were applied to different problems typically encountered in the field of structural bioinformatics in order to assess and compare their performance and suitability for different problems. Each of the approaches developed during this work was capable of improving upon the performance of existing methods in the field. Another major aspect in the experiments was the question, which methodological concept, local, global or a combination of both, offers the most benefits for the specific task of protein binding site comparison, a question that is addressed throughout this thesis

Algorithms for the analysis of protein interaction networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 107-117).In the decade since the human genome project, a major research trend in biology has been towards understanding the cell as a system. This interest has stemmed partly from a deeper appreciation of how important it is to understand the emergent properties of cellular systems (e.g., they seem to be the key to understanding diseases like cancer). It has also been enabled by new high-throughput techniques that have allowed us to collect new types of data at the whole-genome scale. We focus on one sub-domain of systems biology: the understanding of protein interactions. Such understanding is valuable: interactions between proteins are fundamental to many cellular processes. Over the last decade, high-throughput experimental techniques have allowed us to collect a large amount of protein-protein interaction (PPI) data for many species. A popular abstraction for representing this data is the protein interaction network: each node of the network represents a protein and an edge between two nodes represents a physical interaction between the two corresponding proteins. This abstraction has proven to be a powerful tool for understanding the systems aspects of protein interaction. We present some algorithms for the augmentation, cleanup and analysis of such protein interaction networks: 1. In many species, the coverage of known PPI data remains partial. Given two protein sequences, we describe an algorithm to predict if two proteins physically interact, using logistic regression and insights from structural biology. We also describe how our predictions may be further improved by combining with functional-genomic data. 2. We study systematic false positives in a popular experimental protocol, the Yeast 2-Hybrid method. Here, some "promiscuous" proteins may lead to many false positives. We describe a Bayesian approach to modeling and adjusting for this error. 3. Comparative analysis of PPI networks across species can provide valuable insights. We describe IsoRank, an algorithm for global network alignment of multiple PPI networks. The algorithm first constructs an eigenvalue problem that encapsulates the network and sequence similarity constraints. The solution of the problem describes a k-partite graph that is further processed to find the alignment. 4. For a given signaling network, we describe an algorithm that combines RNA-interference data with PPI data to produce hypotheses about the structure of the signaling network. Our algorithm constructs a multi-commodity flow problem that expresses the constraints described by the data and finds a sparse solution to it.by Rohit Singh.Ph.D