Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Annotating Protein Functional Residues by Coupling High-Throughput Fitness Profile and Homologous-Structure Analysis.

Identification and annotation of functional residues are fundamental questions in protein sequence analysis. Sequence and structure conservation provides valuable information to tackle these questions. It is, however, limited by the incomplete sampling of sequence space in natural evolution. Moreover, proteins often have multiple functions, with overlapping sequences that present challenges to accurate annotation of the exact functions of individual residues by conservation-based methods. Using the influenza A virus PB1 protein as an example, we developed a method to systematically identify and annotate functional residues. We used saturation mutagenesis and high-throughput sequencing to measure the replication capacity of single nucleotide mutations across the entire PB1 protein. After predicting protein stability upon mutations, we identified functional PB1 residues that are essential for viral replication. To further annotate the functional residues important to the canonical or noncanonical functions of viral RNA-dependent RNA polymerase (vRdRp), we performed a homologous-structure analysis with 16 different vRdRp structures. We achieved high sensitivity in annotating the known canonical polymerase functional residues. Moreover, we identified a cluster of noncanonical functional residues located in the loop region of the PB1 β-ribbon. We further demonstrated that these residues were important for PB1 protein nuclear import through the interaction with Ran-binding protein 5. In summary, we developed a systematic and sensitive method to identify and annotate functional residues that are not restrained by sequence conservation. Importantly, this method is generally applicable to other proteins about which homologous-structure information is available.ImportanceTo fully comprehend the diverse functions of a protein, it is essential to understand the functionality of individual residues. Current methods are highly dependent on evolutionary sequence conservation, which is usually limited by sampling size. Sequence conservation-based methods are further confounded by structural constraints and multifunctionality of proteins. Here we present a method that can systematically identify and annotate functional residues of a given protein. We used a high-throughput functional profiling platform to identify essential residues. Coupling it with homologous-structure comparison, we were able to annotate multiple functions of proteins. We demonstrated the method with the PB1 protein of influenza A virus and identified novel functional residues in addition to its canonical function as an RNA-dependent RNA polymerase. Not limited to virology, this method is generally applicable to other proteins that can be functionally selected and about which homologous-structure information is available

Identifying network communities with a high resolution

Community structure is an important property of complex networks. An automatic discovery of such structure is a fundamental task in many disciplines, including sociology, biology, engineering, and computer science. Recently, several community discovery algorithms have been proposed based on the optimization of a quantity called modularity (Q). However, the problem of modularity optimization is NP-hard, and the existing approaches often suffer from prohibitively long running time or poor quality. Furthermore, it has been recently pointed out that algorithms based on optimizing Q will have a resolution limit, i.e., communities below a certain scale may not be detected. In this research, we first propose an efficient heuristic algorithm, Qcut, which combines spectral graph partitioning and local search to optimize Q. Using both synthetic and real networks, we show that Qcut can find higher modularities and is more scalable than the existing algorithms. Furthermore, using Qcut as an essential component, we propose a recursive algorithm, HQcut, to solve the resolution limit problem. We show that HQcut can successfully detect communities at a much finer scale and with a higher accuracy than the existing algorithms. Finally, we apply Qcut and HQcut to study a protein-protein interaction network, and show that the combination of the two algorithms can reveal interesting biological results that may be otherwise undetectable.Comment: 14 pages, 5 figures. 1 supplemental file at http://cic.cs.wustl.edu/qcut/supplemental.pd

The Physics of Communicability in Complex Networks

A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.Comment: Review Article. 90 pages, 14 figures. Contents: Introduction; Communicability in Networks; Physical Analogies; Comparing Communicability Functions; Communicability and the Analysis of Networks; Communicability and Localization in Complex Networks; Computability of Communicability Functions; Conclusions and Prespective

Hot-spot analysis for drug discovery targeting protein-protein interactions

Introduction: Protein-protein interactions are important for biological processes and pathological situations, and are attractive targets for drug discovery. However, rational drug design targeting protein-protein interactions is still highly challenging. Hot-spot residues are seen as the best option to target such interactions, but their identification requires detailed structural and energetic characterization, which is only available for a tiny fraction of protein interactions. Areas covered: In this review, the authors cover a variety of computational methods that have been reported for the energetic analysis of protein-protein interfaces in search of hot-spots, and the structural modeling of protein-protein complexes by docking. This can help to rationalize the discovery of small-molecule inhibitors of protein-protein interfaces of therapeutic interest. Computational analysis and docking can help to locate the interface, molecular dynamics can be used to find suitable cavities, and hot-spot predictions can focus the search for inhibitors of protein-protein interactions. Expert opinion: A major difficulty for applying rational drug design methods to protein-protein interactions is that in the majority of cases the complex structure is not available. Fortunately, computational docking can complement experimental data. An interesting aspect to explore in the future is the integration of these strategies for targeting PPIs with large-scale mutational analysis.This work has been funded by grants BIO2016-79930-R and SEV-2015-0493 from the Spanish Ministry of Economy, Industry and Competitiveness, and grant EFA086/15 from EU Interreg V POCTEFA. M Rosell is supported by an FPI fellowship from the Severo Ochoa program. The authors are grateful for the support of the the Joint BSC-CRG-IRB Programme in Computational Biology.Peer ReviewedPostprint (author's final draft

Evolutionary conservation of influenza A PB2 sequences reveals potential target sites for small molecule inhibitors.

The influenza A basic polymerase protein 2 (PB2) functions as part of a heterotrimer to replicate the viral RNA genome. To investigate novel PB2 antiviral target sites, this work identified evolutionary conserved regions across the PB2 protein sequence amongst all sub-types and hosts, as well as ligand binding hot spots which overlap with highly conserved areas. Fifteen binding sites were predicted in different PB2 domains; some of which reside in areas of unknown function. Virtual screening of ~50,000 drug-like compounds showed binding affinities of up to 10.3 kcal/mol. The highest affinity molecules were found to interact with conserved residues including Gln138, Gly222, Ile529, Asn540 and Thr530. A library containing 1738 FDA approved drugs were screened additionally and revealed Paliperidone as a top hit with a binding affinity of -10 kcal/mol. Predicted ligands are ideal leads for new antivirals as they were targeted to evolutionary conserved binding sites

Gcn4p and novel upstream activating sequences regulate targets of the unfolded protein response.

Eukaryotic cells respond to accumulation of unfolded proteins in the endoplasmic reticulum (ER) by activating the unfolded protein response (UPR), a signal transduction pathway that communicates between the ER and the nucleus. In yeast, a large set of UPR target genes has been experimentally determined, but the previously characterized unfolded protein response element (UPRE), an upstream activating sequence (UAS) found in the promoter of the UPR target gene KAR2, cannot account for the transcriptional regulation of most genes in this set. To address this puzzle, we analyzed the promoters of UPR target genes computationally, identifying as candidate UASs short sequences that are statistically overrepresented. We tested the most promising of these candidate UASs for biological activity, and identified two novel UPREs, which are necessary and sufficient for UPR activation of promoters. A genetic screen for activators of the novel motifs revealed that the transcription factor Gcn4p plays an essential and previously unrecognized role in the UPR: Gcn4p and its activator Gcn2p are required for induction of a majority of UPR target genes during ER stress. Both Hac1p and Gcn4p bind target gene promoters to stimulate transcriptional induction. Regulation of Gcn4p levels in response to changing physiological conditions may function as an additional means to modulate the UPR. The discovery of a role for Gcn4p in the yeast UPR reveals an additional level of complexity and demonstrates a surprising conservation of the signaling circuit between yeast and metazoan cells