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

Finding undetected protein associations in cell signaling by belief propagation

External information propagates in the cell mainly through signaling cascades and transcriptional activation, allowing it to react to a wide spectrum of environmental changes. High throughput experiments identify numerous molecular components of such cascades that may, however, interact through unknown partners. Some of them may be detected using data coming from the integration of a protein-protein interaction network and mRNA expression profiles. This inference problem can be mapped onto the problem of finding appropriate optimal connected subgraphs of a network defined by these datasets. The optimization procedure turns out to be computationally intractable in general. Here we present a new distributed algorithm for this task, inspired from statistical physics, and apply this scheme to alpha factor and drug perturbations data in yeast. We identify the role of the COS8 protein, a member of a gene family of previously unknown function, and validate the results by genetic experiments. The algorithm we present is specially suited for very large datasets, can run in parallel, and can be adapted to other problems in systems biology. On renowned benchmarks it outperforms other algorithms in the field.Comment: 6 pages, 3 figures, 1 table, Supporting Informatio

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

Network-based approaches to explore complex biological systems towards network medicine

Network medicine relies on different types of networks: from the molecular level of protein–protein interactions to gene regulatory network and correlation studies of gene expression. Among network approaches based on the analysis of the topological properties of protein–protein interaction (PPI) networks, we discuss the widespread DIAMOnD (disease module detection) algorithm. Starting from the assumption that PPI networks can be viewed as maps where diseases can be identified with localized perturbation within a specific neighborhood (i.e., disease modules), DIAMOnD performs a systematic analysis of the human PPI network to uncover new disease-associated genes by exploiting the connectivity significance instead of connection density. The past few years have witnessed the increasing interest in understanding the molecular mechanism of post-transcriptional regulation with a special emphasis on non-coding RNAs since they are emerging as key regulators of many cellular processes in both physiological and pathological states. Recent findings show that coding genes are not the only targets that microRNAs interact with. In fact, there is a pool of different RNAs—including long non-coding RNAs (lncRNAs) —competing with each other to attract microRNAs for interactions, thus acting as competing endogenous RNAs (ceRNAs). The framework of regulatory networks provides a powerful tool to gather new insights into ceRNA regulatory mechanisms. Here, we describe a data-driven model recently developed to explore the lncRNA-associated ceRNA activity in breast invasive carcinoma. On the other hand, a very promising example of the co-expression network is the one implemented by the software SWIM (switch miner), which combines topological properties of correlation networks with gene expression data in order to identify a small pool of genes—called switch genes—critically associated with drastic changes in cell phenotype. Here, we describe SWIM tool along with its applications to cancer research and compare its predictions with DIAMOnD disease genes

Methods for protein complex prediction and their contributions towards understanding the organization, function and dynamics of complexes

Complexes of physically interacting proteins constitute fundamental functional units responsible for driving biological processes within cells. A faithful reconstruction of the entire set of complexes is therefore essential to understand the functional organization of cells. In this review, we discuss the key contributions of computational methods developed till date (approximately between 2003 and 2015) for identifying complexes from the network of interacting proteins (PPI network). We evaluate in depth the performance of these methods on PPI datasets from yeast, and highlight challenges faced by these methods, in particular detection of sparse and small or sub- complexes and discerning of overlapping complexes. We describe methods for integrating diverse information including expression profiles and 3D structures of proteins with PPI networks to understand the dynamics of complex formation, for instance, of time-based assembly of complex subunits and formation of fuzzy complexes from intrinsically disordered proteins. Finally, we discuss methods for identifying dysfunctional complexes in human diseases, an application that is proving invaluable to understand disease mechanisms and to discover novel therapeutic targets. We hope this review aptly commemorates a decade of research on computational prediction of complexes and constitutes a valuable reference for further advancements in this exciting area.Comment: 1 Tabl

Revisiting Date and Party Hubs: Novel Approaches to Role Assignment in Protein Interaction Networks

The idea of 'date' and 'party' hubs has been influential in the study of protein-protein interaction networks. Date hubs display low co-expression with their partners, whilst party hubs have high co-expression. It was proposed that party hubs are local coordinators whereas date hubs are global connectors. Here we show that the reported importance of date hubs to network connectivity can in fact be attributed to a tiny subset of them. Crucially, these few, extremely central, hubs do not display particularly low expression correlation, undermining the idea of a link between this quantity and hub function. The date/party distinction was originally motivated by an approximately bimodal distribution of hub co-expression; we show that this feature is not always robust to methodological changes. Additionally, topological properties of hubs do not in general correlate with co-expression. Thus, we suggest that a date/party dichotomy is not meaningful and it might be more useful to conceive of roles for protein-protein interactions rather than individual proteins. We find significant correlations between interaction centrality and the functional similarity of the interacting proteins.Comment: 27 pages, 5 main figures, 4 supplementary figure