Laura Bennett

Detection of composite communities in multiplex biological networks

The detection of community structure is a widely accepted means of investigating the principles governing biological systems. Recent efforts are exploring ways in which multiple data sources can be integrated to generate a more comprehensive model of cellular interactions, leading to the detection of more biologically relevant communities. In this work, we propose a mathematical programming model to cluster multiplex biological networks, i.e. multiple network slices, each with a different interaction type, to determine a single representative partition of composite communities. Our method, known as SimMod, is evaluated through its application to yeast networks of physical, genetic and co-expression interactions. A comparative analysis involving partitions of the individual networks, partitions of aggregated networks and partitions generated by similar methods from the literature highlights the ability of SimMod to identify functionally enriched modules. It is further shown that SimMod offers enhanced results when compared to existing approaches without the need to train on known cellular interactions.

Module detection in complex networks using integer optimisation

BackgroundThe detection of modules or community structure is widely used to reveal the underlying properties of complex networks in biology, as well as physical and social sciences. Since the adoption of modularity as a measure of network topological properties, several methodologies for the discovery of community structure based on modularity maximisation have been developed. However, satisfactory partitions of large graphs with modest computational resources are particularly challenging due to the NP-hard nature of the related optimisation problem. Furthermore, it has been suggested that optimising the modularity metric can reach a resolution limit whereby the algorithm fails to detect smaller communities than a specific size in large networks.ResultsWe present a novel solution approach to identify community structure in large complex networks and address resolution limitations in module detection. The proposed algorithm employs modularity to express network community structure and it is based on mixed integer optimisation models. The solution procedure is extended through an iterative procedure to diminish effects that tend to agglomerate smaller modules (resolution limitations).ConclusionsA comprehensive comparative analysis of methodologies for module detection based on modularity maximisation shows that our approach outperforms previously reported methods. Furthermore, in contrast to previous reports, we propose a strategy to handle resolution limitations in modularity maximisation. Overall, we illustrate ways to improve existing methodologies for community structure identification so as to increase its efficiency and applicability.

DyCoNet: A Gephi Plugin for Community Detection in Dynamic Complex Networks

Community structure detection has proven to be important in revealing the underlying organisation of complex networks. While most current analyses focus on static networks, the detection of communities in dynamic data is both challenging and timely. An analysis and visualisation procedure for dynamic networks is presented here, which identifies communities and sub-communities that persist across multiple network snapshots. An existing method for community detection in dynamic networks is adapted, extended, and implemented. We demonstrate the applicability of this method to detect communities in networks where individuals tend not to change their community affiliation very frequently. When stability of communities cannot be assumed, we show that the sub-community model may be a better alternative. This is illustrated through test cases of social and biological networks. A plugin for Gephi, an open-source software program used for graph visualisation and manipulation, named “DyCoNet”, was created to execute the algorithm and is freely available from https://github.com/juliemkauffman/DyCoNet.

DETECTION OF DISJOINT AND OVERLAPPING MODULES IN WEIGHTED COMPLEX NETWORKS

Community structure detection is widely accepted as a means of elucidating the functional properties of complex networks. The problem statement is ever evolving, with the aim of developing more flexible and realistic modeling procedures. For example, a first step in developing a more informative model is the inclusion of weighted interactions. In addition to the standard community structure problem, interest has increased in the detection of overlapping communities. Adopting such constraints may, in some cases, represent a more true to life abstraction of the system under study. In this paper, two novel mathematical programming algorithms for module detection are presented. First, disjoint modules in weighted and unweighted networks are detected by formulating modularity maximization as a mixed integer nonlinear programming (MINLP) model. The solution obtained is then used to detect overlapping modules through a further MINLP model. The inclusion of two parameters controlling the extent of overlapping offers flexibility in user requirements. Comparative results show that these methodologies perform competitively to previously proposed methods. The methodologies proposed here promote the detection of topological relationships in complex systems. Together with the amenable nature of mathematical programming models, we show that both algorithms offer a versatile solution to the community detection problem.

Network-Based Data Integration for Selecting Candidate Virulence Associated Proteins in the Cereal Infecting Fungus Fusarium graminearum

The identification of virulence genes in plant pathogenic fungi is important for understanding the infection process, host range and for developing control strategies. The analysis of already verified virulence genes in phytopathogenic fungi in the context of integrated functional networks can give clues about the underlying mechanisms and pathways directly or indirectly linked to fungal pathogenicity and can suggest new candidates for further experimental investigation, using a ‘guilt by association’ approach. Here we study 133 genes in the globally important Ascomycete fungus Fusarium graminearum that have been experimentally tested for their involvement in virulence. An integrated network that combines information from gene co-expression, predicted protein-protein interactions and sequence similarity was employed and, using 100 genes known to be required for virulence, we found a total of 215 new proteins potentially associated with virulence of which 29 are annotated as hypothetical proteins. The majority of these potential virulence genes are located in chromosomal regions known to have a low recombination frequency. We have also explored the taxonomic diversity of these candidates and found 25 sequences, which are likely to be fungal specific. We discuss the biological relevance of a few of the potentially novel virulence associated genes in detail. The analysis of already verified virulence genes in phytopathogenic fungi in the context of integrated functional networks can give clues about the underlying mechanisms and pathways directly or indirectly linked to fungal pathogenicity and can suggest new candidates for further experimental investigation, using a ‘guilt by association’ approach.

Community structure detection for overlapping modules through mathematical programming in protein interaction networks.

Community structure detection has proven to be important in revealing the underlying properties of complex networks. The standard problem, where a partition of disjoint communities is sought, has been continually adapted to offer more realistic models of interactions in these systems. Here, a two-step procedure is outlined for exploring the concept of overlapping communities. First, a hard partition is detected by employing existing methodologies. We then propose a novel mixed integer non linear programming (MINLP) model, known as OverMod, which transforms disjoint communities to overlapping. The procedure is evaluated through its application to protein-protein interaction (PPI) networks of the rat, E. coli, yeast and human organisms. Connector nodes of hard partitions exhibit topological and functional properties indicative of their suitability as candidates for multiple module membership. OverMod identifies two types of connector nodes, inter and intra-connector, each with their own particular characteristics pertaining to their topological and functional role in the organisation of the network. Inter-connector proteins are shown to be highly conserved proteins participating in pathways that control essential cellular processes, such as proliferation, differentiation and apoptosis and their differences with intra-connectors is highlighted. Many of these proteins are shown to possess multiple roles of distinct nature through their participation in different network modules, setting them apart from proteins that are simply ‘hubs’, i.e. proteins with many interaction partners but with a more specific biochemical role.

A Mathematical Programming Approach to Community Structure Detection in Complex Networks

Abstract The detection of community structure is a widely recognised method of revealing the underlying properties of complex networks in biological, physical and social sciences. The simplest form of the community structure problem is the partitioning of unweighted and undirected networks into disjoint communities. However, module detection in weighted networks or communities with overlapping modules may lead to more realistic applications. Optimisation of the modularity metric is a popular method for community structure detection (Newman and Girvan 2004) and here we extend its use to propose mixed integer nonlinear programming (MINLP) models for (i) partitioning of weighted networks and (ii) detection of overlapping communities. The mathematical programming nature of the methods proposed provide users with an adaptability that may not be available in alternative modelling frameworks. Overall, we show that our methods improve existing methodologies in terms of applicability and adaptability and offer a versatile solution to the community detection problem.

Detection of Multi-clustered Genes and Community Structure for the Plant Pathogenic Fungus Fusarium graminearum

Exploring the community structure of biological networks can reveal the roles of individual genes in the context of the entire biological system, so as to understand the underlying mechanism of interaction. In this study we explore the disjoint and overlapping community structure of an integrated network for a major fungal pathogen of many cereal crops, Fusarium graminearum. The network was generated by combining sequence, protein interaction and co-expression data. We examine the functional characteristics of communities, the connectivity and multi-functionality of genes and explore the contribution of known virulence genes in community structure. Disjoint community structure is detected using a greedy agglomerative method based on modularity optimisation. The disjoint partition is then converted to a set of overlapping communities, where genes are allowed to belong to more than one community, through the application of a mathematical programming method. We show that genes that lie at the intersection of communities tend to be highly connected and multifunctional. Overall, we consider the topological and functional properties of proteins in the context of the community structure and try to make a connection between virulence genes and features of community structure. Such studies may have the potential to identify functionally important nodes and help to gain a better understanding of phenotypic features of a system.