Modular decomposition of protein structure using community detection

As the number of solved protein structures increases, the opportunities for meta-analysis of this dataset increase too. Protein structures are known to be formed of domains; structural and functional subunits that are often repeated across sets of proteins. These domains generally form compact, globular regions, and are therefore often easily identifiable by inspection, yet the problem of automatically fragmenting the protein into these compact substructures remains computationally challenging. Existing domain classification methods focus on finding subregions of protein structure that are conserved, rather than finding a decomposition which spans the full protein structure. However, such a decomposition would find ready application in coarse-graining molecular dynamics, analysing the protein's topology, in de novo protein design and in fitting electron microscopy maps. Here, we present a tool for performing this modular decomposition using the Infomap community detection algorithm. The protein structure is abstracted into a network in which its amino acids are the nodes, and where the edges are generated using a simple proximity test. Infomap can then be used to identify highly intra-connected regions of the protein. We perform this decomposition systematically across 4000 distinct protein structures, taken from the Protein Data Bank. The decomposition obtained correlates well with existing PFAM sequence classifications, but has the advantage of spanning the full protein, with the potential for novel domains. The coarse-grained network formed by the communities can also be used as a proxy for protein topology at the single-chain level; we demonstrate that grouping these proteins by their coarse-grained network results in a functionally significant classification

A modularity based spectral method for simultaneous community and anti-community detection

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrix-based definitions of the modularity of a vertex set. Invariant subspaces associated to extreme eigenvalues of these matrices provide indications on the presence of both kinds of modular structure in the network. The localization of the relevant invariant subspaces can be estimated by looking at particular matrix angles based on Frobenius inner products

Using modular decomposition technique to solve the maximum clique problem

In this article we use the modular decomposition technique for exact solving the weighted maximum clique problem. Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution recursively. Also, we propose algorithms to construct graphs with modules. We show some interesting results, comparing our solution with Ostergard's algorithm on DIMACS benchmarks and on generated graph

Hierarchical modularity in human brain functional networks

The idea that complex systems have a hierarchical modular organization originates in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or "modules-within-modules") decomposition of human brain functional networks, measured using functional magnetic resonance imaging (fMRI) in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I=0.63. The largest 5 modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions

Modules identification in gene positive networks of hepatocellular carcinoma using pearson agglomerative method and Pearson cohesion coupling modularity

In this study, a gene positive network is proposed based on a weighted undirected graph, where the weight represents the positive correlation of the genes. A Pearson agglomerative clustering algorithm is employed to build a clustering tree, where dotted lines cut the tree from bottom to top leading to a number of subsets of the modules. In order to achieve better module partitions, the Pearson correlation coefficient modularity is addressed to seek optimal module decomposition by selecting an optimal threshold value. For the liver cancer gene network under study, we obtain a strong threshold value at 0.67302, and a very strong correlation threshold at 0.80086. On the basis of these threshold values, fourteen strong modules and thirteen very strong modules are obtained respectively. A certain degree of correspondence between the two types of modules is addressed as well. Finally, the biological significance of the two types of modules is analyzed and explained, which shows that these modules are closely related to the proliferation and metastasis of liver cancer. This discovery of the new modules may provide new clues and ideas for liver cancer treatment

Community detection for networks with unipartite and bipartite structure

Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite network consists of one set of nodes and a bipartite network consists of two nonoverlapping sets of nodes with only links joining the nodes in different sets. However, a third type of network exists, defined here as the mixture network. Just like a bipartite network, a mixture network also consists of two sets of nodes, but some nodes may simultaneously belong to two sets, which breaks the nonoverlapping restriction of a bipartite network. The mixture network can be considered as a general case, with unipartite and bipartite networks viewed as its limiting cases. A mixture network can represent not only all the unipartite and bipartite networks, but also a wide range of real-world networks that cannot be properly represented as either unipartite or bipartite networks in fields such as biology and social science. Based on this observation, we first propose a probabilistic model that can find modules in unipartite, bipartite, and mixture networks in a unified framework based on the link community model for a unipartite undirected network [B Ball et al (2011 Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both overlapping and nonoverlapping communities) and apply it to two real-world networks: a southern women bipartite network and a human transcriptional regulatory mixture network. The results suggest that our model performs well for all three types of networks, is competitive with other algorithms for unipartite or bipartite networks, and is applicable to real-world networks.Comment: 27 pages, 8 figures. (http://iopscience.iop.org/1367-2630/16/9/093001

ModuLand plug-in for Cytoscape: determination of hierarchical layers of overlapping network modules and community centrality

Summary: The ModuLand plug-in provides Cytoscape users an algorithm for determining extensively overlapping network modules. Moreover, it identifies several hierarchical layers of modules, where meta-nodes of the higher hierarchical layer represent modules of the lower layer. The tool assigns module cores, which predict the function of the whole module, and determines key nodes bridging two or multiple modules. The plug-in has a detailed JAVA-based graphical interface with various colouring options. The ModuLand tool can run on Windows, Linux, or Mac OS. We demonstrate its use on protein structure and metabolic networks. Availability: The plug-in and its user guide can be downloaded freely from: http://www.linkgroup.hu/modules.php. Contact: [email protected] Supplementary information: Supplementary information is available at Bioinformatics online.Comment: 39 pages, 1 figure and a Supplement with 9 figures and 10 table

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4 figures, 3 table