Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Multipartite Graph Algorithms for the Analysis of Heterogeneous Data

The explosive growth in the rate of data generation in recent years threatens to outpace the growth in computer power, motivating the need for new, scalable algorithms and big data analytic techniques. No field may be more emblematic of this data deluge than the life sciences, where technologies such as high-throughput mRNA arrays and next generation genome sequencing are routinely used to generate datasets of extreme scale. Data from experiments in genomics, transcriptomics, metabolomics and proteomics are continuously being added to existing repositories. A goal of exploratory analysis of such omics data is to illuminate the functions and relationships of biomolecules within an organism. This dissertation describes the design, implementation and application of graph algorithms, with the goal of seeking dense structure in data derived from omics experiments in order to detect latent associations between often heterogeneous entities, such as genes, diseases and phenotypes. Exact combinatorial solutions are developed and implemented, rather than relying on approximations or heuristics, even when problems are exceedingly large and/or difficult. Datasets on which the algorithms are applied include time series transcriptomic data from an experiment on the developing mouse cerebellum, gene expression data measuring acute ethanol response in the prefrontal cortex, and the analysis of a predicted protein-protein interaction network. A bipartite graph model is used to integrate heterogeneous data types, such as genes with phenotypes and microbes with mouse strains. The techniques are then extended to a multipartite algorithm to enumerate dense substructure in multipartite graphs, constructed using data from three or more heterogeneous sources, with applications to functional genomics. Several new theoretical results are given regarding multipartite graphs and the multipartite enumeration algorithm. In all cases, practical implementations are demonstrated to expand the frontier of computational feasibility

DENSE: efficient and prior knowledge-driven discovery of phenotype-associated protein functional modules

<p>Abstract</p> <p>Background</p> <p>Identifying cellular subsystems that are involved in the expression of a target phenotype has been a very active research area for the past several years. In this paper, <it>cellular subsystem </it>refers to a group of genes (or proteins) that interact and carry out a common function in the cell. Most studies identify genes associated with a phenotype on the basis of some statistical bias, others have extended these statistical methods to analyze functional modules and biological pathways for phenotype-relatedness. However, a biologist might often have a specific question in mind while performing such analysis and most of the resulting subsystems obtained by the existing methods might be largely irrelevant to the question in hand. Arguably, it would be valuable to incorporate biologist's knowledge about the phenotype into the algorithm. This way, it is anticipated that the resulting subsytems would not only be related to the target phenotype but also contain information that the biologist is likely to be interested in.</p> <p>Results</p> <p>In this paper we introduce a fast and theoretically guranteed method called <it>DENSE </it>(Dense and ENriched Subgraph Enumeration) that can take in as input a biologist's <it>prior </it>knowledge as a set of query proteins and identify all the dense functional modules in a biological network that contain some part of the query vertices. The density (in terms of the number of network egdes) and the enrichment (the number of query proteins in the resulting functional module) can be manipulated via two parameters γ and <it>μ</it>, respectively.</p> <p>Conclusion</p> <p>This algorithm has been applied to the protein functional association network of <it>Clostridium acetobutylicum </it>ATCC 824, a hydrogen producing, acid-tolerant organism. The algorithm was able to verify relationships known to exist in literature and also some previously unknown relationships including those with regulatory and signaling functions. Additionally, we were also able to hypothesize that some uncharacterized proteins are likely associated with the target phenotype. The DENSE code can be downloaded from <url>http://www.freescience.org/cs/DENSE/</url></p

Low-Diameter Clusters in Network Analysis

In this dissertation, we introduce several novel tools for cluster-based analysis of complex systems and design solution approaches to solve the corresponding optimization problems. Cluster-based analysis is a subfield of network analysis which utilizes a graph representation of a system to yield meaningful insight into the system structure and functions. Clusters with low diameter are commonly used to characterize cohesive groups in applications for which easy reachability between group members is of high importance. Low-diameter clusters can be mathematically formalized using a clique and an s-club (with relatively small values of s), two concepts from graph theory. A clique is a subset of vertices adjacent to each other and an s-club is a subset of vertices inducing a subgraph with a diameter of at most s. A clique is actually a special case of an s-club with s = 1, hence, having the shortest possible diameter. Two topics of this dissertation focus on graphs prone to uncertainty and disruptions, and introduce several extensions of low-diameter models. First, we introduce a robust clique model in graphs where edges may fail with a certain probability and robustness is enforced using appropriate risk measures. With regard to its ability to capture underlying system uncertainties, finding the largest robust clique is a better alternative to the problem of finding the largest clique. Moreover, it is also a hard combinatorial optimization problem, requiring some effective solution techniques. To this aim, we design several heuristic approaches for detection of large robust cliques and compare their performance. Next, we consider graphs for which uncertainty is not explicitly defined, studying connectivity properties of 2-clubs. We notice that a 2-club can be very vulnerable to disruptions, so we enhance it by reinforcing additional requirements on connectivity and introduce a biconnected 2-club concept. Additionally, we look at the weak 2-club counterpart which we call a fragile 2-club (defined as a 2-club that is not biconnected). The size of the largest biconnected 2-club in a graph can help measure overall system reachability and connectivity, whereas the largest fragile 2-club can identify vulnerable parts of the graph. We show that the problem of finding the largest fragile 2-club is polynomially solvable whereas the problem of finding the largest biconnected 2-club is NP-hard. Furthermore, for the former, we design a polynomial time algorithm and for the latter - combinatorial branch-and-bound and branch-and-cut algorithms. Lastly, we once again consider the s-club concept but shift our focus from finding the largest s-club in a graph to the problem of partitioning the graph into the smallest number of non-overlapping s-clubs. This problem cannot only be applied to derive communities in the graph, but also to reduce the size of the graph and derive its hierarchical structure. The problem of finding the minimum s-club partitioning is a hard combinatorial optimization problem with proven complexity results and is also very hard to solve in practice. We design a branch-and-bound combinatorial optimization algorithm and test it on the problem of minimum 2-club partitioning

Enumeration of condition-dependent dense modules in protein interaction networks

Motivation: Modern systems biology aims at understanding how the different molecular components of a biological cell interact. Often, cellular functions are performed by complexes consisting of many different proteins. The composition of these complexes may change according to the cellular environment, and one protein may be involved in several different processes. The automatic discovery of functional complexes from protein interaction data is challenging. While previous approaches use approximations to extract dense modules, our approach exactly solves the problem of dense module enumeration. Furthermore, constraints from additional information sources such as gene expression and phenotype data can be integrated, so we can systematically mine for dense modules with interesting profiles

Recent advances in clustering methods for protein interaction networks

The increasing availability of large-scale protein-protein interaction data has made it possible to understand the basic components and organization of cell machinery from the network level. The arising challenge is how to analyze such complex interacting data to reveal the principles of cellular organization, processes and functions. Many studies have shown that clustering protein interaction network is an effective approach for identifying protein complexes or functional modules, which has become a major research topic in systems biology. In this review, recent advances in clustering methods for protein interaction networks will be presented in detail. The predictions of protein functions and interactions based on modules will be covered. Finally, the performance of different clustering methods will be compared and the directions for future research will be discussed

SECOM: A Novel Hash Seed and Community Detection Based-Approach for Genome-Scale Protein Domain Identification

With rapid advances in the development of DNA sequencing technologies, a plethora of high-throughput genome and proteome data from a diverse spectrum of organisms have been generated. The functional annotation and evolutionary history of proteins are usually inferred from domains predicted from the genome sequences. Traditional database-based domain prediction methods cannot identify novel domains, however, and alignment-based methods, which look for recurring segments in the proteome, are computationally demanding. Here, we propose a novel genome-wide domain prediction method, SECOM. Instead of conducting all-against-all sequence alignment, SECOM first indexes all the proteins in the genome by using a hash seed function. Local similarity can thus be detected and encoded into a graph structure, in which each node represents a protein sequence and each edge weight represents the shared hash seeds between the two nodes. SECOM then formulates the domain prediction problem as an overlapping community-finding problem in this graph. A backward graph percolation algorithm that efficiently identifies the domains is proposed. We tested SECOM on five recently sequenced genomes of aquatic animals. Our tests demonstrated that SECOM was able to identify most of the known domains identified by InterProScan. When compared with the alignment-based method, SECOM showed higher sensitivity in detecting putative novel domains, while it was also three orders of magnitude faster. For example, SECOM was able to predict a novel sponge-specific domain in nucleoside-triphosphatase (NTPases). Furthermore, SECOM discovered two novel domains, likely of bacterial origin, that are taxonomically restricted to sea anemone and hydra. SECOM is an open-source program and available at http://sfb.kaust.edu.sa/Pages/Software.aspx