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WMAXC: a weighted maximum clique method for identifying condition-specific sub-network.

ABSTRACT: Sub-networks can expose complex patterns in an entire bio-molecular network by extracting interactions that depend on temporal or condition-specific contexts. When genes interact with each other during cellular processes, they may form differential co-expression patterns with other genes across different cell states. The identification of condition-specific sub-networks is of great importance in investigating how a living cell adapts to environmental changes. In this work, we propose the weighted MAXimum clique (WMAXC) method to identify a condition-specific sub-network. WMAXC first proposes scoring functions that jointly measure condition-specific changes to both individual genes and gene-gene co-expressions. It then employs a weaker formula of a general maximum clique problem and relates the maximum scored clique of a weighted graph to the optimization of a quadratic objective function under sparsity constraints. We combine a continuous genetic algorithm and a projection procedure to obtain a single optimal sub-network that maximizes the objective function (scoring function) over the standard simplex (sparsity constraints). We applied the WMAXC method to both simulated data and real data sets of ovarian and prostate cancer. Compared with previous methods, WMAXC selected a large fraction of cancer-related genes, which were enriched in cancer-related pathways. The results demonstrated that our method efficiently captured a subset of genes relevant under the investigated condition.

SUBMITTER: Amgalan B

PROVIDER: S-EPMC4141761 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Project description:BackgroundThe maximum clique enumeration (MCE) problem asks that we identify all maximum cliques in a finite, simple graph. MCE is closely related to two other well-known and widely-studied problems: the maximum clique optimization problem, which asks us to determine the size of a largest clique, and the maximal clique enumeration problem, which asks that we compile a listing of all maximal cliques. Naturally, these three problems are NP-hard, given that they subsume the classic version of the NP-complete clique decision problem. MCE can be solved in principle with standard enumeration methods due to Bron, Kerbosch, Kose and others. Unfortunately, these techniques are ill-suited to graphs encountered in our applications. We must solve MCE on instances deeply seeded in data mining and computational biology, where high-throughput data capture often creates graphs of extreme size and density. MCE can also be solved in principle using more modern algorithms based in part on vertex cover and the theory of fixed-parameter tractability (FPT). While FPT is an improvement, these algorithms too can fail to scale sufficiently well as the sizes and densities of our datasets grow.ResultsAn extensive testbed of benchmark graphs are created using publicly available transcriptomic datasets from the Gene Expression Omnibus (GEO). Empirical testing reveals crucial but latent features of such high-throughput biological data. In turn, it is shown that these features distinguish real data from random data intended to reproduce salient topological features. In particular, with real data there tends to be an unusually high degree of maximum clique overlap. Armed with this knowledge, novel decomposition strategies are tuned to the data and coupled with the best FPT MCE implementations.ConclusionsSeveral algorithmic improvements to MCE are made which progressively decrease the run time on graphs in the testbed. Frequently the final runtime improvement is several orders of magnitude. As a result, instances which were once prohibitively time-consuming to solve are brought into the domain of realistic feasibility.

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WMAXC: a weighted maximum clique method for identifying condition-specific sub-network.

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