BackgroundTranscriptome analysis aims at gaining insight into cellular processes through discovering gene expression patterns across various experimental conditions. Biclustering is a standard approach to discover genes subsets with similar expression across subgroups of samples to be identified. The result is a set of biclusters, each forming a specific submatrix of rows (e.g. genes) and columns (e.g. samples). Relevant biclusters can, however, be missed when, due to the presence of a few outliers, they lack the assumed homogeneity of expression values among a few gene/sample combinations. The Max-Sum SubMatrix problem addresses this issue by looking at highly expressed subsets of genes and of samples, without enforcing such homogeneity.ResultsWe present here the K-CPGC algorithm to identify K relevant submatrices. Our main contribution is to show that this approach outperforms biclustering algorithms to identify several gene subsets representative of specific subgroups of samples. Experiments are conducted on 35 gene expression datasets from human tissues and yeast samples. We report comparative results with those obtained by several biclustering algorithms, including CCA, xMOTIFs, ISA, QUBIC, Plaid and Spectral. Gene enrichment analysis demonstrates the benefits of the proposed approach to identify more statistically significant gene subsets. The most significant Gene Ontology terms identified with K-CPGC are shown consistent with the controlled conditions of each dataset. This analysis supports the biological relevance of the identified gene subsets. An additional contribution is the statistical validation protocol proposed here to assess the relative performances of biclustering algorithms and of the proposed method. It relies on a Friedman test and the Hochberg’s sequential procedure to report critical differences of ranks among all algorithms.ConclusionsWe propose here the K-CPGC method, a computationally efficient algorithm to identify K max-sum submatrices in a large gene expression matrix. Comparisons show that it identifies more significantly enriched subsets of genes and specific subgroups of samples which are easily interpretable by biologists. Experiments also show its ability to identify more reliable GO terms. These results illustrate the benefits of the proposed approach in terms of interpretability and of biological enrichment quality. Open implementation of this algorithm is available as an R package.
Summary Allele (or haplotype) networks are often used in phylogeographic studies to display genetic variation within a species or a group of closely related species. A global maximum parsimony approach to infer allele networks, arguably the method of choice to display genetic variation at the intraspecific level, consists in inferring all most parsimonious trees from a DNA sequence alignment and combining the corresponding phylograms into a single graph. However, it has been suggested that, while classic phylogenetic programs generate a single phylogram per most parsimonious tree, deriving all possible phylograms from them would allow identifying additional most parsimonious paths among alleles, thereby improving this network inference method. We test this prediction by analysing both simulated and empirical DNA sequence alignments. For this purpose, a computer program, CPN, was developed to implement the entire procedure, starting with a set of most parsimonious trees and combining all derived phylograms into a network. We show that including all possible most parsimonious phylograms indeed often results in finding additional most parsimonious paths in the network graph, thereby improving the search for a global maximum parsimony solution. We highly recommend the use of this approach in future phylogeographic studies, to ensure that all most parsimonious paths are included in the allele network, instead of an arbitrarily selected subset of those.
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