A procedure is developed to detect statistical correlations stemming from functional interaction by removing the strong phylogenetic signal that leads to the correlations of each site with many others in the sequence. Our method relies upon the accuracy of the alignment but it does not require any assumptions about the phylogeny or the substitution process. The effectiveness of the method was verified using computer simulations and then applied to predict functional interactions between amino acids in the Pfam database of alignments.

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BackgroundBoth differential expression (DE) and differential co-expression (DC) analyses are appreciated as useful tools in understanding gene regulation related to complex diseases. The performance of integrating DE and DC, however, remains unexplored.ResultsIn this study, we proposed a novel analytical approach called DECODE (Differential Co-expression and Differential Expression) to integrate DC and DE analyses of gene expression data. DECODE allows one to study the combined features of DC and DE of each transcript between two conditions. By incorporating information of the dependency between DC and DE variables, two optimal thresholds for defining substantial change in expression and co-expression are systematically defined for each gene based on chi-square maximization. By using these thresholds, genes can be categorized into four groups with either high or low DC and DE characteristics. In this study, DECODE was applied to a large breast cancer microarray data set consisted of two thousand tumor samples. By identifying genes with high DE and high DC, we demonstrated that DECODE could improve the detection of some functional gene sets such as those related to immune system, metastasis, lipid and glucose metabolism. Further investigation on the identified genes and the associated functional pathways would provide an additional level of understanding of complex disease mechanism.ConclusionsBy complementing the recent DC and the traditional DE analyses, DECODE is a valuable methodology for investigating biological functions of genes exhibiting disease-associated DE and DC combined characteristics, which may not be easily revealed through DC or DE approach alone.DECODE is available at the Comprehensive R Archive Network (CRAN): http://cran.r-project.org/web/packages/decode/index.html.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-015-0582-4) contains supplementary material, which is available to authorized users.

Empirical models of substitution are often used in protein sequence analysis because the large alphabet of amino acids requires that many parameters be estimated in all but the simplest parametric models. When information about structure is used in the analysis of substitutions in structured RNA, a similar situation occurs. The number of parameters necessary to adequately describe the substitution process increases in order to model the substitution of paired bases. We have developed a method to obtain substitution rate matrices empirically from RNA alignments that include structural information in the form of base pairs. Our data consisted of alignments from the European Ribosomal RNA Database of Bacterial and Eukaryotic Small Subunit and Large Subunit Ribosomal RNA ( Wuyts et al. 2001. Nucleic Acids Res. 29:175-177; Wuyts et al. 2002. Nucleic Acids Res. 30:183-185). Using secondary structural information, we converted each sequence in the alignments into a sequence over a 20-symbol code: one symbol for each of the four individual bases, and one symbol for each of the 16 ordered pairs. Substitutions in the coded sequences are defined in the natural way, as observed changes between two sequences at any particular site. For given ranges (windows) of sequence divergence, we obtained substitution frequency matrices for the coded sequences. Using a technique originally developed for modeling amino acid substitutions ( Veerassamy, Smith, and Tillier. 2003. J. Comput. Biol. 10:997-1010), we were able to estimate the actual evolutionary distance for each window. The actual evolutionary distances were used to derive instantaneous rate matrices, and from these we selected a universal rate matrix. The universal rate matrices were incorporated into the Phylip Software package ( Felsenstein 2002. http://evolution.genetics.washington.edu/phylip.html), and we analyzed the ribosomal RNA alignments using both distance and maximum likelihood methods. The empirical substitution models performed well on simulated data, and produced reasonable evolutionary trees for 16S ribosomal RNA sequences from sequenced Bacterial genomes. Empirical models have the advantage of being easily implemented, and the fact that the code consists of 20 symbols makes the models easily incorporated into existing programs for protein sequence analysis. In addition, the models are useful for simulating the evolution of RNA sequence and structure simultaneously.