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Background  Several studies have investigated miRNA and mRNA co-expression to identify regulatory networks at the transcriptional level. A typical finding of these studies is the presence of both negative and positive miRNA-mRNA correlations. Negative correlations are consistent with the expected, faster degradation of target mRNAs, whereas positive correlations denote the existence of feed-forward regulations mediated by transcription factors. Both mechanisms have been characterized at the molecular level, although comprehensive methods to represent miRNA-mRNA correlations are lacking. At present, genome-wide studies are able to assess the expression of more than 1000 mature miRNAs and more than 35,000 well-characterized human genes. Even if studies are generally restricted to a small subset of genes differentially expressed in specific diseases or experimental conditions, the number of potential correlations remains very high, and needs robust multivariate methods to be conveniently summarized by a small set of data.    Results  Nonparametric Kendall correlations were calculated between miRNAs and mRNAs differentially expressed in livers of patients with acute liver failure (ALF) using normal livers as controls. Spurious correlations due to the histopathological composition of samples were removed by partial correlations. Correlations were then transformed into distances and processed by multidimensional scaling (MDS) to map the miRNA and mRNA relationships. These showed: (a) a prominent displacement of miRNA and mRNA clusters in ALF livers, as compared to control livers, indicative of gene expression dysregulation; (b) a clustering of mRNAs consistent with their functional annotations [CYP450, transcription factors, complement, proliferation, HLA class II, monocytes/macrophages, T cells, T-NK cells and B cells], as well as a clustering of miRNAs with the same seed sequence; and (c) a tendency of miRNAs and mRNAs to populate distinct regions of the MDS plot. MDS also allowed to visualize the network of miRNA-mRNA target pairs.    Conclusions  Different features of miRNA and mRNA relationships can be represented as thematic maps within the framework of MDS obtained from pairwise correlations. The symmetric distribution of positive and negative correlations between miRNA and mRNA expression suggests that miRNAs are involved in a complex bidirectional molecular network, including, but not limited to, the inhibitory regulation of miRNA targets.    Electronic supplementary material  The online version of this article (doi:10.1186/s12864-015-1971-9) contains supplementary material, which is available to authorized users.

Integrated ordination of miRNA and mRNA expression profiles