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Background  A key problem in systems biology is the determination of the regulatory mechanism corresponding to a phenotype. An empirical approach in this regard is to compare the expression profiles of cells under two conditions or tissues from two phenotypes and to unravel the underlying transcriptional regulation. We have proposed the method BASE to statistically infer the effective regulatory factors that are responsible for the gene expression differentiation with the help from the binding data between factors and genes. Usually the protein-DNA binding data are obtained by ChIP-seq experiments, which could be costly and are condition-specific.    Results  Here we report a definition of binding strength based on a probability model. Using this condition-free definition, the BASE method needs only the frequencies of  cis -motifs in regulatory regions, thereby the inferences can be carried out in silico. The directional regulation can be inferred by considering down- and up-regulation separately. We showed the effectiveness of the approach by one case study. In the study of the effects of polyunsaturated fatty acids (PUFA), namely, docosahexaenoic (DHA) and eicosapentaenoic (EPA) diets on mouse small intestine cells, the inferences of regulations are consistent with those reported in the literature, including PPARα and NFκB, respectively corresponding to enhanced adipogenesis and reduced inflammation. Moreover, we discovered enhanced RORA regulation of circadian rhythm, and reduced ETS1 regulation of angiogenesis.    Conclusions  With the probabilistic definition of  cis-trans  binding affinity, the BASE method could obtain the significances of TF regulation changes corresponding to a gene expression differentiation profile between treatment and control samples. The landscape of the inferred  cis-trans  regulations is helpful for revealing the underlying molecular mechanisms. Particularly we reported a more comprehensive regulation induced by EPA&DHA diet.    Electronic supplementary material  The online version of this article (10.1186/s12859-019-2732-6) contains supplementary material, which is available to authorized users.

The cis-trans binding strength defined by motif frequencies facilitates statistical inference of transcriptional regulation