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Background  The Smad7 protein is negative regulator of the TGF-β signaling pathway, which is upregulated in patients with breast cancer. miRNAs regulate proteins expressions by arresting or degrading the mRNAs. The purpose of this work is to identify a miRNAs profile that regulates the expression of the mRNA coding for Smad7 in breast cancer using the data from patients with breast cancer obtained from the Cancer Genome Atlas Project.    Methods  We develop an automatic search method based on genetic algorithms to find a predictive model based on deep neural networks (DNN) which fit the set of biological data and apply the Olden algorithm to identify the relative importance of each miRNAs.    Results  A computational model of non-linear regression is shown, based on deep neural networks that predict the regulation given by the miRNA target transcripts mRNA coding for Smad7 protein in patients with breast cancer, with R 2  of 0.99 is shown and MSE of 0.00001. In addition, the model is validated with the results  in vivo  and  in vitro  experiments reported in the literature. The set of miRNAs hsa-mir-146a, hsa-mir-93, hsa-mir-375, hsa-mir-205, hsa-mir-15a, hsa-mir-21, hsa-mir-20a, hsa-mir-503, hsa-mir-29c, hsa-mir-497, hsa-mir-107, hsa-mir-125a, hsa-mir-200c, hsa-mir-212, hsa-mir-429, hsa-mir-34a, hsa-let-7c, hsa-mir-92b, hsa-mir-33a, hsa-mir-15b, hsa-mir-224, hsa-mir-185 and hsa-mir-10b integrate a profile that critically regulates the expression of the mRNA coding for Smad7 in breast cancer.    Conclusions  We developed a genetic algorithm to select best features as DNN inputs (miRNAs). The genetic algorithm also builds the best DNN architecture by optimizing the parameters. Although the confirmation of the results by laboratory experiments has not occurred, the results allow suggesting that miRNAs profile could be used as biomarkers or targets in targeted therapies.    Electronic supplementary material  The online version of this article (10.1186/s12976-018-0095-8) contains supplementary material, which is available to authorized users.

Model based on GA and DNN for prediction of mRNA-Smad7 expression regulated by miRNAs in breast cancer