Unveiling gene expression histonic regulative patterns by hyperplanes clustering

In targeted cancer therapy, great relevance is assumed by data-driven investigations on the fundamental mechanisms by which epigenetic modifications cooperate to regulate the transcriptional status of genes. At the high resolution level of genome-wide studies, only general, mean regulative motifs are drawn, with possible multi-functional co-regulative roles remaining concealed. In order to retrieve sharper and more reliable regulative patterns, in this work we propose the application of Kplane regression to partition the set of protein coding genes into clusters with shared regulative mechanisms. Completely data-driven, the approach has computed clusters of genes significantly better fitted by specific linear models than by single regression, and characterized by distinct histonic input patterns and mean measured expression values. 1 Scientific Background Understanding the fundamental mechanisms by which histone marks (HM) and transcription factors (TF) operate to regulate the expression of specific genes is of great interest. Studies revealing the main role played in cancer etiology by gene expression alterations from epigenetic aberrations [1] have recently paved the way to the promising field of targeted cancer therapy, where epigenetic approaches are used to treat cancers in a personalized manner, by kick-starting particular immune responses or bringing back the gene expression levels to the expected ones. Leveraging the large amount of publicly available high-throughput sequencing data, statistical models have been conceived to study the association between gene-related epigenetic signals and messenger RNA (mRNA) abundance at a genome-wide scale [2], with the problem usually framed as a regression task. Genes are samples, signals from HMs and/or TFs are input features and the aim is to predict the response value, i.e., mRNA abundance quantifications. At a genome-wide level, HMs and TFs have been shown to be predictive for mRNA abundance [2], but also to exhibit certain statistical redundancy within themselves, with few works trying to break this last in a data-driven manner. Avoiding the inclusion of biological prior knowledge in statistical modeling is a relevant concern in the context of targeted cancer therapy and personalized medicine: possibly uncharted epigenetic aberrations and anomalies in their regulative effects represent the main objects of analyses. A notable data-driven attempt has been made in [3], where a mixture of Bayesian linear elastic nets revealed to better fit transcriptional regulation w.r. t. a single regression model and to expose distinct predictive relevance of the epigenetic features. Though the models accounting to the mixture in [3] are distinctly defined, genes in the dataset are, however, only softly clustered, as the expression for a gene is the weighted sum of the outputs of all models. Proceedings of CIBB 2018 2 As this soft approach renders interpretative analyses trickier, in this work we inquire into the possibility of performing a hard partitioning of the whole gene set in a datadriven manner, defining clusters where specific linear regression models are fit to learn the regulative dynamics of those gene sub-groups. In such a setting, a one-to-one association between linear models and gene clusters follows, and interpretative analyses are supported at best: regulative patterns can be investigated both at a gene-specific level and, statistically, at a gene-cluster level, and the regulative behavior can be matched with the most represented biological processes within a group. Considered our problem to learn different linear models in a scenario where dynamics are likely to be overlapped, discontinuous, and partially lying on sub-dimensional manifolds, a suited tool is represented by K-plane regression [4] rather than piece-wise linear affine model fitting methods, such as that proposed in [5]. Despite its name, this method is based on a clustering approach; it finds a fixed number of (K) hyperplanes in order to have each point in the training set close to one of the hyperplanes, and all points in a partition as closest as possible in the input feature space. Given the capability of K-plane regression to tackle discontinuous functions and the more flexibility offered by a clustering approach, we built upon this last work to solve our problem. 2 Materials and Methods The aim of this work is modeling epigenetic transcriptional regulation by means of a hard ensemble of linear regression models, each explaining mRNA abundance as a function of epigenetic signals for a specific gene sub-group, i.e., a cluster of genes. All considered measurements are over the K562 immortalized cell line (human blood tissue), and only involve protein coding genes. GENCODE v10 reference annotation for the hg19 assembly was used to retrieve their transcription start sites (TSSs). The Roadmap Epigenomics Mapping Consortium’s (REMC) repository was chosen as the only data source in this work. Genes are epigenetically characterized by data in the form of processed ChIP-seq called peaks only for the m = 12 histone modifications assayed over K562 in REMC (no TF was accounted for). The epigenetic status of the generic gene g is, numerically, an m-dimensional input vector xg. Its elements summarize, each, the g-related status of a specific monitored HM, as the maximum peak enrichment value attained within a symmetric window region of 10 kbases centered on g’s TSS. In accordance to [2], signals closer to the genes’ TSSs (roughly, within promoters) are, indeed, the most valuable for the prediction of gene expression. Considered together for all our n = 19, 794 genes, such vectors form input matrix X , with dimensions n×m. As for the transcriptional characterization of genes, we consider mRNA quantifications, measured by means of RNA-sequencing. The transcriptional status of gene g is encoded by tg = √ ln(1 + τg), where τg is the original mRNA quantification, and the application of two sub-linear, monotonically increasing functions aims at reducing the heteroskedasticity in regression residuals. Finally, consider tg as the (g + 1)-th element in n-dimensional target vector T collecting the transcriptional statuses of all the genes. Together, X and T form our dataset D = 〈X,T 〉, which is going to be partitioned by K-plane regression algorithm that, in our work, is designed to minimize the following objective function: E(Θ) = K−1 ∑