BACKGROUND: In high-throughput experimental biology, it is widely acknowledged that while expression levels measured at the levels of transcriptome and the corresponding proteome do not, in general, correlate well, messenger RNA levels are used as convenient proxies for protein levels. Our interest is in developing data-driven computational models that can bridge the gap between these two levels of measurement at which different mechanisms of regulation may act on different molecular species causing any observed lack of correlations. To this end, we build data-driven predictors of protein levels using mRNA levels and known proxies of translation efficiencies as covariates. Previous work showed that in such a setting, outliers with respect to the model are reliable candidates for post-translational regulation. RESULTS: Here, we present and compare two novel formulations of deriving a protein concentration predictor from which outliers may be extracted in a systematic manner. The first approach, outlier rejecting regression, allows explicit specification of a certain fraction of the data as outliers. In a regression setting, this is a non-convex optimization problem which we solve by deriving a difference of convex functions algorithm (DCA). With post-translationally regulated proteins, one expects their concentrations to be affected primarily by disruption of protein stability. Our second algorithm exploits this observation by minimizing an asymmetric loss using quantile regression and extracts outlier proteins whose measured concentrations are lower than what a genome-wide regression would predict. We validate the two approaches on a dataset of yeast transcriptome and proteome. Functional annotation check on detected outliers demonstrate that the methods are able to identify post-translationally regulated genes with high statistical confidence.

MOTIVATION: Despite much dynamical cellular behaviour being achieved by accurate regulation of protein concentrations, messenger RNA abundances, measured by microarray technology, and more recently by deep sequencing techniques, are widely used as proxies for protein measurements. Although for some species and under some conditions, there is good correlation between transcriptome and proteome level measurements, such correlation is by no means universal due to post-transcriptional and post-translational regulation, both of which are highly prevalent in cells. Here, we seek to develop a data-driven machine learning approach to bridging the gap between these two levels of high-throughput omic measurements on Saccharomyces cerevisiae and deploy the model in a novel way to uncover mRNA-protein pairs that are candidates for post-translational regulation. RESULTS: The application of feature selection by sparsity inducing regression (l₁ norm regularization) leads to a stable set of features: i.e. mRNA, ribosomal occupancy, ribosome density, tRNA adaptation index and codon bias while achieving a feature reduction from 37 to 5. A linear predictor used with these features is capable of predicting protein concentrations fairly accurately (R² = 0.86). Proteins whose concentration cannot be predicted accurately, taken as outliers with respect to the predictor, are shown to have annotation evidence of post-translational modification, significantly more than random subsets of similar size P < 0.02. In a data mining sense, this work also shows a wider point that outliers with respect to a learning method can carry meaningful information about a problem domain.