Mathematical Physics Techniques for Omics Data Integration

Nowadays different types of high-throughput technologies allow us to collect information on the molecular components of biological systems. Each of such technologies is designed to simultaneously collect large sets of molecular data of a specific omic-kind. In order to draw a more comprehensive view of biological processes, experimental data made on different layers have to be integrated and analyzed. The complexity of biological systems, the technological limits, the large number of biological variables and the relatively low number of biological samples make integrative analyses a challenge. Hence, the development of methods for omics integration is one of the most relevant problems computational scientists are addressing nowadays. The most representative and promising techniques for the analysis of omics data are presented and broadly divided into categories. In the literature we notice a growing interest around approaches that use graphs for modeling the relationships among omic variables. In particular we found that algorithms propagating molecular information on networks are being proposed in several applications and are often related to actual physical models. We considered the chemical master equation (CME) framework to model the exchange of information in biological networks as a stochastic process on the network. In this context we defined new algorithms and pipelines for the analysis of omics. In particular we propose two network-based methods with applications to both synthetic and prostate ardenocarcinoma data. In both the applications the molecular alterations are mapped on the protein-protein interaction network. In the first application we defined a novel methodology for extracting modules of connected genes that present the most significant differential molecular information between two classes of samples. In the second application we measure to which degree a distribution of deleterious molecular information on a given network deviates the normal trajectories of information flow using a perturbative approach to the CME.