A multiscale journey through omic sciences for cancer: from somatic copy number aberrations to cellular dynamics via mathematical modelling

The present thesis focuses on the development of robust statistical and computational methods for cancer modelling, with a particular emphasis on the analysis of genomic, transcriptomic, and proteomic data. In the field of genomics, the analysis performed had the objective of detecting and characterizing mutations, with a particular focus on somatic copy number aberrations (SCNAs), defined as the gain or loss of DNA regions. Specifically, this thesis developed a multi-resolution approach for the segmentation of LogR Ratio and B Allele Frequency data, with a focus on the analysis of data with non-homogeneous noise and region-specific signal to noise ratio. With regard to transcriptomic data, this thesis proposes an extension of a widely used SCNA detection pipeline for single-cell data, adapting it to resolve allele-specific configurations and enabling more reliable identification of cancer cell subpopulations. The proposed multi-step method addresses the inherent sparsity and noise of single-cell data, and incorporates novel strategies tailored to omics datasets, including graph-based data integration, state-of-the-art clustering techniques, and probabilistic models. Finally, in the context of proteomics, this thesis proposes a framework for local sensitivity analysis to fine-tune parameters of a Chemical Reaction Network (CRN) modeling key signaling pathways in colorectal cells. By appropriately modifying the network model, it could be possible to simulate mutations induced by SCNAs, and the proposed sensitivity analysis enables the assessment of their effects on cellular dynamics and comparison with the physiological cell state.