PhD Thesis

Biochemical reactions underlying the functioning of cells are inherently stochastic processes. As a consequence, the whole system is noisy and undergoes fluctuations in its fundamental components. Proteins are major players in the life of a cell; their stochastic character manifests itself through striking differences in phenotypes, even in the case of cloned cells exposed to identical environmental conditions. Given the context, it is crucial that models embrace realistic assumptions.

In this thesis we have introduced a new mathematical framework based on Marked Poisson Point Processes (MPPP) to describe the main steps of the production of a specific protein. We were able to overcome the restrictive assumption, crucial in the classical framework, of an exponentially distributed duration of all steps. The non-Markovian description of gene expression obtained through this new framework has allowed us to propose a more realistic model of gene expression, which includes protein elongation step and protein dilution due to volume growth.

We also made the first steps towards a modeling of the production of many proteins, considering interactions as the result of the competition for common resources. The system of production is studied via a mean-field approach both in the underloaded and overloaded regimes of use of the ribosomes. The multi-protein model brings a completely new approach in the domain and marks a new direction in the investigation of protein fluctuations at the cellular level.

In conclusion, the thesis has focused on the study of the stochastic nature of gene expression, by developing different models in order to progress towards a more realistic description of the phenomena. All these studies have been conducted trying to put biology in the foreground, since we believe these models represent a fundamental step in the investigation and understanding of complex biological processes and are a complementary tool to biological experiments.