Protein production is a key process of prokaryotic and eukaryotic cells consuming more that 80% of their resources. The cytoplasm of the cell being a disorganized medium subject to thermal noise, the protein production process has an important stochastic component. In this context the random fluctuations of the number of copies of a given protein in a cell are of primary importance. We discuss the impact of modelling issues of this production process through the use of Markovian and non- Markovian models. Mathematical models of the production of one fixed type of proteins is presented. When several classes of proteins are considered, an important additional aspect has to be taken into account, the limited common resources of the cell (polymerases and ribosomes) used by the production process. A large scale analysis is proposed in this setting. We conclude by an analysis of the impact of some feedback mechanisms to control the fluctuations of the number of proteins.
Joint Work with Renaud Dessalles, Vincent Fromion and Emanuele Leoncini.