A Stochastic Model of the Production of Multiple Proteins in Cells

Source abstract

The production processes of several classes of proteins in prokaryotic cells is investigated. A Markov process is introduced to study how the limited common resources of the cell (like ribosomes) are used. Understanding the impact of this limitation on the production process is a key issue. We focus on the allocation of ribosomes in the case of the production of multiple classes of proteins. Asymptotic results are obtained under a scaling procedure and a realistic biological assumption on the limited number of ribosomes available in the cell. It is shown that, in the limit, the number of nonallocated ribosomes at equilibrium converges in distribution to a Poisson distribution whose parameter satisfies a fixed point equation. It is also shown that the production process of different types of proteins can be seen as independent production processes but with modified parameters.