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Analysis of the Stochastic Variability of Protein Production of Prokaryotic Cells

  • Date : 15/11/2012
  • Place : Rocquencourt, bâtiment 9
  • Guest(s) : Emanuele Leoncini, INRA & Inria Paris - Rocquencourt
  • Organiser(s) : RAP

The protein production, also referred to as gene expression, is a fundamental process within prokaryotic and eukaryotic cells and has been studied over decades by biologists.  Experiments have given direct proof of the stochastic nature of the gene expression.  As a consequence, the concentration of a given protein shows stochastic fluctuations, which may be costly given that the whole protein production process consumes 80% of the resources of a prokaryotic cell.
To analyze the fluctuations of the number of copies of a specific protein, a generalized version of some classical Markovian models of the late 70s is presented. These earlier models assumed an exponential distribution for the duration of the different steps of the production process. Nevertheless, it is well-known that some steps of the gene expression, such as the protein elongation, are not exponentially distributed, showing an almost deterministic duration. By using a new representation of the number of proteins in terms of marked Poisson point process, closed formulas for the fluctuations of the number of proteins are obtained in this general setting.
Our results show in particular that the exponential assumption may, surprisingly, underestimate significantly the variance of the number of proteins when some steps are not exponentially distributed with smaller fluctuations than an exponential random variable. This counter-intuitive result stresses the importance of the statistical assumptions in the protein production process.
Joint work with Vincent Fromion (INRA) and Philippe Robert (INRIA)

Keywords: Paris - Rocquencourt Séminaire RAP