Feedback on dilution in stochastic gene expression: a comparative study of single-cell and population frameworks | Pavol Bokes
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We consider a protein that negatively regulates the rate at which a cell grows. Since less growth means less protein dilution, this mechanism forms a positive feedback loop on the protein concentration. We couple the feedback model with a simple description of the cell cycle, in which a division event is triggered when the cell volume reaches a critical threshold. Following the division we either track only one of the daughter cells (single cell framework) or both cells (population framework). We use the piecewise deterministic Markov process to model a single cell; the population is formalised using the measure-valued Markov process, ie, the population is treated as a sequence of Markov processes. For both frameworks, we find an exact stationary joint distribution of protein concentration and cell volume.
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