Exact solution of a three-stage model of stochastic gene expression including cell-cycle dynamics

Yiling Wang, Zhenhua Yu, Ramon Grima, Zhixing Cao

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The classical three-stage model of stochastic gene expression predicts the statistics of single cell mRNA and protein number fluctuations as a function of the rates of promoter switching, transcription, translation, degradation and dilution. While this model is easily simulated, its analytical solution remains an unsolved problem. Here we modify this model to explicitly include cell-cycle dynamics and then derive an exact solution for the time-dependent joint distribution of mRNA and protein numbers. We show large differences between this model and the classical model which captures cell-cycle effects implicitly via effective first-order dilution reactions. In particular we find that the Fano factor of protein numbers calculated from a population snapshot measurement are underestimated by the classical model whereas the correlation between mRNA and protein can be either over- or underestimated, depending on the timescales of mRNA degradation and promoter switching relative to the mean cell-cycle duration time.

Original languageEnglish
Article number224102
Number of pages19
JournalThe Journal of Chemical Physics
Volume159
Issue number22
Early online date8 Dec 2023
DOIs
Publication statusPublished - 14 Dec 2023

Keywords / Materials (for Non-textual outputs)

  • Proteins/metabolism
  • RNA, Messenger/genetics
  • Promoter Regions, Genetic/genetics
  • Gene Expression
  • Stochastic Processes
  • Models, Genetic

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