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.
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14 December 2023
Research Article|
December 08 2023
Exact solution of a three-stage model of stochastic gene expression including cell-cycle dynamics
Special Collection:
2023 JCP Emerging Investigators Special Collection
Yiling Wang;
Yiling Wang
(Formal analysis, Methodology)
1
Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology
, Shanghai 200237, China
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Zhenhua Yu;
Zhenhua Yu
(Formal analysis, Methodology)
1
Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology
, Shanghai 200237, China
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Ramon Grima
;
Ramon Grima
a)
(Conceptualization, Supervision, Writing – original draft)
2
School of Biological Sciences, The University of Edinburgh
, Max Born Crescent, Edinburgh EH9 3BF, Scotland, United Kingdom
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Zhixing Cao
Zhixing Cao
b)
(Conceptualization, Formal analysis, Funding acquisition, Supervision, Writing – original draft)
1
Key Laboratory of Smart Manufacturing in Energy Chemical Process, Ministry of Education, East China University of Science and Technology
, Shanghai 200237, China
3
Department of Chemical Engineering, Queen’s University
, Kingston, Ontario K7L 3N6, Canada
b)Author to whom correspondence should be addressed: z.cao@queensu.ca
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b)Author to whom correspondence should be addressed: z.cao@queensu.ca
a)
Electronic mail: ramon.grima@ed.ac.uk
J. Chem. Phys. 159, 224102 (2023)
Article history
Received:
August 24 2023
Accepted:
October 04 2023
Citation
Yiling Wang, Zhenhua Yu, Ramon Grima, Zhixing Cao; Exact solution of a three-stage model of stochastic gene expression including cell-cycle dynamics. J. Chem. Phys. 14 December 2023; 159 (22): 224102. https://doi.org/10.1063/5.0173742
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