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Exact solution of a three-stage model of stochastic gene expression including cell-cycle dynamics
Open accessPreprint — published as 10.1063/5.0173742
Abstract
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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Metadata
- Authors
- Wang, Y., Yu, Z., Grima, R., & Cao, Z.
- Affiliations
- East China University of Science and Technology (CN)
- University of Edinburgh (GB)
- Venue
- The Journal of Chemical Physics
- Publisher
- openRxiv
- Published
- 2023-08-31
- Volume
- 159
- Issue
- 22
- ISSN
- 0021-9606 (ISSN-L)
- OpenAlex
- W4389487553
- Cited by
- 14
- References
- 1
- Citations by year
- 2026: 6 · 2025: 6 · 2024: 2
- FWCI
- 1.24
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- cc-by-nc-nd
- Locations
- The Journal of Chemical Physics (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Edinburgh Research Explorer (University of Edinburgh) (submittedVersion, cc-by)
- Funders
- Leverhulme Trust (RPG-2020-327)
- National Natural Science Foundation of China (62073137)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
- Keywords
- stochastic gene expression, three-phase model, cell cycle kinetics, analytical solution, mRNA-protein correlation, Fano factor, promoter switching, mRNA degradation
- MeSH terms
- Models, Genetic, Promoter Regions, Genetic, Proteins, RNA, Messenger, Stochastic Processes, Gene Expression
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