Exact distributions of threshold crossing times of proteins under post-transcriptional regulation by small RNAs
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Abstract
The timings of several cellular events like cell lysis, cell division, or pore formation in endosomes are regulated by the time taken for the relevant proteins to cross a threshold in number or concentration. Since protein synthesis is stochastic, the threshold crossing time is a first passage problem. The exact distributions of these first passage processes have been obtained recently for unregulated and autoregulated genes. Many proteins are however regulated by post-transcriptional regulation, controlled by small noncoding RNAs (sRNAs). Certain mathematical models of gene expression with post-transcriptional sRNA regulation have been recently exactly mapped to models without sRNA regulation. Utilizing this mapping and the exact distributions, we calculate exact results on fluctuations (full distribution, all cumulants, and characteristic times) of protein threshold crossing times in the presence of sRNA regulation. We derive two interesting predictions from these exact results. We show that the size of the fluctuation of the threshold crossing times have a nonmonotonic U-shaped behavior as a function of the rates of binding and unbinding of the sRNA-mRNA complex. Thus there are optimal parameters that minimize noise. Furthermore, the fluctuations in models with sRNA regulation may be higher or lower compared to the model without regulation, depending on the mean protein burst size.
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Barman, H. K., Das, P., & Ali, S. Y. (2025) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.5c04647
Self-citationImpact of variability in cell generation times on cell-to-cell variability of protein concentrationsPreprint
Ali, S. Y., Prasad, A., Singh, A., & Das, D. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.04.23.720286
Self-citation
- Authors
- Ali, S. Y., Prasad, A., & Das, D.
- Affiliations
- Indian Institute of Technology Bombay (IN)
- Colorado State University (US)
- Corresponding author
- Ali, Syed Yunus
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2025-01-03
- Volume
- 111
- Issue
- 1
- Pages
- 014405-014405
- ISSN
- 2470-0045 (ISSN-L)
- 2470-0053
- OpenAlex
- W4406048984
- Cited by
- 2
- References
- 81
- Citations by year
- 2026: 1 · 2025: 1
- FWCI
- 0.60
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- Locations
- Physical review. E (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- Funders
- Indian Institute of Technology Bombay
- 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
- first passage time, post-transcriptional regulation, small RNA, stochastic gene expression, protein fluctuations, exact distribution, noise minimization
- MeSH terms
- Gene Expression Regulation, Models, Biological, Models, Genetic, Proteins, RNA Processing, Post-Transcriptional, RNA, Messenger, Stochastic Processes, Time Factors, RNA, Small Untranslated
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