Abstract
Complex molecular details of transcriptional regulation can be coarse-grained by assuming that reaction waiting times for promoter-state transitions, the mRNA synthesis, and the mRNA degradation follow general distributions. However, how such a generalized two-state model is analytically solved is a long-standing issue. Here we first present analytical formulas of burst-size distributions for this model. Then, we derive an iterative equation for the mRNA moment-generating function, by which mRNA raw and binomial moments of any order can be conveniently calculated. The analytical results obtained in the special cases of phase-type waiting-time distributions not only provide insights into the mechanisms of complex transcriptional regulations but also bring conveniences for experimental data-based statistical inferences.
- Received 10 July 2023
- Accepted 19 January 2024
- Corrected 28 February 2024
DOI:https://doi.org/10.1103/PhysRevE.109.024119
©2024 American Physical Society
Physics Subject Headings (PhySH)
Corrections
28 February 2024
Correction: Incorrect information was used for the affiliation of the fifth author. A new affiliation and affiliation indicator have been inserted.
