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Exact results for gene-expression models with general waiting-time distributions
Jinqiang Zhang1, Aimin Chen2, Huahai Qiu3
1School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China.
Physical Review. E
|March 16, 2024
Summary
This study presents analytical solutions for generalized two-state models of transcriptional regulation, enabling calculation of mRNA moments. These findings offer insights into gene expression mechanisms and aid statistical inference from experimental data.
Area of Science:
- Molecular biology
- Biophysics
- Systems biology
Background:
- Transcriptional regulation involves complex molecular events.
- Generalized two-state models simplify these processes.
- Analytical solutions for such models are challenging.
Purpose of the Study:
- To analytically solve a generalized two-state model for transcriptional regulation.
- To derive formulas for mRNA burst-size distributions.
- To develop methods for calculating mRNA moments.
Main Methods:
- Developed analytical formulas for burst-size distributions.
- Derived an iterative equation for the mRNA moment-generating function.
- Applied phase-type waiting-time distributions for special cases.
Main Results:
- Provided analytical formulas for burst-size distributions.
- Enabled calculation of any order of mRNA raw and binomial moments.
- Demonstrated utility in special cases of phase-type distributions.
Conclusions:
- The generalized two-state model can be analytically solved.
- The derived methods facilitate the study of complex transcriptional regulation.
- The approach aids statistical inference from experimental data.
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