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Ma M, Szavits-Nossan J, Singh A, Grima R. Analysis of a detailed multi-stage model of stochastic gene expression using queueing theory and model reduction. Math Biosci 2024; 373:109204. [PMID: 38710441 DOI: 10.1016/j.mbs.2024.109204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2024] [Revised: 04/03/2024] [Accepted: 04/29/2024] [Indexed: 05/08/2024]
Abstract
We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions. We use these to study the phase diagram of the stochastic model; in particular we derive parametric conditions determining three types of transitions in the properties of mRNA fluctuations: from sub-Poissonian to super-Poissonian noise, from high noise in the nucleus to high noise in the cytoplasm, and from a monotonic increase to a monotonic decrease of the Fano factor with the number of processing stages. In contrast, protein fluctuations are always super-Poissonian and show weak dependence on the number of mRNA processing stages. Our results delineate the region of parameter space where conventional models give qualitatively incorrect results and provide insight into how the number of processing stages, e.g. the number of rate-limiting steps in initiation, splicing and mRNA degradation, shape stochastic gene expression by modulation of molecular memory.
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Affiliation(s)
- Muhan Ma
- School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3BF, UK
| | | | - Abhyudai Singh
- Department of Electrical and Computer Engineering, University of Delaware, Newark DE 19716, USA
| | - Ramon Grima
- School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3BF, UK.
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Hong L, Wang Z, Zhang Z, Luo S, Zhou T, Zhang J. Phase separation reduces cell-to-cell variability of transcriptional bursting. Math Biosci 2024; 367:109127. [PMID: 38070763 DOI: 10.1016/j.mbs.2023.109127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Revised: 12/05/2023] [Accepted: 12/06/2023] [Indexed: 12/25/2023]
Abstract
Gene expression is a stochastic and noisy process often occurring in "bursts". Experiments have shown that the compartmentalization of proteins by liquid-liquid phase separation is conducive to reducing the noise of gene expression. Therefore, an important goal is to explore the role of bursts in phase separation noise reduction processes. We propose a coupled model that includes phase separation and a two-state gene expression process. Using the timescale separation method, we obtain approximate solutions for the expectation, variance, and noise strength of the dilute phase. We find that a higher burst frequency weakens the ability of noise reduction by phase separation, but as the burst size increases, this ability first increases and then decreases. This study provides a deeper understanding of phase separation to reduce noise in the stochastic gene expression with burst kinetics.
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Affiliation(s)
- Lijun Hong
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China; School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province, 510275, PR China
| | - Zihao Wang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China; School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province, 510275, PR China
| | - Zhenquan Zhang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China; School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province, 510275, PR China
| | - Songhao Luo
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China; School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province, 510275, PR China; Department of Mathematics, University of California, Irvine, Irvine, CA 92697, USA
| | - Tianshou Zhou
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China; School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province, 510275, PR China
| | - Jiajun Zhang
- Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, PR China; School of Mathematics, Sun Yat-sen University, Guangzhou, Guangdong Province, 510275, PR China.
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