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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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Wang X, Li Y, Jia C. Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks. J R Soc Interface 2023; 20:20230467. [PMID: 38016635 PMCID: PMC10684348 DOI: 10.1098/rsif.2023.0467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 11/08/2023] [Indexed: 11/30/2023] Open
Abstract
Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner's Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.
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Affiliation(s)
- Xinyu Wang
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, People’s Republic of China
| | - Youming Li
- School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
| | - Chen Jia
- Applied and Computational Mathematics Division, Beijing Computational Science Research Center, Beijing 100193, People’s Republic of China
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Zhdanov VP. Interplay of Cellular mRNA, miRNA and Viral miRNA during Infection of a Cell. Int J Mol Sci 2022; 24:ijms24010122. [PMID: 36613566 PMCID: PMC9820072 DOI: 10.3390/ijms24010122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2022] [Revised: 11/29/2022] [Accepted: 12/15/2022] [Indexed: 12/24/2022] Open
Abstract
The understanding of the kinetics of gene expression in cells infected by viruses is currently limited. As a rule, the corresponding models do not take viral microRNAs (miRNAs) into account. Such RNAs are, however, operative during the replication of some viruses, including, e.g., herpesvirus. To clarify the kinetics of this category (with emphasis on the information available for herpesvirus), I introduce a generic model describing the transient interplay of cellular mRNA, protein, miRNA and viral miRNA. In the absence of viral miRNA, the cellular miRNA is considered to suppress the populations of mRNA and protein due to association with mRNA and subsequent degradation. During infection, the viral miRNA suppresses the population of cellular miRNA and via this pathway makes the mRNA and protein populations larger. This effect becomes appreciable with the progress of intracellular viral replication. Using biologically reasonable parameters, I investigate the corresponding mean-field kinetics and show the scale of the effect of viral miRNAs on cellular miRNA and mRNA. The scale of fluctuations of the populations of these species is illustrated as well by employing Monte Carlo simulations.
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Affiliation(s)
- Vladimir P Zhdanov
- Boreskov Institute of Catalysis, Russian Academy of Sciences, Novosibirsk 630090, Russia
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Yang X, Luo S, Zhang Z, Wang Z, Zhou T, Zhang J. Silent transcription intervals and translational bursting lead to diverse phenotypic switching. Phys Chem Chem Phys 2022; 24:26600-26608. [DOI: 10.1039/d2cp03703c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
For complex process of gene expression, we use theoretical analysis and stochastic simulations to study the phenotypic diversity induced by silent transcription intervals and translational bursting.
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Affiliation(s)
- Xiyan Yang
- School of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou 510521, P. R. China
| | - Songhao Luo
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Zhenquan Zhang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Zihao Wang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Tianshou Zhou
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
| | - Jiajun Zhang
- School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China
- Guangdong Province Key Laboratory of Computational Science, Guangzhou 510275, P. R. China
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