交互式路径随机基因转录模型中 mRNA数量分布的计算

陈欣欣; CHEN Xinxin; 焦锋; JIAO Feng

doi:10.48014/jcss.20240314001

交互式路径随机基因转录模型中 mRNA数量分布的计算

Computation of mRNA Number Distributions in Interactive Pathway Stochastic Gene Transcription Model

中国统计科学学报 2024年第2卷第1期页码[1-9] 下载全文[0.8MB]

摘要

基因表达是一个随机过程, 表现为等基因细胞群单个细胞中mRNA数量的波动性。这种波动可由mRNA数量分布Pm (t) 来刻画, 其中Pm (t) 是指在t时刻产生m个mRNA分子的概率。对于一个给定的随机基因转录模型, 如何求解对应的Pm (t) 精确表达式一直是该领域的研究热点。在现有工作中, 大多数结果是在稳态情形或者特定的参数区域内来求解Pm (t) , 这影响了我们全面理解不同随机基因调控模式对mRNA数量分布的动力学影响。本论文中, 我们探讨了交互式信号路径随机基因转录模型的Pm (t) 计算, 并给出了其在任意系统参数条件下的精确表达式。交互式信号路径模型被成功应用于阐述可诱导基因应对环境变化下的随机转录数据。这项工作为我们进一步研究基因转录的交互式信号路径调控机制提供动力学理论基础。

Abstract

Gene expression is a stochastic process characterized by fluctuations in the amount of mRNA in individual cells of an isogenic cell population. The fluctuation can be characterized by the mRNA number distribution Pm (t) , which denotes the probability of producing m copies of mRNA molecules in one cell at time t. For a given stochastic gene transcription model, how to solve the corresponding Pm (t) exact expression has been a hot research topic in this field. In the existing work, most of the results are solved for Pm (t) in the steady state case or in a specific parameter region, which affects us to fully understand the kinetic effects of different stochastic gene regulation patterns on the distribution of mRNA quantities. In this thesis, we explore the computation of Pm (t) for the cross-talk pathway model and give its exact expression under arbitrary system parameter conditions. The interactive signaling pathway model is successfully applied to elaborate stochastic transcription data of inducible genes in response to environmental changes. This work provides a kinetic theoretical basis for us to further investigate the interactive signaling pathway regulatory mechanism of gene transcription.

DOI	10.48014/jcss.20240314001
文章类型	研究性论文
收稿日期	2024-03-14
接收日期	2024-03-21
出版日期	2024-03-28
关键词	随机基因转录模型, 化学反应主方程, mRNA 数量分布, 超几何函数
Keywords	Stochastic gene transcription model, chemical response master equation, quantitative distribution of mRNA, hypergeometric function
作者	陈欣欣, 焦锋^*
Author	CHEN Xinxin, JIAO Feng^*
所在单位	广州大学数学与信息科学学院, 广州 510006
Company	School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
浏览量	59
下载量	16
参考文献	[1] Munsky B, Neuert G, van Oudenaarden A. Using gene expression noise to understand gene regulation[J]. Science, 2012, 336: 183-187. https://doi.org/10.1126/science.1216379 [2] Sanchez A, Golding I. Genetic determinants and cellular constraints in noisy gene expression[J]. Science, 2013, 342: 1188-1193. https://doi.org/10.1126/science.1242975 [3] Larsson A J M, et al. Genomic encoding of transcriptional burst kinetics[J]. Nature, 2019, 565: 251-254. https://doi.org/10.1038/s41586-018-0836-1 [4] Raj A, Peskin C S, Tranchina D, et al. Stochastic mRNA synthesis in mammalian cells[J]. PLoS Biol, 2006, 4: e309. https://doi.org/10.1038/s41586-018-0836-1 [5] Halpern K B, et al. Bursty gene expression in the intact mammalian liver[J]. Cell, 2015, 58: 147-156. https://doi.org/10.1016/j.molcel.2015.01.027 [6] Dey S S, Foley J E, Limsirichai P, et al. Orthogonal control of expression mean and variance by epigenetic features at different genomic loci[J]. Mol Syst Biol, 2015, 11: 806. https://doi.org/10.15252/msb.20145704 [7] Jiao F, Tang M, Yu J. Distribution profiles and their dynamic transition in stochastic gene transcription[J]. J. Differential Equations, 2013, 254: 3307-3328. https://doi.org/10.1016/j.jde.2013.01.019 [8] Munsky B, Fox Z, Neuert G. Integrating single-molecule experiments and discrete stochastic models to understand heterogeneous gene transcription dynamics[J]. Methods, 2015, 85: 12-21. https://doi.org/10.1016/j.ymeth.2015.06.009 [9] Chen J, Grima R. Dynamical phase diagram of an autoregulating gene in fast switching conditions[J]. J. Chem. Phys, 2020, 152: 174110. https://doi.org/10.1063/5.0007221 [10] Zenklusen D, Larson D R, Singer R H. Single-RNA counting reveals alternative modes of gene expression in yeast[J]. Nat. Struct. Mol. Biol, 2008, 15: 1263-1271. https://doi.org/10.1038/nsmb.1514 [11] Kalmar T, et al. Regulated fluctuations in Nanog expression mediate cell fate decisions in embryonic stem cells[J]. PLoS Biol, 2009, 7: e1000149. https://doi.org/10.1371/journal.pbio.1000149 [12] Senecal A, et al. Transcription factors modulate c-Fos transcriptional bursts[J]. Cell Rep, 2014, 8: 75-83. https://doi.org/10.1016/j.celrep.2014.05.053 [13] Jiao F, Sun Q, Tang M, et al. Distribution modes and their corresponding parameter regions in stochastic gene transcription[J]. SIAM J. Appl. Math, 2015, 75: 2396-2420. https://doi.org/10.1137/151005567 [14] Iyer-Biswas S, Hayot F, Jayaprakash C. Stochasticity of gene products from transcriptional pulsing[J]. Phys. Rev. E, 2009, 79: 031911. https://doi.org/10.1103/PhysRevE.79.031911 [15] Jiao F, Ren J, Yu J. Analytical formula and dynamic profile of mRNA distribution[J]. Discrete Contin. Dyn. Syst. B, 2020, 25: 241-257. https://doi.org/10.3934/dcdsb.2019180 [16] Golding I, Paulsson J, Zawilski S M, et al. Real-time kinetics of gene activity in individual bacteria[J]. Cell, 2005, 123: 1025-1036. DOI: https://doi.org/10.1016/j.cell.2005.09.031 [17] Pelet S, et al. Transient activation of the HOG MAPK pathway regulates bimodal Gene expression[J]. Science, 2011, 332: 732-735. https://doi.org/10.1126/science.1198851 [18] Neuert G, et al. Systematic identification of signal-activated stochastic gene regulation[J]. Science, 2013, 339: 584-587. https://doi.org/10.1126/science.1231456 [19] Fiering S, et al. Single cell assay of a transcription factor reveals a threshold in transcription activated by signals emanating from the T-cell antigen receptor[J]. Genes Dev, 1990, 4: 1823-1834. https://doi.org/10.1101/gad.4.10.1823 [20] Larson D R. What do expression dynamics tell us about the mechanism of transcription[J]. Curr. Opin. Genet. Dev, 2011, 21: 1-9. https://doi.org/10.1016/j.gde.2011.07.010 [21] Zhu C, Han G, Jiao F. Dynamical regulation of mRNA distribution by cross-talking signaling pathways[J]. Complexity, 2020, 20: 6402703. https://doi.org/10.1155/2020/6402703 [22] Macia J, Regot S, Peeters T, et al. Dynamic signaling in the Hog1 MAPK pathway relies on high basal signal transduction[J]. Sci. Signal, 2009, 2, ra13. https://doi.org/10.1126/scisignal.2000056 [23] Jordan A, Defechereux P, Verdin E. The site of HIV-1 integration in the human genome determines basal transcriptional activity and response to Tat transactivation[J]. EMBO J, 2001, 20: 1726-1738. https://doi.org/10.1093/emboj/20.7.1726 [24] Nadal E, Ammerer G, Posas F. Controlling gene expression in response to stress[J]. Nat. Rev. Genet, 2011, 12: 833-845. https://doi.org/10.1038/nrg3055 [25] Aguirre A, Rubio M E, Gallo V. Notch and EGFR pathway interaction regulates neural stem cell number and self-renewal[J]. Nature, 2010, 467: 323-327. https://doi.org/10.1038/nature09347 [26] Yoo A S, Bais C, Greenwald I. Crosstalk between the EGFR and LIN-12/Notch pathways in C. elegans vulval development[J]. Science, 2004, 303: 663-666. https://doi.org/10.1126/science.1091639 [27] Tanji T, Hu X, Weber A N R, et al. Toll and IMD pathways synergistically activate an innate immune response in Drosophila melanogaster[J]. Mol. Cell. Biol, 2007, 27: 4578-4588. https://doi.org/10.1128/MCB.01814-06 [28] Yu J, Tang M, Sun Q. The nonlinear dynamics and fluctuations of mRNA levels in cross-talking pathway acti- vated transcription[J]. J. Theor. Biol, 2014, 363: 223-234. https://doi.org/10.1016/j.jtbi.2014.08.024 [29] Jiao F, Sun Q, Lin G, et al. Distribution profiles in gene transcription activated by the cross-talking pathway. Discrete Contin[J]. Dyn. Syst. B, 2019, 24: 2799-2810. https://doi.org/10.3934/dcdsb.2018275 [30] Tabaka M, Holyst R. Binary and graded evolution in time in a simple model of gene induction[J]. Phys. Rev. E, 2010, 82: 052902. https://doi.org/10.1103/PhysRevE.82.052902 [31] Shahrezaei V, Swain P S. Analytical distributions for stochastic gene expression[J]. Proc. Natl. Acad. Sci, 2009, 105: 17256-17261. https://doi.org/10.1073/pnas.0803850105 [32] Zhou T, Zhang J. Analytical results for a multistategene model[J]. SIAM J Appl Math, 2012, 72: 789-818. https://doi.org/:10.1137/110852887 [33] Sun Q, Cai Z, Zhu C. A novel dynamical regulation ofmRNA distribution by cross-talking pathways[J]. Mathematics, 2022, 10: 1515. https://doi.org/10.3390/math10091515 [34] Jiao F, Zhu C. Regulation of gene activation by competitivecross talking pathways[J]. Biophys. J, 2020, 119: 1204-1214. DOI:10.1016/j.bpj.2020.08.011 [35] Chen L, Lin G, Jiao F. Using average transcription levelto understand the regulation of stochastic gene activation[J]. R. Soc. Open Sci, 2022, 9: 211757. https://doi.org/10.1098/rsos.211757
引用本文	陈欣欣, 焦锋. 交互式路径随机基因转录模型中mRNA数量分布的计算[J]. 中国统计科学学报, 2024, 2(1): 1-9.
Citation	CHEN Xinxin, JIAO Feng. Computation of mRNA number distributions in interactive pathway stochastic gene transcription model[J]. Journal of Chinese Statistical Sciences, 2024, 2(1): 1-9.