随机基因表达模型中表达产物数量分布形态的判别条件

丘芷珊; QIU Zhishan; 盛英; SHENG Ying; 焦锋; JIAO Feng

doi:10.48014/jcss.20250201001

随机基因表达模型中表达产物数量分布形态的判别条件

The Discriminative Conditions for the Distribution Pattern of Expression Products in Stochastic Gene Expression Models

中国统计科学学报 2025年第3卷第1期页码[15-25] 下载全文[1.2MB]

摘要

基因表达本质上是一个随机过程。表达产物数量分布能够全面刻画基因表达的随机行为, 通常呈现出递减、钟形和双峰三种分布形态。文献[21]探讨了耦合最小正负反馈回路的随机基因表达模型, 通过在参数平面上构造两条连续曲线C1和C2, 从理论上给出了模型产生三种分布形态的充分必要条件。然而, 对于任意给定的一组参数, 由于曲线C1和C2无法给出精确表达式, 很难直接并且快速地判断耦合最小正负反馈回路的随机基因表达模型能够产生何种分布形态. 这极大影响了我们利用数学模型针对海量单细胞转录数据的研究. 在该文中, 我们通过对曲线C1和C2的定量刻画, 给出若干产生三种分布形态的系统参数条件。这些参数条件可通过简单的初等函数进行计算, 因此提供了判断随机基因表达模型中表达产物数量分布形态的快速判别方法。

Abstract

Gene expression is essentially a random process. The distribution of expression product quantities can comprehensively describe the stochastic behavior. of gene expression, which typically exhibits three distribution shapes: decaying, bell-shaped, and bimodal. Ref. [21] explores a stochastic gene expression model of minimal coupled positive-plus-negative feedback loop. By constructing two continuous curves C1 and C2 in the parameter phase, the necessary and sufficient conditions for the model to generate three distribution shapes were theoretically provided. However, for any given set of parameters, since the curves C1 and C2 cannot give exact expressions, it is difficult to directly and quickly determine which distribution shape the stochastic gene expression model of a minimal coupled positive-plus-negative feedback loop can generate. This greatly affects our research on massive single cell transcriptomic data using mathematical models. In this paper, we present several system parameter conditions that generate the three distribution shapes by quantitatively characterizing the curves C1 and C2. These parameter conditions can be calculated using simple elementary functions. Thus, a rapid discrimination method for determining the distribution shape of the quantity of expression products in the stochastic gene expression model is provided.

DOI

10.48014/jcss.20250201001

文章类型

研究性论文

收稿日期

2025-02-01

接收日期

2025-02-10

出版日期

2025-03-28

关键词

随机基因表达模型, 正负反馈回路, 化学反应主方程, 表达产物数量分布

Keywords

Stochastic gene transcription model, positive-plus-negative feedback loop, chemical response master equation, quantitative distribution of expression products

作者

丘芷珊, 盛英, 焦锋^*

Author

QIU Zhishan, SHENG Ying, 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 Sciences, Guangzhou University, Guangzhou 510006, China

浏览量

125

下载量

参考文献

[1] Lee T I, Young R A. Transcriptional regulation and its misregulation in disease[J]. Cell, 2013, 152(6): 1237-1251.
https://doi.org/10.1016/j.cell.2013.02.014.
[2] Hamaneh M B, Yu Y K. Relating diseases by integrating gene associations and information flow through protein interaction network[J]. PLoS One, 2014, 9(10): e110936.
https://doi.org/10.1371/journal.pone.0110936.
[3] Kaern M, Elston T C, Blake W J, et al. Stochasticity in gene expression: from theories to phenotypes[J]. Nat Rev Genet, 2005, 6(6): 451-464.
https://doi.org/10.1038/nrg1615.
[4] Sweatt A J, Griffiths C D, Groves S M, et al. Proteomewide copy-number estimation from transcriptomics[J]. Mol Syst Biol, 2024, 20(11): 1230-1256.
https://doi.org/10.1038/s44320-024-00064-3.
[5] Harshbarger B, Feller W. An Introduction to Probability Theory and Its Applications[J]. Volume I. AIBS Bulletin, 1958, 8(1): 32.
https://doi.org/10.1137/1011021.
[6] Davidson E H. The regulatory genome: gene regulatory networks in development and evolution[M]. Elsevier, 2010.
https://doi.org/10.1016/B978-0-12-088563-3.X5000-8.
[7] Shen Orr S S, Milo R, Mangan S, et al. Network motifs in the transcriptional regulation network of Escherichia coli[J]. Nat. Genet, 2002, 31: 64-68.
https://doi.org/10.1038/ng881.
[8] Rosenfeld N, Elowitz M B, Alon U. Negative autoregulation speeds the response times of transcription networks[J]. J. Mol. Biol, 2002, 323: 785-793.
https://doi.org/10.1016/s0022-2836(02)00994-4.
[9] Friedman N, Cai L, Xie X S. Linking stochastic dynamics to population distribution: an analytical framework of gene expression[J]. Phys. Rev. Lett, 2006, 97: 168302.
https://doi.org/10.1103/PhysRevLett.97.168302.
[10] Mackey M C, Tyran-Kaminska M, Yvinec R. Dynamic behavior of stochastic gene expression models in the presence of bursting[J]. SIAM J. Appl. Math, 2013, 73: 1830-1852.
https://doi.org/10.1137/12090229X.
[11] Bokes P, Singh A. Protein copy number distributions for a self-regulating gene in the presence of decoy binding sites[J]. PloS one, 2015, 10: e0120555.
https://doi.org/10.1371/journal.pone.0120555.
[12] 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.
[13] Venturelli O S, El-Samad H, Murray R M. Synergistic dual positive feedback loops established by molecular sequestration generate robust bimodal response[J]. Proc Natl Acad Sci, 2012, 109(48): E3324-3333.
https://doi.org/10.1073/pnas.1211902109.
[14] Choi P J, Cai L, Frieda K, et al. A stochastic single-molecule event triggers phenotype switching of a bacterial cell[J]. Science, 2008, 322(5900): 442-446.
https://doi.org/10.1126/science.1161427.
[15] Liu P, Yuan Z, Huang L, et al. Roles of factorial noise in inducing bimodal gene expression[J]. Phys Rev E Stat Nonlin Soft Matter Phys, 2015, 91(6): 062706.
https://doi.org/10.1103/PhysRevE.91.062706.
[16] Hornos J E M, Schultz D, Innocentini G C P, et al. Selfregulating gene: an exact solution[J]. Phys. Rev. E, 2005, 72: 051907.
https://doi.org/10.1103/PhysRevE.72.051907.
[17] Grima R, Schmidt D R, Newman T J. Steady-state fluctuations of a genetic feedback loop: An exact solution [J]. J. Chem. Phys, 2012, 137(3): 035104.
https://doi.org/10.1063/1.4736721.
[18] Kumar N, Platini T, Kulkarni R V. Exact distributions for stochastic gene expression models with bursting and feedback[J]. Phys. Rev. Lett, 2014, 113: 268105
https://doi.org/10.1103/PhysRevLett.113.268105.
[19] Jia C, Grima R. Small protein number effects in stochastic models of autoregulated bursty gene expression[J]. J. Chem. Phys, 2020, 152(8): 084115.
https://doi.org/10.1063/1.5144578.
[20] Jiao F, Sun Q, Tang M, Yu, 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.
[21] Sheng Y, Lin G, Jiao F, et al. Geometric theory of distribution shapes for autoregulatory gene circuits[R]. To appear in SIAM Journal on Applied Mathematics, 2024.
https://doi.org/10.1101/2024.04.02.587730
[22] Liu P, Yuan Z, Wang H, et al. Decomposition and tunability of expression noise in the presence of coupled feedbacks[J]. Chaos, 2016, 26: 043108.
https://doi.org/10.1063/1.4947202.
[23] Jia C, Yin G G, Zhang M Q, et al. Single-cell stochastic gene expression kinetics with coupled positive-plusnegative feedback[J]. Phys. Rev. E, 2019, 100: 052406.
https://doi.org/10.1103/PhysRevE.100.052406.
[24] Frank W J, Olver, Daniel W L, et al. NIST Digital Library of Mathematical Functions[J]. Annals of Mathematics and Artificial Intelligence, 2003, 38: 105-119.
https://doi.org/10.1023/A:1022915830921

引用本文

芷珊, 盛英, 焦锋. 随机基因表达模型中表达产物数量分布形态的判别条件[J]. 中国统计科学学报, 2025, 3(1): 15-25.

Citation

QIU Zhishan, SHENG Ying, JIAO Feng. The discriminative conditions for the distribution pattern of expression products in stochastic gene expression models[J]. Journal of Chinese Statistical Sciences, 2025, 3(1): 15-25.