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	72
下载量	30
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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.