Analysis of noise effects in Markov and semi-Markov reaction systems

CAO Wenjie; TENG Jiaqi; CHEN Haowen; ZHOU Tianshou

doi:10.13471/j.cnki.acta.snus.ZR20240108

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Analysis of noise effects in Markov and semi-Markov reaction systems

Column of Biomathematics（Contributing editor: ZHOU Tianshou） | 更新时间：2024-11-25

- Analysis of noise effects in Markov and semi-Markov reaction systems
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 63, Issue 6, Pages: 291-300(2024)
- 作者机构：
  
  中山大学数学学院，广东广州 510275
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240108
  CLC： O29
- Published：25 November 2024，
  
  Published Online：25 July 2024，
  
  Received：09 April 2024，
  
  Accepted：02 May 2024
- 稿件说明：
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CAO Wenjie,TENG Jiaqi,CHEN Haowen,et al.Analysis of noise effects in Markov and semi-Markov reaction systems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(06):291-300.
DOI：

CAO Wenjie,TENG Jiaqi,CHEN Haowen,et al.Analysis of noise effects in Markov and semi-Markov reaction systems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(06):291-300. DOI： 10.13471/j.cnki.acta.snus.ZR20240108.

摘要

基因调控网、信号转导网、代谢控制网和蛋白质相互网等生物分子网络是计算系统生物学的主要研究对象. 从随机过程的观点，这些网络可以划分为马氏反应网和非马氏反应网，依赖于分子机制的实验测定. 另一方面，由于生化反应事件是随机发生的，这必然会导致反应物种水平的涨落（即生化反应系统是固有噪声的）. 这种分子噪声可能在自然选择、细胞命运决定、细胞内部过程等起着重要作用. 一个未完全解决的问题是分子噪声的生物学功能是什么. 本文分别分析地导出一般的马氏生化网络和一般的半马氏生化网络中分子噪声对各个反应物种水平影响的计算公式，并对一般的朗之万方程，建立了小噪声影响系统平衡态和特征值的两个实用定理. 此外，以广义生灭过程作为一个例子，分析地显示出分子记忆的效果等同于反馈的引入. 本文的分析结果既有宽广的应用前景，也为基于实验数据的统计推断奠定了基础.

Abstract

Biomoleuclar networks such as gene regulatory networks， signal transduction networks， metabolic control networks， and protein-protein interaction networks， are main research subjects of computational systems biology. From the viewpoint of stochastic process， these networks can be categorized into Markov and non-Markov reaction networks， depending on experimental measurements of molecular mechanisms. On the other hand， biochemical reaction events happen stochastically， so this necessarily leads to fluctuations in reactive species levels （i.e.，biochemical reaction is inherently noisy）. This molecular noise would play an important role in natural selection， cell fate determination， etc. An unsolved issue is what the biological function of molecular noise is. This article analytically derives calculation formulae for the influences of molecular noise on reactive species levels in general Markov and non-Markov reaction networks， and establishes two practical theorems for the influences of small noise on equilibrium states and characteristic values in a generic Langevin equation. In addition， it analytically shows that the effect of molecular memory is equivalent to the introduction of feedback by taking a generalized birth-death process as an example. The analytical results of this paper not only broad applications but also lay a foundation for statistical inferences based on experimental data.

关键词

马氏反应网络半马氏反应网络分子噪声化学主方程

Keywords

Markov reaction networksemi-Markov reactionmolecular noisechemical master equation

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