[1]周天寿.概率主方程的研究综述[J].江西师范大学学报(自然科学版),2015,(01):1-6.
　ZHOU Tianshou.The Review on Study of Probability Master Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2015,(01):1-6.
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概率主方程的研究综述()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2015年01期
页码:
1-6
栏目:
出版日期:
2015-02-10

文章信息/Info

Title:
The Review on Study of Probability Master Equations
作者:
周天寿
中山大学数学与计算科学学院,广东 广州 510275
Author(s):
ZHOU Tianshou
关键词:
反应网络;  概率主方程;  矩封闭方法;  随机模拟
Keywords:
reaction the network;  probability master equation;  moment-closure approach;  stochastic simulation
分类号:
O 242; Q 332
文献标志码:
A
摘要:
反应网络广泛存在于自然系统中.原理上,概率主方程对任何反应网络系统的随机行为提供了最为完整的数学模型.然而,分析和模拟这种类型的方程长期以来是一项挑战性任务.至目前为止,有关问题并没有得到根本解决,相关研究仍在继续.该文对概率主方程的研究进展进行了较为系统和全面的综述,聚焦于若干常用的近似分析方法(如线性噪声逼近、普通矩封闭法、2项矩方法等)与常用的数值方法(如Gillespie随机模拟算法、有限状态映射法、矩封闭格式等).特别地,分析了概率主方程研究取得缓慢进展的主要原因,讨论并提出了可能的解决方案.
Abstract:
Reaction networks exist extensively in natural systems.In principle,probability master equations provide the most complete models of probabilistic behavior for any reaction network systems.However,analysis and simulation of these equations have been a challenging task for a long time; these problems have not been thoroughly unsolved until now and relevant studies are still continuing.This article presents a systematic and comprehensive review on study of probability master equations,focusing on common theoretical analysis methods such as linear noise approximation,common moment-closure methods and binomial moment approach,and common numerical approaches such as Gillespie stochastic simulation approach,finite state mapping method and moment-closure formulations.In particular,some reasons why slow progress is made in study of probability master equations are analyzed,and possible schemes for solving probability master equations are discussed and suggested.

参考文献/References:

[1] Zaikin A N,Zhabotinsky A M.Concentration wave propagation in two-dimensional liquid-phase self-oscillating system [J].Nature,1970,225:535-537.
[2] Thattai M,Van Oudenaarden A.Intrinsic noise in gene regulatory networks [J].Proc Natl Acad Sci U S A,2001,98(15):8614-8619.
[3] 胡长春,周天寿.三类基因振子和它们的基本动力学 [J].江西师范大学学报:自然科学版,2008,32(1):1-5.
[4] Lotka A J.Contribution to the theory of periodic reaction [J].J Phys Chem,1910,14(3):271-274.
[5] Gillespie D T.A general method for numerically simulating the stochastic time evolution of coupled chemical reactions [J].J Comput Phys,1976,22(4):403-434.
[6] 周天寿.基因表达模型的研究进展:概率分布 [J].江西师范大学学报:自然科学版,2012,36(3):221-229.
[7] Zhang Jiajun,Huang Lifang,Zhou Tianshou.Comment on Binomial moment equations for chemical reaction networks [J].Phys Rev Lett,2014,112:088901.
[8] Delbrück M.Statistical fluctuations in autocatalytic reactions [J].J Chem Phys,1940,8(1):120-140.
[9] Van Kampen N G.Stochastic process in physics and chemistry [M].Amsterdam:North-Holland,1992.
[10] Elf J,Ehrenberg M.Fast evaluation of fluctuations in biochemical networks with the linear noise approximation [J].Gen Res,2013,13(11):2475-2484.
[11] Paulsson J.Summing up the noise in gene networks [J].Nature,2004,427:415-418.
[12] Zhang Jiajun,Yuan Zhanjiang,Zhou Tianshou.Physical limits of feedback noise-suppression in biological networks [J].Phys Biol,2009,6(4):046009.
[13] Smadbeck P,Kaznessis Y N.A closure scheme for chemical master equations [J].Proc Natl Acad Sci U S A,2013,110(35):14261-14265.
[14] Zechner C,Ruess J,Krenn P,et al.Moment-based inference predicts bimodality in transient gene expression [J].Proc Natl Acad Sci U S A,2012,109(21):8340-8345.
[15] Grima R.A study of the accuracy of moment-closure approximations for stochastic chemical kinetics [J].J Chem Phys,2012,136(15):154105.
[16] 周天寿.生物系统的随机动力学 [M].北京:科学出版社,2009.
[17] Ale A,Kirk P,Stumpf M P H.A general moment expansion method for stochastic kinetic models [J].J Chem Phys,2013,138(17):174101.
[18] Gibson M A,Bruck J.Efficient exact stochastic simulation of chemical systems with many species and many channels [J].J Phys Chem A,2000,104(9):1876-1889.
[19] Gillespie D T.Approximate accelerated stochastic simulation of chemically reacting systems [J].J Chem Phys,2001,115(4):1716-1733.
[20] Munsky B,Khammash M.The finite state projection algorithm for the solution of the chemical master equation [J].J Chem Phys,2006,124(4):044104.

备注/Memo

备注/Memo:
国家自然科学基金委/重大研究计划/重点支持(91230204)；科技部973项目子课题(2014CB964703)
更新日期/Last Update: 1900-01-01