[1]周天寿.生化反应系统的高维矩阵方程[J].江西师范大学学报(自然科学版),2017,(01):1-5.
 ZHOU Tianshou.The High-Dimensional Matrix Equation for Biochemical Reaction Systems[J].Journal of Jiangxi Normal University:Natural Science Edition,2017,(01):1-5.
点击复制

生化反应系统的高维矩阵方程()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2017年01期
页码:
1-5
栏目:
出版日期:
2017-01-01

文章信息/Info

Title:
The High-Dimensional Matrix Equation for Biochemical Reaction Systems
作者:
周天寿
中山大学数学学院,广东 广州 510275
Author(s):
ZHOU Tianshou
School of Mathematics,Sun Yat-Sen University,Guangzhou Guangdong 510275,China
关键词:
化学主方程 高维矩阵方程 矩阵指数函数 环路算法
Keywords:
chemical master equation high-dimensional matrix equation matrix exponent function cyclic iterative algorithm
分类号:
O 242; Q 332
文献标志码:
A
摘要:
化学主方程对生化反应系统提供了一个建模框架,但它的分析与模拟一直是计算系统生物学的一个难题,到目前为止并没有得到解决.这里,通过引进高维矩阵及其运算规则,首先把化学主方程表示为高维矩阵方程,然后给出了其分析解的形式表示,此外还介绍了一种求解高维矩阵方程的高效数值方法.研究表明:高维矩阵方法似乎解决了化学主方程的分析求解和数值求解问题.
Abstract:
Chemical master equation gives a framework for mathematical modeling of biochemical reaction systems,but its analysis and simulation has been being difficult in the field of computational systems biology.Here,by introducing a high-dimensional matrix and its operators,first the chemical master equation is transformed into a high-dimensional matrix equation,and then a formal expression for the analytical solution to this matrix equation is given.In addition,a 2-order cyclic iterative algorithm is introduced to numerically solve the high-dimensional matrix equation.In a word,the high-dimensional matrix method seems to solve the questions of analytical and numerical solutions to the chemical master equation.

参考文献/References:

[1] Wang Junwei,Zhang Jiajun,Yuan Zhanjiang,et al.Noise-induced switches in network systems of the genetic toggle switch [J].BMC Syst Biol,2007,(1):50-60.
[2] Gammaitoni L,H?nggi P,Jung P,et al.Stochastic resonance [J].Rev Mod Phys,1998,70(1):223-287.
[3] Pikovsky A S,Kurths J.Coherent resonance in a noise-driven excitable system [J].Phys Rev Lett,1997,78(5):775-778.
[4] Zhou Tianshou,Chen Luonan,Aihara K.Molecular communication through stochastic synchronization induced by extracellular fluctuations [J].Phys Rev Lett,2005,95(17):178103.
[5] Teramae J N,Tanaka D.Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators [J].Phys Rev Lett,2004,93(20):204103.
[6] Paulsson J,Berg O G,Ehrenberg M.Stochastic focusing:fluctuation-enhanced sensitivity of intracellular regulation [J].Proc Natl Acad Sci U S A,2000,97(13):7148-7153.
[7] Van Kampen N G.Stochastic processes in physics and chemistry [M].Amsterdam:Elsevier,2007.
[8] 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,2015,39(1):1-6.
[9] 周天寿.基因表达系统的研究进展:概率分布 [J].江西师范大学学报:自然科学版,2012,36(3):221-229.
[10] 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.
[11] 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.
[12] Ale A,Kirk P,Stumpf M P.A general moment expansion method for stochastic kinetic models [J].J Chem Phys,2013,138(17):174101.
[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):1591-1596.
[16] Zhang Jiajun,Nie Qing,Zhou Tianshou.A moment-convergence method for stochastic analysis of biochemical reaction networks [J].J Chem Phys,2016,144(19):194109.
[17] Nie Qing,Zhang Yongtao,Zhao Rui.Efficient semi-implicit schemes for stiff systems [J].J Comput Phys,2006,214(2):521-537.

备注/Memo

备注/Memo:
收稿日期:2016-11-10基金项目:国家自然科学基金委/重大研究计划/集成(91530320)和科技部973课题(2014CB964703)资助项目.作者简介:周天寿(1962-),男,江西新建人,教授,博士生导师,目前主要从事分子系统生物学和计算系统生物学研究.E-mail:mcszhtsh@mail.sysu.edu.cn
更新日期/Last Update: 1900-01-01