Multivariate analysis of noise in genetic regulatory networks

被引:50
作者
Tomioka, R
Kimura, H
Kobayashi, TJ
Aihara, K
机构
[1] Univ Tokyo, Inst Ind Sci, Aihara Lab, Meguro Ku, Tokyo 1538505, Japan
[2] Univ Tokyo, Sch Engn, Dept Math Engn & Informat Phys, Bunkyo Ku, Tokyo 1138656, Japan
[3] Univ Tokyo, Grad Sch Frontier Sci, Dept Complex Sci & Engn, Bunkyo Ku, Tokyo 1138656, Japan
[4] Inst Phys & Chem Res, Bio Mimet Control Res Ctr, Moriyama Ku, Nagoya, Aichi 4630003, Japan
[5] JST, ERATO, Aihara Complex Modelling Project, Shibuya Ku, Tokyo 1510065, Japan
关键词
stochastic gene expression; noise reduction; linear noise approximation; Lyapunov equation; decoupling of a stoichiometric matrix;
D O I
10.1016/j.jtbi.2004.04.034
中图分类号
Q [生物科学];
学科分类号
07 ; 0710 ; 09 ;
摘要
Stochasticity is an intrinsic property of genetic regulatory networks due to the low copy numbers of the major molecular species, such as, DNA, mRNA, and regulatory proteins. Therefore, investigation of the mechanisms that reduce the stochastic noise is essential in understanding the reproducible behaviors of real organisms and is also a key to design synthetic genetic regulatory networks that can reliably work. We use an analytical and systematic method, the linear noise approximation of the chemical master equation along with the decoupling of a stoichiometric matrix. In the analysis of fluctuations of multiple molecular species, the covariance is an important measure of noise. However, usually the representation of a covariance matrix in the natural coordinate system, i.e. the copy numbers of the molecular species, is intractably complicated because reactions change copy numbers of more than one molecular species simultaneously. Decoupling of a stoichiometric matrix, which is a transformation of variables, significantly simplifies the representation of a covariance matrix and elucidates the mechanisms behind the observed fluctuations in the copy numbers. We apply our method to three types of fundamental genetic regulatory networks, that is, a single-gene autoregulatory network, a two-gene autoregulatory network, and a mutually repressive network. We have found that there are multiple noise components differently originating. Each noise component produces fluctuation in the characteristic direction. The resulting fluctuations in the copy numbers of the molecular species are the sum of these fluctuations. In the examples, the limitation of the negative feedback in noise reduction and the trade-off of fluctuations in multiple molecular species are clearly explained. The analytical representations show the full parameter dependence. Additionally, the validity of our method is tested by stochastic simulations. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码:501 / 521
页数:21
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