Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression
Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression
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DOI：
10.1016/j.jmaa.2006.11.043
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发表时间：
2007-09-15
影响因子：
1.3
通讯作者：
Rudnicki, Ryszard
中科院分区：
文献类型：
--
作者：
Bobrowski, Adam;Lipniacki, Tomasz;Rudnicki, Ryszard
本文致力于研究 Lipmacki 等人最近的论文中引入的随机过程。 [T。 Lipniacki, R Paszek, A. Marciniak-Czochra, A.R. Brasier，M. Kimmel，基因表达的转录随机性，J. Theor。生物。 238 (2006) 348-367] 真核生物基因表达建模。从过程的完整生成器开始，我们证明其分布满足（福克-普朗克型）偏微分方程组。然后，我们在对应于该系统的L-1空间中构造一个c(0)马尔可夫半群。论文的主要结果是密度集中所涉及的半群的渐近稳定性。 (c) 2006 Elsevier Inc. 保留所有权利。
The paper is devoted to a stochastic process introduced in the recent paper by Lipmacki et al. [T. Lipniacki, R Paszek, A. Marciniak-Czochra, A.R. Brasier, M. Kimmel, Transcriptional stochasticity in gene expression, J. Theor. Biol. 238 (2006) 348-367] in modelling gene expression in eukaryotes. Starting from the full generator of the process we show that its distributions satisfy a (Fokker-Planck-type) system of partial differential equations. Then, we construct a c(0) Markov semigroup, in L-1 space corresponding to this system. The main result of the paper is asymptotic stability of the involved semigroup in the set of densities. (c) 2006 Elsevier Inc. All rights reserved.