期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2010
卷号：107
期号：18
页码：8171-8176
DOI：10.1073/pnas.0913317107
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The multistep character of transcription, translation, and protein modification inevitably leads to time delays between sensing gene regulatory signals and responding with changed concentrations of functional proteins. However, the interplay between the time-delayed and the stochastic nature of gene regulation has been poorly investigated. Here we present an extension of the linear noise approximation which makes it possible to estimate second moments--variances and covariances--of fluctuations around stationary states in time-delayed systems. The usefulness of the method is exemplified by analyzing two ubiquitous regulatory motifs. In the first system, we show that there is an optimal combination of transcriptional repression and direct product inhibition in determining the activity of an enzyme system. In particular, we demonstrate that direct product inhibition is necessary to avoid deleterious fluctuations in a system when the gene regulatory response is delayed. The second system is an anabolic motif where the substrate fluxes are balanced by time-delayed regulation responding to the substrate concentrations. The extended linear noise approximation makes it possible to show analytically that increased association rate between the substrates leads to a lower product flux because of increasing unbalance in substrate pools.
