title: Costs and constraints from time-delayed feedback in small gene regulatory motifs.
abstract: 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.
authors.affiliation: Department of Mathematics, Uppsala University, SE-751 06 Uppsala, Sweden.
authors.forename: Andreas
authors.initials: A
authors.lastname: Grönlund
authors.forename: Per
authors.initials: P
authors.lastname: Lötstedt
authors.forename: Johan
authors.initials: J
authors.lastname: Elf
mesh_terms: D019281:Dimerization; D005786:Gene Expression Regulation; D008957:Models, Genetic; D013379:Substrate Specificity; D013997:Time Factors; D014158:Transcription, Genetic
references.citation: Nature. 2002 Nov 14;420(6912):186-9
references.pmid: 12432395
references.citation: Nat Rev Mol Cell Biol. 2008 Dec;9(12):981-91
references.pmid: 18971947
references.citation: Q Rev Biophys. 2001 Feb;34(1):1-59
references.pmid: 11388089
references.citation: Genome Res. 2003 Nov;13(11):2475-84
references.pmid: 14597656
references.citation: Science. 2003 Jun 13;300(5626):1718-22
references.pmid: 12805541
references.citation: Proc Natl Acad Sci U S A. 2005 Oct 11;102(41):14593-8
references.pmid: 16199522
references.citation: Biophys J. 2003 Jan;84(1):154-70
references.pmid: 12524272
references.citation: J Bacteriol. 1999 Nov;181(22):6857-64
references.pmid: 10559149
references.citation: Mol Syst Biol. 2008;4:221
references.pmid: 18854820
references.citation: Proc Natl Acad Sci U S A. 2002 Apr 30;99(9):5988-92
references.pmid: 11972055
references.citation: PLoS Biol. 2007 Sep;5(9):e229
references.pmid: 17713988
references.citation: Nat Genet. 2002 May;31(1):64-8
references.pmid: 11967538
references.citation: Biophys J. 2005 Jan;88(1):132-46
references.pmid: 15501947