A genetic timer through noise-induced stabilization of an unstable state

doi:10.1073/pnas.0806349105

A genetic timer through noise-induced stabilization of an unstable state

*Department of Pharmacology, University of Texas Southwestern Medical Center, Dallas, TX 753903;
^†Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom 11, E-08222 Terrassa, Spain; and
^‡Green Center for Systems Biology, University of Texas Southwestern Medical Center, Dallas, TX 75390

Edited by José N. Onuchic, University of California at San Diego, La Jolla, CA, and approved August 27, 2008 (received for review July 1, 2008)

Abstract

Stochastic fluctuations affect the dynamics of biological systems. Typically, such noise causes perturbations that can permit genetic circuits to escape stable states, triggering, for example, phenotypic switching. In contrast, studies have shown that noise can surprisingly also generate new states, which exist solely in the presence of fluctuations. In those instances noise is supplied externally to the dynamical system. Here, we present a mechanism in which noise intrinsic to a simple genetic circuit effectively stabilizes a deterministically unstable state. Furthermore, this noise-induced stabilization represents a unique mechanism for a genetic timer. Specifically, we analyzed the effect of noise intrinsic to a prototypical two-component gene-circuit architecture composed of interacting positive and negative feedback loops. Genetic circuits with this topology are common in biology and typically regulate cell cycles and circadian clocks. These systems can undergo a variety of bifurcations in response to parameter changes. Simulations show that near one such bifurcation, noise induces oscillations around an unstable spiral point and thus effectively stabilizes this unstable fixed point. Because of the periodicity of these oscillations, the lifetime of the noise-dependent stabilization exhibits a polymodal distribution with multiple, well defined, and regularly spaced peaks. Therefore, the noise-induced stabilization presented here constitutes a minimal mechanism for a genetic circuit to function as a timer that could be used in the engineering of synthetic circuits.

Footnotes

^§To whom correspondence should be addressed. E-mail: gurol.suel{at}utsouthwestern.edu
Author contributions: J.G.-O. and G.M.S. designed research; M.T. and J.G.-O. performed research; M.T., J.G.-O., and G.M.S. analyzed data; and J.G.-O. and G.M.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.