Extinction and resurrection in gene networks
- Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0374
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Contributed by José N. Onuchic, October 16, 2008 (received for review August 12, 2008)
Abstract
When gene regulatory networks operate in regimes where the number of protein molecules is so small that the molecular species are on the verge of extinction, the death and resurrection of the species greatly modifies the attractor landscape. Deterministic models and the diffusion approximation to the master equation break down at the limits of protein populations in a way very analogous to the breakdown of geometrical optics that occurs at distances <1 wavelength of light from edges. Stable stochastic attractors arise from extinction and resurrection events that are not predicted by the deterministic description. With this view, we explore the attractors of the regular toggle switch and the exclusive switch, focusing on the effects of cooperative binding and the production of protein in bursts. Our arguments suggest that the stability of lysogeny in the λ-phage may be influenced by such extinction phenomena.
Footnotes
- 2To whom correspondence should be addressed. E-mail: jonuchic{at}ucsd.edu
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Author contributions: D.S., A.M.W., J.N.O., and P.G.W. designed research; D.S. performed research; D.S. contributed new reagents/analytic tools; D.S. and A.M.W. analyzed data; and D.S., A.M.W., J.N.O., and P.G.W. wrote the paper.
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↵1Present address: Princeton Center for Theoretical Science, Princeton University, Princeton, NJ 08544.
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The authors declare no conflict of interest.
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This article contains supporting information online at www.pnas.org/cgi/content/full/0810366105/DCSupplemental.
- © 2008 by The National Academy of Sciences of the USA
