Deterministic characterization of stochastic genetic circuits
- *Center for Theoretical Biological Physics and Department of Physics, University of California at San Diego, La Jolla, CA 92093-0374; and
- ‡Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1
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Edited by Michael S. Waterman, University of Southern California, Los Angeles, CA, and approved March 12, 2007 (received for review November 26, 2006)
Abstract
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corrections due to the molecular noise. The method allows the steady-state behavior of the stochastic model to be easily computed, facilitates the mapping of stability phase diagrams that include stochastic effects, and reveals how model parameters affect noise susceptibility in a manner not accessible to numerical simulation. By way of illustration we consider two genetic circuits: a bistable positive-feedback loop and a negative-feedback oscillator. We find in the positive feedback circuit that translational activation leads to a far more stable system than transcriptional control. Conversely, in a negative-feedback loop triggered by a positive-feedback switch, the stochasticity of transcriptional control is harnessed to generate reproducible oscillations.
Footnotes
- †To whom correspondence should be addressed. E-mail: mscott{at}ctbp.ucsd.edu
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Author contributions: M.S., T.H., and B.I. performed research and wrote the paper.
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The authors declare no conflict of interest.
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This article is a PNAS Direct Submission.
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This article contains supporting information online at www.pnas.org/cgi/content/full/0610468104/DC1.
- Abbreviation:
- ESA,
- effective stability approximation.
- © 2007 by The National Academy of Sciences of the USA
