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Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations


  • Thomas B. Kepler
  • Timothy C. Elston


Transcriptional regulation is subject to significant stochasticity due partly to the random waiting times among synthesis and degradation reactions involving a finite collection of transcripts. Additional stochasticity is attributable to the random transitions among the discrete operator states controlling the rate of transcription. We develop a Markov model to which these random reactions are intrinsic as well as a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the ``underlying'' deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

Suggested Citation

  • Thomas B. Kepler & Timothy C. Elston, 2001. "Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations," Working Papers 01-06-033, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:01-06-033

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    References listed on IDEAS

    1. Martin Shubik, 2000. "The Theory of Money," Working Papers 00-03-021, Santa Fe Institute.
    2. Arthur, W Brian, 1989. "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," Economic Journal, Royal Economic Society, vol. 99(394), pages 116-131, March.
    3. Kiyotaki, Nobuhiro & Wright, Randall, 1989. "On Money as a Medium of Exchange," Journal of Political Economy, University of Chicago Press, vol. 97(4), pages 927-954, August.
    4. Dubey, Pradeep & Mas-Colell, Andreau & Shubik, Martin, 1980. "Efficiency properties of strategies market games: An axiomatic approach," Journal of Economic Theory, Elsevier, vol. 22(2), pages 339-362, April.
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    Cited by:

    1. Xu, Yong & Zhu, Ya-nan & Shen, Jianwei & Su, Jianbin, 2014. "Switch dynamics for stochastic model of genetic toggle switch," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 461-466.

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    Gene regulation; Markov processes; biological networks; bifurcations; first passage times;

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