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Research Article

Delay-induced stochastic oscillations in gene regulation

Dmitri Bratsun, Dmitri Volfson, Lev S. Tsimring, and Jeff Hasty
PNAS October 11, 2005 102 (41) 14593-14598; https://doi.org/10.1073/pnas.0503858102
Dmitri Bratsun
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Dmitri Volfson
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Lev S. Tsimring
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Jeff Hasty
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  1. Edited by Nancy J. Kopell, Boston University, Boston, MA (received for review May 10, 2005)

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Abstract

The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale.

  • master equation
  • stochastic delay equations
  • noise
  • time delay
  • systems biology

Footnotes

  • ↵ § To whom correspondence should be addressed at: Department of Bioengineering, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0412. E-mail: hasty{at}ucsd.edu.

  • This paper was submitted directly (Track II) to the PNAS office.

  • Abbreviation: DG, direct Gillespie.

  • Copyright © 2005, The National Academy of Sciences
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Delay-induced stochastic oscillations in gene regulation
Dmitri Bratsun, Dmitri Volfson, Lev S. Tsimring, Jeff Hasty
Proceedings of the National Academy of Sciences Oct 2005, 102 (41) 14593-14598; DOI: 10.1073/pnas.0503858102

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Delay-induced stochastic oscillations in gene regulation
Dmitri Bratsun, Dmitri Volfson, Lev S. Tsimring, Jeff Hasty
Proceedings of the National Academy of Sciences Oct 2005, 102 (41) 14593-14598; DOI: 10.1073/pnas.0503858102
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Proceedings of the National Academy of Sciences of the United States of America: 102 (41)
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    • Abstract
    • Delayed Protein Degradation
    • Stochastic Simulations: Modified Gillespie Method
    • Negative Feedback with Delayed Production
    • Negative Feedback with Dimerization
    • Discussion
    • Acknowledgments
    • Footnotes
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