DNA looping increases the range of bistability in a stochastic model of the lac genetic switch

Tyler M. Earnest, Elijah Roberts, Michael Assaf, Karin Dahmen, Zaida Luthey-Schulten

Research output: Contribution to journalArticlepeer-review

Abstract

Conditions and parameters affecting the range of bistability of the lac genetic switch in Escherichia coli are examined for a model which includes DNA looping interactions with the lac repressor and a lactose analogue. This stochastic gene-mRNA-protein model of the lac switch describes DNA looping using a third transcriptional state. We exploit the fast bursting dynamics of mRNA by combining a novel geometric burst extension with the finite state projection method. This limits the number of protein/mRNA states, allowing for an accelerated search of the model's parameter space. We evaluate how the addition of the third state changes the bistability properties of the model and find a critical region of parameter space where the phenotypic switching occurs in a range seen in single molecule fluorescence studies. Stochastic simulations show induction in the looping model is preceded by a rare complete dissociation of the loop followed by an immediate burst of mRNA rather than a slower build up of mRNA as in the two-state model. The overall effect of the looped state is to allow for faster switching times while at the same time further differentiating the uninduced and induced phenotypes. Furthermore, the kinetic parameters are consistent with free energies derived from thermodynamic studies suggesting that this minimal model of DNA looping could have a broader range of application.

Original languageEnglish (US)
Article number026002
JournalPhysical Biology
Volume10
Issue number2
DOIs
StatePublished - Apr 1 2013

ASJC Scopus subject areas

  • Biophysics
  • Structural Biology
  • Molecular Biology
  • Cell Biology

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