title: DNA looping increases the range of bistability in a stochastic model of the lac genetic switch.
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.
authors: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
authors: Emmy E
authors: EE
authors: Earnest
authors: Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
authors: Elijah
authors: E
authors: Roberts
authors: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
authors: Michael
authors: M
authors: Assaf
authors: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
authors: Karin
authors: K
authors: Dahmen
authors: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL, USA.|Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, USA.
authors: Zaida
authors: Z
authors: Luthey-Schulten
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004269:DNA, Bacterial / Q000737:chemistry / Q000235:genetics*; D004926:Escherichia coli / Q000737:chemistry / Q000235:genetics*; D007763:Lac Operon; D056968:Lac Repressors / Q000235:genetics*; D008957:Models, Genetic; D009690:Nucleic Acid Conformation; D012333:RNA, Messenger / Q000235:genetics; D013269:Stochastic Processes
chemical_list: D004269:DNA, Bacterial; D056968:Lac Repressors; D012333:RNA, Messenger