DNA looping increases the range of bistability in a stochastic model of thelacgenetic 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.

Modeling the effect of transcriptional noise on switching in gene networks in a genetic bistable switch

“…5. As reported earlier [39][40][41], our analysis of the three-state promoter model shows that the gene expression level is strongly affected by the promoter architecture. Also, in the twostate promoter model, one can introduce a non-exponential protein degradation step instead of a simple Poisson process.…”

“…However, these simple thermodynamic models can only compute the mean and not the higher moments of protein/mRNA distributions. As shown in the previous section, we can not only use our approach to calculate the mean and the variance of the protein/ mRNA distributions but to also obtain the mean switching time between active and inactive promoter states for a complex promoter architecture such as the three-state promoter model [39][40][41] as shown in Fig. 5.…”

Protein Distributions from a Stochastic Model of the lac Operon of E. coli with DNA Looping: Analytical solution and comparison with experiments

“…1 [14]–[16], but these studies do not give analytical expressions for the steady state protein distribution. The literature also contains several stochastic models of gene regulation for which analytical solutions were obtained [11], [17]–[24], but they do not account for the presence of multiple auxiliary operators and DNA looping.…”

Effects of DNA replication on mRNA noise

“…Many of these works have also considered forms of transcriptional regulation wherein a gene can switch between active and inactive transcriptional states [either through the binding of a transcription factor (8,13,14,19,20) or through structural changes to the DNA that may occlude transcription start sites (21,22)]. More recently, researchers have begun to venture beyond the steadystate approximation to address sources of noise that are tied to cell cycle-dependent processes.…”