Subsequently, by means of numerical simulations of a more detailed model, we demonstrate that the stochastic stabilization effect is generic for this kind of architecture. Finally, in the Discussion section, we present the main conclusions and discuss about the applicability and relevance of our study. In the context of genetic circuits, a definition of stochastic bifurcation has been previously proposed, based on experimental data or results from gene network models. In general, a stochastic bifurcation is characterized by a qualitative change in one of the observables of the stochastic process. In the case of a bistable system, one may consistently identify two subpopulations of cells whose states are distributed around the two stable states. We will follow this approach and define the stochastic system as monostable if its steady state probability distribution is unimodal and bistable if its distribution is bimodal. More complex stochastic bifurcations has been proposed, for example in the case of systems with oscillatory dynamics. In the context of gene regulatory circuits, the chemical kinetics formalism that address the different processes underlying regulation leads to a Master equation representation. By using the auto-activating genetic switch as a case study, we have shown that the biochemical intrinsic noise may induce a shift in the position of the bifurcation points such that the region of parameter values for which the stationary probability distribution is bimodal increases with fluctuations with respect to the deterministic situation. In particular, the low state stability is extended; an effect that we call stochastic stabilization and that we have shown that, in essence, does not depend on the colored character of the fluctuations. The perturbative method that we have introduced is general and can be applied to any stochastic system describing a gene regulatory network. Yet, we point out that the method is limited to the case of one-dimensional stochastic differential equations for which the general solution of the stationary probability density can be written explicitly. Nonetheless, we have shown by means of simulations of a more detailed model, that the stochastic stabilization phenomenon does not depend on this particular detail thus suggesting a generic phenomenon in positive feedback switches. AbMole Miglitol Previous studies have also found that noise changes the position and even the number of stable states. In this regard, our study provides a theoretical framework to predict and understand such phenomenology. The results of the detailed model differ quantitatively from the simple model when fluctuations are considered. In particular, the probability AbMole Lomitapide Mesylate distributions and the range of values for which the latter are bimodal are different. Thus, although the deterministic descriptions of both models are totally equivalent this is not true when considering the biochemical fluctuations. In fact, the dynamics at steady state are quite different and we find that in the detailed model the switching rate from the low to the high state is slower than in the simplified model. These results are in agreement with other studies about genetic switches: for example in the case of the genetic toggle switch it has been shown that protein-protein interactions can be safely eliminated but protein-DNA interactions, even though are also fast, lead to noticeable changes in the switching rates if neglected. It is also interesting to place our findings in the context of the role played by different noisy sources, gene switching, translational and transcriptional, for defining the global attractor of bistable systems.
It has been recently shown that the modulation of the intensity of these fluctuations can actually condition
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