Figure 4.

Example of failure of local linearization and LNA. This figure demonstrates the application of LNA to the system described by Vilar et al. (2002). We use the same equations and parameters as in the original article. In a certain parameter regime, the mesoscopic system displays periodic oscillation, whereas the macroscopic model describes an asymptotically stable steady state (A). As can be seen in B, the LNA well describes the Fano-factor for the repressor and repressor-inhibitor complex up to a certain value for the decay rate for the repressor (δ_R 0.0275h^-1). Above this point, the system displays large stochastic fluctuations and for even higher values (δ_R > 0.05h^-1) also periodic oscillations that cannot be described by the LNA. However, the large fluctuations predicted by LNA indicate that a more thorough stochastic analysis should be conducted. At the bifurcation, at δ_R 0.101h^-1, the macroscopic steady state loses stability and the oscillations are described also by a macroscopic model.