Stability of an autocatalytic biochemical system in the presence of noise perturbations

The stability of an autocatalytic biochemical system (Moran & Goldbeter, 19 84, Biophys. Chem. 20, 149-156) in the presence of perturbations due to noi se is investigated. In the absence of noise, Moran & Goldbeter (1984) showe d that the model system admits the phenomena of both hard excitation and bi rhythmicity. Hard excitation is the coexistence of a stable steady state wi th a stable oscillation, and birhythmicity is the coexistence of two stable oscillatory regimes. This work shows that noise may switch the system from a state having a smaller basin of attraction to one with a larger basin of attraction. The inverse switching is not observed. The stability of a stat e in the presence of noise depends on both the size of basin of attraction and the dynamical behaviour. When the noise amplitude is above a critical v alue, the distinction between two coexisting attractors are lost. Based on these results, the roles of a recycling enzyme in the stability of the syst em under noise perturbations are analysed. It is concluded that, for a fixe d input rate, increasing the activity of the recycling enzyme enhances the stability of the steady state for hard excitations, although this does not change the net flux of the system.