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

Liu, J. and Crawford, J. W. (1998) Stability of an autocatalytic biochemical system in the presence of noise perturbations. Mathematical Medicine and Biology, 15(4), pp. 339-350. (doi: 10.1093/imammb/15.4.339)

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The stability of an autocatalytic biochemical system (Moran & Goldbeter, 1984, Biophys. Chem. 20, 149–156) in the presence of perturbations due to noise is investigated. In the absence of noise, Moran & Goldbeter (1984) showed that the model system admits the phenomena of both hard excitation and birhythmicity. Hard excitation is the coexistence of a stable steady state with 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 state 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 value, the distinction between two coexisting attractors are lost. Based on these results, the roles of a recycling enzyme in the stability of the system under noise perturbations are analysed. It is concluded that, for a fixed 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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Crawford, Professor John
Authors: Liu, J., and Crawford, J. W.
College/School:College of Social Sciences > Adam Smith Business School > Management
Journal Name:Mathematical Medicine and Biology
Publisher:Oxford University Press for IMA
ISSN (Online):1477-8602
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