Skip Navigation

Mathematical Medicine and Biology 1998 15(4):339-350; doi:10.1093/imammb/15.4.339
© 1998 by Institute of Mathematics and its Applications
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by LIU, J.
Right arrow Articles by CRAWFORD, J. W.
Right arrow Search for Related Content
PubMed
Right arrow Articles by LIU, J.
Right arrow Articles by CRAWFORD, J. W.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

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

JUNLI LIU{dagger} and JOHN W. CRAWFORD

Centre for Nonlinear Systems in Biology, Scottish Crop Research Institute Dundee, DD2 5DA, UK

{dagger}Author to whom correspondence should be addressed. Email: jliu{at}scriiari.ac.uk

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.

Keywords: relative stability of states; coexistence of attractors; noise-induced transition; basin of attraction


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.