Journal of Mathematical Chemistry

, Volume 49, Issue 2, pp 531–545 | Cite as

Globally attractive oscillations in open monosubstrate allosteric enzyme reactions

Original Paper

Abstract

Here we study the dynamical properties of glycolytic and other similar biochemical oscillation-generating processes by means of the analysis of a model proposed by Golbdeter and Lefever (Bioph J 13:1302–1315, 1972) in a reduced form proposed by Keener and Sneyd (Mathematical physiology, chap 1, Springer Verlag, Berlin, 2009). After showing that the orbits of the system are bounded, we give some conditions for the existence of oscillations and for the global arrest of them. Then, after deriving an equivalent Lienard-Newton’s equation we assess uniqueness and the global stability of the arising limit cycle. Finally, we shortly investigate the possibility of breaking of the spatial symmetry. Some biological remarks end the work.

Keywords

Limit cycles Glycolysis Global stability Lienard’s equation Turing’s bifurcations 

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Experimental OncologyEuropean Institute of OncologyMilanoItaly

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