Dynamics of biochemical oscillators in a large number of interacting cells

Item Type:	Article
Title:	Dynamics of biochemical oscillators in a large number of interacting cells
Creators Name:	Wolf, J. and Heinrich, R.
Abstract:	We investigated here minimal models for coupled metabolic oscillators in cell suspensions. They are based on a feedback-activation mechanism, proposed for the explanation of the glycolytic oscillations. Despite the simplicity of the models we found a wide variety of complex dynamical phenomena. Depending on the kinetic parameters interacting cells may oscillate synchronous or asynchronous. It was shown, that there are different possibilities for asynchronous oscillations. (a) Depending on the type of coupling regular asynchronous behaviour may occur near to the boundary of stability. This type of behaviour was only possible, if the coupling metabolite belongs to the pool of products of the autocatalytic reaction. (b) Leaving the near neighbourhood of the points of Hopf-bifurcations in both models nonregular asynchronous behaviour may arise by secondary symmetry breaking bifurcations, either from the branch of synchronous oscillations or from the branch of regular asynchronous oscillations. In model II the coupling opens the possibility of multiple steady states. The whole population may be within different stable steady states or different oscillatory modes. The results of our study may be helpful for the interpretation of experimental data in this field. The mechanism of interaction, which was investigated here, has been proposed for many biological systems. Especially for yeast cell suspensions the question of the coupling intermediates is studied intensively. In recent time acetaldehyde was reported to be the synchronizer of the oscillations [5], but this substance was shown to desynchronize the oscillations too [4]. Without discussing the problem, whether or not this substance mediates the coupling, we want to emphasize that any metabolite may play the role of a synchronizer as well as that of a desynchronizer. Moreover we have demonstrated that the regular asynchronous oscillations may lead to the phenomenon of hidden oscillations, where it may be difficult to observe cellular oscillations.
Keywords:	Cell Population, Coupled Oscillators, Synchronization, Stability, Bifurcation Analysis
Source:	Nonlinear Analysis Theory Methods & Applications
ISSN:	0362-546X
Publisher:	Elsevier
Volume:	30
Number:	3
Page Range:	1835-1845
Date:	December 1997
Official Publication:	https://doi.org/10.1016/S0362-546X(96)00346-X

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