Equality of average and steady-state levels in some nonlinear models of biological oscillations

Theory in Biosciences = Theorie in Den Biowissenschaften
Beate KnokeStefan Schuster

Abstract

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi-Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins-Selkov model of glycolytic oscillations and two-dimensional Lotka-Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property...Continue Reading

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Citations

Feb 17, 2010·Theory in Biosciences = Theorie in Den Biowissenschaften·Beate KnokeStefan Schuster
Jul 2, 2016·Journal of Theoretical Biology·Alexandra-M Reimers, Arne C Reimers
Apr 8, 2020·Royal Society Open Science·Ravindra GardeStefan Schuster

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