An Oscillatory Reaction with Constant Input of Reactants

3 An Oscillatory Reaction with Constant Input of Reactants 

Consider the following model for the reaction mechanism of the beginning part of glycolysis (Fig. 16.3) [6] for the production of the energy rich chemical species ATP (adenosine triphosphate), which is the universal energy coinage in biochemical reactions. 

In the first reaction glucose reacts with ATP to produce ADP and PEP the enzyme for this first step is hexokinase the notation is similar for the remaining reaction steps, with the enzymes as indicated. The rate of influx of glucose into the system is constant. Due to the feedback mechanisms in both the PFK and PK reactions chemical oscillations of some species may occur, see Fig. 16.4. These oscillations have been observed [1] and are also obtained from numerical solutions of the deterministic mass action rate equations of the model in Fig. 16.1 for given glucose inflow conditions, see Fig. 16.4. 

The four different periods of oscillations are for different experimental conditions for a given set of experimental conditions all species oscillate with the same period. For lower glucose inflow oscillations cease and the system is in a stable stationary state (a node or a focus). 

In Fig. 16.5 we plot the period of chemical oscillations in the system vs. the total adenine nucleotide concentration, that is the sum of the concentrations of ATP, ADP and AMP, labelled A(MDT)P, for several values of influx conditions. At low values of A(MDT)P there are no oscillations. The oscillations appear at the marginal stability point, and after that the period varies. 

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