Control analysis of glycolytic oscillations

The principles involved in the control of the frequency of sustained metabolic oscillations are developed in the context of glycolytic oscillations in Saccharomyces cerevisiae. To this purpose, an existing mathematical model that describes the experimentally obtained oscillations was simplified to a core model. Frequency, relative phase, average concentrations and amplitudes of the oscillations were well approximated by writing the two remaining metabolic variables of the core model (representing [ATP] and [hexose]) as harmonic functions of time and by requiring them to fulfill the differential equations. The extent to which an enzyme (-conglomerate) controls the frequency in a sustained oscillation is defined as the log-log derivative of that frequency with respect to enzyme activity. In both the full model and the core model this control of frequency and the control over the average concentrations proved to be distributed over the enzymes. We identified a summation theorem, stating that the sum of such control coefficients over all processes equals unity for frequency and zero for the average concentrations.