Abstract
The role of enzyme co-operativity in the mechanism of metabolic periodicities is analyzed quantitatively by study of the Hill coefficient in a concerted model for an allosteric enzyme activated by its reaction product. This model applies to the regulation of phosphofructokinase, which produces glycolytic oscillations in yeast and muscle. Periodic behavior takes place around a non-equilibrium, unstable stationary state. The minimum Hill coefficient associated with instability of the steady state is determined as a function of the number of protomers constituting the enzyme. Positive co-operativity is always a necessary prerequisite for sustained oscillations, although the requirement for co-operativity is significantly reduced when the concentration of the product varies much faster than that of the substrate. Suppression of periodic behavior by positive or negative effectors follows from the decrease of enzyme co-operativity below a threshold. The results are discussed in relation to the molecular basis of glycolytic oscillations.
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