THRESHOLDS AND OSCILLATIONS IN ENZYMATIC CASCADES

We determine the conditions in which sustained oscillations develop in a model for a bicyclic enzyme cascade regulated by negative feedback. The model, based on a cascade of two phosphorylation-dephosphorylatio n cycles, was previously proposed (Goldbeter, A. Proc. Natl. Acad. Sci . U.S.A. 1991, 88, 9107) as a minimal cascade model for the mitotic os cillator driving the early cell division cycles in amphibian embryos. We analyze the role of thresholds in the mechanism of oscillatory beha vior by constructing stability diagrams as a function of the main para meters of the model. The thresholds arise from the phenomenon of zero- order ultrasensitivity naturally associated with the kinetics of phosp horylation-dephosphorylation cycles (Goldbeter, A.; Koshland, D. E., J r. Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 6840). The analysis shows t hat if the existence of a threshold in each of the two cycles markedly favors the periodic operation of the cascade, a single threshold suff ices for sustained oscillatory behavior. Oscillations may even arise i n the absence of any threshold in a small region of parameter space, b ut their amplitude is very much reduced. The model provides an example of biochemical oscillator based on negative feedback in which nonline ar amplification, instead of being due to allosteric cooperativity, re sults from the ultrasensitivity that arises from the kinetics of phosp horylation-dephosphorylation cycles.