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The Temperature-Compensated Goodwin Model Simulates Many Circadian Clock Properties

Goodwin's model oscillator, which consists of a negative feedback loop within a single gene expression pathway (1963, 1965), was modified in order to demonstrate temperature compensation, a characteristic property of circadian oscillators. Temperature effects were introduced into the oscillatory mechanism by means of the Arrhenius equation. This term may provide a simplified estimate of the complicated temperature-dependence of actual cellular processes. Temperature compensation within the oscillatory mechanism was achieved by balancing the effect of different temperatures on amplifying processes and on stabilizing processes (antagonistic balance; Ruoff, 1994). Apart from temperature compensation, the modified Goodwin oscillator showed other characteristic properties of circadian clocks including: 
 
(i) temperature entrainment even by temperature cycles of rather low amplitude (1 °C), 
 
(ii) phase shifts by temperature pulses or steps of different signs (up or down) and different amplitudes, giving rise to phase response curves similar to those reported, for example, inNeurospora crassa(Francis & Sargent 1979; Rensinget al., 1987; Nakashima, 1987). 
 
A single change in one of the reaction rates of the model oscillator not only caused a change in the period length but also abolished temperature compensation. This closely corresponds to the effects observed after a single point mutation of the clock gene (frq7) inNeurospora crassa(Aronsonet al., 1994b). Limit cycle oscillations were damped at permanently low temperatures, however the period of the damped oscillations was still temperature compensated.