Amplitude/Temperature-Compensation: Data and Models

Stuart Brody (October 27, 2010)

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Amplitude is a measurable parameter of an oscillator, yet it is often not considered as a variable, Amplitude can be measured in several ways: 1) as an output of an oscillator; 2) directly as the amplitude of a "key" clock protein; or 3) indirectly via a Phase-response curve. Data will be presented for a particular mutant (frq7) of Neurospora which shows how the amplitude was altered in all three of the measures listed above. A model will be presented based on limit-cycle expansion which accounts for these observations.

Temperature affects the amplitude of circadian oscillators in almost all systems studied. Data will be presented to illustrate how an increase in temperature leads to an increase in amplitude of these oscillators from many organisms. This increase in amplitude is proposed to be the mechanism of temperature-compensation, ie. to compensate for the increase in rates at a higher temperature, there is an expansion of the limit-cycle. This model is designated as the temperature-amplitude model, or the "T-A" model. A combination of this model with the one mentioned above predicts how much the midpoint of an oscillator will change when the temperature is raised, a feature not found in other models.

To determine if the temperature-amplitude relationship was a general one, a model callled the "degrade and fire" model was explored. This model simulates the known in vivo oscillations of a synthetic circuit, the arabinose circuit, constructed in E. coli. Data will be presented showing how the change in the activation energy of just one reaction can increase the amplitude of this oscillator, and can convert this non- temperature-compensated oscillator into a temperature-compensated oscillator.

Work done in collaboration with Lev Tsimring.