Adaptive Temperature Compensation in Circadian Oscillations

A temperature independent period and temperature entrainment are two defining features of circadian oscillators. A default model of distributed temperature compensation satisfies these basic facts yet is not easily reconciled with other properties of circadian clocks, such as many mutants with altered but temperature compensated periods. The default model also suggests that the shape of the circadian limit cycle and the associated phase response curves (PRC) will vary since the average concentrations of clock proteins change with temperature. We propose an alternative class of models where the twin properties of a fixed period and entrainment are structural and arise from an underlying adaptive system that buffers temperature changes. These models are distinguished by a PRC whose shape is temperature independent and orbits whose extrema are temperature independent. They are readily evolved by local, hill climbing, optimization of gene networks for a common quality measure of biological clocks, phase anticipation. Interestingly a standard realization of the Goodwin model for temperature compensation displays properties of adaptive rather than distributed temperature compensation. Author Summary: Circadian clocks are biological oscillators which evolved to couple the internal rhythm of animals, plants and even some bacteria to the alternation of light and day. Circadian oscillators are temperature compensated, i.e. they keep a 24-h period irrespective of the temperature of the organism. This is surprising, since many biochemical parameters, including average concentration of clock proteins, vary with temperature. From dynamical system theory, we therefore expect changes in both period and relative lengths of features in the phase response curve which are not seen. We couple mathematical modelling and computational evolution of gene networks to formulate a novel explanation for temperature compensation that accords better with experimental facts than alternatives. Our model has deep mathematical connections with the process of biochemical adaptation, by which cells respond to temporal gradients of signals rather than their absolute value.