Oscillation and Input Compensation in the Cyanobacterial Kai Proteins

The purified Kai protein oscillator remarkably recapitulates many of the qualitative features of circadian clocks in living organisms. Here I review the phenomenology of this system with a focus on how the Kai oscillator is special compared to generic biochemical oscillators. A key feature is that many external perturbations couple much more strongly to the amplitude than to the period of oscillations. This property is the basis of the ability of the oscillator to entrain to cycling environments while maintaining free-running rhythms that are always near 24 h. In contrast, internal perturbations that alter the structure of KaiC can cause large changes in the period. Explaining the molecular mechanism that underlies the sensitivity of period and amplitude to perturbations is a major remaining challenge that lies at the heart of clock physiology. I propose a toy mathematical model based on speculative biochemical assumptions that may shed some light on how the period and amplitude of the Kai protein oscillator arise.