Homeostasis of the period of post-translational biochemical oscillators

Generally, circadian clocks or biological oscillations are resistant to external conditions such as temperature and nutrient concentration. We propose that enzyme-limited competition provides a general mechanism of homeostasis of the period of post-translational oscillators based on protein modifications, and demonstrate it by nutrient compensation in a theoretical model of cyanobacterial circadian clock. The rate change by nutrient concentration is counterbalanced by the amount of available free enzyme, which occurs because of the competition among the various substrates for the limited enzyme. The temperature and nutrient compensation are determined by the postulate that the catalytic modification reactions are rate limiting.