Optimal Regulation of Circadian Clock

A circadian clock (sometimes called a circadian oscillator or rhythm) oscillates roughly once every 24 hours, enabling us to organize our physical and mental activities at the time that is most optimal. The Nobel Prize in physiology or medicine in 2017 was awarded to the scientists who discovered the molecular mechanisms controlling the circadian clock.[1] In this thesis, we study the circadian clock in a physical and mathematical setting. The modified Kuramoto model which describes the synchronization between coupled oscillators is chosen as the equation of motion to study the circadian clock of living organisms. More specifically, we picture our physical system as two individual oscillators, one the solar-cycle oscillator and the other an internal-clock oscillator of a living organism. As in the real world, there is always random noise that prevents living organisms from having perfect knowledge of the outside world. Noise can either come from the environmental background or uncertainty in the internal processing of the organism. The deterministic and stochastic versions of the modified Kuramoto model are separately analyzed. The cost analysis based on the phase synchronization between the two oscillators in both deterministic and stochastic environments can reflect the optimization problem of an organism’s circadian clock. Our approach of analyzing the circadian clock can provide us an insight to regulate the operation of a circadian clock within a noisy environment and with internal noise.