Stochastic Phase Oscillator Models for Circadian Clocks

Abstract

Periodic environments like we experience on the surface of planet earth lead living organisms to evolve molecular anticipation devices known a circadian clocks. The word circadian refers to the period of these oscillations which last about (circa) one day (dies). A frequently felt manifestation of this oscillator is experienced by travelers crossing timezones, when the local external cues are suddenly set out of phase with respect to our internal timing, resulting in a discomfort called jetlag. Although we might be less conscious about them, the circadian pacemaker also regulates a number of our basic daily physiological functions such as hourly changes in our body temperature or heart beat rate. Such clocks are found throughout the tree of life, in bacteria, plants, insects, funghi, vertebrates and mammals. Since the 1970s1, genetics and molecular biology has begun to disentangle the molecular circuitries by which cell-autonomous oscillations can be maintained, and how external light or temperature entrainment cues are relayed to this pacemaker. The three defining characteristics of these oscillators is that (i) rhythms persists in constant conditions (after external cues have been removed); (ii) phases can be reset by light, temperature or hormone pulses; (iii) the period of oscillation is temperature compensated in a physiological range. A commonality across the many species whose oscillators were studied is the recurrence of negative feedback circuits among the core clock genes2. Several species including Arabidopsis Thaliana, Drosophila melanogaster and mouse, use interlocked feedback loops, with up to three loops in Arabidopsis.3,4 The resulting redundancy is thought to provide not only robustness,5 but also the necessary flexibility to allow accurate timekeeping despite seasonal changes in photoperiod duration 3 or temperature variations.