Stochastic and Deterministic Analysis of Circadian Clocks |
Circadian clocks govern vital daily behaviors in most organisms. Of particular interest is the clock in mammals, which resides in the hypothalamic suprachiasmatic nucleus (SCN).
Its behavior is regulated by a hierarchy of mechanisms. The cells of the SCN each contain transcription feedback networks, which induce cell-autonomous oscillations showing a large degree of variability.
Via intercellular communication, the population of individual oscillators synchronize to form an SCN-level oscillator with much less variability.
The SCN level oscillator is then synchronized to its environment via the process of entrainment with the daily light/dark cycle. To study the circadian clock, we use discrete stochastic methods to capture the variability at the lowest levels, and differential equations to study the clock at the highest levels. At all levels, we are interested in the timing, or phase, behavior of oscillators because it is key to proper synchronization and entrainment behavior. The standard method for studying phase behavior in circadian clocks is the phase response curve (PRC). Along with the PRC, we use an analytical analog called the parametric impulse PRC (pIPRC).
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