Circadian rhythms are observed in many species from Drosophila to humans. In Drosophila, per mRNA is synthesized by the transcription of the per gene which is translated into PER protein in cytoplasm. Huge amount of PER is accumulated in the cytoplasm before PER is transported into the nucleus and suppress the expression of per gene.
[1] By comparing several models of different complexity, we prove that a sustained oscillation is more likely to occur if the kinetics the transport to the nucleus have cooperativity with a nonlinear dependence on the substrate concentration.
[2] We show that the saturation in any of the reactions included in the feedback loop (in-loop reaction steps) suppresses the oscillation, whilst the saturation of degradation steps (branch reaction steps) makes the oscillation more likely to occur.
[3] Free-running period of circadian clock is not exactly 24h. It is not clear why the free-running period is of the order of 21.5h in Neurospora and 24.2h in humans, instead of precisely 24h. From model for circadian rhythms in Neurospora and Drosophila, we demonstrate how the entrainment of these rhythms is affected by the free-running period and by the amplitude of the external light-dark cycle.
[4] Free-running period of any organisms remains unchanged with temperature increase. It is unknown which molecular process, generating circadian rhythms does play most decisive role for temperature compensated period. Through analyzing the elasticity of free-running period with respect to reaction speed, we consider plausible sensitivity of each reaction to temperature, which generate temperature compensation of circadian period.