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Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics
Fig 2
A light driven network of two coupled phase oscillators, representing the Per and Bmal-Rev loops, is able to reproduce experimental free-running and light perturbation data.
A) Illustration of the phase oscillator concept. B) Schematic drawing of our conceptual model of light-driven, interlocked intra-cellular feedback loops. C) Isoclines of constant phase difference between the Per and the Bmal-Rev loops, color-coded for different values of β. Black lines denote the borders of synchronization between the Per and Bmal-Rev loops as determined by Eq (4) in Section Materials and Methods. Isoclines of constant Δθ⋆ = −0.7π, corresponding to the experimentally observed phase difference of approximately 9 h between Per1 and Bmal1 expression in the time domain, are plotted and color-coded for different values of β, ranging from 
to 
in 20 equidistant steps. The experimentally observed oscillation period τ⋆ ≈ 24.53h and phase difference has been estimated by cosine fits to Per1 and Bmal1 circadian gene expressions from high-throughput transcriptome data of 48h length at 2h sampling intervals [33], see S3 Fig. General distributions of phase differences Δθ⋆ within the range of synchronization between Per and Bmal-Rev loops for different values of β are depicted in S4 Fig D) Dynamics of experimentally observed Per1 and Bmal1 gene expression rhythms can be reproduced by the concpetual oscillator model. Bold lines denote the cosine of oscillation phases θP(t) and θR(t) of the corresponding Per and Bmal-Rev loop. E) Weakly coupled Per and Bmal-Rev loops can account for a faster re-entrainment of Per1 compared to Bmal1 gene expression oscillations after a 6h phase advancing jet-lag.
doi: https://doi.org/10.1371/journal.pcbi.1007330.g002