Figure 2.

The model of Goldbeter including our extension does not differ from the original model of Goldbeter if the molecular clock is in the phase of the external Zeitgeber. (a) Time curves where the superscript u indicates that these time curves stem from the extended model consisting of (6) and (2) to (5) with (7) for $\phi =0$ and $\alpha =0.05$. (b) Time curve of the external stimulus u defined in (7), of M calculated from the model (1) to (5) and of $M^u$ calculated from (6) and (2) to (5) with (7) for $\phi =0$ and $\alpha =0.05$. For the figure (c) and (d) the external stimulus induces a shift of the molecular clock’s phase of 12 h where the experiment is as in (a) and (b) but with $\phi =\pi$. The external stimulus induces a shift of the molecular clock’s phase of about 6 h in (e) and (f) where the experiment is as in (a) and (b) with $\phi =\frac{\pi }{2}$. Units and and dimensions: abscissa t: time in hours, ordinate U: amount of substance (M, $M^u$ mRNA, $P_i^u$, $\left\{0,,,1,,,2,,,N\right\},$ protein, u intensity of illumination).