Figure 5.

A peripheral oscillator coupled in antiphase to the molecular clock. (a) Time curves of the second oscillator where the agents $\tilde{M}$, ${\tilde{P}}_0$, ${\tilde{P}}_1$, ${\tilde{P}}_2$ and ${\tilde{P}}_N$ fulfill analog equations corresponding to (1) to (5) where (2) is replaced by (11) and $\tilde{\alpha }=0.5$. (b) Time curve of the external stimulus u defined in (16), of M calculated from the model (1) to (5), of $\tilde{M}$ calculated by an analogous model like (1) to (5) where (2) is replaced by (11) with $\tilde{\alpha }=0.5$ and of $M^u$ calculated from (1) to (5) where (2) is replaced by (8) with $\alpha =1$ for (16). In (c) and (d) a peripheral oscillator coupled in phase to the molecular clock. (c) Time curves of the second oscillator where the agents $\tilde{M}$, ${\tilde{P}}_0$, ${\tilde{P}}_1$, ${\tilde{P}}_2$ and ${\tilde{P}}_N$ fulfill analog equations corresponding to (1) to (5) where (2) is replaced by (12) with $\tilde{\alpha }=0.5$, $\beta =2$. (d) Time curve of the external stimulus u defined in (16), of M calculated from the model (1) to (5), of $\tilde{M}$ calculated by an analogous model like (1) to (5) where (2) is replaced by (12) with $\tilde{\alpha }=0.5$, $\beta =2$ and of $M^u$ calculated from (1) to (5) where (2) is replaced by (8) with $\alpha =1$ for (16). In (e) the time curve of the external stimulus u defined in (16) where $M^u$ and $\tilde{M}$ are calculated as in (a) and (b). The quantity ${\tilde{M}}^p$ is calculated by an analogous model as $\tilde{M}$ where (11) is replaced by (13) with ${\alpha }^P=0.5$. After the transient, we have a shift of about 12.7 h between $M^u$ and $\tilde{M}$ and of about 15.8 h between $M^u$ and ${\tilde{M}}^p$. Units and dimensions: abscissa t: time in hours, ordinate U: amount of substance (M, $M^u$, $\tilde{M}$, ${\tilde{M}}^P$ mRNA, ${\tilde{P}}_i$, $\left\{0,,,1,,,2,,,N\right\},$ protein, u intensity of illumination).