Figure 3.

Simulation of the dynamics of Dbp, Per2, and Homer1a expression. (A) Simulation of the time course of Dbp (upper), Per2 (middle), and Homer1a (lower panel) expression in the brain. For Dbp and Per2, a driven and damped harmonic oscillator was assumed with as periodic driving force either the sleep-wake distribution (for Dbp: dark-gray signal at bottom of panel indicates minutes spent asleep in consecutive 5-min intervals) or the changes in plasma corticosterone levels (for Per2: dark-gray signal at bottom of panel, amplitude set to 1.0; see Figure 4). These recurrent forces initiate and set the phase of the circadian expression pattern in Dbp and Per2 (gray line) in baseline (see Methods and Results for details). For Dbp the force exerted during the four 6-h sleep deprivations (SDep; ZT0-6 orange; ZT6-12: yellow; ZT12-18: green; ZT18-24: blue) is zero as no sleep was present. For Per2 it was assumed that the force was the same for the 4 sleep deprivations and to follow a square-wave function, the amplitude of which was optimized by fitting to the empirical expression data. Simulations were run for 10 days prior to sleep-deprivation-onset in order to reach steady state oscillations (days 1-8 not shown). Changes in Homer1a expression were simulated according to the same assumption as EEG delta power (see Methods and Figure 5); i.e., expression increases during 4-s epochs scored as wakefulness and REMS and decreases during 4-s epochs scores as NREM sleep according to exponential saturating functions (gray line). The simulation presented was performed using the sleep-wake distribution of an individual mouse (dark-gray signal at bottom of graph; min of waking/5min interval). Gray and red symbols are the predicted expression levels at the timepoints the empirical samples were taken during baseline and after sleep deprivation, respectively (see Figure 1 and panels B). Light gray areas denote the dark periods. (B) Comparison of the predicted (left) and observed (right panel) expression levels for Dbp, Per2, and Homer1a. Empirical data were averaged for the 3 inbred strains (see Figure 1) during baseline (gray lines and symbols) and sleep deprivation (red dashed lines and symbols).