Figure 1.
Basic concepts of entrainment (a) Schematic of a circadian rhythm entrained by 24 h LD cycles. The square-wave light cycles represent the zeitgeber cycle used in the experiments of this study also known as T-cycle. Note that upon complete entrainment, the phase angle relation between rhythmic variable and zeitgeber cycle is constant. (b) Schematic of the entrainment region where the oscillator period is locked to the external period in a 1∶1 relation. The entrainment region is dependent on zeitgeber period (T) and zeitgeber strength and is also known as 1∶1 Arnold tongue. For a constant zeitgeber strength, the entrainment region is confined between its lower (Tlow) and upper (Thigh) limit of entrainment. Outside the entrainment region, the oscillators show no stable phase relation. Within the entrainment region, the oscillator can be locked to shorter (22 h) and longer (26 h) than 24 h period. The oscillator state variable is typically plotted as a 24 h double-plotted actogram (c–e), i.e. with activity on day n followed by day n + 1 horizontally, succeeded by days n + 1 and n + 2 on the next line, etc. The actogram of an oscillator entrained to 22, 24 and 26 h typically shows positive slope, vertical and negative slope stripes, respectively. Within the entrainment region, the oscillator is locked to the external rhythm and thus the spectra of the oscillator state variable shows only one main component with the period of the zeitgeber (g–i). Thus, the spectral component for different zeitgeber periods leads to a line of slope one (f) and the normalized power of this unique component leads to a resonance-like curve (j). (c–j) was generated with the oscillator model discussed below. Further details are given in §9.