Synchronization-Induced Rhythmicity of Circadian Oscillators in the Suprachiasmatic Nucleus
Figure 4
Single-Cell Rhythmicity Implies Synchrony
(A–C) Phase space of a network of two oscillators showing possible dynamic behaviors. Each panel represents a condition that was simulated in the previous subsection. The inlets show what kind of coupling was considered (spirals, damped oscillators; solid arrows, normal coupling [K = 0.9]; dashed arrows, weak coupling [K = 0.3]; red and green arrows, paracrine and autocrine coupling, respectively). The axes show the differences of Per/Cry mRNA and PER/CRY complex concentrations between the two oscillators. This way, two oscillators can be represented in a 2-D space.
(A) Normal, wild-type condition. The oscillators are normally coupled (autocrine and paracrine coupling), and the result is a regular, clock-like cycle denoting synchrony.
(B) Dispersed condition. Oscillators with autocrine activation only are rhythmic, but quickly run out of phase. The result is an irregular cycle as phase differences are not constant.
(C) Weak coupling. Oscillators with weak paracrine and autocrine coupling damp out to a steady state.
(D) Stable steady state of Per/Cry mRNA under constant input. The minimal and maximal values of rhythmic input signals (variable X2) under normal coupling conditions are indicated by the dashed lines.
(E) Phase space of a single oscillator with constant input. Because the intracellular oscillator is 7-D, we had to reduce the phase space from seven to two dimensions, and we chose a projection plane for which the trajectory was closest to a spiral.