Figure 1.
Schematic representation of the SCN neuron model.
The gene expression model was obtained from a published study by Leloup and Goldbeter (2003), whereas the intracellular calcium model was adapted from Goldbeter et. al (1990). VIP expressed as a function of firing frequency was responsible for the rhythmic release of GABA. Because our model describes a single SCN cell, we assumed that the VIP and GABA concentrations acting on the cell membrane were the same as the released concentrations. In that sense our model assumes autocrine responses. The signaling cascade that activates Per transcription was adapted from To et. al (2007) to include the effects of intracellular calcium. Extracellular post-synaptic currents involve AMPA and NMDA receptors activated in a constant phase relationship to the Na+ and Ca2+ concentrations, respectively.
Figure 2.
Oscillatory profiles of individual cellular clocks.
Rhythmic profiles of the potassium (A), sodium (B), calcium (C), Ca2+-activated potassium (D), excitatory (E) and inhibitory (F) currents. Intracellular calcium (G), Per mRNA (H) and the firing rate (I) also displayed oscillations that peaked during the subjective day. The arrows in Fig. 2G denote CT 1.5, which is the time Cain peaks. The gray and black bars on the top of each figure represent the alternation between the subjective day (gray) and night (black) that compose a 24h circadian cycle in constant darkness.
Table 1.
Circadian phase of SCN model components relative to a calcium peak at CT 1.5.
Figure 3.
Intracellular calcium dynamics affect the circadian oscillatory behavior.
Circadian profiles of the firing rate (A), intracellular calcium concentration (C) and Per mRNA concentration (D) are shown for the control (black line), ryanodine blockade (red dashed line) and nimodipine application (blue dotted line). B). % decrease in the firing rate, Per mRNA concentration, Ca2+ current (ICa) and cytosolic calcium concentration during the circadian night (green bars) and day (red bars) as a result of ryanodine blockade. E) % decrease in the firing rate, Per mRNA concentration, Ca2+ current (ICa) and Ca2+ -activated K+ current (IKCa) during the circadian night (green bars) and day (red bars) as a result of nimodipine application. ** denotes very small changes of the perturbed value compared to the control.
Figure 4.
GABA concentrations affect the circadian oscillatory behavior.
A). % IPSC change during the subjective night (black solid line) and day (red dashed line) as a function of % GABA decrease B). % firing frequency change during the subjective night (black solid line) and day (red dashed line) as a function of % GABA decrease. C) % IPSC change during the subjective night (black solid line) and day (red dashed line) as a function of % GABA increase. D). % firing frequency change during subjective night (black solid line) and day (red dashed line) as a function of % GABA increase. E). Circadian profiles of the firing frequency are shown for the control (black line), complete GABA blockade (red dotted line) and maximum GABA application (blue dashed line).
Figure 5.
Effects of VIP on circadian rhythmicity.
Circadian profiles of firing rate (A) and Per mRNA (B) for the control (black line), VIP blockade (red dashed line) and VIP application (blue dotted line). C) % amplitude decrease in firing rate, Per mRNA and IPSCs as a result of VIP blockade. D) % amplitude increase in firing rate, Per mRNA and IPSCs as a result of VIP application.
Figure 6.
Cytosolic calcium levels regulate circadian behavior.
Circadian profiles of Per mRNA (A) and firing rate (B) are shown for the control (black line), 50% reduced cytosolic Ca2+ concentration (red dashed line) and 50% increased cytosolic Ca2+ concentration (blue dotted line) compared to the control. C). Per mRNA (red dashed line) and firing rate (black solid line) amplitudes as a function of the cytosolic calcium concentration. D). The period of the core oscillator as a function of the cytosolic calcium concentration. The circles in 6C and 6D represent nominal values of the model.
Figure 7.
Correlating electrophysiology with gene expression.
A). Mean firing rate (black solid line) and mean VIP concentration (red dashed line) as a function of the applied extracellular current (I). B). Mean VIP concentration (red dashed line) and mean Per mRNA levels (black solid line) versus the mean firing rate.
Table 2.
Model parameter values.
Table 3.
Initial conditions of the 20 ODEs characterizing the single cell model.