A molecular model for intercellular synchronization in the mammalian circadian clock

Abstract

The mechanisms and consequences of synchrony among heterogeneous oscillators are poorly understood in biological systems. We present a multicellular, molecular model of the mammalian circadian clock that incorporates recent data implicating the neurotransmitter vasoactive intestinal polypeptide (VIP) as the key synchronizing agent. The model postulates that synchrony arises among circadian neurons because they release VIP rhythmically on a daily basis and in response to ambient light. Two basic cell types, intrinsically rhythmic pacemakers and damped oscillators, are assumed to arise from a distribution of Period gene transcription rates. Postsynaptic neurons show time-of-day dependent responses to VIP binding through a signaling cascade that activates Period mRNA transcription. The heterogeneous cell ensemble model self-synchronizes, entrains to ambient light-dark cycles, and desynchronizes in constant bright light or upon removal of VIP signaling. The degree of synchronicity observed depends on cell-specific features (e.g., mean and variability of parameters within the rhythm-generating loop), in addition to the more commonly studied effect of intercellular coupling strength. These simulations closely replicate experimental data and predict that heterogeneous oscillations (e.g., sustained, damped, and arrhythmic) arise from small differences in the molecular parameters between cells, that damped oscillators participate in entrainment and synchrony of the ensemble of cells, and that constant light desynchronizes oscillators by maximizing VIP release.

FIGURE 1

Schematic of the mechanisms modeled to generate and synchronize circadian rhythms in the SCN. A core transcription-translation negative feedback loop provides the drive on rhythmic communication between cells and responds to synchronizing signals from neighboring cells. Within this loop, two transcription factors (CLOCK and BMAL1) form dimers to activate transcription of the Per gene. This activation is rhythmically suppressed and restored approximately every 24 h as the inhibitory PER and CRY proteins accumulate and then degrade. One hypothesized output of this clockwork is the circadian regulation of VIP release. VIP binds to the G-protein coupled receptor, VPAC2, to increase intracellular calcium and activate CREB. At specific phases in the circadian cycle, activated CREB induces Per transcription and shifts the phase of the circadian clock. Increases in intracellular calcium also mediate the phase-resetting effects of light and the release of available VIP. In a light-dark cycle, VIP was assumed to be constitutively released throughout the light phase. In constant darkness, VIP release was assumed to be controlled by intracellular Per mRNA levels.

FIGURE 2

Weight factors used for the coupling of neurons placed on a two-dimensional grid. The solid circle represents the neuron of interest and has a weight factor of 1 on itself. The other weight factors are assumed to be inversely proportional to the distance away from the neuron of interest.

FIGURE 3

Synchronization of circadian neurons under constant darkness. The basal transcription rate of Per mRNA was subjected to a zero mean, normally distribution perturbation to obtain a desired fraction of neurons that display sustained oscillations in the absence of VIP signaling. Variations in the free-running periods of these intrinsic oscillators were generated by introducing zero mean, normally distributed perturbations to eight kinetic parameters in the core oscillator. (A) The fraction of intrinsically rhythmic cells versus the standard deviation in the Per mRNA basal transcription rate for ensembles of 100 neurons. The eight kinetic parameters were subjected to perturbation with a standard deviation of 10%. The error bars indicate the standard deviation in the rhythmic cell fraction across 10 runs. (B) The average period of the intrinsically rhythmic cells versus the standard deviation in the kinetic parameter for ensembles of 100 neurons. The Per mRNA basal transcription rate was subjected to perturbation with a standard deviation of 10%. The error bars indicate the standard deviation in the mean period across 10 runs. (C) Population synchronization dynamics of 400 circadian neurons when the Per mRNA basal transcription rate and the kinetic parameters were subjected to perturbations with a standard deviation of 10%. The population synchronized in the presence of VIP signaling despite the highly asynchronous initial state and the lack of photic input. (D) A high degree of synchrony (SI > 0.8) was obtained after three oscillation cycles (∼80 h).

FIGURE 4

Effect of random perturbations in the core oscillator on the synchronization of circadian neurons under constant darkness. Eight core oscillator parameters were subjected to zero mean, normally distributed perturbations with standard deviations of 0%, 10%, 20%, 30%, or 80%. Additionally, the basal transcription rate of Per mRNA was perturbed with a standard deviation of 10% such that ∼40% of the neurons were intrinsic oscillators. (A) The synchronization index is shown at zero time for the uncoupled population and at nine cycles for the coupled population of 400 neurons. The population failed to achieve substantial synchronization (SI > 0.6) for standard deviations >30%. (B) The distribution of periods is shown at zero time for the intrinsic oscillators in the uncoupled populations and at the ninth cycle for all cells in the coupled populations. VIP signaling increased the mean period and reduced the standard deviation of the period distribution. (C) The synchronization index (SI) at the ninth cycle and the order parameter (R) from the last five cycles versus the standard deviation in the kinetics parameters k₁–k₈ for ensembles of 100 neurons. The error bars indicate standard deviations across 10 independent runs.

FIGURE 5

Effect of eliminating VIP signaling on the synchronization of 400 neurons under constant darkness. Cellular heterogeneities were introduced as in Fig. 3. The initial cell state was generated by simulating the cell ensemble until a high degree of synchrony was achieved. To mimic the loss of VIP signaling, the extent of VPAC2 saturation was set to zero at t = 72 h. (A) Approximately 60% of the neurons failed to exhibit rhythmicity after two cycles following elimination of VIP signaling. Synchrony was disrupted in the remaining 40% of rhythmic neurons. (B) When averaged across the cell population, the expression of Per and Bmal1 mRNAs decreased and the expression of Cry mRNA increased following the loss of VIP signaling. (C) The synchronization index (SI) showed that the population lost phase coherence after removal of VIP signaling.

FIGURE 6

Effect of VIP agonist on the synchronization of 400 VIP −/− neurons under constant darkness. Cellular heterogeneities were introduced as in Fig. 3. The maximum VIP release rate was set to zero for each neuron, thereby eliminating VIP signaling. As a result, only ∼40% of the neurons displayed circadian rhythms. Daily pulses of VIP agonist were mimicked by setting the extent of VPAC2 saturation to its maximum value of unity when the agonist was applied (t = 48, 72, 96, 120, and 144 h). The agonist was assumed to be provided in excess and to have an effect that lasted 3 h. (A) Daily agonist applications induced rhythmicity in most neurons and resulted in synchronization of the cell population. Single neuron rhythmicity was maintained following the elimination of agonist pulses at t = 144 h. (B) When averaged across the cell population, the expression of Bmal1 mRNA increased and the expression of Per and Cry mRNAs was maintained constant following the removal of agonist pulses. (C) The synchronization index (SI) showed that population synchrony was slowly lost following the elimination of agonist pulses.

FIGURE 7

The effect of photic input on the synchronization of 400 neurons. Cellular heterogeneities were introduced as in Fig. 3. (A) Synchronization dynamics under repeated light-dark cycles implemented by imposing a square wave in the light-induced calcium stimulus. During the light phase, the VPAC2 receptors were saturated due to the constitutive release of VIP. The Per mRNA level peaked during the day, and a higher degree of synchrony was achieved than in constant darkness. (B) Synchronization dynamics under constant bright light implemented by setting the light-induced calcium stimulus and the extent of VPAC2 saturation to their maximum values. Although all the individual cells remained rhythmic, population synchrony was strongly disrupted. (C) The synchronization index (SI) showed that population synchrony was enhanced by light-dark cycles and lost during constant light.