A Theoretical Study of Glucagon-Mediated Feedback in the Mammalian Circadian Clock

The circadian clock is closely linked to glucose regulation, but the dynamical consequences of specific metabolic feedback pathways on core clock regulation remain incompletely understood. In this study, we developed a theoretical metabolic-circadian model incorporating a REV-ERBα-glucagon-glucose feedback pathway. The model extends a previously established mammalian circadian clock framework by introducing glucagon-mediated regulation of blood glucose and glucose-dependent modulation of Rev-erbα transcription. Using this model, we examined how the feedback pathway affects circadian oscillations, the sensitivity of period and amplitude to parameter perturbations, and phase-related responses under light stimulation and light–dark cycles. Simulations of the feedback-related parameters showed that the glucose-to-clock feedback strength had a marked effect on oscillation period and amplitude, motivating a further assessment of whether regular circadian dynamics were preserved under parameter perturbations. We therefore analyzed both one-parameter perturbations and simultaneous perturbations of all model parameters. For one-parameter scans, we quantified not only the oscillatory boundaries but also the period variation and the amplitude variation of Per and Rev-erbα within the oscillatory ranges. For simultaneous all-parameter perturbations, Latin hypercube sampling was used to compare coupled and uncoupled models under bounded perturbation ranges. The coupled model showed a higher fraction of regular circadian oscillations under local perturbations, mainly by reducing the probability of rhythm loss. We further examined phase responses and light–dark entrainment to assess how the feedback affects dynamical properties beyond period and amplitude. In the phase-response analysis, the feedback reduced excessive phase shifts in the model, suggesting a possible phase-response robustness effect in this theoretical framework. These theoretical results suggest that the REV-ERBα-glucagon-glucose feedback pathway may be relevant to circadian regulation under fasting-associated metabolic conditions.