Hypothesis and Theory: A Two-Process Model of Torpor-Arousal Regulation in Hibernators

Hibernating mammals drastically lower their metabolic rate (MR) and body temperature (T_b) for up to several weeks, but regularly rewarm and stay euthermic for brief periods. It has been hypothesized that the necessity for rewarming is due to the accumulation or depletion of metabolites, or the accrual of cellular damage that can be eliminated only in the euthermic state. Recent evidence for significant inverse relationships between the duration of torpor bouts (TBD) and MR in torpor strongly supports this hypothesis. We developed a new mathematical model that simulates hibernation patterns. The model involves an hourglass process H (Hibernation) representing the depletion/accumulation of a crucial enzyme/metabolite, and a threshold process H_thr. Arousal, modelled as a logistic process, is initiated once the exponentially declining process H reaches H_thr. We show that this model can predict several phenomena observed in hibernating mammals, namely the linear relationship between TMR and TBD, effects of ambient temperature on TBD, the modulation of torpor depth and duration within the hibernation season, (if process H_thr undergoes seasonal changes). The model does not need but allows for circadian cycles in the threshold T, which lead to arousals occurring predominantly at certain circadian phases, another phenomenon that has been observed in certain hibernators. It does not however, require circadian rhythms in T_b or MR during torpor. We argue that a two-process regulation of torpor-arousal cycles has several adaptive advantages, such as an easy adjustment of TBD to environmental conditions as well as to energy reserves and, for species that continue to forage, entrainment to the light-dark cycle.