Abstract
The two-process model (2pm) of sleep regulation is not only a conceptual framework but consists of mathematical equations that have meaning and structure. Despite the apparent simplicity of its graphical representation, the mathematical structure of the 2pm is complex and falls within the wider class of coupled oscillator models. The structure of the 2pm is very similar to models that have been used to capture other physiological phenomena such as cardiac arrhythmias, breathing and the integrate-and-fire behaviour of neurons. The 2pm is also intimately related to neuronal mutual inhibition models for the alternation between sleep and wake. Here we discuss how the relationship between neuronal models of sleep regulation and the 2pm model provides new insights into the physiological interpretation of the circadian thresholds of the 2pm and parameter values. We analyse the mathematical structure of the 2pm and how this structure relates to sleep patterns observed in the absence of 24-h time cues, in different species and in early childhood. We discuss how extending the 2pm to include a light-circadian pacemaker process allows for quantitative modelling of the effects of artificial light on sleep duration and sleep timing relative to the 24 hour day. Overall, we highlight how understanding the mathematical structure of the 2pm and its extensions provides alternative, not immediately intuitive, perspectives on the drivers of sleep phenotypes. We show that changes in sleep timing and the phase relationship between sleep and circadian rhythms may occur not only as a result of changes in the circadian pacemaker but also as a result of changes in sleep homeostasis, neuronal processes associated with excitability or the light environment. Analysis of the mathematical structure of the 2pm brings the opportunity to quantitatively predict the effect of interventions to support sleep and circadian alignment in individuals of all ages, including those with neurodegenerative disorders.
Competing Interest Statement
The authors have declared no competing interest.