Owls, larks and tongues – sleep timing in the two-process model of sleep-wake regulation #

Rachel Bernasconi, Derk-Jan Dijk, Anne Skeldon

11:50 Wednesday in 2Q42.

Part of the Mathematical modelling of sleep and circadian rhythms: from molecular mechanisms to policy session.

Abstract #

NOTE: This talk replaces the previously-scheduled talk by Abishek Upadhyay et al., which has been cancelled. It has then moved from the start of this MS to talk 5.

Rachel Bernasconi: 1 ; Derk-Jan Dijk: 2,3 ; Anne Skeldon: 1,3 1Department of Mathematics, University of Surrey, Guildford, UK 2Surrey Sleep Research Centre, Department of Clinical and Experimental Medicine, University of Surrey, Guildford, UK 3UK Dementia Research Institute, Care Research and Technology Centre at Imperial College, London and the University of Surrey, Guildford, UK

The average person is estimated to spend a third of their life asleep. Despite this, a large proportion of the population regularly experience insufficient sleep or suffer from sleep disorders. These have been linked to poorer health outcomes, with a multinational survey by RAND suggesting inadequate sleep increases mortality by up to 13%. The complexity and importance of sleep means that interdisciplinary approaches including mathematical modelling are valuable to develop insight. Since its formulation in the early 1980s, the two-process model of sleep-wake regulation has been at the forefront of sleep modelling. The model suggests that two oscillators – one capturing the daily cycle of the body’s ‘clock’ system and the other representing sleep need – interact to generate sleep/wake rhythms. The two-process model has provided many insights into both the overall patterns of sleep and how performance is affected when we are sleep deprived. However, there remain aspects of sleep that have not yet been described using the two-process framework. For example, preferred sleep timing varies across the population, from ‘early birds’ (larks) to ‘night owls’. While a full explanation of these preferences requires the addition of another oscillator describing the interaction of the sleep-wake regulatory system with light, we will show that the original two-process model can replicate the experimental observation that larks wake up at a later time in their biological clock than owls. Specifically, we derive expressions for the relative phase of the two oscillators in the two-process model and relate them to the underpinning Arnold ‘tongue’ structure that captures when sleep and the body clock are synchronised. Our work is of biological significance as it not only allows us to reproduce variations in sleep phase across healthy individuals like larks and owls, but also provides the groundwork for study into various disease states where poorly timed sleep is a contributing factor.