The complexity and commonness of the two-process model of sleep regulation from a mathematical perspective.

npj Biological Timing and Sleep Pub Date : 2025-01-01 Epub Date: 2025-06-18 DOI:10.1038/s44323-025-00039-z
Anne C Skeldon, Derk-Jan Dijk
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Abstract

The two-process model (2pm) of sleep regulation is a conceptual framework and consists of mathematical equations. It shares similarities with models for cardiac, respiratory and neuronal rhythms and falls within the wider class of coupled oscillator models. The 2pm is related to neuronal mutual inhibition models of sleep-wake regulation. The mathematical structure of the 2pm, in which the sleep-wake cycle is entrained to the circadian pacemaker, explains sleep patterns in the absence of 24 h time cues, in different species and in early childhood. Extending the 2pm with a process describing the response of the circadian pacemaker to light creates a hierarchical entrainment system with feedback which permits quantitative modelling of the effect of self-selected light on sleep and circadian timing. The extended 2pm provides new interpretations of sleep phenotypes and provides quantitative predictions of effects of sleep and light interventions to support sleep and circadian alignment in individuals, including those with neurodegenerative disorders.

从数学角度看睡眠调节双过程模型的复杂性与共性。
睡眠调节的两过程模型(2pm)是一个概念框架,由数学方程组成。它与心脏、呼吸和神经节律的模型有相似之处,属于更广泛的耦合振荡器模型。下午2点与睡眠-觉醒调节的神经元相互抑制模式有关。下午2点的睡眠-觉醒周期受昼夜节律起搏器支配的数学结构,解释了不同物种和儿童早期在没有24小时时间线索的情况下的睡眠模式。通过描述昼夜节律起搏器对光线的反应过程,将下午2点延长,从而创建了一个带有反馈的分层诱导系统,该系统允许对自我选择的光线对睡眠和昼夜节律时间的影响进行定量建模。延长的下午2点为睡眠表型提供了新的解释,并提供了睡眠和光照干预效果的定量预测,以支持个体的睡眠和昼夜节律一致性,包括那些患有神经退行性疾病的人。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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