Model integration of circadian and sleep-wake driven contributions to rhythmic gene expression reveals novel regulatory principles

Transcriptome studies aim at gaining insight into the molecular pathways underlying biological processes. Analyses of gene-expression dynamics in research on circadian rhythms and sleep homeostasis describe these two processes independently, using separate models such as sinusoidal oscillations and exponential saturating functions. Rhythmically expressed genes are, however, influenced by both processes. We therefore implemented a driven, damped harmonic oscillator model which can accommodate both types of dynamics by varying the degree of damping. This makes it possible to estimate the contribution of circadian and sleep-wake driven influences on the expression of a gene within the framework of a single model. We applied the model to cortex, liver, and blood data obtained in mice and humans. The model reliably captured a wide range of rhythmic dynamics under various experimental conditions, including the long-term amplitude reduction of cortical clock-gene rhythms observed after sleep deprivation. Cortical gene expression was generally influenced more by sleep-wake driven than circadian factors, while the opposite was observed in liver and blood. Importantly, the model suggested that sleep-wake state can alter gene expression with a delayed, long-lasting response not previously considered. Our model further predicted that, perhaps paradoxically, the gain in sleep time after sleep deprivation, delayed re-establishing baseline expression rhythms of intrinsically oscillatory transcripts indicating that similar to insufficient sleep, also excess sleep can impact rhythmic gene expression. Because of the tissue- and gene-specific responses, sleep deprivation led to a profound intra- and inter-tissue desynchronization which in the cortex lasted well beyond phenotypic sleep-wake recovery. The results demonstrate that analyzing rhythmic gene expression must take the complex interactions between circadian and sleep-wake influences into account. The model is a versatile tool with a low number of free parameters to fit and predict gene expression under a variety of conditions relevant to society. ### Competing Interest Statement The authors have declared no competing interest.