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Abstract We study the impact of light on the mammalian circadian system using the theory of phase response curves. Using a recently developed ansatz we derive a low-dimensional macroscopic model for the core circadian clock in mammals. Significantly, the variables and parameters in our model have physiological interpretations and may be compared with experimental results. We focus on the effect of four key factors which help shape the mammalian phase response to light: heterogeneity in the population of oscillators, the structure of the typical light phase response curve, the fraction of oscillators which receive direct light input and changes in the coupling strengths associated with seasonal day-lengths. We find these factors can explain several experimental results and provide insight into the processing of light information in the mammalian circadian system. In particular, we find that the sensitivity of the circadian system to light may be modulated by changes in the relative coupling forces between the light sensing and non-sensing populations. Finally, we show how seasonal day-length, after-effects to light entrainment and seasonal variations in light sensitivity in the mammalian circadian clock are interrelated. 

Abstract Study Objectives Examine the ability of a physiologically based mathematical model of human circadian rhythms to predict circadian phase, as measured by salivary dim light melatonin onset (DLMO), in children compared to other proxy measurements of circadian phase (bedtime, sleep midpoint, and wake time). Methods As part of an ongoing clinical trial, a sample of 29 elementary school children (mean age: 7.4 ± .97 years) completed 7 days of wrist actigraphy before a lab visit to assess DLMO. Hourly salivary melatonin samples were collected under dim light conditions (<5 lx). Data from actigraphy were used to generate predictions of circadian phase using both a physiologically based circadian limit cycle oscillator mathematical model (Hannay model), and published regression equations that utilize average sleep onset, midpoint, and offset to predict DLMO. Agreement of proxy predictions with measured DLMO were assessed and compared. Results DLMO predictions using the Hannay model outperformed DLMO predictions based on children’s sleep/wake parameters with a Lin’s Concordance Correlation Coefficient (LinCCC) of 0.79 compared to 0.41–0.59 for sleep/wake parameters. The mean absolute error was 31 min for the Hannay model compared to 35–38 min for the sleep/wake variables. Conclusion Our findings suggest that sleep/wake behaviors were weak proxies of DLMO phase in children, but mathematical models using data collected from wearable data can be used to improve the accuracy of those predictions. Additional research is needed to better adapt these adult models for use in children. Clinical Trial The i Heart Rhythm Project: Healthy Sleep and Behavioral Rhythms for Obesity Prevention https://clinicaltrials.gov/ct2/show/NCT04445740. 

Mathematical models have a long and influential history in the study of human circadian rhythms. Accurate predictive models for the human circadian light response have been used to study the impact of a host of light exposures on the circadian system. However, generally, these models do not account for the physiological basis of these rhythms. We illustrate a new paradigm for deriving models of the human circadian light response. Beginning from a high-dimensional model of the circadian neural network, we systematically derive low-dimensional models using an approach motivated by experimental measurements of circadian neurons. This systematic reduction allows for the variables and parameters of the derived model to be interpreted in a physiological context. We fit and validate the resulting models to a library of experimental measurements. Finally, we compare model predictions for experimental measurements of light levels and discuss the differences between our model’s predictions and previous models. Our modeling paradigm allows for the integration of experimental measurements across the single-cell, tissue, and behavioral scales, thereby enabling the development of accurate low-dimensional models for human circadian rhythms.