Impact of Light Schedules and Model Parameters on the Circadian Outcomes of Individuals.

Key differences exist between individuals in terms of certain circadian-related parameters, such as intrinsic period and sensitivity to light. These variations can differentially impact circadian timing, leading to challenges in accurately implementing time-sensitive interventions. In this work, we parse out these effects by investigating the impact of parameters from a macroscopic model of human circadian rhythms on phase and amplitude outputs. Using in silico light data designed to mimic commonly studied schedules, we assess the impact of parameter variations on model outputs to gain insight into the different effects of these schedules. We show that parameter sensitivity is heavily modulated by the lighting routine that a person follows, with darkness and shift work schedules being the most sensitive. We develop a framework to measure overall sensitivity levels of the given light schedule and furthermore decompose the overall sensitivity into individual parameter contributions. Finally, we measure the ability of the model to extract parameters given light schedules with noise and show that key parameters like the circadian period can typically be recovered given known light history. This can inform future work on determining the key parameters to consider when personalizing a model and the lighting protocols to use when assessing interindividual variability.

Validation of the Entrainment Signal Regularity Index and associations with children's changes in BMI.

OBJECTIVE: This study examined the validity of a novel metric of circadian health, the Entrainment Signal Regularity Index (ESRI), and its relationship to changes in BMI during the school year and summer. METHODS: In a longitudinal observational data set, this study examined the relationship between ESRI score and children's (n = 119, 5- to 8-year-olds) sleep and physical activity levels during the school year and summer, differences in ESRI score during the school year and summer, and the association of ESRI score during the school year and summer with changes in BMI across those time periods. RESULTS: The ESRI score was higher during the school year (0.70 ± 0.10) compared with summer (0.63 ± 0.11); t(111) = 5.484, p < 0.001. Whereas the ESRI score at the beginning of the school year did not significantly predict BMI change during the school year (ß = 0.05 ± 0.09 SE, p = 0.57), having a higher ESRI score during summer predicted smaller increases in BMI during summer (ß = -0.22 ± 0.10 SE, p = 0.03). CONCLUSIONS: Overall, children demonstrated higher entrainment regularity during the school year compared with the summer. During summer, having a higher entrainment signal was associated with smaller changes in summertime BMI. This effect was independent of the effects of children's sleep midpoint, sleep regularity, and physical activity on children's BMI.

Estimating circadian phase in elementary school children: leveraging advances in physiologically informed models of circadian entrainment and wearable devices.

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.

Seasonality and light phase-resetting in the mammalian circadian rhythm.

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.

Integrating wearable data into circadian models.

The emergence of wearable health sensors in the last decade has the potential to revolutionize the study of sleep and circadian rhythms. In particular, recent progress has been made in the use of mathematical models in the prediction of a patient's internal circadian state using data measured by wearable devices. This is a vital step in our ability to identify optimal circadian timing for health interventions. We review the available data for fitting circadian phase models with a focus on wearable data sets. Finally, we review the current modeling paradigms and explore avenues for developing personalized parameter sets in limit cycle oscillator models in order to further improve prediction accuracy.

Macroscopic Models for Human Circadian Rhythms.

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.

Potential circadian and circannual rhythm contributions to the obesity epidemic in elementary school age children.

Children gain weight at an accelerated rate during summer, contributing to increases in the prevalence of overweight and obesity in elementary-school children (i.e., approximately 5 to 11 years old in the US). Int J Behav Nutr Phys Act 14:100, 2017 explained these changes with the "Structured Days Hypothesis" suggesting that environmental changes in structure between the school year and the summer months result in behavioral changes that ultimately lead to accelerated weight gain. The present article explores an alternative explanation, the circadian clock, including the effects of circannual changes and social demands (i.e., social timing resulting from societal demands such as school or work schedules), and implications for seasonal patterns of weight gain. We provide a model for understanding the role circadian and circannual rhythms may play in the development of child obesity, a framework for examining the intersection of behavioral and biological causes of obesity, and encouragement for future research into bio-behavioral causes of obesity in children.

Macroscopic models for networks of coupled biological oscillators.

The study of synchronization of coupled biological oscillators is fundamental to many areas of biology including neuroscience, cardiac dynamics, and circadian rhythms. Mathematical models of these systems may involve hundreds of variables in thousands of individual cells resulting in an extremely high-dimensional description of the system. This often contrasts with the low-dimensional dynamics exhibited on the collective or macroscopic scale for these systems. We introduce a macroscopic reduction for networks of coupled oscillators motivated by an elegant structure we find in experimental measurements of circadian protein expression and several mathematical models for coupled biological oscillators. The observed structure in the collective amplitude of the oscillator population differs from the well-known Ott-Antonsen ansatz, but its emergence can be characterized through a simple argument depending only on general phase-locking behavior in coupled oscillator systems. We further demonstrate its emergence in networks of noisy heterogeneous oscillators with complex network connectivity. Applying this structure, we derive low-dimensional macroscopic models for oscillator population activity. This approach allows for the incorporation of cellular-level experimental data into the macroscopic model whose parameters and variables can then be directly associated with tissue- or organism-level properties, thereby elucidating the core properties driving the collective behavior of the system.

Collective phase response curves for heterogeneous coupled oscillators.

Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakaguchi-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.

Buffering by gene duplicates: an analysis of molecular correlates and evolutionary conservation.

BACKGROUND: One mechanism to account for robustness against gene knockouts or knockdowns is through buffering by gene duplicates, but the extent and general correlates of this process in organisms is still a matter of debate. To reveal general trends of this process, we provide a comprehensive comparison of gene essentiality, duplication and buffering by duplicates across seven bacteria (Mycoplasma genitalium, Bacillus subtilis, Helicobacter pylori, Haemophilus influenzae, Mycobacterium tuberculosis, Pseudomonas aeruginosa, Escherichia coli), and four eukaryotes (Saccharomyces cerevisiae (yeast), Caenorhabditis elegans (worm), Drosophila melanogaster (fly), Mus musculus (mouse)). RESULTS: In nine of the eleven organisms, duplicates significantly increase chances of survival upon gene deletion (P-value < or = 0.05), but only by up to 13%. Given that duplicates make up to 80% of eukaryotic genomes, the small contribution is surprising and points to dominant roles of other buffering processes, such as alternative metabolic pathways. The buffering capacity of duplicates appears to be independent of the degree of gene essentiality and tends to be higher for genes with high expression levels. For example, buffering capacity increases to 23% amongst highly expressed genes in E. coli. Sequence similarity and the number of duplicates per gene are weak predictors of the duplicate's buffering capacity. In a case study we show that buffering gene duplicates in yeast and worm are somewhat more similar in their functions than non-buffering duplicates and have increased transcriptional and translational activity. CONCLUSION: In sum, the extent of gene essentiality and buffering by duplicates is not conserved across organisms and does not correlate with the organisms' apparent complexity. This heterogeneity goes beyond what would be expected from differences in experimental approaches alone. Buffering by duplicates contributes to robustness in several organisms, but to a small extent--and the relatively large amount of buffering by duplicates observed in yeast and worm may be largely specific to these organisms. Thus, the only common factor of buffering by duplicates between different organisms may be the by-product of duplicate retention due to demands of high dosage.