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Abstract From smart work scheduling to optimal drug timing, there is enormous potential in translating circadian rhythms research results for precision medicine in the real world. However, the pursuit of such effort requires the ability to accurately estimate circadian phase outside of the laboratory. One approach is to predict circadian phase noninvasively using light and activity measurements and mathematical models of the human circadian clock. Most mathematical models take light as an input and predict the effect of light on the human circadian system. However, consumer-grade wearables that are already owned by millions of individuals record activity instead of light, which prompts an evaluation of the accuracy of predicting circadian phase using motion alone. Here, we evaluate the ability of four different models of the human circadian clock to estimate circadian phase from data acquired by wrist-worn wearable devices. Multiple datasets across populations with varying degrees of circadian disruption were used for generalizability. Though the models we test yield similar predictions, analysis of data from 27 shift workers with high levels of circadian disruption shows that activity, which is recorded in almost every wearable device, is better at predicting circadian phase than measured light levels from wrist-worn devices when processed by mathematical models. In those living under normal living conditions, circadian phase can typically be predicted to within 1 h, even with data from a widely available commercial device (the Apple Watch). These results show that circadian phase can be predicted using existing data passively collected by millions of individuals with comparable accuracy to much more invasive and expensive methods. 

Which suggestions for behavioral modifications, based on mathematical models, are most likely to be followed in the real world? We address this question in the context of human circadian rhythms. Jet lag is a consequence of the misalignment of the body’s internal circadian (~24-hour) clock during an adjustment to a new schedule. Light is the clock’s primary synchronizer. Previous research has used mathematical models to compute light schedules that shift the circadian clock to a new time zone as quickly as possible. How users adjust their behavior when provided with these optimal schedules remains an open question. Here, we report data collected by wearables from more than 100 travelers as they cross time zones using a smartphone app, Entrain . We find that people rarely follow the optimal schedules generated through mathematical modeling entirely, but travelers who better followed the optimal schedules reported more positive moods after their trips. Using the data collected, we improve the optimal schedule predictions to accommodate real-world constraints. We also develop a scheduling algorithm that allows for the computation of approximately optimal schedules "on-the-fly" in response to disruptions. User burnout may not be critically important as long as the first parts of a schedule are followed. These results represent a crucial improvement in making the theoretical results of past work viable for practical use and show how theoretical predictions based on known human physiology can be efficiently used in real-world settings. 

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 Background Gene-set analyses measure the association between a disease of interest and a “set" of genes related to a biological pathway. These analyses often incorporate gene network properties to account for differential contributions of each gene. We extend this concept further—defining gene contributions based on biophysical properties—by leveraging mathematical models of biology to predict the effects of genetic perturbations on a particular downstream function. Results We present a method that combines gene weights from model predictions and gene ranks from genome-wide association studies into a weighted gene-set test. We demonstrate in simulation how such a method can improve statistical power. To this effect, we identify a gene set, weighted by model-predicted contributions to intracellular calcium ion concentration, that is significantly related to bipolar disorder in a small dataset (P = 0.04; n = 544). We reproduce this finding using publicly available summary data from the Psychiatric Genomics Consortium (P = 1.7 × 10−4; n = 41,653). By contrast, an approach using a general calcium signaling pathway did not detect a significant association with bipolar disorder (P = 0.08). The weighted gene-set approach based on intracellular calcium ion concentration did not detect a significant relationship with schizophrenia (P = 0.09; n = 65,967) or major depression disorder (P = 0.30; n = 500,199). Conclusions Together, these findings show how incorporating math biology into gene-set analyses might help to identify biological functions that underlie certain polygenic disorders. 

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. 

Multisite phosphorylation of the PERIOD 2 (PER2) protein is the key step that determines the period of the mammalian circadian clock. Previous studies concluded that an unidentified kinase is required to prime PER2 for subsequent phosphorylation by casein kinase 1 (CK1), an essential clock component that is conserved from algae to humans. These subsequent phosphorylations stabilize PER2, delay its degradation, and lengthen the period of the circadian clock. Here, we perform a comprehensive biochemical and biophysical analysis of mouse PER2 (mPER2) priming phosphorylation and demonstrate, surprisingly, that CK1δ/ε is indeed the priming kinase. We find that both CK1ε and a recently characterized CK1δ2 splice variant more efficiently prime mPER2 for downstream phosphorylation in cells than the well-studied splice variant CK1δ1. While CK1 phosphorylation of PER2 was previously shown to be robust to changes in the cellular environment, our phosphoswitch mathematical model of circadian rhythms shows that the CK1 carboxyl-terminal tail can allow the period of the clock to be sensitive to cellular signaling. These studies implicate the extreme carboxyl terminus of CK1 as a key regulator of circadian timing.