A dual-feedback loop model of the mammalian circadian clock for multi-input control of circadian phase.

The molecular circadian clock is driven by interlocked transcriptional-translational feedback loops, producing oscillations in the expressions of genes and proteins to coordinate the timing of biological processes throughout the body. Modeling this system gives insight into the underlying processes driving oscillations in an activator-repressor architecture and allows us to make predictions about how to manipulate these oscillations. The knockdown or upregulation of different cellular components using small molecules can disrupt these rhythms, causing a phase shift, and we aim to determine the dosing of such molecules with a model-based control strategy. Mathematical models allow us to predict the phase response of the circadian clock to these interventions and time them appropriately but only if the model has enough physiological detail to describe these responses while maintaining enough simplicity for online optimization. We build a control-relevant, physiologically-based model of the two main feedback loops of the mammalian molecular clock, which provides sufficient detail to consider multi-input control. Our model captures experimentally observed peak to trough ratios, relative abundances, and phase differences in the model species, and we independently validate this model by showing that the in silico model reproduces much of the behavior that is observed in vitro under genetic knockout conditions. Because our model produces valid phase responses, it can be used in a model predictive control algorithm to determine inputs to shift phase. Our model allows us to consider multi-input control through small molecules that act on both feedback loops, and we find that changes to the parameters of the negative feedback loop are much stronger inputs for shifting phase. The strongest inputs predicted by this model provide targets for new experimental small molecules and suggest that the function of the positive feedback loop is to stabilize the oscillations while linking the circadian system to other clock-controlled processes.

A classification approach to estimating human circadian phase under circadian alignment from actigraphy and photometry data.

The time of dim light melatonin onset (DLMO) is the gold standard for circadian phase assessment in humans, but collection of samples for DLMO is time and resource-intensive. Numerous studies have attempted to estimate circadian phase from actigraphy data, but most of these studies have involved individuals on controlled and stable sleep-wake schedules, with mean errors reported between 0.5 and 1 hour. We found that such algorithms are less successful in estimating DLMO in a population of college students with more irregular schedules: Mean errors in estimating the time of DLMO are approximately 1.5-1.6 hours. We reframed the problem as a classification problem and estimated whether an individual's current phase was before or after DLMO. Using a neural network, we found high classification accuracy of about 90%, which decreased the mean error in DLMO estimation-identifying the time at which the switch in classification occurs-to approximately 1.3 hours. To test whether this classification approach was valid when activity and circadian rhythms are decoupled, we applied the same neural network to data from inpatient forced desynchrony studies in which participants are scheduled to sleep and wake at all circadian phases (rather than their habitual schedules). In participants on forced desynchrony protocols, overall classification accuracy dropped to 55%-65% with a range of 20%-80% for a given day; this accuracy was highly dependent upon the phase angle (ie, time) between DLMO and sleep onset, with the highest accuracy at phase angles associated with nighttime sleep. Circadian patterns in activity, therefore, should be included when developing and testing actigraphy-based approaches to circadian phase estimation. Our novel algorithm may be a promising approach for estimating the onset of melatonin in some conditions and could be generalized to other hormones.

Developmental patterning of peptide transcription in the central circadian clock in both sexes.

Introduction: Neuropeptide signaling modulates the function of central clock neurons in the suprachiasmatic nucleus (SCN) during development and adulthood. Arginine vasopressin (AVP) and vasoactive intestinal peptide (VIP) are expressed early in SCN development, but the precise timing of transcriptional onset has been difficult to establish due to age-related changes in the rhythmic expression of each peptide. Methods: To provide insight into spatial patterning of peptide transcription during SCN development, we used a transgenic approach to define the onset of Avp and Vip transcription. Avp-Cre or Vip-Cre males were crossed to Ai9+/+ females, producing offspring in which the fluorescent protein tdTomato (tdT) is expressed at the onset of Avp or Vip transcription. Spatial patterning of Avp-tdT and Vip-tdT expression was examined at critical developmental time points spanning mid-embryonic age to adulthood in both sexes. Results: We find that Avp-tdT and Vip-tdT expression is initiated at different developmental time points in spatial subclusters of SCN neurons, with developmental patterning that differs by sex. Conclusions: These data suggest that SCN neurons can be distinguished into further subtypes based on the developmental patterning of neuropeptide expression, which may contribute to regional and/or sex differences in cellular function in adulthood.

Later energy intake relative to mathematically modeled circadian time is associated with higher percentage body fat.

OBJECTIVE: Later circadian timing of energy intake is associated with higher body fat percentage. Current methods for obtaining accurate circadian timing are labor- and cost-intensive, limiting practical application of this relationship. This study investigated whether the timing of energy intake relative to a mathematically modeled circadian time, derived from easily collected ambulatory data, would differ between participants with a lean or overweight/obesity body fat percentage. METHODS: Participants (N = 87) wore a light- and activity-measuring device (actigraph) throughout a cross-sectional 30-day study. For 7 consecutive days within these 30 days, participants used a time-stamped-picture phone application to record energy intake. Body fat percentage was recorded. Circadian time was defined using melatonin onset from in-laboratory collected repeat saliva sampling or using light and activity or activity data alone entered into a mathematical model. RESULTS: Participants with overweight/obesity body fat percentages ate 50% of their daily calories significantly closer to model-predicted melatonin onset from light and activity data (0.61 hours closer) or activity data alone (0.86 hours closer; both log-rank p < 0.05). CONCLUSIONS: Use of mathematically modeled circadian timing resulted in similar relationships between the timing of energy intake and body composition as that observed using in-laboratory collected metrics. These findings may facilitate use of circadian timing in time-based interventions.

Neural circuit models for evidence accumulation through choice-selective sequences.

Decision making is traditionally thought to be mediated by populations of neurons whose firing rates persistently accumulate evidence across time. However, recent decision-making experiments in rodents have observed neurons across the brain that fire sequentially as a function of spatial position or time, rather than persistently, with the subset of neurons in the sequence depending on the animal's choice. We develop two new candidate circuit models, in which evidence is encoded either in the relative firing rates of two competing chains of neurons or in the network location of a stereotyped pattern ("bump") of neural activity. Encoded evidence is then faithfully transferred between neuronal populations representing different positions or times. Neural recordings from four different brain regions during a decision-making task showed that, during the evidence accumulation period, different brain regions displayed tuning curves consistent with different candidate models for evidence accumulation. This work provides mechanistic models and potential neural substrates for how graded-value information may be precisely accumulated within and transferred between neural populations, a set of computations fundamental to many cognitive operations.

An Anticipatory Scheme for the Model Predictive Control of Circadian Phase for Expected Environmental Light Changes.

The circadian system is critical to timing biological functions in anticipation of daily environmental light changes, but much previous work on the development of molecular control inputs to shift the phase of the circadian system has applied model predictive control (MPC) without considering expected environmental light changes. We augment the MPC algorithm to develop an anticipatory control algorithm, which has advantages over MPC in achieving scheduled phase shifts (as occurs with jet lag and shiftwork). We further extend the algorithm in a model switching control scheme to account for changes in the light environment. Taken together, these two enhancements to the standard MPC framework allow for better control of the circadian oscillator in more realistic environments by anticipating environmental light changes.

Compensating for Sensor Error in the Model Predictive Control of Circadian Clock Phase.

The circadian oscillator regulates many critical biological functions; misalignment between the phase of this oscillator and the environment has been linked to adverse health outcomes. Thus, shifting the circadian phase of the oscillator to align with the environment using either light or small molecule pharmaceuticals as control inputs is desired. One challenge to controlling circadian phase is that the magnitude and direction of the phase shift caused by these inputs is dependent on the phase at which the input is delivered. Simulations show that model predictive control (MPC) can successfully shift the phase of the circadian clock using perfect knowledge of the current phase of the system. However, methods to assess circadian phase continuously in real time, as would be needed to implement MPC in vivo, are limited in their accuracy. Here, we explore the impact of imperfect sensing on our ability to control circadian phase. While some pathological patterns of sensor error can make control impossible, we show that by assuming errors in the phase sensor are bounded to be sufficiently small, we can bound the error of our MPC algorithm. We propose using the expected phase response curve to improve control when sensor error is present.