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

Abstract

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.

Synergies of Multiple Zeitgebers Tune Entrainment

“…An alternative to the design of full entrainment schedules are short drug pulses to adaptively shift circadian phases at the subsequent day. This modelling approach was used to study the relative strength of the negative and the positive feedback loop of the circadian clock (Brown and Doyle, 2020) and to investigate interindividual variabilities in response to circadian drugs (Kim et al, 2013).…”

From circadian clock mechanism to sleep disorders and jet lag: Insights from a computational approach

“…Recent studies point to alternative approaches to altering the period, phase and amplitude of the circadian clock in order to achieve therapeutic effects [152][153][154][155][156][157]. These promising approaches which can also benefit from the study of molecular models to pinpoint potential molecular targets [34,63,158], are based on the use of small molecules that interact with components of the circadian clock so as to modify its amplitude or/and its phase with respect to the LD cycle. Clock-enhancing small molecules (CEMs) [156] represent a new approach to treat a variety of circadian clock-related physiological disorders, beyond those that impinge on the sleep-wake cycle.…”

The shades of grey in adipose tissue reprogramming

“…The molecular machinery of the circadian system has been elegantly reviewed here [ 167 , 168 ]. Briefly, our internal timekeeper is based on transcription–translation feedback loops consisting of circadian locomotor output cycles kaput (CLOCK)–brain and muscle ARNT-like 1 (BMAL1) heterodimers and their target clock genes Period ( PER 1-3) , Cryptochrome ( CRY 1-2 ), REV-ERB and retinoic acid-related orphan receptor ( ROR ).…”