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We propose a stochastic distributed delay model together with a Markov random field prior and a measurement model for bioluminescence-reporting to analyse spatio-temporal gene expression in intact networks of cells. The model describes the oscillating time evolution of molecular mRNA counts through a negative transcriptional-translational feedback loop encoded in a chemical Langevin equation with a probabilistic delay distribution. The model is extended spatially by means of a multiplicative random effects model with a first order Markov random field prior distribution. Our methodology effectively separates intrinsic molecular noise, measurement noise, and extrinsic noise and phenotypic variation driving cell heterogeneity, while being amenable to parameter identification and inference. Based on the single-cell model we propose a novel computational stability analysis that allows us to infer two key characteristics, namely the robustness of the oscillations, i.e. whether the reaction network exhibits sustained or damped oscillations, and the profile of the regulation, i.e. whether the inhibition occurs over time in a more distributed versus a more direct manner, which affects the cells’ ability to phase-shift to new schedules. We show how insight into the spatio-temporal characteristics of the circadian feedback loop in the suprachiasmatic nucleus (SCN) can be gained by applying the methodology to bioluminescence-reported expression of the circadian core clock gene Cry1 across mouse SCN tissue. We find that while (almost) all SCN neurons exhibit robust cell-autonomous oscillations, the parameters that are associated with the regulatory transcription profile give rise to a spatial division of the tissue between the central region whose oscillations are resilient to perturbation in the sense that they maintain a high degree of synchronicity, and the dorsal region which appears to phase shift in a more diversified way as a response to large perturbations and thus could be more amenable to entrainment., Author summary We develop a method for estimating and modelling transcriptional processes in living tissue samples using a model which approximates the end product of a series of complex chemical interactions using a density function—and thus is amenable to parameter estimation—but can realistically account for the intrinsic noise and rhythm generation inherent in the single-cell. The model incorporates a form of dependence between nearby cells using a spatial prior distribution over the parameters. The model thus describes the cyclical behaviour of the production of the population of some molecular species within cells, along with the spatial variation of the process across a network of cells. This approach is suitable for modelling circadian gene expression in the suprachiasmatic nucleus (SCN), the region of the brain which is responsible for the ‘circadian master clock’ which coordinates the bodies daily rhythms. This model is applied to three sample tissues from mice SCN. Based on the inferred dynamic behaviour of the cells, we are able to divide the organ into two regions: a central core in which the rhythm is intrinsic and resilient and the more entrainable outer region which is much more heavily influenced by external stimuli. The findings highlight a trade-off between resilient cyclic behaviour and ability to adapt to environmental cues.

A molecular circadian clock exists not only in the brain, but also in most cells of the body. Research over the past two decades has demonstrated that it directs daily rhythmicity of nearly every aspect of metabolism. It also consolidates sleep-wake behavior each day into an activity/feeding period and a sleep/fasting period. Otherwise, sleep-wake states are mostly controlled by hypothalamic and thalamic regulatory circuits in the brain that direct overall brain state. Recent evidence suggests that hypothalamic control of appetite and metabolism may be concomitant with sleep-wake regulation, and even share the same control centers. Thus, circadian control of metabolic pathways might be overlaid by sleep-wake control of the same pathways, providing a flexible and redundant system to modify metabolism according to both activity and environment.

The hypothalamic suprachiasmatic nuclei (SCN) are the principal mammalian circadian timekeeper, co-ordinating organism-wide daily and seasonal rhythms. To achieve this, cell-autonomous circadian timing by the ~20,000 SCN cells is welded into a tight circuit-wide ensemble oscillation. This creates essential, network-level emergent properties of precise, high-amplitude oscillation with tightly defined ensemble period and phase. Although synchronised, regional cell groups exhibit differentially phased activity, creating stereotypical spatiotemporal circadian waves of cellular activation across the circuit. The cellular circuit pacemaking components that generate these critical emergent properties are unknown. Using intersectional genetics and real-time imaging, we show that SCN cells expressing vasoactive intestinal polypeptide (VIP) or its cognate receptor, VPAC2, are neurochemically and electrophysiologically distinct, but together they control de novo rhythmicity, setting ensemble period and phase with circuit-level spatiotemporal complexity. The VIP/VPAC2 cellular axis is therefore a neurochemically and topologically specific pacemaker hub that determines the emergent properties of the SCN timekeeper., Circadian activity modulation in the suprachiasmatic nucleus (SCN) is a network-level emergent property that requires neuropeptide VIP signaling, yet the precise cellular mechanisms are unknown. Patton et al. show that cells expressing VIP or its receptor VPAC2 together determine these emergent properties of the SCN.