This study was supported by the Bundesministerium für Bildung und Forschung, Germany (FKZ: 13N13160 and 13N13162) and Intellux GmbH, Germany.

A simple three-component negative feedback loop is a recurring motif in biochemical oscillators. This motif oscillates as it has the three necessary ingredients for oscillations: a three-step delay, negative feedback, and nonlinearity in the loop. However, to oscillate, this motif under the common Goodwin formulation requires a high degree of cooperativity (a measure of nonlinearity) in the feedback that is biologically “unlikely.” Moreover, this recurring negative feedback motif is commonly observed augmented by positive feedback interactions. Here we show that these positive feedback interactions promote oscillation at lower degrees of cooperativity, and we can thus unify several common kinetic mechanisms that facilitate oscillations, such as self-activation and Michaelis-Menten degradation. The positive feedback loops are most beneficial when acting on the shortest lived component, where they function by balancing the lifetimes of the different components. The benefits of multiple positive feedback interactions are cumulative for a majority of situations considered, when benefits are measured by the reduction in the cooperativity required to oscillate. These positive feedback motifs also allow oscillations with longer periods than that determined by the lifetimes of the components alone. We can therefore conjecture that these positive feedback loops have evolved to facilitate oscillations at lower, kinetically achievable, degrees of cooperativity. Finally, we discuss the implications of our conclusions on the mammalian molecular clock, a system modeled extensively based on the three-component negative feedback loop.

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Robust synchronization is a critical feature of several systems including the mammalian circadian clock. The master circadian clock in mammals consists of about 20000 ‘sloppy’ neuronal oscillators within the hypothalamus that keep robust time by synchronization driven by inter-neuronal coupling. The complete understanding of this synchronization in the mammalian circadian clock and the mechanisms underlying it remain an open question. Experiments and computational studies have shown that coupling individual oscillators can achieve robust synchrony, despite heterogeneity and different network topologies. But, much less is known regarding the mechanisms and circuits involved in achieving this coupling, due to both system complexity and experimental limitations. Here, we computationally study the coupling mediated by the primary coupling neuropeptide, vasoactive intestinal peptide (VIP) and its canonical receptor, VPAC2R, using the transcriptional elements and generic mode of VIP-VPAC2R signaling. We find that synchrony is only possible if VIP (an inducer of Per expression) is released in-phase with activators of Per expression. Moreover, anti-phasic VIP release suppresses coherent rhythms by moving the network into a desynchronous state. Importantly, experimentally observed rhythms in VPAC2R have little effect on network synchronization, but can improve the amplitude of the SCN network rhythms while narrowing the network entrainment range. We further show that these findings are valid across several computational network models. Thus, we identified a general design principle to achieve robust synchronization: An activating coupling agent, such as VIP, must act in-phase with the activity of core-clock promoters. More generally, the phase of coupling is as critical as the strength of coupling from the viewpoint of synchrony and entrainment.

Synchrony of spawning in many hermatypic corals, typically a few nights after the full moon, is putatively dependent on solar and lunar light cycles in conjunction with other possible cues such as tides and temperature. We analyze here the contributions of separate components of light dynamics, because the effects of twilight and lunar skylight on coral spawning synchrony have previously been conflated and the alternative hypothesis that these components have differential contributions as proximate cues has not been tested. Moonlight-dependent changes in spectra during twilight, rates of decreasing twilight intensities, and changes in lunar photoperiod were experimentally decoupled using programmed light-emitting diodes and compared for their separate effects on spawning synchrony in Acropora humilis. Effects on synchrony under the control of synthetic lunar cues were greatest in response to changes in lunar photoperiod; changes in light intensities and spectra had lesser influence. No significant differences among treatment responses were found at the circa-diel time scale. We conclude that spawning synchrony on a particular lunar night and specific time of night is a threshold response to differential periods of darkness after twilight that is primarily influenced by lunar photoperiod and secondarily by discrete optical components of early nocturnal illumination.

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In mammals, a network of coupled neurons within the hypothalamus coordinates physiological rhythms with daily changes in the environment. In each neuron, delayed negative transcriptional feedbacks generate oscillations, albeit noisy and unreliable ones. Coupling mediated by diffusible neuropeptides lends precision and robustness to circadian rhythms. The double knockout of Cryptochrome Cry turns adult mice arrhythmic. But, remarkably, double knockout neonates continue to show robust oscillation much like wild-type neonates and appear to lose rhythmicity with development. We study quantitatively dispersed neurons and brain slices from wild-type and Cry double knockout mice to understand the links between single cell rhythmicity and intercellular coupling. We quantify oscillator properties of dispersed cells using nonlinear regression and study bifurcations diagrams of network models. We find that varying just three parameters-oscillator strength, strength of coupling, and timing of coupling-can reproduce experimentally observed features. In particular, modeling reveals that minor changes in timing of coupling can destroy synchronization as observed in adult slices from knockout mice.

SummaryIn many organisms, the circadian clock drives rhythms in the transcription of clock-controlled genes that can be either circadian (∼24-hr period) or ultradian (<24-hr period). Ultradian rhythms with periods that are a fraction of 24 hr are termed harmonics. Several harmonic transcripts were discovered in the mouse liver, but their functional significance remains unclear. Using a model-based analysis, we report for the first time ∼7-hr third harmonic transcripts in Neurospora crassa, a well-established fungal circadian model organism. Several third harmonic genes are regulated by female fertility 7 (FF-7), whose transcript itself is third harmonic. The knockout of circadian output regulator CSP1 superimposes circadian rhythms on the third harmonic genes, whereas the knockout of stress response regulator MSN1 converts third harmonic rhythms to second harmonic rhythms. The 460 ∼7-hr genes are co-regulated in two anti-phasic groups in multiple genotypes and include kinases, chromatin remodelers, and homologs of harmonic genes in the mouse liver.