Mammalian circadian clocks have a hierarchical organization, governed by the suprachiasmatic nucleus (SCN) in the hypothalamus. The brain itself contains multiple loci that maintain autonomous circadian rhythmicity, but the contribution of the non-SCN clocks to this hierarchy remains unclear. We examine circadian oscillations of clock gene expression in various brain loci and discovered that in mouse, robust, higher amplitude, relatively faster oscillations occur in the choroid plexus (CP) compared to the SCN. Our computational analysis and modeling show that the CP achieves these properties by synchronization of “twist” circadian oscillators via gap-junctional connections. Using an in vitro tissue coculture model and in vivo targeted deletion of the Bmal1 gene to silence the CP circadian clock, we demonstrate that the CP clock adjusts the SCN clock likely via circulation of cerebrospinal fluid, thus finely tuning behavioral circadian rhythms.

We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e., a state with coexisting regions of complete and partial synchrony, emerges via a supercritical bifurcation from a homogeneous state and thus does not require preparation of special initial conditions. We develop a theory of chimera based on the equations for the local complex order parameter in the Ott-Antonsen approximation. Applying a numerical linear stability analysis, we also describe the instability of the chimera and transition to phase turbulence with persistent patches of synchrony. Populations of coupled oscillators is a paradigmatic model of nonlinear science, with numerous applications from purely physical ones like Josephson junction arrays and coupled lasers to biologically and even socially important [1]. While in globally coupled ensembles and in networks one is mostly interested in the features of synchronization and desynchronization, spatially extended oscillating systems demonstrate a variety of patternforming phenomena. One of the most spectacular recent findings are the so-called chimera states (CSs) which are observed in otherwise completely synchronizable oscillatory media if the system starts from specially prepared initial state. CSs are characterized by the coexistence of regions with locally synchronized oscillators and regions where the oscillators phases are not locked but yet not completely incoherent. CSs were initially discovered and explained theoretically in [2], and then received more analytical treatment in [3]. Following those pioneering works on CSs, a large body of observations and analysis of similar regimes has been recently published, see [4] and references therein.In this Letter, we add another species to the zoo of chimeras. The crucial difference is that our CS does not require special initial conditions: It emerges from a general initial state and is thus denoted as self-emerging. CS is stable close to the bifurcation, but with a further variation of the parameter it becomes turbulent, so that synchronous and partially synchronous patches intermingle irregularly. The key elements of our model are Stuart-Landau oscillators, coupled through an exponentially decaying kernel as in the original chimera setup, but with a difference that the coupling is nonlinear in the sense of [5]. First, we numerically demonstrate the existence of CS and then explain it in the phase dynamics framework with the help of reduced equations for the local order parameter. Our main theoretical tools are the equations for the complex order parameter in the socalled Ott-Antonsen (OA) approximation [6]. It exploits a parametrization of the probability density for ensembles of sinusoidally coupled phase oscillators and results in a closed equation for the order parameter. The OA ansatz is closely related to the Watanabe-Strogatz theory [7] which is exact but does not yield closed equations in terms of the order parameter. A connection between these two theories h...

The endogenous circadian timing system has evolved to synchronize an organism to periodically recurring environmental conditions. Those external time cues are called Zeitgebers. When entrained by a Zeitgeber, the intrinsic oscillator adopts a fixed phase relation to the Zeitgeber. Here, we systematically study how the phase of entrainment depends on clock and Zeitgeber properties. We combine numerical simulations of amplitude-phase models with predictions from analytically tractable models. In this way we derive relations between the phase of entrainment to the mismatch between the endogenous and Zeitgeber period, the Zeitgeber strength, and the range of entrainment. A core result is the “180° rule” asserting that the phase varies over a range of about 180° within the entrainment range. The 180° rule implies that clocks with a narrow entrainment range (“strong oscillators”) exhibit quite flexible entrainment phases. We argue that this high sensitivity of the entrainment phase contributes to the wide range of human chronotypes.

Circadian clocks are endogenous oscillators driving daily rhythms in physiology. The cell-autonomous clock is governed by an interlocked network of transcriptional feedback loops. Hundreds of clock-controlled genes (CCGs) regulate tissue specific functions. Transcriptome studies reveal that different organs (e.g. liver, heart, adrenal gland) feature substantially varying sets of CCGs with different peak phase distributions. To study the phase variability of CCGs in mammalian peripheral tissues, we develop a core clock model for mouse liver and adrenal gland based on expression profiles and known cis-regulatory sites. ‘Modulation factors’ associated with E-boxes, ROR-elements, and D-boxes can explain variable rhythms of CCGs, which is demonstrated for differential regulation of cytochromes P450 and 12 h harmonics. By varying model parameters we explore how tissue-specific peak phase distributions can be generated. The central role of E-boxes and ROR-elements is confirmed by analysing ChIP-seq data of BMAL1 and REV-ERB transcription factors.