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Exposed to the constant light, the master clock located in the bilaterally paired suprachiasmatic nucleus (SCN) above the optic chiasma exhibits three rhythmic behaviors in hamsters. Some hamsters remain or lose circadian rhythms due to synchronization or desynchronization between the SCN neurons, respectively. Interestingly, the other hamsters show a phenomenon called “split”, in which the left SCN and right SCN oscillate with a stable anti-phase. In this paper, a modified Kuramoto model is built to explain these three rhythmic behaviors, where the phase-shift of cellular coupling is taken into account. Three cases of phase-shifts are considered, including that first case exists in all the SCN neurons, second case exists between the left and right SCN, and the last case exists within each group. We found that the phase-shift is able to induce the anti-phase synchronization between the left SCN and right SCN in the former two cases, but eliminate this anti-phase synchronization in the latter case. Our findings provide an alternative explanation for the emergency of the split and shed light on the collective behaviors of the SCN neurons.

Most of the systems in an organism (human included) function in a regular daily rhythm. Hypothalamo-pituitary-adrenocortical (HPA) axis, although mostly known for its role in stress response, probably has a role in conveying rhythmic signals from the major pacemaker, suprachiazmatic nucleus (SCN), to the periphery. A general qualitative nonphenomenological mathematical model of the HPA axis is constructed and its dynamics is examined using linear stability analysis and Roushe's theorem. The results show that this system is asymptotically stable, i.e. it does not generate circadian oscillations, but only responds to the external pacemaker.

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus is considered as the master circadian pacemaker. Each cell in the SCN contains an autonomous molecular clock, and the SCN is composed of multiple single-cell circadian oscillators. The fundamental question is how the individual cellular oscillators, expressing a wide range of periods, interact and assemble to achieve phase synchronization. In natural conditions, the interaction between the SCN neurons is non-negligible and coupling between cells in the SCN is achieved partly by neurotransmitters. Though there have been a lot of works about the synchronization of circadian oscillators coupled by neurotransmitter, most of the works are based on numerical simulation with little theoretical analysis. In this paper, from the theoretical analysis, we prove that the clocks can be synchronized by the neurotransmitter with mathematical knowledge. Our results also show that the coupling among neurons can synchronize circadian oscillators but the synchronized oscillators are not with period of 24 h, which indicates that environmental cues are necessary to entrain oscillators with period of 24 h. This work can offer theoretical basis to study circadian synchronization in a numerical or experimental way.

The luteinizing hormone (LH) is released by the pituitary in discrete pulses. Electro-physiological studies in monkeys have demonstrated that sharp intermittent increases in the electrical activity of a hypothalamic pulse generator (HPG) are associated in a one-to-one manner with the occurrence of LH pulses in the plasma and exhibits a circadian modulation. In order to investigate the temporal structure of the HPG, we develop a semi-parametric stochastic point process model generalizing the Cox's periodic regression model. We apply this approach to the study of memory range of the process underlying HPG activity, using experimental data from one ovariectomized rhesus monkey. A non-parametric approach is also described.

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• ASIA-PACIFIC — Importance of Redox Homeostasis in Potential Treatment of Disease
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• ASIA-PACIFIC — Cataloguing Cancer “fingerprints” to Map Cancer Genomes
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Judgment periodicity of biological time series data is important and done widely to find the circadian expression of genes, monthly change of hormones, etc. To keep complete reproducibility of judgment is a problem because popular judgment methods such as curve fitting, Fourier analysis, etc. need judgment criteria determined by analysts considering experimental conditions and results (level, S/N, distribution, etc.) based on their experience. Judgment results are often affected by analysts' subjects. Reproducible criterion determination is therefore strongly needed. We propose introducing the information criterion to replace analysts' criteria. A judgment algorithm by combining Bayesian information criterion (BIC) and discrete Fourier transform (DFT) has been developed and has proved its ability through application to mice microarray data and finding of circadian genes. Our method, named "Piccolo", shows higher sensitivity than the simple DFT (without BIC) method with reproducibility, and can be fully automated.

We present three different simplest realistic models of the circadian pacemaker that can be interpreted in molecular terms: Goodwin model, piece-wise Goodwin model and delay model. The main purpose is to investigate how the common parameters in these three model affect the dynamical behavior. In particular, the existence and stability of periodic solutions of three models are studied, and the parameter space where the steady state becomes unstable is given which can be used to compare the effect of parameters on the oscillations of three models. Furthermore, the effects of parameters on the period of periodic solutions and phase response curves are investigated and discussed. Our results confirm that all three models can be used to simulate the realistic circadian rhythms. However, in practice, which model is chosen depends on the real data.

This paper presents an alternative representation of a system of differential equations qualitatively showing the behavior of the biological rhythm of a crayfish during their transition from juvenile to adult stages. The model focuses on the interaction of four cellular oscillators coupled by diffusion of a hormone, a parameter $\mu$ is used to simulate the quality of communication among the oscillators, in biological terms, it measures developmental maturity of the crayfish. Since some quorum-sensing mechanism is assumed to be responsible for the synchronization of the biological oscillators, it is natural to investigate the possibility that the underlying diffusion process is not standard, i.e. it may be a so-called anomalous diffusion. In this case, it is well understood that diffusion equations with fractional derivatives describe these processes in a more realistic way. The alternative formulation of these equations contains fractional operators of Liouville–Caputo and Caputo–Fabrizio type. The numerical simulations of the equations reflect synchronization of ultradian rhythms leading to a circadian rhythm. The classical behavior is recovered when the order of the fractional derivative is $\gamma =1$. We discuss possible biological implications.

Circadian rhythms of the living organisms are 24hr oscillations found in behavior, biochemistry and physiology. Under constant conditions, the rhythms continue with their intrinsic period length, which are rarely exact 24hr. In this paper, we examine the effects of light on the phase of the gene expression rhythms derived from the interacting feedback network of a few clock genes, taking advantage of a computer simulation with Cell Illustrator. The simulation results suggested that the interacting circadian feedback network at the molecular level is essential for phase dependence of the light effects, observed in mammalian behavior. Furthermore, the simulation reproduced the biological observations that the range of entrainment to shorter or longer than 24hr light-dark cycles is limited, centering around 24hr. Application of our model to inter-time zone flight successfully demonstrated that 6 to 7 days are required to recover from jet lag when traveling from Tokyo to New York.