Delay model of circadian gene expression with two negative feedback loops

In this theoretical paper we propose a quantitative minimal model for circadian gene expression based on two negative feedback loops. We perform numerical simulations to analyse its dynamics and parameter sensitivities in free-running conditions, and verify the entrainability by a single periodic driver. We furthermore apply two simultaneously acting external drivers, leading to aperiodic oscillations in the case of a single-loop system. These can be turned into regular periodic oscillations by introduction of a second loop. Our studies confirm the increasing evidence that multiple feedback loops increase the robustness of regulatory systems, and stress the particular situation of systems that are close to transition from free-running oscillation to steady-state behaviour. We discuss possible molecular realisations of the featured feedback loops and suggest the application of complex patterns of external stimulation as a generally useful approach to assess the functionality of models of circadian systems.     

Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm

A mechanism for generating circadian rhythms has been of major interest in recent years. After the discovery of per and tim, a model with a simple feedback loop involving per and tim has been proposed. However, it is recognized that the simple feedback model cannot account for phenotypes generated by various mutants. A recent report by Glossop, Lyons & Hardin [Science286, 766 (1999)] on Drosophila suggests involvement of another feedback loop by dClk that is interlocked with per-tim feedback loop. In order to examine whether interlocked feedback loops can be a basic mechanism for circadian rhythms, a mathematical model was created and examined. Through extensive simulation and mathematical analysis, it was revealed that the interlocked feedback model accounts for the observations that are not explained by the simple feedback model. Moreover, the interlocked feedback model has robust properties in oscillations.     

A circadian oscillator model based on empirical data

A model based on the van der Pol equation has been developed to predict the pattern of adaptation of aircrew and other travellers to rapid time-zone transitions, when the exposure to light cannot be quantified. The parameters of the model include the stiffness (mu) and the intrinsic period (T0), which together define the free-running period, and the external force (F). The parameter values were estimated by using a simplex minimization technique to fit the output from the model to body temperature data from 12 individuals before, and over a 12-day period immediately after, a 10-h eastward transition between London and Sydney. Data were collected at three equally spaced points during each sleep period and at the end of four 45-min rest periods during the day. The fitting procedure enabled the parameters of the temperature rhythm to be estimated after correcting for the masking effect of sleep. The average estimates of mu (0.38 h) and T0 (24.24 h) were close to earlier estimates based on forced desynchronization experiments, and the mean free-running period, calculated from these, was 24.50 h. The mean value of the external force F (0.54) was surprisingly high, and this may reflect the strong outdoor light levels during the days in Sydney. Estimates of phase, based on the model solutions, suggested that 11 subjects adapted by a phase delay and 1 by a phase advance. However, the amplitude of the rhythms was much reduced at times when the phase was changing rapidly. Simulations using the range of the model parameters for the 12 individuals predicted that adaptation to within 1 h after a 10-h eastward transition would be achieved within between 3 and 11 days. However, since these predictions are dependent on the choice of external force, estimates may need to be more conservative in real-life situations when light exposure cannot be measured.     

Biochemical characterization of the recombinant human Drosophila homologues Timekeeper and Andante involved in the Drosophila circadian oscillator

The Drosophila clock proteins timekeeper (CK2α^Tik) and andante (CK2β^And) are mutated CK2α and CK2β subunits, respectively.In order to revisit the hypothesis concerning a perturbation of the β/β and/or α/β subunit association, involving the andante mutant we have cloned, expressed and purified the recombinant andante mutant CK2β^And and a CK2 holoenzyme composed of CK2β^And and the wildtype CK2α subunit. Biochemical analyses using gel filtration analysis, inhibitor and heat treatment, as well as urea denaturation studies did not yield significant differences between the wildtype holoenzyme (α₂β₂) and a holoenzyme containing wildtype CK2α and andante CK2β^And.The timekeeper mutant, CK2α^Tik has been reported to show a significant reduction in enzyme activity. In order to closely investigate the reason for this reduction in activity, we have also cloned and expressed the human homologue of Drosophila timekeeper. Using a CK2 holoenzyme containing the human timekeeper mutant and the wildtype CK2β subunit we could confirm a strongly reduced activity towards CK2 substrates, but also a significant reduction in the autophosphorylation of the CK2β in the absence of any substrate. Based on a structure-based model we postulate that the mutation M161K in Drosophila (i.e. M163K in human) is responsible for the drastic loss of activity, where the lysine residue may cause improper binding of the tri-nucleotide.     

A role for the Drosophila fragile X-related gene in circadian output

Mutations that abolish expression of an X-linked gene, FMR1, result in the pathogenesis of fragile X syndrome, the most common form of inherited mental retardation. To understand the normal function of the FMR1 protein, we have produced fly strains bearing deletions in a Drosophila homolog of FMR1 (dfmr1). Since fragile X patients show a number of abnormal behaviors including sleep problems, we investigated whether a loss-of-function mutation of dfmr1 affect circadian behavior. Here we show that under constant darkness (DD), a lack of dfmr1 expression causes arrhythmic locomotor activity, but in light:dark cycles, their behavioral rhythms appear normal. In addition, the clock-controlled eclosion rhythm is normal in DFMR1-deficient flies. These results suggest that DFMR1 plays a critical role in the circadian output pathway regulating locomotor activity in Drosophila.     

Revised limit cycle oscillator model of human circadian pacemaker

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer's model has been replaced with a higher order limit cycle oscillator so that the system's amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer's model has been refined so that the peak sensitivity to light on the limit cycle now occurs approximately 4 h before the core body temperature minimum (CBTmin) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT,n now corresponds to 0.8 h after the minimum of x (x(min) in this refined model rather than to the exact timing of x(min) as in Kronauer's model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff's rule.     

Identification of neuromedin S and its possible role in the mammalian circadian oscillator system

The discovery of neuropeptides has resulted in an increased understanding of novel regulatory mechanisms of certain physiological phenomena. Here we identify a novel neuropeptide of 36 amino-acid residues in rat brain as an endogenous ligand for the orphan G protein-coupled receptor FM-4/TGR-1, which was identified to date as the neuromedin U (NMU) receptor, and designate this peptide 'neuromedin S (NMS)' because it is specifically expressed in the suprachiasmatic nuclei (SCN) of the hypothalamus. NMS shares a C-terminal core structure with NMU. The NMS precursor contains another novel peptide. NMS mRNA is highly expressed in the central nervous system, spleen and testis. In rat brain, NMS expression is restricted to the core of the SCN and has a diurnal peak under light/dark cycling, but remains stable under constant darkness. Intracerebroventricular administration of NMS in rats activates SCN neurons and induces nonphotic type phase shifts in the circadian rhythm of locomotor activity. These findings suggest that NMS in the SCN is implicated in the regulation of circadian rhythms through autocrine and/or paracrine actions.