|
The circadian rhythm pervades the whole organism from the level of the proteins to the activity of the whole body and its interaction with the environment. In natural conditions, the circadian clock is controlled by a periodic and very reliable external light-dark cycle and is phase-locked to it. In mammals the circadian pacemaker is located in the suprachiasmatic nucleus of the hypothalamus and consists of two paired nuclei, each containing ~ 10,000 neurons. The neurons are controlled by protein concentrations of a genetic clock circuit. Interestingly, the circadian clock is able to produce precise self-sustained oscillations under constant light conditions. By high and constant light the circadian clock undergoes a transition from the rhythmic regime to an arrhythmic behaviour without any clear rhythm in the activity.
We model the circadian pacemaker on the genetic level and investigate an large ensemble of non-identical Goodwin oscillators globally coupled by neurotransmitters [1]. The Goodwin oscillator describes the interplay amongst the clock mRNA, the clock protein, and the transcriptional inhibitor. The collective activity of all oscillators generates an overt rhythm that can be e.g. the motor activity or the body temperature. The dynamics of a single cell is affected by light and intercellular coupling. According to ref. [2] we assume an influence of the light intensity on the coupling strength in such a way that increasing light reduces the coupling. The different eigen-frequencies of the individual Goodwin oscillators cause a de-synchronisation, hence the overt-rhythm undergoes a transition from self-oscillations to a steady state for increasing light whereas the individual non-identical genetic oscillators preserve their self-oscillations for all light conditions but de-synchronise amongst them for large light levels. We are interested in constructive effects of noise in the environmental light on the circadian overt rhythm. We found a noise induced overt rhythm generation for constant light intensities that evoke an arrhythmic response in the noise-free case. The noise has a resonance-like influence on the overt rhythm with a clear maximum at an optimal noise intensity. Due to the absence of any external pacemaker or periodic signal, because we are working under constant light conditions, the resonance found in the overt rhythm versus the noise intensity is a kind of Coherence Resonance (CR) [3]. The resonance can be observed only in the overt rhythm and not at the level of the individual oscillators, hence we found a joint effect of noise, coupling and the synchronisation amongst the oscillators. Noteworthy, the noise-induced rhythm generation only needs a very small synchronisation level. [1] D. Gonze, S. Bernard, C. Waltermann, A. Kramer and H. Herzel, "Spontaneous Synchronization of Coupled Circadian Oscillators'', Biophysical Journal vol 89, 120 (2005). [2] A. Díez-Noguera, "A functional model of the circadian system based on the degree of intercommunication in a complex system'', Am J Physiol. vol 267, R1118 (1994). [3] A. Pikovsky, J. Kurths, "Coherence Resonance in a Noise-Driven Excitable System'', Phys. Rev. Lett. vol 78, 775 (1997). |
|