The Research Of Fluctuations-Induced Circadian Oscillations In Gene Regulation Network Of Biological Clock

Smolen et al. have proposed a reduced circadian oscillator model including two variables in gene regulation network of Drosophila[Biophys. J. 83, 2349 (2002)]. As an important control element for circadian oscillator, light controls circadian rhythms of Drosophila by enhancing the degradation of phosphory-lated TIM. We introduce the fluctuation of light into this deterministic model and study the influence of light noise on circadian oscillator model by using Langevin Equations firstly. When the light-controlled parameter is slightly beyond the bifurcation point and system is a stable steady state, it is found that the circadian oscillations can be induced by the light fluctuation. For the small and large noise intensities, the rhythmicity of supra-threshold circadian oscillations induced by the light fluctuation is un-conspicuous. For the moderate noise intensity, however, the circadian oscillations are clearly observed. There is an optimal light noise intensity at which a remarkable circadian coherent oscillation is observed, which implies a significant resonance phenomenon in the sense of preferred biological circadian oscillations, which is the well known coherence resonance. The signal-to-noise ratio and characteristic correlation both confirm our result. This result shows that the light fluctuation plays a constructive role in the Drosophila circadian oscillations. Time delay can control the coherence of noise-induced circadian oscillations and the strength of coherent resonance achieves a maximum under a moderate time delay.Secondly we study the influence of molecular fluctuations on circadian oscillator model. The molecular fluctuations become important because of the low number of molecules involved in such genetic regulatory networks. To assessthe effect of molecular noise, we perform stochastic simulations by Gillespie's algorithm after decomposing the deterministic model into elementary reaction steps. We find molecular noise can also induce supra-threshold circadian oscillations. Because the circadian oscillations can occur already with a limited number protein molecules, in the range of tens, the supra-threshold circadian oscillations are very robust.Noise inducing the circadian oscillations shows noises can induce internal order of a nonlinear system and play constructive role at the cellular level. It is very important for the biological clock to maintain robust circadian oscillations and furthermore control the rhythmic metabolism and behavior accurately. Those parameters such as D and k_dp may provide targets for pharmacological intervention. And some special purposes of gene therapy, such as the treatment of physiological disorder, may be reached by the control of such parameters.