Mathematical Models For Light Entrainment Of Neurospora System

Organism usually shows the consistency of body’s activities and variability of rhythm within a cycle of 24 hours. Meanwhile organism interior exists a rhythm phenonmenon of perceiving time which also controlled by the time. These rhythm phenonmenons are known as biological clock. We take the neurospora system for an example to study the effects of light for entrainment of biological clock.This paper mainly studies two core issues. First,we find a experimental phenomenon that the experimental results have not been published by Professor Guo Jinhu of Zhongshan University in the biological experiments. When light entrainment of the neurospora system uses the longer photoperiods, rhythm of the system changes along with the cycle of light. However, when light entrainment of the neurospora system uses frequent photoperiods, rhythm of the system restores the endogenous cycle. We establish an ODE Mathematical model of neurospora biological systems beacaue for this problem. We combine the computer simulation and biological experiment to analysis the reason. Second, We establish further simplified mathematical model of the system again. Then we establish Quasi standard map according to the further simplified mathematical model to study synchronization conditions for light entrainment of neurospora circadian clock.The paper shows the main results and contributions. First, we establish an ODE mathematical model according to the real neurospora system. Appling the computer simulation and analysis, we confirm some impor-tant parameters(for example Hypo-FRQ) of the neurospora system model which have an very important effect on the first core problem. And the result provides a direction for further research on biological experiment. Second, we establish a new mathematical model of iterative map from the ODE mathematical model. The simplified mathematical model is more convenient to analysis the changes of extreme points in the model, compared to the original model. At the same time, we analyse the synchronization condition of coupled oscillators for light entrainment of the neurospora model according to the mapping. When the ratio of two oscillator periods is a rational number, the coupling of the light entrainment of the neurospora system can achieves synchronization. When the ratio of two oscillator periods is an irrational number, the coupling of the light entrainment of the neurospora system not achieves synchronization.