Dynamical Mechanism For Singularity Behaviour Of Biological Circadian Clock

Biological circadian clock refers to the changes of life activities on a24-hour cycle,also known as circadian rhythm.Activities like the photosynthesis of plants,or feeding,body activity,sleeping of animals,will show the circadian rhythm.In fact,life activities on a 24-hour cycle are the changes of molecular concentration of cells in bodies on a 24-hour cycle.Circadian singularity behavior is a phenomenon of the abolishment of these circadian rhythmicities of organisms by a critical stimulus(such as light pulse or temperature step-up).In the laboratory,this kind of phenomenon have been found in neurospora,hamster,and human beings by changing light intensity and temperature.Based on the experiment,this paper use Gonze et al's three-dimensional model of neurospora to study the dynamical mechanism of singularity behavior of biological circadian clock.The following are main results and conclusions of this paper.(1)First of all,we use the three-dimensional model of neuronspora to establish ODE(ordinary differential equation),and through the computer simulation,we found that,under a specific light stimulation,the singularity behavior of circadian rhythm is caused by the collaboration of the desynchronization and the loss of oscillation amplitude.(2)Secondly,through the theoretical analysis of three-dimensional kinetic equation of neurospora,we found that the system has a one-dimensional stable manifold and a two-dimensional unstable manifold.When the cells are stimulated near the stable manifold,the periodic change rhythm of molecular concentration in cells will be abolished,and thus the circadian singularity behavior happens.(3)At last,in order to study the influence of some parameters on the circadian singularity behavior,we establish a regular three-dimensional model on the basis of three-dimensional neurospora model.We get some theoretical results through the theoretical analysis and numerical calculation:(a)For a single cell,if the unit vector of light stimulation (?) (?x,?y,?z)(?x,?y can't be 0 at the same time)is given,there exist the only stimulus phase and the only instantaneous stimulus intensity k to elicit the circadian singularity behavior.(b)For a group of cells among which phase differences between cells are not quite big,if the unit vector of light stimulation (?) (?x,?y,?z)(?x,?y can't be 0 at the same time)is given,there exist the particular range of stimulus phase and instantaneous stimulus intensity k to elicit the circadian singularity behavior.(c)When studying the influences of parameter on the circadian singularity behavior,we reached the following three conclusions:(i)under the condition of constant cells amplitude,the smaller the phase difference between cells is,the more difficult the circadian singularity behavior happens.(ii)under the condition of constant phase difference between cells,the greater the cells amplitude get,the more difficult the circadian singularity behavior will happens.(iii)for the probability of the occurrence of circadian singularity behavior,the influence of the change of the phase difference between cells is greater than that of the change of cells amplitude circadian clockAs is known to us that many diseases have something to do with the decrease or loss of the circadian clock amplitude of a people.That is to say,the appearance of circadian singularity behavior can pose threats to human's life and health.In this case,it is of considerable realistic significance to study how to prevent the circadian singularity behavior from happening.In this study,based on the combination of the computer simulation,theories analysis,and experimental data analysis,we explore further the dynamical mechanism of singularity behavior of biological circadian clock and the related influencing parameters.It will provide a reference for those who want to control the appearance of the circadian singularity behavior.