| The physiological and behavioral activities of living beings are synchronized with the natural light-dark cycle generated by the rotation of the earth,and exhibit a circadian rhythm of approximately 24 hours.Circadian rhythms in mammals are orchestrated by an endogenous clock called the suprachiasmatic nucleus(SCN),the SCN neurons can maintain self-oscillating and remain synchronized through the coupling with neurotransmitters,resulting in the output of a circadian rhythm with a uniform period to the external environment.The period in constant condition(under constant darkness or constant light)is called the free running period(FRP),which varies among different species or individuals within the same species,ranging from 22 to 28 hours.Meanwhile,the SCN,as the master clock in mammals,not only regulates the circadian rhythms in physiological and behavioral activities,but also acts as one of the main control nodes in the brain,inducing scalar invariance over a wide range of time in the temporal patterns of physiological activities such as heart rate,multi-unit electrical activity,and behavioral activity.To explain why different species or individuals within the same species exhibit different the free running periods,and why the SCN can induce the scalar invariance over a wide range of time in the temporal patterns of physiological activities such as heart rate,multi-unit electrical activity,and behavioral activity,in this thesis,we conducted researches on these,specifically:(1)A globally coupled Poincaré model based on the heterogeneity in light-sensitivity of the SCN neurons is established exposed to the constant light.The numerical simulations show that the presence of a critical value for the heterogeneity degree of the light sensitivity with different coupling strength.When the the heterogeneity degree is below the critical value,the ventrolateral par(VL)and the dorsomedial part(DM)remain synchronized,and the FRP increase with the increase of the degree of heterogeneity in the sensitivity.The periods of the VL regions and the DM regions disperse when the heterogeneity degree is larger than this critical value,and the synchronization between the regions is lost,because the period of the VL increases with increasing the heterogeneity degree,whereas the period of DM decreases with increasing the heterogeneity degree.Moreover,the numerical simulations follow that with the increase of the coupling strength both the critical value and the critical free running period increase.The relationships of the FRP for each subregion to the heterogeneity degree on completely random network,WS small-world network,NW small-world network and BA scale-free networkare consistent with the main results,and the relationship between the FRP for each subgroup and the heterogeneity degree in light-sensitivity is not alternated by the difference in the neuronal intrinsic periods qualitatively.And the theoretical results are almost consistent with the numerical simulations.Therefore,the reason why different species or one animal exhibit different free running periods may be due to the varying degrees of the heterogeneity in light-sensitivity of their SCN neurons to the light information.(2)A locally coupled Poincaré model based on the network topology(the Nearestneighbor coupled network,the NW small world network,the ER random network and the BA scale free network.)of the SCN neurons is established exposed to the constant light.The results show that the FRP is longest in the BA network,because the BA network is characterized by the most heterogeneous structure among these four types of networks.These findings are not affected by the average node degree of the SCN network,the value of relaxation rate of the SCN neuronal oscillators,the intensity of constant light or the scale of SCN network.In the theoretical analysis,the star network is selected as the SCN network structure,and the analytical results are consistent with the numerical simulations.Thus,the reason why different species or one animal exhibit different free running periods may be due to the varying network topologies of the SCN neurons.(3)With only 200 data points in the bioluminescence time series,a method which is tailored to measure scale-invariance in shorter time series(with a minimum of only around 100 data points),is correlation-dependent balance estimation of diffusion entropy(c BEDE),which is applied in the present study.The scale-invariant behavior of the individual neurons within each slice or the SCN slice as a whole(network)was measured by using the c BEDE method,respectively.For comparison,the scale-invariant behavior in so-called shuffled time series was also examined.The results show that the scaling exponent of the individual neurons or the SCN slice as a whole is significantly larger for the washout condition(closer to 1)than for TTX,within each slice,respectively.Moreover,the upper time limit for the scale-invariant range is significantly larger in the washout condition(46.8 h)than during TTX application.The scaling exponent is around 0.5 for both the TTX and washout conditions,which is indicative of complete randomness in the data.This shows that our results found in the actual data are not coincidental.Our findings show that the scale-invariance of the SCN can already be found at the level of the individual neurons,and that the coupling between SCN neurons plays a decisive role in this.Therefore,this may be the underlying reason why the SCN can induce the scale invariance in the temporal patterns of physiological activities such as heart rate,multi-unit electrical activity,and behavioral activity.Our findings contribute to the understanding of how the heterogeneity in lightsensitivity as well as the network structure of the SCN neurons influences the circadian behaviors,and of the scale-invariant behaviors in the circadian rhythm in mammals. |
