Models Of Circadian Rhythms In Mammals Under Different Light Conditions

In mammals, there is an endogenous clock named suprachiasmatic nucleus (SCN) which controls the circadian rhythms of physiological activities and behaviors. SCN has two main functions. One is that when there is no external periodic signal, SCN has the ability to keep circadian rhythms with the period close to 24h. The other one is that SCN can keep the same period as outside under proper periodic signal. These two main functions are decided by the collective behaviors of thousands of neurons in SCN. These neurons can self-oscillate with periods ranging from 22h to 28h. They are coupled through transmitters and synchronize to reach a uniform period, and then SCN sends this periodic signal to other parts of the body. From the view of network, the SCN is a network with thousands of nodes, where the neurons are regard as nodes and the couplings between neurons are identified as edges. In this thesis we consider the SCN network as an all-to-all network. After understanding the SCN network, it’s necessary to understand the dynamical behavior of one single neuron for studying on the collective behaviors of all neurons. Here we choose Goodwin oscillators to represent the dynamical behavior of individual neurons. Based on these intrinsic factors, i.e., the topology and dynamical model, we can study the influence of external light conditions on SCN network. In this thesis, we discuss three different light conditions:Under darkness, the free running periods are varied among different species. In Chapter 4, an explanation will be represented for the experimental finding. The inductive ability is varied to different transmitters among different neurons, thus we suppose that the inductive ability is dispersed, i.e. the coupling strength is dispersed in coupled Goodwin oscillators. The numerical results from Goodwin model and the analytical results from phase model show that the free running period is in contrast to the dispersion of coupling strength. The free running periods are varied among different species in that the dispersions of coupling are different in different species.Under constant light, the left and right nucleus of SCN show synchronized, "split" and lost rhythms. Indie et al. found that there are two anti-phase oscillator groups in phase model based on the activity feedback which has a～12h time delay to SCN. In Chapter 5, we apply this kind of feedback to Goodwin model which has amplitude information in additional to phase information. In different regions of parameter plane, synchronization, anti-synchronization and amplitude death are found and these three collective behaviors are corresponding to synchronization, "split" and lost rhythms. Furthermore, we find that the term of feedback with time delay has an impact on the period of SCN.Under proper periodic light-dark cycle, SCN can keep the period as the same as external period. When the period of external light-dark cycle is 22h, there is dissociation between VL (ventrolateral part) and DM (dorsomedial part) part of SCN, i.e., the period of VL is 22h as that of external signal while the period of DM is the free running period. But when the period of external dark-cycle is 26h, it’s hard to dissociate between VL and DM. In Chapter 6, Goodwin model is used to explain this phenomenon. In our model, there is only a part of neuron oscillators that can accept the light signal because the neurons of VL can directly receive the light signal from retina. Additionally, we discuss the dispersion of coupling strength as in Chapter 4. We find that this kind of dispersion helps SCN entrainment to light-dark cycle with period of 26h, while doesn’t help SCN entrainment to light-dark cycle with period of 22h. Furthermore we find that with this kind of dispersion, it’s easier to dissociate between VL and DM under light-dark cycle with period of 22h than with period of 26h. This finding is in consistent with experimental finding.The influence of light condition from outside on SCN network is considered in this thesis. Next step, we will discuss the impact of the factors from inside. For example, the topology of SCN network has an effect on the period of SCN and the ability of SCN entrainment to light-dark cycle with different periods.