Dissociation between two subgroups of the suprachiasmatic nucleus affected by the number of damped oscillated neurons

Motif structure for the four subgroups within the suprachiasmatic nuclei affects its entrainment ability

Circadian rhythms of physiological and behavioral activities are regulated by a central clock. This clock is located in the bilaterally symmetrical suprachiasmatic nucleus (SCN) of mammals. Each nucleus contains a light-sensitive group of neurons, named the ventrolateral (VL) part, with the rest of the neurons being insensitive to light, named the dorsomedial (DM) group. While the coupling between the VL and DM subgroups have been investigated quite well, the communication among the four subgroups across the nuclei did not get a lot of attention. In this article, we theoretically analyzed seven motiflike connection patterns to investigate the network of the two nuclei of the SCN as a whole in relation to the function of the SCN. We investigated the entrainment ability of the SCN and found that the entrainment range is larger in the motifs containing a link between the two VL parts across the nuclei, but it is smaller in the motifs that contain a link between the two DM parts across the nuclei. The SCN may strengthen or weaken connections between the left and right nucleus to accomodate changes in external conditions, such as resynchronization after a jet lag, adjustment to photoperiod or for the aging SCN.

Heterogeneity in relaxation rate improves the synchronization of oscillatory neurons in a model of the SCN

The circadian rhythms in mammals, that are regulated by the suprachiasmatic nucleus (SCN) of the brain, have been observed even in the absence of a light-dark cycle. The SCN is composed of about 10 000 autonomous neuronal oscillators, which are heterogenous in many oscillatory properties, including the heterogeneity in relaxation rates. Although the relaxation rate affects the entrainability of the SCN as a whole, not much is known about the reasons why the heterogeneity in relaxation rate exists. In the present study, based on a Poincaré model, we examine whether the heterogeneity in the relaxation rate affects the synchronization of the SCN neuronal oscillators under constant darkness. Both our simulations and theoretical results show that the heterogeneity improves the synchronization. Our findings provide an alternative explanation for the existence of the heterogeneity in the SCN neurons and shed light on the effect of neuronal heterogeneity on the collective behavior of the SCN neurons.

Dependence of the entrainment on the ratio of amplitudes between two subgroups in the suprachiasmatic nucleus

Organisms can be synchronized not only to the natural 24-h light-dark cycle but also to artificial non-24-h cycles. Interestingly, when the period of the cycle is far from 24 h, organisms may show complicated behavioral patterns. For example, exposed to a 22-h light-dark cycle, in behavioral activity of rats, a phenomenon called "dissociation" emerges, i.e., one periodic component shows a 22-h period and the other shows a period close to the endogenous period of the animal (around 24 h). It has been found that these two components are regulated by two subgroups of the suprachiasmatic nucleus (SCN), respectively, with the ventrolateral part regulating the 22-h component and the dorsomedial part regulating the other component. In the present study, based on a mathematical model, we will examine how the ratio of amplitudes between these two subgroups affects the entrainment of the SCN to the external 22-h light-dark cycle. Our results show that the dissociation happens when the ratio is smaller than 1 and the maximal entrainment (synchronization) ability of the SCN to the external cycle is obtained when the ratio is larger than 1. Our finding sheds light on the dissociation between the subgroups and suggests that the heterogeneity in the amplitudes alter the entrainment ability of the SCN.

Globally fixed-time synchronization of coupled neutral-type neural network with mixed time-varying delays

This paper mainly studies the globally fixed-time synchronization of a class of coupled neutral-type neural networks with mixed time-varying delays via discontinuous feedback controllers. Compared with the traditional neutral-type neural network model, the model in this paper is more general. A class of general discontinuous feedback controllers are designed. With the help of the definition of fixed-time synchronization, the upper right-hand derivative and a defined simple Lyapunov function, some easily verifiable and extensible synchronization criteria are derived to guarantee the fixed-time synchronization between the drive and response systems. Finally, two numerical simulations are given to verify the correctness of the results.

Dispersion of the intrinsic neuronal periods affects the relationship of the entrainment range to the coupling strength in the suprachiasmatic nucleus

Living beings on the Earth are subjected to and entrained (synchronized) to the natural 24-h light-dark cycle. Interestingly, they can also be entrained to an external artificial cycle of non-24-h periods. The range of these periods is called the entrainment range and it differs among species. In mammals, the entrainment range is regulated by a main clock located in the suprachiasmatic nucleus (SCN) which is composed of 10 000 neurons in the brain. Previous works have found that the entrainment range depends on the cellular coupling strength in the SCN. In particular, the entrainment range decreases with the increase of the cellular coupling strength, provided that all the neuronal oscillators are identical. However, the SCN neurons differ in the intrinsic periods that follow a normal distribution in a range from 22 to 28 h. In the present study, taking the dispersion of the intrinsic neuronal periods into account, we examined the relationship between the entrainment range and the coupling strength. Results from numerical simulations and theoretical analyses both show that the relationship is altered to be paraboliclike if the intrinsic neuronal periods are nonidentical, and the maximal entrainment range is obtained with a suitable coupling strength. Our results shed light on the role of the cellular coupling in the entrainment ability of the SCN network.

The asymmetry of the entrainment range induced by the difference in intrinsic frequencies between two subgroups within the suprachiasmatic nucleus

The rhythms of physiological and behavioral activities in mammals, which are regulated by the main clock suprachiasmatic nucleus (SCN) in the brain, can not be only synchronized to the natural 24 h light-dark cycle, but also to cycles with artificial periods. The range of the artificial periods that the animal can be synchronized to is called entrainment range. In the absence of the light-dark cycle, the animal can also maintain the circadian rhythm with an endogenous period close to 24 h. Experiments found that the entrainment range is not symmetrical with respect to the endogenous period. In the present study, an explanation is given for the asymmetry based on a Kuramoto model which describes the neuronal network of the SCN. Our numerical simulations and theoretical analysis show that the asymmetry results from the difference in the intrinsic frequencies between two subgroups of the SCN, as well as the entrainment range is affected by the difference.

Entrainment range of the suprachiasmatic nucleus affected by the difference in the neuronal amplitudes between the light-sensitive and light-insensitive regions

Mammals not only can be synchronized to the natural 24-h light-dark cycle, but also to a cycle with a non-24-h period. The range of the period of the external cycle, for which the animals can be entrained to, is called the entrainment range, which differs among species. The entrainment range as a characteristic of the animal is determined by the main circadian clock, i.e., the suprachiasmatic nucleus (SCN) in the brain. The SCN is composed of ∼10000 heterogeneous neurons, which can be divided into two subgroups, i.e., the ventrolateral subgroup (VL) directly receiving the light information from the retina and relaying the information to the dorsomedial subgroup (DM). Among the SCN neurons, the amplitudes are different; however, it is unclear that the amplitude is related to the location of the neurons in experiments. In the present study, we examined the effect of the difference in the neuronal amplitude between the VL and the DM on the entrainment range of the SCN, based on a mathematical model, i.e., the Poincaré model, which is used to describe the circadian clock. We find that the maximal entrainment range is obtained when the difference is equal to a critical point. If the difference of the amplitudes of the VL neurons to the amplitudes of the DM neurons is smaller than a critical point, with the increase of the difference, the entrainment range of the SCN increases, while if the difference is larger than the critical point, the entrainment range decreases with the increase of the difference. Our finding may give a potential explanation for the diversity of the entrainment range among species.