Disassortative Network Structure Improves the Synchronization between Neurons in the Suprachiasmatic Nucleus.

In mammals, an endogenous clock located in the suprachiasmatic nucleus (SCN) of the brain regulates the circadian rhythms of physiological and behavioral activities. The SCN is composed of about 20,000 neurons that are autonomous oscillators with nonidentical intrinsic periods ranging from 22 h to 28 h. These neurons are coupled through neurotransmitters and synchronized to form a network, which produces a robust circadian rhythm of a uniform period. The neurons, which are the nodes in the network, are known to be heterogeneous in their characteristics, which is reflected in different phenotypes and different functionality. This heterogeneous nature of the nodes of the network leads to the question as to whether the structure of the SCN network is assortative or disassortative. Thus far, the disassortativity of the SCN network has not been assessed and neither have its effects on the collective behaviors of the SCN neurons. In the present study, we build a directed SCN network composed of hundreds of neurons for a single slice using the method of transfer entropy, based on the experimental data. Then, we measured the synchronization degree as well as the disassortativity coefficient of the network structure (calculated by either the out-degrees or the in-degrees of the nodes) and found that the network of the SCN is a disassortative network. Furthermore, a positive relationship is observed between the synchronization degree and disassortativity of the network, which is confirmed by simulations of our modeling. Our finding suggests that the disassortativity of the network structure plays a role in the synchronization between SCN neurons; that is, the synchronization degree increases with the increase of the disassortativity, which implies that a more heterogeneous coupling in the network of the SCN is important for proper function of the SCN.

A Patient Suffering From Neurodegenerative Disease May Have a Strengthened Fractal Gait Rhythm.

Scale invariance in stride series, namely, the series shows similar patterns across multiple time scales, is used widely as a non-invasive identifier of health assessment. Detailed calculations in the literature with standard tools, such as de-trended fluctuation analysis and wavelet transform modulus maxima seem to lead a conclusion that patients suffering from neurodegenerative diseases have weakened fractal gait rhythm compared with healthy persons. These variance-based methods are dynamical mechanism dependent, namely, for some dynamical process the scale invariance cannot be detected qualitatively, while for some others the scale invariance can be detected correctly, but the estimated value of scaling exponent is not correct. Generally, we have limited knowledge on the dynamical mechanism. What is more, the stride series for the patients have a typical finite length of ~300, which may lead to unreasonable statistical fluctuations to the evaluation procedure. Hence, how a neurodegenerative disorder disease affects the scale invariance is still an open problem. In this paper the balanced estimation of diffusion entropy (cBEDE) is used to overcome the limitations. The volunteers include healthy individuals and patients with/without freezing of gait (FOG). It is found that scale invariance exists widely in the gait time series for all the individuals. The average of scaling exponents for patients suffering from FOG is similar with or larger than that for healthy individuals, and similar with that for patients without FOG. The patients not suffering from FOG have an average of scaling exponent significantly larger than that for healthy people. From the results estimated by cBEDE, we can conclude that a patient may have an increased scaling exponent, which is contradictory qualitatively with that in the literatures.