Phase Synchronization Based on Regions Heterogeneity in Suprachiasmatic Nucleus

Abstract

Based on the suprachiasmatic nucleus (SCN) structure and molecular biology, numerous significant results have been obtained via some well-designed network-models as regards to circadian rhythm, in which synchronized cells can be entrained by a 24-h light-dark cycle. However, existing models cannot explain the phase synchronization clearly, such as jet lag. In this paper, a modified Kuramoto model in SCN network is proposed. Results show that the model exhibits some prominent characteristics of phase synchronization. The results obtained in this model also provide some deep insights for the mechanism of circadian rhythm, and lay a foundation for further discussion and analysis. Introduction Mammalian behavior rhythms are dominated by a central pacemaker located in the suprachiasmatic nucleus (SCN), which is composed of about 20,000 oscillating neurons [1]. The dissociated neurons have scattered periods between 20 and 28 hours [2]. There are quantities of research on circadian rhythm in single cell level [3, 4]. According to these research, several clock proteins exhibit periodical oscillation, including PERIOD(PER1,2,3), FRQENCY(FRQ1,2), CRYPTOCHROME(CRY1,2). Hence, it is reasonable to assume that limit cycles can be generated in the circadian system [5]. Based on these facts, Goodwin model, Poincare model and some Kuramoto-type models have been applied to circadian system [6-9]. SCN can be divided into ventral-lateral (VL) subregion and dorsal-medial (DM) subregion, which have different functions and topologies. VL and DM are light sensitive and insensitive respectively. VL, about a quarter of SCN, is entrained by the external light-dark cycle, while DM shows free-running oscillation except that it receives light signals via VL [10]. In topology, VL is a small-world network while DM is a nearest neighbor network, moreover, neurons in VL directly affect neurons in DM and the intercellular coupling in DM is weak [10]. Accordingly, it is necessary to divide SCN into VL and DM to discuss phases of neuronal oscillators. Neurons in SCN form a network consists of heterogeneous oscillators, which emerges a robust circadian rhythm. Although the structures of CRY, CLOCK and BMAL have been verified, the mechanism of circadian rhythms is still not clear. To explain the mechanism of circadian rhythms, phase synchronization is also necessary to be considered as well as period synchronization. In this paper, a modified Kuramoto model is proposed to discuss the effect of structure parameter on the phase synchronization. The modified Kuramoto model Neural oscillators have the similar periods and phases to make the circadian rhythm work well. So it is necessary to discuss phase synchronization or entrainment. In recent research [11], VL is denoted with a WS small-world network matrix A, while DM is denoted with a cyclic matrix B. Based on single-direction dissemination of light signal, the coupling from VL to DM is denoted by International Industrial Informatics and Computer Engineering Conference (IIICEC 2015) © 2015. The authors Published by Atlantis Press 711 C. Connectivity matrix of neurons in SCN can be described as 0 A C D B   =    , where ij D indicates a directed connectivity from neuron i to neuron j. For simplicity, periodical light signal is denoted by sinusoidal function, and the modified Kuramoto model system is displayed as follows.