Xu Jinshan, Gu Changgui, Pumir Alain, Garnier Nicolas, Liu Zonghua
Department of Physics, East China Normal University, Shanghai 200062, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041903. doi: 10.1103/PhysRevE.86.041903. Epub 2012 Oct 8.
The synchronization of biological activity with the alternation of day and night (circadian rhythm) is performed in the brain by a group of neurons, constituting the suprachiasmatic nucleus (SCN). The SCN is divided into two subgroups of oscillating cells: the ventrolateral (VL) neurons, which are exposed to light (photic signal), and the dorsomedial (DM) neurons, which are coupled to the VL cells. When the coupling between these neurons is strong enough, the system synchronizes with the photic period. Upon increasing the cell coupling, the entrainment of the DM cells has been recently shown to occur via a very sharp (jumping) transition when the period of the photic input is larger than the intrinsic period of the cells. Here, we characterize this transition with a simple realistic model. We show that two bifurcations possibly lead to the disappearance of the endogenous mode. Using a mean-field model, we show that the jumping transition results from a supercritical Hopf-like bifurcation. This finding implies that both the period and strength of the stimulating photic signal, and the relative fraction of cells in the VL and DM compartments, are crucial in determining the synchronization of the system.
生物活动与昼夜交替（昼夜节律）的同步是由构成视交叉上核（SCN）的一组神经元在大脑中完成的。SCN分为两个振荡细胞亚群：暴露于光（光信号）的腹外侧（VL）神经元，以及与VL细胞耦合的背内侧（DM）神经元。当这些神经元之间的耦合足够强时，系统就会与光周期同步。最近研究表明，当光输入周期大于细胞的固有周期时，随着细胞耦合的增加，DM细胞的夹带会通过非常急剧（跳跃）的转变发生。在这里，我们用一个简单的现实模型来描述这种转变。我们表明，两种分岔可能导致内源性模式的消失。使用平均场模型，我们表明跳跃转变是由超临界霍普夫型分岔引起的。这一发现意味着，刺激光信号的周期和强度，以及VL和DM区室中细胞的相对比例，在决定系统的同步方面都至关重要。
