Indic Premananda, Schwartz William J, Paydarfar David
Department of Neurology, University of Massachusetts Medical School, Worcester, MA 01655, USA.
J R Soc Interface. 2008 Aug 6;5(25):873-83. doi: 10.1098/rsif.2007.1248.
Nonlinear interactions among coupled cellular oscillators are likely to underlie a variety of complex rhythmic behaviours. Here we consider the case of one such behaviour, a doubling of rhythm frequency caused by the spontaneous splitting of a population of synchronized oscillators into two subgroups each oscillating in anti-phase (phase-splitting). An example of biological phase-splitting is the frequency doubling of the circadian locomotor rhythm in hamsters housed in constant light, in which the pacemaker in the suprachiasmatic nucleus (SCN) is reconfigured with its left and right halves oscillating in anti-phase. We apply the theory of coupled phase oscillators to show that stable phase-splitting requires the presence of negative coupling terms, through delayed and/or inhibitory interactions. We also find that the inclusion of real biological constraints (that the SCN contains a finite number of non-identical noisy oscillators) implies the existence of an underlying non-uniform network architecture, in which the population of oscillators must interact through at least two types of connections. We propose that a key design principle for the frequency doubling of a population of biological oscillators is inhomogeneity of oscillator coupling.
耦合细胞振荡器之间的非线性相互作用可能是多种复杂节律行为的基础。在此，我们考虑一种此类行为的情况，即由一群同步振荡器自发分裂为两个反相振荡的子群（相位分裂）导致的节律频率加倍。生物相位分裂的一个例子是饲养在持续光照下的仓鼠昼夜运动节律的频率加倍，其中视交叉上核（SCN）中的起搏器被重新配置，其左右两半部分反相振荡。我们应用耦合相位振荡器理论表明，稳定的相位分裂需要通过延迟和/或抑制性相互作用存在负耦合项。我们还发现，纳入实际生物学限制（SCN包含有限数量的非相同噪声振荡器）意味着存在潜在的非均匀网络架构，其中振荡器群体必须通过至少两种类型的连接进行相互作用。我们提出，生物振荡器群体频率加倍的一个关键设计原则是振荡器耦合的不均匀性。
