Goldbeter Albert, Gonze Didier, Houart Gerald, Leloup Jean-Christophe, Halloy Jose, Dupont Genevieve
Unite de Chronobiologie theorique, Faculte des Sciences, Universite Libre de Bruxelles, Campus Plaine, C.P. 231, B-1050 Brussels, Belgium.
Chaos. 2001 Mar;11(1):247-260. doi: 10.1063/1.1345727.
We present an overview of mechanisms responsible for simple or complex oscillatory behavior in metabolic and genetic control networks. Besides simple periodic behavior corresponding to the evolution toward a limit cycle we consider complex modes of oscillatory behavior such as complex periodic oscillations of the bursting type and chaos. Multiple attractors are also discussed, e.g., the coexistence between a stable steady state and a stable limit cycle (hard excitation), or the coexistence between two simultaneously stable limit cycles (birhythmicity). We discuss mechanisms responsible for the transition from simple to complex oscillatory behavior by means of a number of models serving as selected examples. The models were originally proposed to account for simple periodic oscillations observed experimentally at the cellular level in a variety of biological systems. In a second stage, these models were modified to allow for complex oscillatory phenomena such as bursting, birhythmicity, or chaos. We consider successively (1) models based on enzyme regulation, proposed for glycolytic oscillations and for the control of successive phases of the cell cycle, respectively; (2) a model for intracellular Ca(2+) oscillations based on transport regulation; (3) a model for oscillations of cyclic AMP based on receptor desensitization in Dictyostelium cells; and (4) a model based on genetic regulation for circadian rhythms in Drosophila. Two main classes of mechanism leading from simple to complex oscillatory behavior are identified, namely (i) the interplay between two endogenous oscillatory mechanisms, which can take multiple forms, overt or more subtle, depending on whether the two oscillators each involve their own regulatory feedback loop or share a common feedback loop while differing by some related process, and (ii) self-modulation of the oscillator through feedback from the system's output on one of the parameters controlling oscillatory behavior. However, the latter mechanism may also be viewed as involving the interplay between two feedback processes, each of which might be capable of producing oscillations. Although our discussion primarily focuses on the case of autonomous oscillatory behavior, we also consider the case of nonautonomous complex oscillations in a model for circadian oscillations subjected to periodic forcing by a light-dark cycle and show that the occurrence of entrainment versus chaos in these conditions markedly depends on the wave form of periodic forcing. (c) 2001 American Institute of Physics.
我们概述了代谢和遗传控制网络中导致简单或复杂振荡行为的机制。除了对应于向极限环演化的简单周期性行为外，我们还考虑了复杂的振荡行为模式，如爆发型的复杂周期性振荡和混沌。还讨论了多个吸引子，例如稳定稳态与稳定极限环之间的共存（硬激发），或两个同时稳定的极限环之间的共存（双节律性）。我们通过一些作为选定示例的模型，讨论了导致从简单振荡行为向复杂振荡行为转变的机制。这些模型最初是为了解释在各种生物系统的细胞水平上实验观察到的简单周期性振荡而提出的。在第二阶段，对这些模型进行了修改，以允许出现复杂的振荡现象，如爆发、双节律性或混沌。我们依次考虑：（1）基于酶调节的模型，分别用于糖酵解振荡和细胞周期连续阶段的控制；（2）基于运输调节的细胞内Ca(2+)振荡模型；（3）基于盘基网柄菌细胞中受体脱敏的环磷酸腺苷振荡模型；以及（4）基于遗传调节的果蝇昼夜节律模型。确定了导致从简单振荡行为向复杂振荡行为转变的两类主要机制，即（i）两种内源性振荡机制之间的相互作用，其可以有多种形式，明显的或更微妙的，这取决于这两个振荡器各自是否涉及自身的调节反馈回路，或者是否共享一个共同的反馈回路，同时在一些相关过程上有所不同；以及（ii）振荡器通过系统输出对控制振荡行为的参数之一的反馈进行自我调制。然而，后一种机制也可以被视为涉及两个反馈过程之间的相互作用，每个反馈过程都可能能够产生振荡。尽管我们的讨论主要集中在自主振荡行为的情况，但我们也考虑了在一个受明暗周期周期性强迫的昼夜振荡模型中的非自主复杂振荡情况，并表明在这些条件下同步与混沌的出现明显取决于周期性强迫的波形。（c）2001美国物理研究所。
