Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100-DK Copenhagen, Denmark.
J Theor Biol. 2012 Aug 21;307:205-10. doi: 10.1016/j.jtbi.2012.04.011. Epub 2012 Apr 21.
We analyze a class of network motifs in which a short, two-node positive feedback motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point and a stable limit cycle coexist. At the bifurcation point the period of the oscillations diverges. Further, intrinsic noise can make the system switch between oscillatory state and the stationary state spontaneously. We find that this switching also occurs in previous models of circadian clocks that use this combination of positive and negative feedbacks. Our results suggest that real-life circadian systems may need specific regulation to prevent or minimize such switching events.
我们分析了一类网络基元，其中在三节点负反馈环中插入了一个短的双节点正反馈基元。我们证明，这样的网络可以经历分岔，达到一个稳定的平衡点和稳定的极限环共存的状态。在分岔点，振荡的周期发散。此外，内在噪声可以使系统自发地在振荡状态和静止状态之间切换。我们发现，这种切换也发生在以前使用这种正反馈和负反馈组合的生物钟模型中。我们的结果表明，现实生活中的生物钟系统可能需要特定的调节来防止或最小化这种切换事件。
