A simple negative feedback loop of interacting genes or proteins has the potential to generate sustained oscillations. However, many biological oscillators also have a positive feedback loop, raising the question of what advantages the extra loop imparts. Through computational studies, we show that it is generally difficult to adjust a negative feedback oscillator’s frequency without compromising its amplitude, whereas with positive-plus-negative feedback, one can achieve a widely tunable frequency and near-constant amplitude. This tunability makes the latter design suitable for biological rhythms like heartbeats and cell cycles that need to provide a constant output over a range of frequencies. Positive-plus-negative oscillators also appear to be more robust and easier to evolve, rationalizing why they are found in contexts where an adjustable frequency is unimportant.
In the early embryonic cell cycle, Cdc2-cyclin B functions like an autonomous oscillator, whose robust biochemical rhythm continues even when DNA replication or mitosis is blocked. At the core of the oscillator is a negative feedback loop; cyclins accumulate and produce active mitotic Cdc2-cyclin B; Cdc2 activates the anaphase-promoting complex (APC); the APC then promotes cyclin degradation and resets Cdc2 to its inactive, interphase state. Cdc2 regulation also involves positive feedback, with active Cdc2-cyclin B stimulating its activator Cdc25 (refs 5-7) and inactivating its inhibitors Wee1 and Myt1 (refs 8-11). Under the correct circumstances, these positive feedback loops could function as a bistable trigger for mitosis, and oscillators with bistable triggers may be particularly relevant to biological applications such as cell cycle regulation. Therefore, we examined whether Cdc2 activation is bistable. We confirm that the response of Cdc2 to non-degradable cyclin B is temporally abrupt and switch-like, as would be expected if Cdc2 activation were bistable. We also show that Cdc2 activation exhibits hysteresis, a property of bistable systems with particular relevance to biochemical oscillators. These findings help establish the basic systems-level logic of the mitotic oscillator.
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