We consider a model of extracellular signal-regulated kinase regulation by dual-site phosphorylation and dephosphorylation, which exhibits bistability and oscillations, but loses these properties in the limit in which the mechanisms underlying phosphorylation and dephosphorylation become processive. Our results suggest that anywhere along the way to becoming processive, the model remains bistable and oscillatory. More precisely, in simplified versions of the model, precursors to bistability and oscillations (specifically, multistationarity and Hopf bifurcations, respectively) exist at all “processivity levels”. Finally, we investigate whether bistability and oscillations can exist together.

我们考虑了通过双位磷酸化和去磷酸化的细胞外信号调节激酶调控的模型，该模型表现出双稳性和振荡，但是在磷酸化和去磷酸化的基础机制变为可处理的极限范围内失去了这些特性。我们的结果表明，在进行过程的任何地方，该模型都保持双稳态和振荡。更准确地说，在模型的简化版本中，双稳态和振荡（分别是多平稳性和Hopf分支）分别存在于所有“过程级”。最后，我们研究双稳态和振动是否可以同时存在。