PDF(Pubmed)
Abstract：
Ordered distributive double phosphorylation is a recurrent motif in intracellular signaling and control. It is either sequential (where the site phosphorylated last is dephosphorylated first) or cyclic (where the site phosphorylated first is dephosphorylated first). Sequential distributive double phosphorylation has been extensively studied and an inequality involving only the catalytic constants of kinase and phosphatase is known to be sufficient for multistationarity. As multistationarity is necessary for bistability it has been argued that these constants enable bistability. Here we show for cyclic distributive double phosphorylation that if its catalytic constants satisfy an analogous inequality, then Hopf bifurcations and hence sustained oscillations can occur. Hence we argue that in distributive double phosphorylation (sequential or distributive) the catalytic constants enable non-trivial dynamics. In fact, if the rate constant values in a network of cyclic distributive double phosphorylation satisfy this inequality, then a network of sequential distributive double phosphorylation with the same rate constant values will show multistationarity-albeit for different values of the total concentrations. For cyclic distributive double phosphorylation we further describe a procedure to generate rate constant values where Hopf bifurcations and hence sustained oscillations can occur. This may, for example, allow for an efficient sampling of oscillatory regions in parameter space. Our analysis is greatly simplified by the fact that it is possible to reduce the network of cyclic distributive double phosphorylation to what we call a network with a single extreme ray. We summarize key properties of these networks.
摘要：
有序分布双磷酸化是细胞内信号传导和控制中的复发性基序。它是顺序的(其中最后磷酸化的位点首先去磷酸化)或环状的(其中首先磷酸化的位点首先去磷酸化)。已经广泛研究了顺序分布双磷酸化，并且已知仅涉及激酶和磷酸酶的催化常数的不等式足以实现多平稳性。由于多平稳性对于双稳态是必需的，因此有人认为这些常数可以实现双稳态。在这里，我们显示对于循环分布双磷酸化，如果其催化常数满足类似的不等式，然后Hopf分叉，因此可能会发生持续的振荡。因此，我们认为，在分布双重磷酸化（顺序或分布）中，催化常数能够实现非平凡的动力学。事实上,如果循环分布双磷酸化网络中的速率常数满足此不等式，然后，具有相同速率恒定值的顺序分布双重磷酸化网络将显示多平稳性-尽管总浓度的不同值。对于循环分布双磷酸化，我们进一步描述了一种生成速率恒定值的程序，其中Hopf分叉并因此发生持续振荡。这可能,例如,允许在参数空间中对振荡区域进行有效采样。由于可以将循环分布双重磷酸化的网络简化为我们所说的具有单个极端射线的网络，因此我们的分析大大简化了。我们总结了这些网络的关键属性。
