混合机制磷酸化系统中振荡的出现
Emergence of oscillations in a mixed-mechanism phosphorylation system
摘要：
这项工作调查的振荡出现在一个最简单的细胞信号网络表现出的振荡，即双位点磷酸化和去磷酸化网络（徒劳的循环），其中磷酸化的机制是进行性的，而去磷酸化的一个是分配（或反之亦然）。最近Suwanmajo和Krishnan证明了这个网络产生振荡的事实。我们的结果，这显着扩展了他们的分析，如下。首先，在总量的三维空间中，具有稳定与不稳定稳态的系统之间的边界是由单个赫尔维茨行列式的消失所定义的表面。其次，这个表面一般由简单的Hopf分支。接下来，模拟表明，当稳态不稳定时，振荡是常态。最后，通过一个霍普夫分岔振荡的出现是由催化和缔合常数的分配部分的机制：如果这些速率常数满足两个不等式，那么系统一般承认一个霍普夫分岔。我们的证明是使劳斯-赫维茨标准，一个霍普夫分歧标准，由于杨，和一个单项参数化的稳定状态。
英文摘要：
This work investigates the emergence of oscillations in one of the simplest cellular signaling networks exhibiting oscillations, namely, the dual-site phosphorylation and dephosphorylation network (futile cycle), in which the mechanism for phosphorylation is processive while the one for dephosphorylation is distributive (or vice-versa). The fact that this network yields oscillations was shown recently by Suwanmajo and Krishnan. Our results, which significantly extend their analyses, are as follows. First, in the three-dimensional space of total amounts, the border between systems with a stable versus unstable steady state is a surface defined by the vanishing of a single Hurwitz determinant. Second, this surface consists generically of simple Hopf bifurcations. Next, simulations suggest that when the steady state is unstable, oscillations are the norm. Finally, the emergence of oscillations via a Hopf bifurcation is enabled by the catalytic and association constants of the distributive part of the mechanism: if these rate constants satisfy two inequalities, then the system generically admits a Hopf bifurcation. Our proofs are enabled by the Routh-Hurwitz criterion, a Hopf-bifurcation criterion due to Yang, and a monomial parametrization of steady states.
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