过程多位点磷酸化反应系统的全局收敛性
An All-Encompassing Global Convergence Result for Processive Multisite Phosphorylation Systems
摘要：
磷酸化，即酶介导的磷酸基团添加到分子上，是生物学中普遍存在的化学机制。多位点磷酸化，即磷酸基团添加到单个分子的多个位点，可以是分布性的或进行性的。分配系统可以是稳定的，而过程系统最近被证明是全局稳定的。然而，这种全局收敛结果仅被证明是进行性磷酸化/去磷酸化的特定机制（即所有催化反应都是可逆的）。因此，我们将这一结果推广到允许进行性磷酸化网络，其中每个反应可能是不可逆的，也考虑到可能的产物抑制。我们通过定义一个包罗万象的进程网络来实现这一点，该网络封装了所有这些方案，然后诉诸于Marcondes de Freitas，Wiuf和Feliu的最新结果，这些结果通过单调系统理论和网络/图约简（对应于去除中间复合物）来断言全局收敛。我们的研究结果形成了一个案例研究的问题时，全球收敛的反应和/或中间复合物被添加到或从网络中删除。
英文摘要：
Phosphorylation, the enzyme-mediated addition of a phosphate group to a molecule, is a ubiquitous chemical mechanism in biology. Multisite phosphorylation, the addition of phosphate groups to multiple sites of a single molecule, may be distributive or processive. Distributive systems can be bistable, while processive systems were recently shown to be globally stable. However, this global convergence result was proven only for a specific mechanism of processive phosphorylation/dephosphorylation (namely, all catalytic reactions are reversible). Accordingly, we generalize this result to allow for processive phosphorylation networks in which each reaction may be irreversible, and also to account for possible product inhibition. We accomplish this by defining an all-encompassing processive network that encapsulates all of these schemes, and then appealing to recent results of Marcondes de Freitas, Wiuf, and Feliu that assert global convergence by way of monontone systems theory and network/graph reductions (which correspond to removal of intermediate complexes). Our results form a case study into the question of when global convergence is preserved when reactions and/or intermediate complexes are added to or removed from a network.
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