代谢循环的顽固根源
The Stubborn Roots of Metabolic Cycles
摘要：
对代谢网络结构进行分类的努力已经产生了非常详细的、基因组规模的细胞生化反应图谱。不幸的是，这些图谱无法捕捉代谢反应的动力学细节，而只能提供\textit{topological}信息来进行预测。因此，研究经常考虑代谢网络的拓扑结构在多大程度上决定其动态行为，而不考虑动力学细节。在这里，我们研究了一类称为非自催化代谢循环的代谢网络，并分析证明了一个关于其稳态稳定性的公开猜想。重要的是，我们的研究结果是不变的动力学参数，速率定律，平衡通量和代谢物浓度的选择。出乎意料的是，我们的证明暴露了一个基本的，但显然是公开的问题，定位两个多项式S = P+Q的和的根，当被加数多项式P和Q的根是已知的。我们得出两个新的结果命名的顽固根定理，提供了充分的条件下，S的根保持定性相同的根P.我们的工作说明了如何互补反馈，从经典领域，如动力系统，生物学，反之亦然，可以暴露基本的和潜在的被忽视的问题。
英文摘要：
Efforts to catalogue the structure of metabolic networks have generated highly detailed, genome-scale atlases of biochemical reactions in the cell. Unfortunately, these atlases fall short of capturing the kinetic details of metabolic reactions, instead offering only \textit{topological} information from which to make predictions. As a result, studies frequently consider the extent to which the topological structure of a metabolic network determines its dynamic behavior, irrespective of kinetic details. Here, we study a class of metabolic networks known as non-autocatalytic metabolic cycles, and analytically prove an open conjecture regarding the stability of their steady-states. Importantly, our results are invariant to the choice of kinetic parameters, rate laws, equilibrium fluxes, and metabolite concentrations. Unexpectedly, our proof exposes an elementary but apparently open problem of locating the roots of a sum of two polynomials S = P+Q, when the roots of the summand polynomials P and Q are known. We derive two new results named the Stubborn Roots Theorems, which provide sufficient conditions under which the roots of S remain qualitatively identical to the roots of P. Our work illustrates how complementary feedback, from classical fields like dynamical systems to biology and vice versa, can expose fundamental and potentially overlooked questions.
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