不稳定的核心是化学反应网络不稳定的根源

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-03-06 DOI:10.1098/rspa.2023.0694
Nicola Vassena, Peter F. Stadler
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引用次数: 0

摘要

在生化网络中,超线性增长和振荡等复杂动力学特征通常被认为是自催化作用的结果。对于包括广义质量作用动力学和迈克尔-门顿动力学在内的一大类参数丰富的动力学模型,我们表明,化学计量矩阵的某些子矩阵,即所谓的不稳定核心,足以使反应网络具有不稳定性,并有可能产生这种复杂的动力学行为。子矩阵的行列式区分了具有单一实正特征值的不稳定正反馈和不具有实正特征值的不稳定负反馈。自催化核心正是梅兹勒矩阵的不稳定正反馈。因此,化学网络中存在与自催化无关的动态不稳定源。我们利用这种直觉来设计具有超线性增长和振荡的非自动催化生化网络。
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Unstable cores are the source of instability in chemical reaction networks

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes generalized mass action kinetics and Michaelis–Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction network to admit instability and potentially give rise to such complex dynamical behaviour. The determinant of the submatrix distinguishes unstable-positive feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive feedbacks that are Metzler matrices. Thus there are sources of dynamical instability in chemical networks that are unrelated to autocatalysis. We use such intuition to design non-autocatalytic biochemical networks with superlinear growth and oscillations.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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