Origin of exponential growth in nonlinear reaction networks.
Origin of exponential growth in nonlinear reaction networks.
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DOI：
10.1073/pnas.2013061117
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发表时间：
2020-11-10
影响因子：
11.1
通讯作者：
Jacobs-Wagner C
中科院分区：
文献类型：
--
作者：
Lin WH;Kussell E;Young LS;Jacobs-Wagner C
自然系统（例如细胞和生态系统）通常由具有非线性通量函数（例如米氏动力学和密度依赖选择）的反应网络（例如代谢网络或食物网）组成。尽管具有复杂的非线性，但从长远来看，这些系统通常表现出简单的指数增长。非线性网络如何实现指数增长仍然难以捉摸。我们的工作从数学角度证明了通量函数的多元可扩展性和重新调整系统的遍历性这两个原理如何保证明确的增长率。通过将数学的一个强大分支——遍历理论与生物学的生长研究联系起来，我们的理论框架可以概括各种生长模式（从平衡生长到周期性、准周期性甚至混沌行为），极大地扩展了可以研究的生长系统的类型。指数增长的系统在自然界中普遍存在，涵盖从单细胞的生化反应网络到生态系统的食物网的所有尺度。非线性系统中指数增长如何出现在数学上尚不清楚。在这里，我们描述了一个通用的理论框架，它揭示了长期增长的基本原理：通量函数的可扩展性和重新调整系统的遍历性。我们的理论表明，非线性通量不仅可以产生平衡生长，还可以产生振荡或混沌生长模式，解释了在细胞周期和生态系统中观察到的非平衡动力学。我们的数学框架广泛用于预测自然和合成网络的长期增长率、分析系统噪声和扰动的影响、验证增长率的经验和现象学定律以及研究自动催化和网络演化。
Natural systems (e.g., cells and ecosystems) generally consist of reaction networks (e.g., metabolic networks or food webs) with nonlinear flux functions (e.g., Michaelis–Menten kinetics and density-dependent selection). Despite their complex nonlinearities, these systems often exhibit simple exponential growth in the long term. How exponential growth emerges from nonlinear networks remains elusive. Our work demonstrates mathematically how two principles, multivariate scalability of flux functions and ergodicity of the rescaled system, guarantee a well-defined growth rate. By connecting ergodic theory, a powerful branch of mathematics, to the study of growth in biology, our theoretical framework can recapitulate various growth modalities (from balanced growth to periodic, quasi-periodic, or even chaotic behaviors), greatly expanding the types of growing systems that can be studied. Exponentially growing systems are prevalent in nature, spanning all scales from biochemical reaction networks in single cells to food webs of ecosystems. How exponential growth emerges in nonlinear systems is mathematically unclear. Here, we describe a general theoretical framework that reveals underlying principles of long-term growth: scalability of flux functions and ergodicity of the rescaled systems. Our theory shows that nonlinear fluxes can generate not only balanced growth but also oscillatory or chaotic growth modalities, explaining nonequilibrium dynamics observed in cell cycles and ecosystems. Our mathematical framework is broadly useful in predicting long-term growth rates from natural and synthetic networks, analyzing the effects of system noise and perturbations, validating empirical and phenomenological laws on growth rate, and studying autocatalysis and network evolution.
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影响因子：
48
作者：
Godin, Michel;Delgado, Francisco Feijo;Son, Sungmin;Grover, William H.;Bryan, Andrea K.;Tzur, Amit;Jorgensen, Paul;Payer, Kris;Grossman, Alan D.;Kirschner, Marc W.;Manalis, Scott R.
通讯作者：
Manalis, Scott R.
影响因子：
0.9
作者：
Farmer, Roger E. A.
通讯作者：
Farmer, Roger E. A.
影响因子：
3.6
作者：
Bender, David A.
通讯作者：
Bender, David A.
影响因子：
16.6
作者：
Ferrezuelo, Francisco;Colomina, Neus;Aldea, Marti
通讯作者：
Aldea, Marti
影响因子：
5.4
作者：
Arnold, PB;Moore, GD;Yaffe, LG
通讯作者：
Yaffe, LG