Origin of exponential growth in nonlinear reaction networks

Wei Hsiang Lin, Edo Kussell, Lai Sang Young, Christine Jacobs-Wagner

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)27795-27804
Number of pages10
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number45
StatePublished - Nov 10 2020


  • Exponential growth | reaction networks | systems biology | ergodic theory

ASJC Scopus subject areas

  • General


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