Origin of exponential growth in nonlinear reaction networks

• DOI: 10.1073/pnas.2013061117
• Publication Date: 2020-10-23T00:00:27Z
• Authors: Wei-Hsiang Lin; Edo Kussell; Lai-Sang Young; Christine Jacobs-...
• Keywords: 0303 health sciences; 03 medical and health sciences; Nonlinear Dynamics; Physical Sciences; Growth; Models, Theoretical; Models, Biological; Ecosystem; Biological Phenomena

Significance 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.