Origin of Exponential Growth in Nonlinear Reaction Networks
Origin of exponential growth in nonlinear reaction networks Wei-Hsiang Lina,b,c,d,e,1, Edo Kussellf,g, Lai-Sang Youngh,i,j, and Christine Jacobs-Wagnera,b,c,d,e,k,1 aMicrobial Science Institute, Yale University, West Haven, CT 06516; bDepartment of Molecular, Cellular and Developmental Biology, Yale University, New Haven, CT 06511; cHoward Hughes Medical Institute, Yale University, New Haven, CT 06510; dDepartment of Biology, Stanford University, Palo Alto, CA 94305; eChemistry, Engineering & Medicine for Human Health (ChEM-H) Institute, Stanford University, Palo Alto, CA 94305; fCenter of Genomics and Systems Biology, Department of Biology, New York University, New York, NY 10003; gDepartment of Physics, New York University, New York, NY 10003; hCourant Institute of Mathematical Science, New York University, New York, NY 10012; iSchool of Mathematics, Institute for Advanced Study, Princeton, NJ 08540; jSchool of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540; and kDepartment of Microbial Pathogenesis, Yale School of Medicine, New Haven, CT 06510 Contributed by Christine Jacobs-Wagner, September 10, 2020 (sent for review June 24, 2020; reviewed by Jeff Gore and Ned S. Wingreen) Exponentially growing systems are prevalent in nature, spanning For example, the levels of metabolites and proteins can oscillate all scales from biochemical reaction networks in single cells to food during cell growth (13–15). The abundance of species in eco- webs of ecosystems. How exponential growth emerges in nonlin- systems can also oscillate (6) or exhibit nonperiodic fluctuations ear systems is mathematically unclear. Here, we describe a general (7). Yet, the biomass of these systems increases exponentially theoretical framework that reveals underlying principles of long- (6, 7, 16).
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