ArticlePLoS computational biology2023
Mathematical properties of optimal fluxes in cellular reaction networks at balanced growth.
Article in PLoS computational biology, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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5 citing papers in PubMed.
- Enzyme kinetics shapes the growth response of metabolic networks.PLoS computational biology · 2026Article
- GBA Solver: a user-friendly web server for growth balance analysis.Bioinformatics (Oxford, England) · 2025Article
- A comprehensive review of computational cell cycle models in guiding cancer treatment strategies.NPJ systems biology and applications · 2024Review
- Costs of ribosomal RNA stabilization affect ribosome composition at maximum growth rate.Communications biology · 2024Article
- Turnover number predictions for kinetically uncharacterized enzymes using machine and deep learning.Nature communications · 2023Article
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4 authors.
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Abstract
The physiology of biological cells evolved under physical and chemical constraints, such as mass conservation across the network of biochemical reactions, nonlinear reaction kinetics, and limits on cell density. For unicellular organisms, the fitness that governs this evolution is mainly determined by the balanced cellular growth rate. We previously introduced growth balance analysis (GBA) as a general framework to model and analyze such nonlinear systems, revealing important analytical properties of optimal balanced growth states. It has been shown that at optimality, only a minimal subset of reactions can have nonzero flux. However, no general principles have been established to determine if a specific reaction is active at optimality. Here, we extend the GBA framework to study the optimality of each biochemical reaction, and we identify the mathematical conditions determining whether a reaction is active or not at optimal growth in a given environment. We reformulate the mathematical problem in terms of a minimal number of dimensionless variables and use the Karush-Kuhn-Tucker (KKT) conditions to identify fundamental principles of optimal resource allocation in GBA models of any size and complexity. Our approach helps to identify from first principles the economic values of biochemical reactions, expressed as marginal changes in cellular growth rate; these economic values can be related to the costs and benefits of proteome allocation into the reactions' catalysts. Our formulation also generalizes the concepts of Metabolic Control Analysis to models of growing cells. We show how the extended GBA framework unifies and extends previous approaches of cellular modeling and analysis, putting forward a program to analyze cellular growth through the stationarity conditions of a Lagrangian function. GBA thereby provides a general theoretical toolbox for the study of fundamental mathematical properties of balanced cellular growth.
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