Abstract
The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. Mathematical models that maximize this balanced growth rate while accounting for mass conservation, reaction kinetics, and limits on dry mass per volume are inevitably non-linear. Here, we develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, GBA unveils fundamental quantitative principles of cellular resource allocation and growth; it accurately predicts the relationship between growth rates and ribosome concentrations in E. coli and yeast and between growth rate and dry mass density in E. coli.
Highlights
The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition
The mass conservation in chemical reaction networks is commonly described through a stoichiometric matrix N, where rows correspond to metabolites and each column describes the mass balance of one reaction[26]
The insight that optimal, density-constrained states of balanced growth are elementary growth states (EGSs) allowed us to derive the balance equations (Eq (10)); as any balanced growth state (BGS) can be expressed as a weighted average of EGSs (Theorem 3), our results allow a general characterization of the solution space of balanced growth
Summary
The biological fitness of microbes is largely determined by the rate with which they replicate their biomass composition. We develop a general theory for such models, termed Growth Balance Analysis (GBA), which provides explicit expressions for protein concentrations, fluxes, and growth rates. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that are related to metabolic control coefficients. Numerical growth rate optimization predicted qualitatively the growth-rate dependencies of cellular ribosome content, cell size, and the emergence of overflow metabolism We term this general modeling scheme Growth Balance Analysis (GBA). The most popular such method is flux balance analysis (FBA)[12,13]
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