Abstract:

Mathematical models are an important tool for understanding and predicting the complex behavior of biological cells. This behavior is driven by nonlinear physical constraints that cannot be fully captured in current modeling frameworks, which rely on simplified linear optimizations and phenomenological assumptions about cell biomass composition. Importantly, the critical trade-off between cell resource investment in reactants and catalysts of biochemical reactions can only be fully captured by models that incorporate nonlinear kinetic rate laws. When these kinetic models also account for catalyst production, limited density and dilution by growth of all components, they become holistic models capable of explaining the entire cell composition as a result of a nonlinear optimization problem.

This advantage of predicting the entire biomass composition from first principles comes at the cost of the much more difficult study of nonlinear optimization problems, as opposed to the simple study of linear models. Here, we summarize the need for this next generation of nonlinear cell models of growing cells, and present some recent developments on the mathematical foundation that simplifies the analytical study of such models, leading to general principles relevant to all growing cells. These analytical properties provide a quantitative way to understand the economics of the cell from first principles, in particular revealing the fundamental trade-offs in proteome allocation.

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