A Thermodynamic Framework Linking Black Box Growth models with Genome Scale Metabolite models

Genome scale metabolic models provide detailed mechanistic descriptions of cellular metabolism, whereas black box growth models capture physiological behaviors using a small number of effective parameters. However, the quantitative relationship between these two modeling scales remains unclear. In this study, we develop a thermodynamic framework that connects black box growth models with thermodynamically constrained genome scale metabolic models. By linking black box model parameters with Gibbs energy dissipation rates derived from genome scale metabolic models, we demonstrate that coarse grained physiological descriptions can be obtained from detailed metabolic networks while preserving their thermodynamic foundation. We validate this framework in both Escherichia coli and yeast, showing that the resulting black box models reproduce key physiological behaviors, including growth dynamics, biomass yield, and overflow metabolism observed experimentally. Our results indicate that black box growth models and genome scale metabolic models are connected through shared thermodynamic constraints, revealing a consistent thermodynamic basis across different levels of metabolic description. This framework provides a general approach for integrating detailed metabolic networks with simple black box growth models and enables efficient multiscale modeling of cellular metabolism.