COBRA-k: A powerful framework bridging constraint-based and kinetic metabolic modeling

Mathematical modeling is key to understanding cellular metabolism. Two common approaches are kinetic modeling and constraint-based reconstruction and analysis (COBRA). COBRA models analyze steady-state fluxes using linear constraints but lack kinetic detail. Kinetic models offer mechanistic descriptions via differential equations but require (often unknown) kinetic parameters and enzyme concentrations. To bridge this gap, we introduce COBRA-k, a framework integrating nonlinear kinetic rate laws into COBRA models to consistently constrain metabolic fluxes, enzyme abundances, and metabolite concentrations. COBRA-k enables flexible exploration of metabolic steady states with optimization techniques, even with incomplete parametrization. COBRA-k models require solving computationally demanding mixed-integer nonlinear programs. We therefore developed a dedicated iterative algorithm, implemented in an open-source Python package. We applied COBRA-k to a large-scale Escherichia coli model, demonstrating its effectiveness and revealing holistic metabolic insights. For example, it accurately predicts and explains the phenomenon of high intracellular glutamate concentration. COBRA-k combines the flexibility of COBRA with kinetic precision, offering a powerful tool for predictive metabolic modeling and engineering.