A hybrid response surface–ODE framework for multiscale predictions of microalgae growth dynamics

Accurately predicting microbial growth across varying environmental conditions and cultivation scales remains a central challenge in mathematical biology. ODE models offer mechanistic interpretability but typically rely on fixed kinetic parameters, restricting their validity to narrow operating ranges. Data-driven approaches such as Response Surface Methodology (RSM) [Breig et al., 2021] accommodate parameter variability yet either disregard temporal dynamics or risk generating biologically implausible trajectories. We propose a hybrid framework embedding bounded, biologically interpretable RSM surfaces into ODE systems, letting kinetic parameters vary continuously with environmental factors. We validate the framework on microalgae cultures grown in microplates (200 µL) and flasks (50 mL), spanning 85 combinations of light intensity and nutrient availability for a total of over 1,300 growth curves. The model captures nonlinear light–nutrient interactions, predicts growth trajectories under untested conditions, and consistently outperforms classical mechanistic benchmarks [Kambe et al., 2022, Martínez et al., 2020]. We further show that microplate- and flask-derived parameter surfaces are related through morphological transformations, suggesting that the functional structure of growth responses is conserved across a 250-fold volume increase. This opens perspectives for high-throughput screening strategies [Wolf et al., 2024] where small-scale experiments inform larger-scale bioprocess design