Model reduction in microalgae culture: an application of Tikhonov's theorem

Michaelis–Menten kinetics have long provided a framework for enzymatic reactions, and Monod directly extended this analogy to microbial populations growing under substrate limitation. Multiplicative composition of the Monod model are now widely used to represent growth on multiple substrates, particularly in the case of microalgae, photosynthetic unicellular organisms of increasing relevance for research and industry. To go beyond these models, we represent microalgal growth using biochemical reaction networks (BioCRNs), which provide a simplified yet mechanistic view of algae–environment interactions. Since such networks naturally lead to large systems of ordinary differential equations (ODEs), Tikhonov's theorem provides a powerful tool for reducing their complexity by exploiting the multiple time scales of biological processes. Applying this approach iteratively to a BioCRN of photoautotrophic growth, we fitted the model to experimental growth curves, obtaining quantitative estimates of reaction rates. This approach confirms the presence of multiple time scales; such as light absorption, nutrient uptake, and cell division; and allows us to assess their biological consistency. This reduction establishes a formal link between mechanistic BioCRN models and classical ODEs of Monod or logistic type, thereby providing both theoretical insight and practical validation.