Dynamic biokinetic and hybrid modelling of nitrogen–carbon interactions governing photo-fermentative biomass growth and biohydrogen production by Rhodopseudomonas palustris

Rhodopseudomonas palustris produces biohydrogen throughout its growth phases, albeit constrained by complex carbon–nitrogen (C-N) interactions that poses significant modelling challenges. Using glycerol (as C source) and glutamate (as N source), this study generated datasets at four initial glycerol concentrations (10, 25, 50, and 75 mM) and developed two frameworks: a unified biokinetic model incorporating C–N interactions via a new parameter K 1 , and a hybrid model combining simplified mechanistic structure with polynomial regression to capture nonlinearities, an approach not previously reported for this biosystem. Using 10, 50, and 75 mM for training, the models achieved average errors of 15.7% (biokinetic) and 17.5% (hybrid), with deviations attributed to limited and noisy data. Over 85% activation of polynomial terms confirmed strong nonlinearity, consistent with K 1 interpretations. For the unseen 25 mM case, errors increased to 32.27% and 111.06%, respectively, highlighting overfitting but providing new insights for future DoE, optimisation and scale-up.