From observable fermentation data to hidden cell states: A modeling study of a mixotrophic Clostridium coculture under perfusion mode

Microbial cocultures exhibit complex population dynamics that are difficult to interpret because internal physiological states are only partially observable. In particular, active and dormant cell states can influence system-level behavior but are rarely resolved from standard fermentation measurements. In this study, we present a hybrid modeling framework that combines structured population-state reconstruction with sparse identification of nonlinear dynamics (SINDy) to analyze a Clostridium acetobutylicum - Clostridium ljungdahlii coculture under perfusion mode. The framework estimates active C a c and C l j biomass-equivalent trajectories from observable biomass and activity measurements, reconstructs dormant populations as model-constrained latent states, and uses these states to identify extracellular metabolite dynamics. After accounting for first-principles perfusion transport, SINDy identified sparse biological reaction terms associated with organic acid turnover, solvent formation, and acetone-to-isopropanol conversion. The resulting model captured active-biomass and metabolite trajectories and suggested that the coculture dynamics are consistent with acid-associated state transitions and sequential metabolic exchange. This framework provides a transparent strategy for interpreting partially observed microbial cocultures while explicitly treating dormant biomass as a latent reconstructed state.