Mono and Polyauxic Growth Kinetic Models

Abstract: Accurate modeling of microbial growth curves is essential for understanding and optimizing bioprocesses in biotechnology and environmental engineering. While classical monoauxic models such as Monod, Boltzmann, and Gompertz are widely used, they often lack biological interpretability or fail to capture the complex, multiphasic growth patterns observed in systems with mixed substrates or microbial communities. This paper presents a methodological framework for reparametrizing the Boltzmann and Gompertz equations, assigning direct biological significance to each parameter and enabling their application to both monoauxic and polyauxic (multi-phase) growth scenarios. Polyauxic growth is modeled as a weighted sum of sigmoidal functions, with constraints for model identifiability and biological plausibility. Robust parameter estimation is achieved using a Lorentzian loss function, combined with a global-local optimization strategy (Particle Swarm Optimization and Nelder-Mead), and systematic outlier exclusion using the ROUT method. Model parsimony is enforced via established information criteria. This workflow enables reliable, reproducible, and interpretable extraction of kinetic parameters from complex growth data and is broadly applicable to other fields where sigmoidal patterns are observed.