Mono- and Polyauxic Growth Kinetics: A Semi-Mechanistic Framework for Complex Biological Dynamics

Area of Science:

• Bioprocess Engineering
• Mathematical Biology
• Microbial Kinetics

Background:

• Industrial bioprocess design requires accurate microbial growth kinetic models.
• Classical models struggle with multiphasic (polyauxic) growth and lack biological interpretability.
• Mechanistic models are often too complex for real-world applications.

Purpose of the Study:

• To develop a unified semi-mechanistic mathematical framework for microbial growth kinetics.
• To explicitly define key kinetic parameters like maximum specific reaction rate and lag phase duration.
• To accurately model polyauxic growth using constrained sigmoidal phases.

Main Methods:

• Reformulated Boltzmann and Gompertz equations into semi-mechanistic forms.
• Represented polyauxic growth as a weighted sum of sigmoidal phases with biological constraints.
• Employed a two-stage optimization (Differential Evolution + L-BFGS-B) for nonlinear regression.
• Utilized Charbonnier loss and outlier removal for data robustness.
• Applied information criteria (AIC, BIC) for model parsimony.

Main Results:

• The framework successfully modeled complex microbial growth, including polyauxic behaviors.
• Demonstrated that single-phase models can obscure critical metabolic shifts in co-digestion.
• Validated the approach using experimental anaerobic digestion data.
• Ensured parameter identifiability, temporal consistency, and biological plausibility.

Conclusions:

• The proposed framework offers a robust and interpretable approach to microbial kinetic modeling.
• It overcomes limitations of classical and mechanistic models for industrial bioprocesses.
• Provides a more accurate representation of microbial dynamics, especially in mixed cultures and complex substrates.