Analytical solution for a hybrid Logistic‐Monod cell growth model in batch and continuous stirred tank reactor culture

• Published in: Biotechnology and bioengineering Vol. 117; no. 3; pp. 873 - 878
• Main Author: Xu, Peng
• Format: Journal Article
• Language: English
• Published: United States Wiley Subscription Services, Inc 01.03.2020; John Wiley and Sons Inc
• Subjects: analytical solution; Bacteria; batch and CSTR culture; Biomass; Bioreactors; Biotechnology; Carrying capacity; Cell culture; Cell Culture Techniques; Cell growth; Cell Proliferation; Communication to the Editor; Constraining; Continuously stirred tank reactors; Exact solutions; Fermentation; Growth models; Growth rate; hybrid model; Kinetics; logistic growth; Logistic Models; Mathematical models; Models, Biological; monod equation; Nutrients; Optimization; Organic chemistry; Reactors; Substrate inhibition; cell growth; hybrid model; analytical solution; logistic growth; batch and CSTR culture; monod equation
• ISSN: 0006-3592; 1097-0290; 1097-0290
• DOI: 10.1002/bit.27230

Monod and Logistic growth models have been widely used as basic equations to describe cell growth in bioprocess engineering. In the case of the Monod equation, the specific growth rate is governed by a limiting nutrient, with the mathematical form similar to the Michaelis–Menten equation. In the case of the Logistic equation, the specific growth rate is determined by the carrying capacity of the system, which could be growth‐inhibiting factors (i.e., toxic chemical accumulation) other than the nutrient level. Both equations have been found valuable to guide us build unstructured kinetic models to analyze the fermentation process and understand cell physiology. In this work, we present a hybrid Logistic‐Monod growth model, which accounts for multiple growth‐dependent factors including both the limiting nutrient and the carrying capacity of the system. Coupled with substrate consumption and yield coefficient, we present the analytical solutions for this hybrid Logistic‐Monod model in both batch and continuous stirred tank reactor (CSTR) culture. Under high biomass yield (Yx/s) conditions, the analytical solution for this hybrid model is approaching to the Logistic equation; under low biomass yield condition, the analytical solution for this hybrid model converges to the Monod equation. This hybrid Logistic‐Monod equation represents the cell growth transition from substrate‐limiting condition to growth‐inhibiting condition, which could be adopted to accurately describe the multi‐phases of cell growth and may facilitate kinetic model construction, bioprocess optimization, and scale‐up in industrial biotechnology. Monod and Logistic growth models have been widely used to describe cell growth. Here Xu presents the analytical solution for a hybrid Logistic‐Monod equation accounting for both the substrate and carrying capacity of the system. Incorporating growth‐inhibition into the Monod equation captures cellular physiological transition from substrate‐limiting condition to growth‐inhibiting condition, which may facilitate bioprocess optimization when this hybrid model is integrated with existing process control software.