The Gompertz model and its applications in microbial growth and bioproduction kinetics: Past, present and future

The Gompertz model, initially proposed for human mortality rates, has found various applications in growth analysis across the biotechnological field. This paper presents a comprehensive review of the Gompertz model's applications in the biotechnological field, examining its past, present, and future. The past of the Gompertz model was examined by tracing its origins to 1825, and then it underwent various modifications throughout the 20th century to increase its applicability in biotechnological fields. The Zwietering-modified version has proven to be a versatile tool for calculating the lag-time and maximum growth rate/quantity in microbial growth. In addition, the present applications of the Gompertz model to microbial growth kinetics and bioproduction (e.g., hydrogen, methane, caproate, butanol, and hexanol production) kinetics have been comprehensively summarized and discussed. We highlighted the importance of standardized citations and guidance on model selection. The Zwietering-modified Gompertz model and the Lay-modified Gompertz model are recommended for describing microbial growth kinetics and bioproduction kinetics, recognized for their widespread use and provision of valuable kinetics information. Finally, in response to the current Gompertz models' focus on internal mortality, the modified Makeham-Gompertz models that consider both internal/external mortality were introduced and validated for microbial growth and bioproduction kinetics with good fitting performance. This paper provides a perspective of the Gompertz model and offers valuable insights that facilitate the diverse applications of this model in microbial growth and bioproduction kinetics.