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 (
When studying observations of chemical reaction dynamics, closed form equations based on a putative mechanism may not be available. Yet when sufficient data from experimental observations can be obtained, even without knowing what exactly the physical meaning of the parameter settings or recorded variables are, data‐driven methods can be used to construct minimal (and in a sense, robust) realizations of the system. The approach attempts, in a sense, to circumvent physical understanding, by building intrinsic “information geometries” of the observed data, and thus enabling prediction without physical/chemical knowledge. Here we use such an approach to obtain evolution equations
- Publication Date:
- NSF-PAR ID:
- 10056125
- Journal Name:
- Israel Journal of Chemistry
- Volume:
- 58
- Issue:
- 6-7
- Page Range or eLocation-ID:
- p. 787-794
- ISSN:
- 0021-2148
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Sponsoring Org:
- National Science Foundation
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