Washout and non-washout solutions of a system describing microbial fermentation process under the influence of growth inhibitions and maximal concentration of yeast cells

• Published in: Mathematical biosciences 2017-07, Vol.289, p.40-50
• Main Authors: Kasbawati, Gunawan, Agus Yodi, Sidarto, Kuntjoro Adjie
• Format: Article
• Language: English
• Subjects: (Non-)washout solution; Bifurcation analysis; Cell density; Colony Count, Microbial; Dilution; Ethanol; Ethanol - metabolism; Fermentation; Fermentation - drug effects; Glucose; Glucose - metabolism; Glucose - pharmacology; Growth inhibition; Mathematical models; Microorganisms; Oscillations; Parameters; Saccharomyces cerevisiae - cytology; Saccharomyces cerevisiae - drug effects; Saccharomyces cerevisiae - growth & development; Saccharomyces cerevisiae - metabolism; Steady state; Studies; Substrate inhibition; Unstructured fermentation model; Yeast
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2017.04.003

•On the derived unstructured model of fermentation process we find two types of steady state solution, namely washout and non-washout solutions that respectively describe the disappearance and the coexistence of the yeast cells and the two products.•There exists a feasible region for operating parameters the inlet glucose and the dilution rate in which the washout solution disappears.•Regarding the non-washout solution, three types of region are obtained in which the fermentation system admits a unique locally stable solution, a unique locally stable solution towards which other nearby solutions exhibit damped oscillations, and multiple solutions where one is locally stable while the other is unstable.•There exists an optimal inlet glucose at which the highest stable steady state solutions of yeast cells and products are reached. There also exists a critical inlet glucose at which the non-washout solution jumped to the washout solution.•Increasing the carrying capacity of the yeast cells expands the feasible region of the inlet glucose in which the non-washout solution appears. An unstructured model for the growth of yeast cell on glucose due to growth inhibitions by substrate, products, and cell density is discussed. The proposed model describes the dynamical behavior of fermentation system that shows multiple steady states for a certain regime of operating parameters such as inlet glucose and dilution rate. Two types of steady state solutions are found, namely washout and non-washout solutions. Furthermore, different numerical impositions to the two parameters put in evidence three results regarding non-washout solution: a unique locally stable non-washout solution, a unique locally stable non-washout solution towards which other nearby solutions exhibit damped oscillations, and multiple non-washout solutions where one is locally stable while the other is unstable. It is also found an optimal inlet glucose which produces the highest cell and ethanol concentration.