A dynamic cell cycling model for growth of baker's yeast and its application in profit optimization

A cell cycling model for unequal budding yeast Saccharomyces cerevisiae is proposed and verified by steady state data from experiments available in the literature. This model can be used to determine the relative fraction of the cells in any cycling phase or with any genealogical age during fermentation. As the quality of yeast is strongly influenced by the cycling process, the model could therefore be used to control the quality of the harvested yeast cells. The input of the cell cycling model is the specific growth rate , which is obtained from a metabolic model for S. cerevisiae proposed earlier. With this extended model system not only the quality control, but also the whole economical profit optimization can be carried out. Simulations were done to optimize the profit of a commercial scale baker's yeast production process by manipulating substrate feeding rate and substrate concentration under different aeration rates, fermentation periods and other conditions applied in industry.List of Symbols B h budding phase - C _d1, C _d2, C _p1' parameters in cycling phase equations - C _p2, C _b1, C _b2, d _s m Sauter-diameter - E kg/m³ ethanol concentration - E1, E2 state variables in the metabolic model - E _G mean relative gas hold-up - f parameter vector of the regulation model - F system matrix of the regulation model - F or F(t) m³/h substrate feeding rate - Fr Froude number - FBC, FDC, FPC % fraction of daughter cells, unbudded daughter cells and unbudded parent cells - g m/s² acceleration of gravity - K _B1–3, K _EG parameters in metabolic model - K ₃, K _Ad , L ₃ K ₃ E, K_O, K_S limitation constants for ethanol, oxygen and substrate - k _La h^–1 volumetric mas transfer coefficient - m _ATP mol(gh)^–1 maintenance coefficient - nb, nd, np number of cycling age intervals in budding cycling phase, unbudded daughter cycling phase and unbudded parent cycling phase - Nt number of total cells - OF mg/dm³ concentration of dissolved oxygen - P kg total yeast product in dry weight - P/O effectiveness of oxidative phosphorylation - q _O20 mol(gh)^–1 minimum specific oxygen uptake ability - q _O2 mol(gh)^–1 specific oxygen uptake rate - q _O2max mol(gh)^–1 maximum q _O2 given by metabolic regulation - q _s mol(gh)^–1 specific glucose uptake rate - q _Smax mol(gh)^–1 maximum q _S - R(·) switch function - r _Ac mol(gh)^–1 specific acetyl-CoA-consumption rate - r _Acmax saturation rate of r _Ac - r _E1 mol(gh)^–1 specific ethanol production rate - r _E2 mol(gh)^–1 specific ethanol uptake rate - r _SO mol(gh)^–1 minimum value of r _Smax - r _s mol(gh)^–1 specific rate of glycolysis - r _Smax mol(gh)^–1 maximum specific rate of gluconeogenesis given by metabolic regulation - S kg/m³ total reduced sugar concentration - S _R kg/m³ substrate concentration in feed - T h cell number doubling time - T _f h fermentation period - Ud h unbudded daughter phase - Up h unbudded parent phase - V _F m³ volume of liquid phase in fermentor - V _G m³/h aeration rate - w _sg m/s superficial gas velocity - X kg/m³ dried cell concentration - Y _ATP g(molATP)^–1 yield coefficient of ATP - z state vector in regulation model - the factor of fermentative activity decrease caused by budding cells - or(t) h^–1 specific growth rate - h discrete unit of cycling age