TABLE 1.
Equations used for primary model development
| Model | Equationa |
|---|---|
| Cell growth | dX/dt = [μmax × (1 − X/Xmax)n − α] × X when t > λ |
| Sugar consumption (maltose) | dM/dt = −1/YX/M × dX/dt − mM × X |
| Sugar consumption (fructose) | dF/dt = −1/YX/F × dX/dt − mF × X |
| Lactic acid production | dL/dt = −1/YL/S × (dM/dt + dF/dt) |
| Bacteriocin production | dB/dt = kB × dX/dt − kinact × X × B |
Abbreviations: X, biomass concentration (in grams of CDM per liter); Xmax, maximum attainable biomass concentration (in grams of CDM per liter); μmax, maximum specific growth rate (per hour); t, time (in hours); λ, duration of the lag phase (in hours); n, inhibition exponent; α, specific rate of death (per hour); M, residual maltose concentration (in grams of maltose per liter); F, residual fructose concentration (in grams of fructose per liter); mM, maintenance coefficient for maltose (in grams of maltose per gram of CDM per hour); mF, maintenance coefficient for fructose (in grams of fructose per gram of CDM per hour); YX/M, cell yield coefficient for maltose (in grams of CDM per gram of maltose); YX/F, cell yield coefficient for fructose (in grams of CDM per gram of fructose); L, amount of lactic acid produced (in grams of lactic acid per liter); YL/M, yield coefficient for lactic acid production based on maltose (in grams of lactic acid per gram of maltose); YL/F, yield coefficient for lactic acid production based on fructose (in grams of lactic acid per gram of fructose); B, soluble bacteriocin activity (in arbitrary units [AU] per liter); kB, specific bacteriocin production (in AU per gram of CDM); kinact, apparent rate of bacteriocin inactivation (in liters per gram of CDM per hour).