Abstract
This work concerns mathematical modeling of the rate of microbial growth on inhibitory levels of nutrients as affected by pH, concentration of the nutrients, temperature, cultivation method, and method of data analysis. Candida utilis (ATCC 9226) was grown with sodium acetate as growthβlimiting carbon and energy source in mineral salts medium in shake flask and continuous cultures to study inhibition by excess acetate. Differential shake flask cultures were grown at low yeast concentrations at temperatures (T) of 25 and 30Β°C, pH's between 5.5 and 7.0, and acetate concentrations (S) between 0.25 and 3.0% (w/v). Growth data were exponential with correlation coefficients greater than 0.995 in 49 of 56 experiments; the lowest correlation coefficient was 0.986. Specific growth rates (ΞΌ) determined by graphical methods showed only fair correlation with those determined by regression analysis. Both sets of specific growth rate data were grouped at constant T and pH and fitted to the three parameter equation,
The improvement in use of the fitted equation instead of the mean value was significant with greater than 70% confidence in all (14 groups) and 90% confidence in only half of the data groups; the correlation does not improve with the increasing acetate inhibition at lower pH. Both defects in the model and insufficient data at each pH are responsible. A modified six parameters with hydrogen ion concentration(H^+^) as follows:
Specific growth rates calculated with the six parameter equation matched observed values in all groups of isothermal data better than the means with greater than 99% confidence. The six parameter model adequately represents effects of acetate and hydrogen ion concentrations under constant or slowly changing environmental conditions and balanced growth; although better models probably exist. Thus steadyβstste and transient continuous culture experiments agreed with many published growth yields, but specific growth rates could only be predicted qualitatively from the model fit to the shake flask data. The data and present models could be incorporated into published models for transient growth at low nutrient concentrations to correlate and perhaps predict microbial growth kinetics over a much wider range of growth conditions than now possible.