summaryHigh substrate concentrations inhibit growth and may distort the metabolism of microorganisms. Mechanisms causing substrate inhibition are discwed and used to derive several mathematical models representative of the entire concentration range, including stimulation of growth by low substrate concentrations. These kinetic models are tested with a variety of batch culture measurements of specific growth rate and respiration rate at widely-ranging substrate concentrations. Using one of t.he kinetic models, equations are developed for batch, continuous, and exponential-feed reactors. Comparison of results obtained in continuous culture with results from exponential-feed culture systems is shown to offer a novel experimental method for evaluating the effect of the cell age distribution on the properties and metabolic activity of a culture.

SummaryInhibitory substrate levels are common in industrial fermentations and in biological waste-water treatment of many industrial wastes. Continuous microbial cultures are unstable to certain disturbances, such as shock loading by inhibitory substrates. Two feedback proportional control strategies are analyzed and compared for a simple model culture assumed representable by the culture concentrations of biomass and a single rate-limiting and growth-limiting nutrient (substrate)). One control strategy, the well known turbidostat, consists of adjusting culture holding time (e.g., by flow rate adjustment) in response to deviations in turbidity or some other measure of culture biomass concentration. The other control strategy is to adjust holding time in response to deviations in limiting nutrient concentrations in the culture. This second control. strategy, termed the nutristat, can be superior to the turbidosJat i? many applications. The sign and magnitude of the dimensionless group { ( X / I ; D ) ( d p / d S ] ; ), is shown to be an important determinant in the behavior of the open loop and the two closed loop processes. This characteristic group is positive when the specific growth rate is increased by increases in the nutrient concentration, zero when the growth rate is unaffected by the nutrient concentration, and negative in the presence of nutrient or substrate inhibition.The effects of process modifications and of modeling assumptions on the control of the process are discussed and more sophisticated control schemes are also proposed.

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SummaryThis 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 uiilis (ATCC 9226) was grown with sodium acetate as growth-limiting 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 30°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 ( p ) 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 increaaing acetate inhibition a t lower pH. Both defects in the model and insufficient data a t each pH are responsible. A modified six parameter model was developed to include pH effects by varying five of six parameters with hydrogen ion concentration (H+) aa follows: JACKSON AND EDWARDS99% 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 steady-stste 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.