• KSBB Journal
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• v.13 no.6
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• pp.730-734
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• 1998

The mathematical model of specific growth rate of Saccharomyces cerevisiae ATCC 24858 is proposed as a function of sugar and ethanol concentrations by the combination of Andrew's equation and Aiba's equation. The maximum concentration of sugar Sm, which was the highest concentration of sugar not having any effect on the growth inhibition, was 150 g/L and the substrate inhibition was expressed as a function of (S-Sm). The maximum specific growth inhibition, was 150 g/L and the substrate inhibition was expressed as a function of (S-Sm). The maximum specific growth rate ${\mu}m$, Monod's constant Ks, and Andrew's inhibition constant KI were 0.49 hr-1, 19 g/L, and 139 g/L, respectively. The maximum ethanol concentration, Pm, which did not show any inhibition effect on the specific growth rate was found to be 2 g/L. Therefore, the ethanol inhibition was represented as a function of (P-Pm). The final mathematical model for the specific growth rate of the microorganism in this work is proposed as the following. And the average percent of errors between the calculated specific growth rate and the experimental values was 5.96%.

• Journal of Environmental Science International
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• v.9 no.1
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• pp.75-80
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• 2000

Kinetic data for the acid phase anaerobic digestion were presented in this study and the constants were determined with acid production rate and gas production rate. Process models based on continuous culture theory were used to describe the characteristics of the acid forming microorganisms and to enable further development toward utilization of the process in a more rational manner. Acid phase digestion can be separated with appropriate manipulation of hydraulic retention time in anaerobic digestion. Kinetic analysis of data from the various hydraulic retention times using a phase specific model obtained form the acid phase indicated maximum specific growth rate of 0.40/h, saturation constant of 2,000mgCOD.$\ell$, yield coefficient of 0.35 mgVSS/msCOD utilized and decay constant of 0.04/h for the acid production rate. Similar analysis of data for the gas production rate indicated maximum specific growth rate of 0.003/h, saturation constant of 2,200mgCOD/$\ell$, yield coefficient of 0.035 mgVSS/mgCOD utilized and decay constant of 0.06/h.

• Journal of Korean Society of Environmental Engineers
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• v.27 no.4
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• pp.409-413
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• 2005

A method to estimate the autotrophic maximum specific growth rate is presented in this paper. First of all, the concentration of nitrifier is simulated based on the amount of N nitrified, the sludge age and the default value for the decay coefficient. Secondly the OUR of the sludge with access of ammonia is measured. The maximum specific growth rate can be calculated as ${\mu}_{max,A}\;=\;OUR_{max,A}/Y_A$. It was demonstrated that the maximum specific growth rate of autotrophic biomass is not a constants but a time variable parameter. It is concluded that using $OUR_{max,A}$ for dynamic estimating maximum specific growth rate is a good approach and that using a constant value for the maximum specific growth rate over a longer period of time could not predict the performance of activated sludge plants.

• Microbiology and Biotechnology Letters
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• v.25 no.3
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• pp.235-239
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• 1997

Chlorococcum littorale has been grown in high $CO_2$ concentrations to utilize $CO_2$ gas in the polluted air. The effect of incident light intensity on the specific growth rate is expressed by a photoinhibition model, showing half- saturation constant, $K_0\;as\;8\;(W/m^2)$ and inhibition constant, Ki as 35 $(W/m^2)$. The maximum specific growth rate was also estimated as 0.095 (1/day) under this condition. This strain maintained the optimum growth rate in 20% of $CO_2$ gas but 50% of input $CO_2$ gas is the maximum concentration considering the economical efficiency. The maximum Specific $CO_2$ consumption rate, $qCO_2$ was measured as 17.48 (mg $CO_2/g$ dry wt./day) in batch cultivation, 11.2 (mg $CO_2/g$ dry wt./day) in fed-batch cultivation and 10.87 (mg $CO_2/g$ dry wt./day) at 0.065 (1/day) of dilution rate in continuous cultivation. The chemical composition of the biomass obtained from this process showed 32.5% of protein, 27.5% of lipid, 16.5% of carbohydrate and ash 11.7%.

• Journal of Microbiology and Biotechnology
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• v.17 no.7
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• pp.1221-1225
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• 2007

A ${\beta}$-ionone-resistant mutant strain isolated from the red yeast Xanthophyllomyces dendrorhous KCTC 7704 was used for batch and continuous fermentation kinetic studies with glucose media in a 2.5-1 jar fermentor at $22^{\circ}C$ and pH 4.5. The kinetic pattern of growth and carotenoid concentration in the batch fermentations exhibited a so-called mixed-growth-associated product formation, possibly due to the fact that the content of intracellular carotenoids depends on the degree of physical maturation toward adulthood. To determine the maximum specific growth rate constant (${\mu}_m$) and Monod constant ($K_s$) for the mutant, glucose-limited continuous culture studies were performed at different dilution rates within a range of $0.02-0.10\;h^{-1}$. A reciprocal plot of the steady-state data (viz., reciprocal of glucose concentration versus residence time) obtained from continuous culture experiments was used to estimate a ${\mu}_m$ of $0.15\;h^{-1}$ and $k_s$ of 1.19 g/l. The carotenoid content related to the residence time appeared to assume a typical form of saturation kinetics. The maximum carotenoid content ($X_m$) for the mutant was estimated to be $1.04\;{\mu}g/mg$ dry cell weight, and the Lee constant ($k_m$), which was tentatively defined in this work, was found to be 3.0 h.

• Korean Journal of Food Science and Technology
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• v.37 no.2
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• pp.194-198
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• 2005

Growth curves of Listeria monocytogenes in modified surimi-based imitation crab (MIC) broth were obtained by measuring cell concentration in MIC broth at different culture conditions [initial cell numbers, $1.0{\times}10^{2},\;1.0{\times}10^{3}\;and\;1.0{\times}10^{4}$, colony forming unit (CFU)/mL; temperature, 15, 20, 25, 37, and $40^{\circ}C$] and applied to Gompertz model to determine microbial growth indicators, maximum specific growth rate constant (k), lag time (LT), and generation time (GT). Maximum specific growth rate of L. monocytogenes increased rapidly with increasing temperature and reached maximum at $37^{\circ}C$, whereas LT and GT decreased with increasing temperature and reached minimum at $37^{\circ}C$. Initial cell number had no effect on k, LT, and GT (p > 0.05). Polynomial and square root models were developed to express combined effects of temperature and initial cell number using Gauss-Newton Algorism. Relative coefficients of experimental k and predicted k of polynomial and square root models were 0.92 and 0.95, respectively, based on response surface model. Results indicate L. monocytogenes growth was mainly affected by temperature and square root model was more effective than polynomial model for growth prediction.

• Journal of Microbiology and Biotechnology
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• v.21 no.6
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• pp.652-658
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• 2011

The growth kinetics of Streptomyces noursei NRRL 5126 was investigated under different aeration and agitation combinations in a 5.0 l stirred tank fermenter. Poly-${\varepsilon}$-lysine biosynthesis, cell mass formation, and glycerol utilization rates were affected markedly by both aeration and agitation. An agitation speed of 300 rpm and aeration rate at 2.0 vvm supported better yields of 1,622.81 mg/l with highest specific productivity of 15 mg/l.h. Fermentation kinetics performed under different aeration and agitation conditions showed poly- ${\varepsilon}$-lysine fermentation to be a growth-associated production. A constant DO at 40% in the growth phase and 20% in the production phase increased the poly-${\varepsilon}$-lysine yield as well as cell mass to their maximum values of 1,992.35 mg/l and 20.73 g/l, respectively. The oxygen transfer rate (OTR), oxygen utilization rate (OUR), and specific oxygen uptake rates ($qO_2$) in the fermentation broth increased in the growth phase and remained unchanged in the stationary phase.

• Korean Journal of Food Science and Technology
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• v.37 no.6
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• pp.1012-1017
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• 2005

Predictive growth model of putrefactive bacteria of surimi-based imitation crab in the modified surimi-based imitation crab (MIC) broth was investigated. The growth curves of putrefactive bacteria were obtained by measuring cell number in MIC broth under different conditions (Initial cell number, $1.0{\times}10^2,\;1.0{\times}10^3$ and $1.0{\times}10^4$ colony forming unit (CFU)/mL; temperature, $15^{\circ}C,\;20^{\circ}C\;and\;25^{\circ}C$) and applied them to Gompertz model. The microbial growth indicators, maximum specific growth rate constant (k), lag time (LT) and generation time (GT), were calculated from Gompertz model. Maximum specific growth rate (k) of putrefactive bacteria was become fast with rising temperature and fastest at $25^{\circ}C$. LT and GT were become short with rising temperature and shortest at $25^{\circ}C$. There were not significant differences in k, LT and GT by initial cell number (p>0.05). Polynomial model, $k=-0.2160+0.0241T-0.0199A_0$, and square root model, $\sqrt{k}=0.02669$ (T-3.5689), were developed to express the combination effects of temperature and initial cell number, The relative coefficient of experimental k and predicted k of polynomial model was 0.87 from response surface model. The relative coefficient of experimental k and predicted k of square root model was 0.88. From above results, we found that the growth of putrefactive bacteria was mainly affected by temperature and the square root model was more credible than the polynomial model for the prediction of the growth of putrefactive bacteria.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.40 no.2
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• pp.95-101
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• 2007

We investigated the growth and phosphate uptake of a toxic dinoflagellate, Gymnodinium catenatum, isolated from Yeosuhae Bay, South Korea. A short-term phosphate uptake experiment revealed that its maximum uptake and the half-saturation constant were 1.39 pmol/cell/hr and $2.65{\mu}M$, respectively. In a semicontinuous culture, the maximum specific growth rate and minimum phosphorus cell quota of G. catenatum were 0.39/day and 1.27 pmol/cell, respectively. Thus, G. catenatum is a poor competitor in terms of inorganic nutrient use and is unlikely to form blooms in Yeosuhae Bay.

• Journal of Korean Society of Water and Wastewater
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• v.27 no.4
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• pp.457-468
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• 2013

Based on the activated sludge model(ASM), a mathematical model which represents the aerobic sludge digestion by sequencing batch reactor(SBR) combined with ultrasonic treatment was composed and performed in this study. Aerobic digestion using sequencing batch reactor(SBR) equipped with ultrasound treatment was also experimented for the purpose of parameter calibration. Most of the presented kinetic parameters in ASM or ASM2 could be used for the aerobic digestion of sludge but the parameters related in hydrolysis and decay rate needed modification. Hydrolysis rate constant of organic matter in aerobic condition was estimated at $0.3day^{-1}$ and the maximum growth rate for autotrophs in aerobic condition was $0.618day^{-1}$. Solubilization reactions of particulate organics and nitrogen by ultrasonication was added in this kinetic model. The solubilization rate is considered to be proportional to the specific energy which is defined by specific ultrasound power and sonication time. The solubilization rate constant by ultrasonication was estimated at $0.202(W/L)^{-1}day^{-1}$ in this study. Autotrophs as well as heterotrophs also decomposed by ultrasonic treatment and the nitrification reaction was limited by the lack of autotrophs accumulation in the digester.