• Title/Summary/Keyword: Gompertz equation

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Development of Predictive Growth Models for Staphylococcus aureus and Bacillus cereus on Various Food Matrices Consisting of Ready-to-Eat (RTE) Foods

  • Kang, Kyung-Ah;Kim, Yoo-Won;Yoon, Ki-Sun
    • Food Science of Animal Resources
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    • v.30 no.5
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    • pp.730-738
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    • 2010
  • We developed predictive growth models for Staphylococcus aureus and Bacillus cereus on various food matrices consisting primarily of ready-to-eat (RTE) foods. A cocktail of three S. aureus strains, producing enterotoxins A, C, and D, or a B. cereus strain, were inoculated on sliced bread, cooked rice, boiled Chinese noodles, boiled bean sprouts, tofu, baked fish, smoked chicken, and baked hamburger patties at an initial concentration of 3 log CFU/g and stored at 8, 10, 13, 17, 24, and $30^{\circ}C$. Growth kinetic parameters were determined by the Gompertz equation. The square-root and Davey models were used to determine specific growth rate and lag time values, respectively, as a function of temperature. Model performance was evaluated based on bias and accuracy factors. S. aureus and B. cereus growth were most delayed on sliced bread. Overall, S. aureus growth was significantly (p<0.05) more rapid on animal protein foods than carbohydrate-based foods and vegetable protein foods. The fastest growth of S. aureus was observed on smoked chicken. B. cereus growth was not observed at 8 and $10^{\circ}C$. B. cereus growth was significantly (p<0.05) more rapid on vegetable protein foods than on carbohydrate-based foods. The secondary models developed in this study showed suitable performance for predicting the growth of S. aureus and B. cereus on various food matrices consisting of RTE foods.

A Response Surface Model Based on Absorbance Data for the Growth Rates of Salmonella enterica Serovar Typhimurium as a Function of Temperature, NaCl, and pH

  • Park, Shin-Young;Seo, Kyo-Young;Ha, Sang-Do
    • Journal of Microbiology and Biotechnology
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    • v.17 no.4
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    • pp.644-649
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    • 2007
  • Response surface model was developed for predicting the growth rates of Salmonella enterica sv. Typhimurium in tryptic soy broth (TSB) medium as a function of combined effects of temperature, pH, and NaCl. The TSB containing six different concentrations of NaCl (0, 2, 4, 6, 8, and 10%) was adjusted to an initial of six different pH levels (pH 4, 5, 6, 7, 8, 9, and 10) and incubated at 10 or $20^{\circ}C$. In all experimental variables, the primary growth curves were well $(r^2=0.900\;to\;0.996)$ fitted to a Gompertz equation to obtain growth rates. The secondary response surface model for natural logarithm transformations of growth rates as a function of combined effects of temperature, pH, and NaCl was obtained by SAS's general linear analysis. The predicted growth rates of the S. Typhimurium were generally decreased by basic (9, 10) or acidic (5, 6) pH levels or increase of NaCl concentrations (0-8%). Response surface model was identified as an appropriate secondary model for growth rates on the basis of coefficient determination $(r^2=0.960)$, mean square error (MSE=0.022), bias factor $(B_f=1.023)$, and accuracy factor $(A_f=1.164)$. Therefore, the developed secondary model proved reliable predictions of the combined effect of temperature, NaCl, and pH on growth rates for S. Typhimurium in TSB medium.

Validation of Predictive Liquid Model Systems for the Growth of Listeria monocytogenes and Yersinia enterocolitica on Pork at Various Temperatures

  • Rho, Min-Jeong;Chung, Myung-Sub;Kim, Jeong-Weon;Park, Ji-Yong
    • Food Science and Biotechnology
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    • v.14 no.1
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    • pp.42-45
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    • 2005
  • The present study was carried out to envisage the aerobic growth of Listeria monocytogenes and Yersinia enterocolitica on pork, which is one of the major meat sources in Korea. The results were compared with the previously developed predictive model systems for the verification of microbial growth in a real situation during pork processing. Pork loin samples (8.0 g, 5 mm thick) were aseptically prepared and inoculated with each pathogen by immersing into the respective inoculums for one min. Each of the samples were then wrapped with PE film and stored at 5, 10, and $15^{\circ}C$ up to 36 days to measure the growth profile of the respective pathogens. The growth parameters were calculated by using Gompertz equation and were compared with the previously reported data. The predicted generation time (GT) of L. monocytogenes at 5, 10 and $15^{\circ}C$ was 28.74, 7.85 and 4.02 hr, respectively, and for Y. enterocolitica was 10.29, 4.74 and 2.50 hr, at the same temperatures respectively. In this study, the GT values predicted on pork were slightly higher than the values predicted in other studies using liquid model systems. Unlike previous reports, both the pathogens were found to grow at $5^{\circ}C$ on pork. This finding recommends the necessity of controlling the growth of both the pathogens during the slaughtering process and distribution.

Kinetic Behavior of Salmonella on Low NaNO2 Sausages during Aerobic and Vacuum Storage

  • Ha, Jimyeong;Gwak, Eunji;Oh, Mi-Hwa;Park, Beomyoung;Lee, Jeeyeon;Kim, Sejeong;Lee, Heeyoung;Lee, Soomin;Yoon, Yohan;Choi, Kyoung-Hee
    • Food Science of Animal Resources
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    • v.36 no.2
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    • pp.262-266
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    • 2016
  • This study evaluated the growth kinetics of Salmonella spp. in processed meat products formulated with low sodium nitrite (NaNO2). A 5-strain mixture of Salmonella spp. was inoculated on 25-g samples of sausages formulated with sodium chloride (NaCl) (1.0%, 1.25%, and 1.5%) and NaNO2 (0 and 10 ppm) followed by aerobic or vacuum storage at 10℃ and 15℃ for up to 816 h or 408 h, respectively. The bacterial cell counts were enumerated on xylose lysine deoxycholate agar, and the modified Gompertz model was fitted to the Salmonella cell counts to calculate the kinetic parameters as a function of NaCl concentration on the growth rate (GR; Log CFU/g/h) and lag phase duration (LPD; h). A linear equation was then fitted to the parameters to evaluate the effect of NaCl concentration on the kinetic parameters. The GR values of Salmonella on sausages were higher (p<0.05) with 10 ppm NaNO2 concentration than with 0 ppm NaNO2. The GR values of Salmonella decreased (p<0.05) as NaCl concentration increased, especially at 10℃. This result indicates that 10 ppm NaNO2 may increase Salmonella growth at low NaCl concentrations, and that NaCl plays an important role in inhibiting Salmonella growth in sausages with low NaNO2.

Prediction of Listeria monocytogenes Growth Kinetics in Sausages Formulated with Antimicrobials as a Function of Temperature and Concentrations

  • Bang, Woo-Suk;Chung, Hyun-Jung;Jin, Sung-Sik;Ding, Tian;Hwang, In-Gyun;Woo, Gun-Jo;Ha, Sang-Do;Bahk, Gyung-Jin;Oh, Deog-Hwan
    • Food Science and Biotechnology
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    • v.17 no.6
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    • pp.1316-1321
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    • 2008
  • This study was conducted to develop a model to describe the effect of antimicrobials [potassium sorbate (PS), potassium lactate (PL), and combined PL and sodium diacetate (SDA, PLSDA)] on the growth parameters of Listeria monocytogenes such as specific growth rate (SGR) and lag phase periods (LT) in air-dried raw sausages as a function of storage temperature (4, 10, 16, and $25^{\circ}C$). Results showed that the SGR of L monocytogenes was dependent on the storage temperature and level of antimicrobials used. The most effective treatment was the 4% PLSDA, followed by the 2% PLSDA and 4% PL and 0.2% PS exhibited the least antimicrobial effect. Increased growth rates were observed with increasing storage temperatures from 4 to $25^{\circ}C$. The growth data were fitted with a Gompertz equation to determine the SGR and LT of the L. monocytogenes. Six polynomial models were developed for the SGR and LT to evaluate the effect of PS (0.1, 0.2%) and PL (2,4%) alone and PLSDA (2, 4%) on the growth kinetics of L. monocytogenes from 4 to $25^{\circ}C$.

Growth and Production of Sinonovacula constricta (Bivalvia) from the Hwaseong Tidal Flat in the Namyang Bay, Korea (가리맛조개(Sinonovacula constricta: Bivalvia)의 성장과 생산 (경기 남양만 화성조간대))

  • Koh, Chul-Hwan;Yang, Mee-Ra;Chang, Won-Keun
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.2 no.1
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    • pp.21-30
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    • 1997
  • The present study reports the density, growth and production of a razor clam, Sinollovacula constricta, which is known to be one of the important fishreies catches from the Korean tidal flat. The annual yield reached to about 6,000 metric tons per year till 1994. The study was conducted on the Hwaseong tidal flat located on the central west coast, 40 kilometers south-west from Seoul. The annual yield of the razor clam in this area reached to about 50% of the total catch from the whole Korean coast. Samples were colleted monthly at 14 occasions from May 1992 to August 1993. Density of S. constricta ranged from 92~165 individuals per square meter during the study period. General trend of decreasing density was observed when the animal became older, but an exception was the year class of 1991 whose density was lower than that of 1990. The size of the shell was clearly separated into two classes during fall and winter (from September to February), however, the maximum frequency of the length of small size classes moved to right after February. It indicates a fast growth of young clams from spring to summer. Fast growth of the shell could also be examined by the growth curve. The shell growth of the whole life span was described by the von Bertalanffy equation of $L_t=89.3{\times}[1{\exp}\{-0.58{\times}(t+0.73\}]$. The growth in flesh dry weight was well fitted to the Gompertz growth model with the equation, $W_t=5.00{\times}{\exp}\{-4.31{\times}{\exp}(-0.043{\times}t)\}$. The clam lost about 30% of the body weight during spawning in August. The annual production calculated based on the data from September 1992 to August 1993 amounted to 150 g $DW{\cdot}m^{-2}{\cdot}yr^{-1}$ which was 2~50 fold higher than those of other bivalves occurred in Korea. This estimate was patitioned by each year classes; 87.5 by 1992, 53.4 by 1991, 59.0 by 1990 and -30.0 g $DW{\cdot}m^{-2}{\cdot}yr^{-1}$ by 1989 year class.

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Growth and Predictive Model of Wild-type Salmonella spp. on Temperature and Time during Cut and Package Processing in Cold Pork Meats (냉장돈육 가공공정 온도와 시간에서의 Wild-type Salmonella spp.의 성장특성 및 예측모델)

  • Song, Ju Yeon;Kim, Yong Soo;Hong, Chong Hae;Bahk, Gyung Jin
    • Journal of Food Hygiene and Safety
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    • v.28 no.1
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    • pp.7-12
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    • 2013
  • This study presents the influence on growth properties determined using a novel predictive growth model of wild-type Salmonella spp. KSC 101 by variations in the temperature and time during cut packaging in cold, uncooked pork meat. The experiment performed for model development included an arrangement of different temperatures ($0^{\circ}C$, $5^{\circ}C$, $10^{\circ}C$, $15^{\circ}C$, and $20^{\circ}C$) and time durations (0, 1, 2, and 3 hours) that reflect actual pork-cut and packaging processes. No growth was observed at $0^{\circ}C$ and $5^{\circ}C$, whereas some growth was observed at $10^{\circ}C$, $15^{\circ}C$, and $20^{\circ}C$, with a mean increase of only 0.34 log CFU/g. The growth observed at $20^{\circ}C$ was more robust than that observed at $15^{\circ}C$, but the difference was not statistically significant (p > 0.05). However, compared with PMP (Pathogen Modeling Program), the wild-type Salmonella spp. KSC 101 showed a more rapid growth. We used the Gompertz 4 parameter equation as the primary model, and the exponential decay formula as the secondary model. The estimated $R^2$ values were 0.99 or higher. The developed model was evaluated by comparison of the experimental and predictive values, and the values were in agreement with the ${\pm}0.5$ log CFU/g, although the RMSE (Root mean square error) value was 0.103, which indicates a slight overestimation. Therefore, we suggest that the developed predictive growth model would be useful as a tool for evaluating sanitation criteria in pork cut-packaging processes.

Prediction of Growth of Escherichia coli O157 : H7 in Lettuce Treated with Alkaline Electrolyzed Water at Different Temperatures

  • Ding, Tian;Jin, Yong-Guo;Rahman, S.M.E.;Kim, Jai-Moung;Choi, Kang-Hyun;Choi, Gye-Sun;Oh, Deog-Hwan
    • Journal of Food Hygiene and Safety
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    • v.24 no.3
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    • pp.232-237
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    • 2009
  • This study was conducted to develop a model for describing the effect of storage temperature (4, 10, 15, 20, 25, 30 and $35^{\circ}C$) on the growth of Escherichia coli O157 : H7 in ready-to-eat (RTE) lettuce treated with or without (control) alkaline electrolyzed water (AIEW). The growth curves were well fitted with the Gompertz equation, which was used to determine the specific growth rate (SGR) and lag time (LT) of E. coli O157 : H7 ($R^2$ = 0.994). Results showed that the obtained SGR and LT were dependent on the storage temperature. The growth rate increased with increasing temperature from 4 to $35^{\circ}C$. The square root models were used to evaluate the effect of storage temperature on the growth of E. coli O157 : H7 in lettuce samples treated without or with AIEW. The coefficient of determination ($R^2$), adjusted determination coefficient ($R^2_{Adj}$), and mean square error (MSE) were employed to validate the established models. It showed that $R^2$ and $R^_{Adj}$ were close to 1 (> 0.93), and MSE calculated from models of untreated and treated lettuce were 0.031 and 0.025, respectively. The results demonstrated that the overall predictions of the growth of E. coli O157: H7 agreed with the observed data.

Predictive Modeling for the Growth of Listeria monocytogenes as a Function of Temperature, NaCl, and pH

  • PARK SHIN YOUNG;CHOI JIN-WON;YEON JIHYE;LEE MIN JEONG;CHUNG DUCK HWA;KIM MIN-GON;LEE KYU-HO;KIM KEUN-SUNG;LEE DONG-HA;BAHK GYUNG-JIN;BAE DONG-HO;KIM KWANG-YUP;KIM CHEOL-HO
    • Journal of Microbiology and Biotechnology
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    • v.15 no.6
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    • pp.1323-1329
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    • 2005
  • A mathematical model was developed for predicting the growth kinetics of Listeria monocytogenes in tryptic soy broth (TSB) as a function of combined effects of temperature, pH, and NaCl. The TSB containing four different concentrations of NaCl (2, 4, 5, and $10\%$) was initially adjusted to six different pH levels (pH 5, 6, 7, 8, 9, and 10) and incubated at 4, 10, 25, or 37$^{circ}C$. In all experimental variables, the primary growth curves were well fitted ($r^{2}$=0.982 to 0.998) to a Gompertz equation to obtain the lag time (LT) and specific growth rate (SGR). Surface response models were identified as appropriate secondary models for LT and SGR on the basis of coefficient determination ($r^{2}$=0.907 for LT, 0.964 for SGR), mean square error (MSE=3.389 for LT, 0.018 for SGR), bias factor ($B_{1}$B,=0.706 for LT, 0.836 for SGR), and accuracy factor ($A_{f}$=1.567 for LT, 1.213 for SGR). Therefore, the developed secondary model proved reliable predictions of the combined effect of temperature, NaCl, and pH on both LT and SGR for L. monocytogenes in TSB.

Reproduction and Early Life History of Gunnel, Pholis fangi in the Yellow Sea off Korea (한국 서해 흰베도라치 (Pholis fangi)의 생식과 초기 생활사)

  • Hwang, Sun-Do;Lee, Tae-Won
    • Korean Journal of Ichthyology
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    • v.13 no.1
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    • pp.6-18
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    • 2001
  • Larvae of the gunnel Pholis fangi were collected in coastal waters off Daecheon with a bag net from March to June, 1988, and with a ring larva net in February 1989. Maturity and spawning period were analyzed by examination of the gonads of adult fish collected with a bag net from May 1998 through November 1999. In February, the larvae were widely distributed in the outer and inner Cheonsu Bay. From March to April the larvae were present mainly the inner bay; they were absent there in May and found mainly in the outer bay. After June, few gunnel larvae were collected in the study area. This suggests a seaward movement of gunnel from the nursery grounds of the bay to offshore feeding grounds. The otolith of larvae smaller than 10 mm in total length did not show a distinct growth stop. The growth stop is believed to be formed in the early larval stage when the total length is about 10 mm. This period coincides with the time of shoreward migration, suggesting a metabolic change during this period. At a total length of 30 to 40 mm, the shape of the otolith changes from spherical to elongate. Daily growth rate in length was estimated by the Gompertz equation, which is represented as follows: TL = 6.702exp{2.925"1-exp (-0.008 t)"} ($r^2=0.94$, N = 92) Assuming daily deposition of growth increments in the otolith, the time of first growth increment formation was shown to be from December to January. Gonad observations show that Pholis fangi spawns from November to December. So, the hatching time is thought to be about one month.

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