Mathematical Modeling of Microbial Growth: A Review

Skinner, Guy E.; Larkin, John W.; Rhodehamel, E. Jeffery

doi:10.1111/j.1745-4565.1994.tb00594.x

Cited by 79 publications

(61 citation statements)

References 90 publications

(137 reference statements)

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“…This, the logistic model and other predictive models are commonly used to determine important kinetic parameters relating to bacterial growth (Zwietering et al, 1990;Skinner et al, 1994). However, this is the first report to provide a simultaneous quantitative evaluation of kinetic parameters (m, LPD and MPD) for native M. aeruginosa in culture media at different temperatures by modelling all points along the curve (minimum 8 points) using the Gompertz function.…”

Section: Discussionmentioning

confidence: 99%

Mathematical modeling of Microcystis aeruginosa growth and [D-Leu1] microcystin-LR production in culture media at different temperatures

et al. 2017

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A B S T R A C TThe effect of temperature (26 C, 28 C, 30 C and 35 C) on the growth of native CAAT-3-2005 Microcystis aeruginosa and the production of Chlorophyll-a (Chl-a) and Microcystin-LR (MC-LR) were examined through laboratory studies. Kinetic parameters such as specific growth rate (m), lag phase duration (LPD) and maximum population density (MPD) were determined by fitting the modified Gompertz equation to the M. aeruginosa strain cell count (cells mL À1 ). A 4.8-fold increase in m values and a 10.8-fold decrease in the LPD values were found for M. aeruginosa growth when the temperature changed from 15 C to 35 C. The activation energy of the specific growth rate (Em) and of the adaptation rate (E 1 /LPD) were significantly correlated (R 2 = 0.86). The cardinal temperatures estimated by the modified Ratkowsky model were minimum temperature = 8.58 AE 2.34 C, maximum temperature = 45.04 AE 1.35 C and optimum temperature = 33.39 AE 0.55 C.Maximum MC-LR production decreased 9.5-fold when the temperature was increased from 26 C to 35 C. The maximum production values were obtained at 26 C and the maximum depletion rate of intracellular MC-LR was observed at 30-35 C. The MC-LR cell quota was higher at 26 and 28 C (83 and 80 fg cell À1 , respectively) and the MC-LR Chl-a quota was similar at all the different temperatures (0.5-1.5 fg ng À1 ).The Gompertz equation and dynamic model were found to be the most appropriate approaches to calculate M. aeruginosa growth and production of MC-LR, respectively. Given that toxin production decreased with increasing temperatures but growth increased, this study demonstrates that growth and toxin production processes are uncoupled in M. aeruginosa. These data and models may be useful to predict M. aeruginosa bloom formation in the environment.

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Section: Discussionmentioning

confidence: 99%

Mathematical modeling of Microcystis aeruginosa growth and [D-Leu1] microcystin-LR production in culture media at different temperatures

et al. 2017

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“…Many reviews and discussions concerning their applicability have been published (28,32,35,38). But the prediction of the lag time in foods still seems difficult to obtain and it is necessary to improve predictions (20,37).…”

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Influence of Stress on Individual Lag Time Distributions of Listeria monocytogenes

Guillier

Pardon

Augustin

2005

Appl Environ Microbiol

114

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The effects of nine common food industry stresses on the times to the turbidity (T d ) distribution of Listeria monocytogenes were determined. It was established that the main source of the variability of T d for stressed cells was the variability of individual lag times. The distributions of T d revealed that there was a noticeable difference in response to the stresses encountered by the L. monocytogenes cells. The applied stresses led to significant changes of the shape, the mean, and the variance of the distributions. The variance of T d of wells inoculated with single cells issued from a culture in the exponential growth phase was multiplied by at least 6 and up to 355 for wells inoculated with stressed cells. These results suggest stress-induced variability may be important in determining the reliability of predictive microbiological models.

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“…Single endpoint modeling is used to predict a single phenomenon, e.g., lag-phase duration, the time required to reach a predetermined population density, toxin production, or the probability of these events occurring (27). Such models have been referred to as the first attempts to predict the risk associated with foods (38).…”

mentioning

confidence: 99%

Modeling of Combined Processing Steps for Reducing Escherichia coli O157:H7 Populations in Apple Cider

Uljas

Schaffner

Duffy

et al. 2001

Appl Environ Microbiol

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Probabilistic models were used as a systematic approach to describe the response of Escherichia coli O157:H7 populations to combinations of commonly used preservation methods in unpasteurized apple cider. Using a complete factorial experimental design, the effect of pH (3.1 to 4.3), storage temperature and time (5 to 35°C for 0 to 6 h or 12 h), preservatives (0, 0.05, or 0.1% potassium sorbate or sodium benzoate), and freeze-thaw (F-T; ؊20°C, 48 h and 4°C, 4 h) treatment combinations (a total of 1,600 treatments) on the probability of achieving a 5-log 10 -unit reduction in a three-strain E. coli O157:H7 mixture in cider was determined. Using logistic regression techniques, pH, temperature, time, and concentration were modeled in separate segments of the data set, resulting in prediction equations for: (i) no preservatives, before F-T; (ii) no preservatives, after F-T; (iii) sorbate, before F-T; (iv) sorbate, after F-T; (v) benzoate, before F-T; and (vi) benzoate, after F-T. Statistical analysis revealed a highly significant (P < 0.0001) effect of all four variables, with cider pH being the most important, followed by temperature and time, and finally by preservative concentration. All models predicted 92 to 99% of the responses correctly. To ensure safety, use of the models is most appropriate at a 0.9 probability level, where the percentage of false positives, i.e., falsely predicting a 5-log 10 -unit reduction, is the lowest (0 to 4.4%). The present study demonstrates the applicability of logistic regression approaches to describing the effectiveness of multiple treatment combinations in pathogen control in cider making. The resulting models can serve as valuable tools in designing safe apple cider processes.

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Mathematical Modeling of Microbial Growth: A Review

Cited by 79 publications

References 90 publications

Mathematical modeling of Microcystis aeruginosa growth and [D-Leu1] microcystin-LR production in culture media at different temperatures

Mathematical modeling of Microcystis aeruginosa growth and [D-Leu1] microcystin-LR production in culture media at different temperatures

Influence of Stress on Individual Lag Time Distributions of Listeria monocytogenes

Modeling of Combined Processing Steps for Reducing Escherichia coli O157:H7 Populations in Apple Cider

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