Modeling the pressure inactivation dynamics of Escherichia coli

Modeling the pressure inactivation of Escherichia coli and Salmonella typhimurium in sapote mamey ( Pouteria sapota (Jacq.) H.E. Moore & Stearn) pulp

High hydrostatic pressure inactivation kinetics of Escherichia coli ATCC 25922 and Salmonella enterica subsp. enterica serovar Typhimurium ATCC 14028 ( S. typhimurium) in a low acid mamey pulp at four pressure levels (300, 350, 400, and 450 MPa), different exposure times (0-8 min), and temperature of 25 ± 2℃ were obtained. Survival curves showed deviations from linearity in the form of a tail (upward concavity). The primary models tested were the Weibull model, the modified Gompertz equation, and the biphasic model. The Weibull model gave the best goodness of fit ( R²_adj > 0.956, root mean square error < 0.290) in the modeling and the lowest Akaike information criterion value. Exponential-logistic and exponential decay models, and Bigelow-type and an empirical models for b'( P) and n( P) parameters, respectively, were tested as alternative secondary models. The process validation considered the two- and one-step nonlinear regressions for making predictions of the survival fraction; both regression types provided an adequate goodness of fit and the one-step nonlinear regression clearly reduced fitting errors. The best candidate model according to the Akaike theory information, with better accuracy and more reliable predictions was the Weibull model integrated by the exponential-logistic and exponential decay secondary models as a function of time and pressure (two-step procedure) or incorporated as one equation (one-step procedure). Both mathematical expressions were used to determine the t_d parameter, where the desired reductions ( 5D) (considering d = 5 ( t₅) as the criterion of 5 Log₁₀ reduction (5 D)) in both microorganisms are attainable at 400 MPa for 5.487 ± 0.488 or 5.950 ± 0.329 min, respectively, for the one- or two-step nonlinear procedure.

Evaluation of Different Dose-Response Models for High Hydrostatic Pressure Inactivation of Microorganisms

Modeling of microbial inactivation by high hydrostatic pressure (HHP) requires a plot of the log microbial count or survival ratio versus time data under a constant pressure and temperature. However, at low pressure and temperature values, very long holding times are needed to obtain measurable inactivation. Since the time has a significant effect on the cost of HHP processing it may be reasonable to fix the time at an appropriate value and quantify the inactivation with respect to pressure. Such a plot is called dose-response curve and it may be more beneficial than the traditional inactivation modeling since short holding times with different pressure values can be selected and used for the modeling of HHP inactivation. For this purpose, 49 dose-response curves (with at least 4 log10 reduction and ≥5 data points including the atmospheric pressure value (P = 0.1 MPa), and with holding time ≤10 min) for HHP inactivation of microorganisms obtained from published studies were fitted with four different models, namely the Discrete model, Shoulder model, Fermi equation, and Weibull model, and the pressure value needed for 5 log10 (P₅) inactivation was calculated for all the models above. The Shoulder model and Fermi equation produced exactly the same parameter and P₅ values, while the Discrete model produced similar or sometimes the exact same parameter values as the Fermi equation. The Weibull model produced the worst fit (had the lowest adjusted determination coefficient (R²adj) and highest mean square error (MSE) values), while the Fermi equation had the best fit (the highest R²adj and lowest MSE values). Parameters of the models and also P₅ values of each model can be useful for the further experimental design of HHP processing and also for the comparison of the pressure resistance of different microorganisms. Further experiments can be done to verify the P₅ values at given conditions. The procedure given in this study can also be extended for enzyme inactivation by HHP.

Biological approach to modeling of Staphylococcus aureus high-hydrostatic-pressure inactivation kinetics

Graphs for survival under high hydrostatic pressure (450 MPa; 25°C; citrate-phosphate buffer, pH 7.0) of stationary-growth-phase cells of eight Staphylococcus aureus strains were found to be nonlinear. The strains could be classified into two groups on the basis of the shoulder length. Some of them showed long shoulders of up to 20 min at 450 MPa, while others had shoulders of <3.5 min. All strains showed tails. No significant differences in the inactivation rate were found during the log-linear death phase among the eight strains. The entry into stationary growth phase resulted both in an increase in shoulder length and in a decrease in the inactivation rate. However, whereas shoulder length proved to depend on sigma B factor activity, the inactivation rate did not. Recovery in anaerobiosis decreased the inactivation rate but did not affect the shoulder length. Addition of the minimum noninhibitory concentration of sodium chloride to the recovery medium resulted in a decrease in shoulder length and in an increase in the inactivation rate for stationary-growth-phase cells. In the tail region, up to 90% of the population remained sensitive to sodium chloride.

Prediction of a required log reduction with probability for Enterobacter sakazakii during high-pressure processing, using a survival/death interface model

A probabilistic model for predicting Enterobacter sakazakii inactivation in trypticase soy broth (TSB) and infant formula (IF) by high-pressure processing was developed. The modeling procedure is based on a previous model (S. Koseki and K. Yamamoto, Int. J. Food Microbiol. 116:136-143, 2007) that describes the probability of death of bacteria. The model developed in this study consists of a total of 300 combinations of pressure (400, 450, 500, 550, or 600 MPa), pressure-holding time (1, 3, 5, 10, or 20 min), temperature (25 or 40 degrees C), inoculum level (3, 5, or 7 log(10) CFU/ml), and medium (TSB or IF), with each combination tested in triplicate. For each replicate response of E. sakazakii, survival and death were scored with values of 0 and 1, respectively. Data were fitted to a logistic regression model in which the medium was treated as a dummy variable. The model predicted that the required pressure-holding times at 500 MPa for a 5-log reduction in IF with 90% achievement probability were 26.3 and 7.9 min at 25 and 40 degrees C, respectively. The probabilities of achieving 5-log reductions in TSB and IF by treatment with 400 MPa at 25 degrees C for 10 min were 92 and 3%, respectively. The model enabled the identification of a minimum processing condition for a required log reduction, regardless of the underlying inactivation kinetics pattern. Simultaneously, the probability of an inactivation effect under the predicted processing condition was also provided by taking into account the environmental factors mentioned above.

Predictive modelling of the recovery of Listeria monocytogenes on sliced cooked ham after high pressure processing

This study examined bacterial recovery on sliced cooked ham that was inoculated with Listeria monocytogenes, treated by high pressure processing (HPP) and then stored at 10 degrees C for 70 days. The number of L. monocytogenes on the ham inoculated with 5 log(10) CFU/g was initially reduced by HPP at 500 MPa for 10 min to below the detectable level (10 CFU/g). However, the bacterial count gradually increased during storage, and exceeded the initial inoculum level at the end of the 70-day period, having risen by 7-8 log(10) CFU/g. A novel predictive model was therefore developed to estimate the recovery of L. monocytogenes during storage after HPP. Recovery of L. monocytogenes was defined as the detection of >10(2) CFU/g bacteria, in view of the relevant food safety objectives of L. monocytogenes. At each 14-day sampling session, the ham was scored as either 1 or 0 indicating bacterial recovery or no bacterial recovery, respectively. The data were then subjected to a simple linear logistic regression model, which provided a good fit as indicated by the performance statistics. Using this model, we estimated the minimum HPP conditions necessary for the required storage periods. Additionally, as the developed model was based on logistic regression, the probability of the recovery of L. monocytogenes during storage after HPP was estimated. Our model not only calculated the appropriate shelf life and process conditions, but also provided a method for evaluating the risk of the recovery of pathogenic bacteria during storage.

A novel approach to predicting microbial inactivation kinetics during high pressure processing

The inactivation kinetics of Escherichia coli (ATCC 25922) during high pressure processing (HPP) was examined from 200 to 400 MPa in 50 MPa increments at 15 degrees C. Although the time course of HPP-induced E. coli inactivation in 0.1% peptone water successfully fitted the Weibull function, this procedure involved curve fitting, and not prediction. The objective of this study was to develop a novel HPP-induced microbial inactivation model to simulate the inactivation kinetics under various pressure conditions. The maximum inactivation rate during HPP was calculated from the inactivation curves at different pressure conditions on a semi-log plot. The relationship between the square root of the absolute value of the inactivation rate (k(max)) and treatment pressure was linear (R(2)=0.99). The linear relationship between k(max) and treatment pressure also successfully described independent data from other studies in the literature. Overall, the newly developed differential equation model, into which was substituted the square root function of the inactivation rate, was capable of simulating the inactivation kinetics during HPP at constant pressure. Additionally, the model could successfully describe the inactivation kinetics during HPP using other researchers' data. The accuracy of prediction of the new model was comparable to that derived from Weibull or modified Gompertz fitting to the observed data. Furthermore, the new model could successfully simulate the inactivation kinetics during dynamic pressure conditions, which included come-up time, changes in holding pressure during treatment, and pressure-release time. Moreover, the effect of pulsed pressure treatment was also simulated successfully using this model. Therefore, the modeling procedure presented in this study will contribute to the advancement of predictive modeling for HPP-induced microbial inactivation.

New mathematical modeling approach for predicting microbial inactivation by high hydrostatic pressure

A new primary model based on a thermodynamically consistent first-order kinetic approach was constructed to describe non-log-linear inactivation kinetics of pressure-treated bacteria. The model assumes a first-order process in which the specific inactivation rate changes inversely with the square root of time. The model gave reasonable fits to experimental data over six to seven orders of magnitude. It was also tested on 138 published data sets and provided good fits in about 70% of cases in which the shape of the curve followed the typical convex upward form. In the remainder of published examples, curves contained additional shoulder regions or extended tail regions. Curves with shoulders could be accommodated by including an additional time delay parameter and curves with tails shoulders could be accommodated by omitting points in the tail beyond the point at which survival levels remained more or less constant. The model parameters varied regularly with pressure, which may reflect a genuine mechanistic basis for the model. This property also allowed the calculation of (a) parameters analogous to the decimal reduction time D and z, the temperature increase needed to change the D value by a factor of 10, in thermal processing, and hence the processing conditions needed to attain a desired level of inactivation; and (b) the apparent thermodynamic volumes of activation associated with the lethal events. The hypothesis that inactivation rates changed as a function of the square root of time would be consistent with a diffusion-limited process.

Modelling the bacterial survival/death interface induced by high pressure processing

The survival/death interface model was developed for prediction of inactivation of Listeria monocytogenes by high pressure processing (HPP). The model was derived from data sets comprising 360 combinations of environmental factors such as pressure (200, 300 400, and 500 MPa), pressure-holding time (1, 3, 5, 10, 20, 30 min), pH (3, 4, 5, 6, 7), and inoculum level (3, 5, 7 log(10) CFU/ml). The determination of survival/death of L. monocytogenes after HPP was confirmed by the presence/absence of colony forming ability on non-selective agar plates after 30 days of incubation at 20 degrees C in broth to take into account recovery of HPP-induced injured cells. The developed linear logistic model with time logarithmically transformed gave a degree of agreement between probabilities predicted by the fitted model and all observations as 99.3% concordant. The model provided a good fit to the data as shown by performance statistics. The developed interface model in the present study provided requisite process conditions for the target effect of HPP on L. monocytogenes. In addition to using the simple linear logistic model, a polynomial logistic model was also fitted to the data where pressure-holding time was not logarithmically transformed. That model did not produce a better fit to the data and resulted in some potentially misleading predictions. Optimization of HPP could be accomplished using the model developed in this study. Furthermore, choice in processing factors allows for processing flexibility in HPP and specifies the process criteria that are incorporated into the HACCP plan.