Dynamic model of heat inactivation kinetics for bacterial adaptation

Modeling Salmonella spp. inactivation in chicken meat subjected to isothermal and non-isothermal temperature profiles

Salmonella genus has foodborne pathogen species commonly involved in many outbreaks related to the consumption of chicken meat. Many studies have aimed to model bacterial inactivation as a function of the temperature. Due to the large heterogeneity of the results, a unified description of Salmonella spp. inactivation behavior is hard to establish. In the current study, by evaluating the root mean square errors, mean absolute deviation, and Akaike and Bayesian information criteria, the double Weibull model was considered the most accurate primary model to fit 61 datasets of Salmonella inactivation in chicken meat. Results can be interpreted as if the bacterial population is divided into two subpopulations consisting of one more resistant (2.3% of the total population) and one more sensitive to thermal stress (97.7% of the total population). The thermal sensitivity of the bacteria depends on the fat content of the chicken meat. From an adapted version of the Bigelow secondary model including both temperature and fat content, 90% of the Salmonella population can be inactivated after heating at 60 °C of chicken breast, thigh muscles, wings, and skin during approximately 2.5, 5.0, 9.5, and 57.4 min, respectively. The resulting model was applied to four different non-isothermal temperature profiles regarding Salmonella growth in chicken meat. Model performance for the non-isothermal profiles was evaluated by the acceptable prediction zone concept. Results showed that >80% of the predictions fell in the acceptable prediction zone when the temperature changes smoothly at temperature rates lower than 20 °C/min. Results obtained can be used in risk assessment models regarding contamination with Salmonella spp. in chicken parts with different fat contents.

Variability in the heat resistance of Listeria monocytogenes under dynamic conditions can be more relevant than that evidenced by isothermal treatments

Heterogeneity in the response of microbial cells to environmental conditions is inherent to every biological system and can be very relevant for food safety, potentially being as important as intrinsic and extrinsic factors. However, previous studies analyzing variability in the microbial response to thermal treatments were limited to data obtained under isothermal conditions, whereas in the reality, environmental conditions are dynamic. In this article we analyse both empirically and through mathematical modelling the variability in the microbial response to thermal treatments under isothermal and dynamic conditions. Heat resistance was studied for four strains of Listeria monocytogenes (Scott A, CECT 4031, CECT 4032 and 12MOB052), in three different matrices (buffered peptone water, pH 7 Mcllvaine buffer and semi-skimmed milk). Under isothermal conditions, between-strain and between-media variability had no impact in the heat resistance, whereas it was very relevant for dynamic conditions. Therefore, the differences observed under dynamic conditions can be attributed to the variability in the ability for developing stress acclimation. The highest acclimation was observed in strain CECT 4031 (10-fold increase of the D-value), while the lowest acclimation was observed in strain CECT 4032 (50% increase of the D-value). Concerning the different media, acclimation was higher in buffered peptone water and semi-skimmed milk than in Mcllvaine buffer of pH 7.0. To the knowledge of the authors, this is the first research work that specifically analyses the variability of microbial adaptation processes that take place under dynamic conditions. It highlights that microbial heat resistance under dynamic conditions are sometimes determined by mechanisms that cannot be observed when cells are treated in isothermal conditions (e.g. acclimation) and can also be affected by variability. Consequently, empirical evidence on variability gathered under isothermal conditions should be extrapolated with care for dynamic conditions.

Describing the Individual Spore Variability and the Parameter Uncertainty in Bacterial Survival Kinetics Model by Using Second-Order Monte Carlo Simulation

The objective of this study was to separately describe the fitting uncertainty and the variability of individual cell in bacterial survival kinetics during isothermal and non-isothermal thermal processing. The model describing bacterial survival behavior and its uncertainties and variabilities during non-isothermal inactivation was developed from survival kinetic data for Bacillus simplex spores under fifteen isothermal conditions. The fitting uncertainties in the parameters used in the primary Weibull model was described by using the bootstrap method. The variability of individual cells in thermotolerance and the true randomness in the number of dead cells were described by using the Markov chain Monte Carlo (MCMC) method. A second-order Monte Carlo (2DMC) model was developed by combining both the uncertainties and variabilities. The 2DMC model was compared with reduction behavior under three non-isothermal profiles for model validation. The bacterial death estimations were validated using experimentally observed surviving bacterial count data. The fitting uncertainties in the primary Weibull model parameters, the individual thermotolerance heterogeneity, and the true randomness of inactivated spore counts were successfully described under all the iso-thermal conditions. Furthermore, the 2DMC model successfully described the variances in the surviving bacterial counts during thermal inactivation for all three non-isothermal profiles. As a template for risk-based process designs, the proposed 2DMC simulation approach, which considers both uncertainty and variability, can facilitate the selection of appropriate thermal processing conditions ensuring both food safety and quality.

Kinetics of different bioreactor systems with Acidithiobacillus ferrooxidans for ferrous iron oxidation

The relative performance of two biofilm-based airlift reactors using different kinds of packing materials and one fixed bed biofilm reactor with a homemade packing material of high specific area (~ 1000 m2/m3) was addressed. The bioreactors operated under ferrous iron loading rates in the range of 8–120 mol Fe(II)/m3 h. Acidithiobacillus ferrooxidans cells immobilized in the three bioreactors afforded the reactions for an extended period of 120 days of continuous operation at the dilution rates of 0.2, 0.4, 0.7, 1 and 1.2 h−1. The maximum ferrous iron oxidation rates achieved in this study at a hydraulic residence time of 1.2 h were about 91, 68 and 51 mol Fe(II)/m3 h for the fixed bed, airlift1, and airlft2 bioreactors. The performance data from the fixed-bed bioreactor offered a higher potential for ferrous iron oxidation because of fast biofilm development, the formation of a thick biofilm, and lower sensitivity to shear, which enhanced the startup time of the bioreactor and the higher reactor productivity. Proper kinetic models were also presented for both the startup period and the steady-state process.

Stochastic modeling of variability in survival behavior of Bacillus simplex spore population during isothermal inactivation at the single cell level using a Monte Carlo simulation

The control of bacterial reduction is important to maintain food safety during thermal processing. The goal of this study was to illustrate and describe variability in bacterial population behavior during thermal processing as a probability distribution based on individual cell heterogeneity regarding heat resistance. Toward this end, we performed a Monte Carlo simulation via computer, and compared and validated the simulated estimations with observed values. Weibullian fitted parameters were estimated from the kinetic survival data of Bacillus simplex during thermal treatment at 94 °C. The variability in reductions of bacterial sporular populations was illustrated using Monte Carlo simulation based on the Weibull distribution of the parameters. In particular, variabilities in viable spore counts and survival probability of the B. simplex spore population were simulated in various replicates. We also experimentally determined the changes in survival probability and distributions of survival spore counts; notably, these were successfully predicted by the Monte Carlo simulation based on the kinetic parameters. The kinetic parameter-based Monte Carlo simulation could thus successfully illustrate bacterial population behavior variability during thermal processing as a probability distribution. The simulation approach may contribute to improving food quality through risk-based processing designs and enhance risk assessment model accuracy.

Relevance of the Induced Stress Resistance When Identifying the Critical Microorganism for Microbial Risk Assessment

Decisions regarding microbial risk assessment usually have to be carried out with incomplete information. This is due to the large number of possible scenarios and the lack of specific data for the problem considered. Consequently, risk assessment studies are based on the information obtained with a small number of bacterial cells which are considered the most heat resistant and/or more capable of multiplying during storage. The identification of the most resistant strains is usually based on D and z-values, normally estimated from isothermal experiments. This procedure omits the potential effect that the shape of the dynamic thermal profile applied in industry has on the microbial inactivation. One example of such effects is stress acclimation, which is related to a physiological response of the cells during sub-lethal treatments that increases their resistance. In this article, we use a recently published mathematical model to compare the development of thermal resistance for Escherichia coli K12 MG1655 and E. coli CECT 515 using inactivation data already published for these strains. Based only on the isothermal experiments, E. coli K12 MG1655 would be identified as more resistant to the thermal treatment than the CECT 515 strain in the 50-65°C temperature range. However, we conclude that stress acclimation is strain (and/or media)-dependent; the CECT 515 strain has a higher capacity for developing a stress acclimation than K12 MG1655 (300% increase of the D-value for CECT 515, 50% for K12 MG1655). It, thus, has the potential to be more resistant to the thermal treatment than the K12 MG1655 strain for some conditions allowing acclimation. A methodology is proposed to identify for which conditions this may be the case. After calibrating the model parameters representing acclimation using real experimental data, the applicability of the proposed approach is demonstrated using numerical simulations, showing how the CECT 515 strain can be more resistant for some heating profiles. Consequently, the most resistant bacterial strain to a dynamic heating profile should not be identified based only on isothermal experiments (D- and z-value). The relevance of stress acclimation for the treatment studied should also be evaluated.

Mathematical quantification of the induced stress resistance of microbial populations during non-isothermal stresses

This contribution presents a mathematical model to describe non-isothermal microbial inactivation processes taking into account the acclimation of the microbial cell to thermal stress. The model extends the log-linear inactivation model including a variable and model parameters quantifying the induced thermal resistance. The model has been tested on cells of Escherichia coli against two families of non-isothermal profiles with different constant heating rates. One of the families was composed of monophasic profiles, consisting of a non-isothermal heating stage from 35 to 70°C; the other family was composed of biphasic profiles, consisting of a non-isothermal heating stage followed by a holding period at constant temperature of 57.5°C. Lower heating rates resulted in a higher thermal resistance of the bacterial population. This was reflected in a higher D-value. The parameter estimation was performed in two steps. Firstly, the D and z-values were estimated from the isothermal experiments. Next, the parameters describing the acclimation were estimated using one of the biphasic profiles. This set of parameters was able to describe the remaining experimental data. Finally, a methodology for the construction of diagrams illustrating the magnitude of the induced thermal resistance is presented. The methodology has been illustrated by building it for a biphasic temperature profile with a linear heating phase and a holding phase. This diagram provides a visualization of how the shape of the temperature profile (heating rate and holding temperature) affects the acclimation of the cell to the thermal stress. This diagram can be used for the design of inactivation treatments by industry taking into account the acclimation of the cell to the thermal stress.

Explicit numerical solutions of a microbial survival model under nonisothermal conditions

Differential equations used to describe the original and modified Geeraerd models were, respectively, simplified into an explicit equation in which the integration of the specific inactivation rate with respect to time was numerically approximated using the Simpson's rule. The explicit numerical solutions were then used to simulate microbial survival curves and fit nonisothermal survival data for identifying model parameters in Microsoft Excel. The results showed that the explicit numerical solutions provided an easy way to accurately simulate microbial survival and estimate model parameters from nonisothermal survival data using the Geeraerd models.

Evaluation of Salmonella thermal inactivation model validity for slow cooking of whole-muscle meat roasts in a pilot-scale oven

Sublethal heating can increase subsequent thermal resistance of bacteria, which may compromise the validity of thermal process validations for slow-roasted meats. Therefore, this research evaluated the accuracy of a traditional log-linear inactivation model, developed via prior laboratory-scale isothermal tests, and a novel path-dependent model accounting for sublethal injury, applied to pilot-scale slow cooking of whole-muscle roasts. Irradiated turkey breasts, beef rounds, and pork loins were inoculated with an eight-serovar Salmonella cocktail via vacuum tumble marination in a salt-phosphate marinade. The resulting initial Salmonella population in the geometric center (core) was 7.0, 6.3, and 6.3 log CFU/g for turkey, beef, and pork, respectively. Seven different cooking schedules representing industry practices were evaluated in a pilot-scale, moist-air convection oven. Core temperatures recorded during cooking were used to calculate lethality real-time via the log-linear model. The path-dependent model reduced the bias (mean residual) and root mean square error by 4.24 and 4.60 log CFU/g respectively, in turkey; however, the new model did not reduce the prediction error in beef or pork. Overall, results demonstrated that slow-cooked roasts, processed to a computed lethality at or near that required by the regulatory performance standards, as calculated with a state-dependent model, may be underprocessed.

Evaluating the predictive ability of a path-dependent thermal inactivation model for salmonella subjected to prior sublethal heating in ground turkey, beef, and pork

Pathogen thermal inactivation models currently available to and used by industry consider only the present state of the product when predicting inactivation rates. However, bacteria subjected to sublethal thermal injury can develop partial protection against lethal temperatures. The objective of this study was to extend the capabilities of a previously published path-dependent Salmonella inactivation model by accounting for longer sublethal heating periods and different substrates and to test this new model against independent data. Ground samples of irradiated (> 10 kGy) turkey breast, beef round, and pork loin were inoculated with an eight-serovar Salmonella cocktail and subjected to 53 nonisothermal treatments (in triplicate) that combined a linear heating rate (1, 2, 3, 4, or 7 K/min), a variable length sublethal holding period (at 40, 45, or 50°C), a lethal holding temperature (55, 58, 61, or 64°C), and a nominal target kill (3- or 5-log reductions) (n = 159 for each meat species). When validated against nonisothermal data from similar treatments, traditional state-dependent model predictions resulted in root mean squared errors (RMSEs) of 2.9, 2.2, and 4.6 log CFU/g for turkey, beef, and pork, respectively. RMSEs for the new path-dependent model were 0.90, 0.81, and 0.82 log CFU/g for the same species, respectively, with reductions in error of 63 to 82 % relative to the state-dependent model. This new path-dependent model can significantly reduce error from the state-dependent model and could become a useful tool for assuring product safety, particularly relative to slow heating processes.

Effect of the medium characteristics and the heating and cooling rates on the nonisothermal heat resistance of Bacillus sporothermodurans IC4 spores

In recent years, highly thermo-resistant mesophilic spore-forming bacteria belonging to the species Bacillus sporothermodurans have caused non-sterility problems in industrial sterilization processes. The aim of this research was to evaluate the effect of the heating medium characteristics (pH and buffer/food) on the thermal inactivation of B. sporothermodurans spores when exposed to isothermal and non-isothermal heating and cooling treatments and the suitability of non-linear Weibull and Geeraaerd models to predict the survivors of these thermal treatments. Thermal treatments were carried out in pH 3, 5 and 7 McIlvaine buffer and in a courgette soup. Isothermal survival curves showed shoulders that were accurately characterized by means of both models. A clear effect of the pH of the heating medium was observed, decreasing the D120 value from pH 7 to pH 3 buffer down to one third. Differences in heat resistance were similar, regardless of the model used and were kept at all temperatures tested. The heat resistance in courgette soup was similar to that shown in pH 7 buffer. When the heat resistance values obtained under isothermal conditions were used to predict the survival in the non-isothermical experiments, the predictions estimated the experimental data quite accurately, both with Weibull and Geeraerd models.

Re-shaping models of E. coli population dynamics in livestock faeces: increased bacterial risk to humans?

Dung-pats excreted directly on pasture from grazing animals can contribute a significant burden of faecal microbes to agricultural land. The aim of this study was to use a combined field and modelling approach to determine the importance of Escherichia coli growth in dung-pats when predicting faecal bacteria accumulation on grazed grassland. To do this an empirical model was developed to predict the dynamics of an E. coli reservoir within 1ha plots each grazed by four beef steers for six months. Published first-order die-off coefficients were used within the model to describe the expected decline of E. coli in dung-pats. Modelled estimates using first-order kinetics led to an underestimation of the observed E. coli land reservoir, when using site-specific die-off coefficients. A simultaneous experiment determined the die-off profiles of E. coli within fresh faeces of beef cattle under field relevant conditions and suggested that faecal bacteria may experience growth and re-growth in the period post defecation when exposed to a complex interaction of environmental drivers such as variable temperature, UV radiation and moisture levels. This growth phase in dung-pats is not accounted for in models based on first-order die-off coefficients. When the model was amended to incorporate the growth of E. coli, equivalent to that observed in the field study, the prediction of the E. coli reservoir was improved with respect to the observed data and produced a previously unquantified step-change improvement in model predictions of the accumulation of these faecal bacteria on grasslands. Results from this study suggest that the use of first-order kinetic equations for determining land-based reservoirs of faecal bacteria should be approached with caution and greater emphasis placed on accounting for actual survival patterns observed under field relevant conditions.