A Combined Model for Growth and Subsequent Thermal Inactivation of Brochothrix thermosphacta

Modeling naturally-occurring Vibrio parahaemolyticus in post-harvest raw shrimps

There is little known about the growth and survival of naturally-occurring Vibrio parahaemolyticus in harvested raw shrimps. In this study, the fate of naturally-occurring V. parahaemolyticus in post-harvest raw shrimps was investigated from 4℃ to 30℃ using real-time PCR combined with propidium monoazide (PMA-qPCR). The Baranyi-model was used to fit the growth and survival data. A square root model and non-linear Arrhenius model was then used to quantify the parameters derived from the Baranyi-model. The results showed that naturally-occurring V. parahaemolyticus were slowly inactivated at 4℃ and 7℃ with deactivation rates of 0.019 Log CFU/g/h and 0.025 Log CFU/g/h. Conversely, at 15, 20, 25, and 30 °C, the average maximum growth rates (μmax) of naturally-occurring V. parahaemolyticus were determined to be 0.044, 0.105, 0.179 and 0.336 Log CFU/g/h, accompanied by the average lag phases (λ) of 15.5 h, 7.3 h, 4.4 h and 3.7 h. The validation metrics, Af and Bf, for both the square root model and non-linear, indicating that the model had a good ability to predict the growth behavior of naturally-occurring V. parahaemolyticus in post-harvest raw shrimps. Furthermore, a comparative exploration between the growth of artificially contaminated V. parahaemolyticus in cooked shrimps and naturally-occurring V. parahaemolyticus in post-harvest raw shrimps revealed intriguing insights. While no substantial distinction in deactivation rates emerged at 4 °C and 7 °C (P > 0.05), a discernible disparity in growth rates was observable at 15 °C, 20 °C, 25 °C, and 30 °C, with the former surpassing the latter. Which indicated the risk of V. parahaemolyticus using models derived from cooked shrimps may be biased. Our study also unveiled a discernible seasonal effect. The μmax and λ of V. parahaemolyticus in shrimps harvested in summer were similar to those harvested in autumn, while the initial and maximum bacterial concentration harvested in summer were higher than those harvested in autumn. This predictive microbiology model of naturally-occurring V. parahaemolyticus in raw shrimps provides relevance to modelling growth in situ.

Lethality Validation for Human Pathogenic Salmonella enterica on Chicken Feathers and Blood during Simulated Commercial Low-Temperature Dry Rendering

Poultry rendering is the process of upcycling inedible poultry carcass materials into useful animal food/feed components as well as other valuable commercial products. Microbiological safety validation is nonetheless critical to ensuring the prevention of food safety hazard(s) transmission. This study determined the death kinetics of the thermotolerant Salmonella enterica serovar Senftenberg isolate 775W in chicken feathers and blood in low-temperature dry rendering (i.e., no direct contact with heating medium) to validate pathogen inactivation in commercial processing. Chicken feathers and blood were inoculated with Salmonella Senftenberg 775W and heated to 60, 70, or 80 °C for up to 60, 20, and 5 min, respectively. Three identically completed replicates (N = 3) for each product were conducted. Pathogen inactivation data were fitted to a non-linear model, providing for the detection and characterization of shoulder, log-linear death, and tailing components in death curves. The analysis showed a >7-log10 reduction in Salmonella was achieved across all processing temperatures, with t7D values (time for 7.0 log-cycle lethality) ranging from 21.68, 7.30, and 4.26 min for feathers and 18.38, 5.03, and 2.79 min in blood at 60, 70, and 80 °C, respectively. Study findings validate that low-temperature processing conditions can inactivate Salmonella in poultry-rendered offal.

Effects of osmotic stress on Listeria monocytogenes ATCC 7644: persistent cells and heat resistance

Persistent bacteria are a microbial subpopulation that, exposed to bactericidal treatment, is killed at a slower rate than the rest of the population they are part of. They can be triggered either following stress or stochastically without external signals. The hallmark of persistent bacteria is the biphasic killing curve, a sign that, within a microbial population, two subpopulations are inactivated at a different rate. Furthermore, when plated into a fresh medium and in the absence of stressors, persistent bacteria typically remain in the lag phase longer before resuming active replication. This study aims to evaluate in vitro whether the formation of persistent cells in a strain of Listeria monocytogenes can be triggered by exposure to osmotic stress and if this phenomenon can increase heat resistance in the bacterial population. In a first experiment, the lag time distribution of a L. monocytogenes strain grown in a 6% NaCl broth was evaluated using the software ScanLag. A stationary phase broth culture was inoculated on agar plates placed on an office scanner inside an incubator at 37°C. The plates were scanned every 20' for 4 days and the acquired images were automatically elaborated with the aid of MatLab software in order to evaluate the appearance times of every single colony. The experiment was also carried out on a control culture obtained by growing the strain in the broth without salt. In a second experiment, the same broth cultures, after proper dilutions to rebalance NaCl concentration, were subjected to a heat treatment at 51°C and the death curves obtained were parameterized using the GinaFit system. Results showed that the lag phase of 31.40% of the salt culture colonies was long enough to suppose the formation of persistent bacteria. Analyses of the thermal survival curves showed that the shoulder and tail model was the one that best represented the inactivation trend of the salt culture, unlike the control culture, whose trend was essentially linear. Results of the present study show how exposure to salt could induce the formation of persistent bacteria in a L. monocytogenes strain. The last raises concerns as persistent cells may not only be undetected with common analytical techniques but they even show a greater heat resistance.

Predicting the Simultaneous Oxidation of Ammonia, Nitrite, and m-cresol and Microbial Growth in a Sequencing Batch Reactor with a Kinetic Model Using Inhibition and Inactivation Effects

The kinetic model derived in this study was able to adequately predict the simultaneous oxidation of ammonia, nitrite, and m-cresol and microbial growth using nitrifying sludge in a sequencing batch reactor. Time-varying inhibition and inactivation effects were successfully incorporated in the process kinetics to account for the past cell exposure history to m-cresol increasing concentrations (up to 150 mg C L^-1). The initial concentration of the microbial species (ammonia and nitrite oxidizers, heterotrophs) was evaluated using pyrosequencing of DNA samples of the consortium. These measurements allowed to establish a model that explicitly handles specific reaction rates and to enhance the practical identifiability of the model parameters. A single simulation run was used to adequately predict the kinetic behavior of the main variables throughout the 242 cycles using a single set of initial conditions in the first cycle. This kind of dynamic model may be used as a helpful predictive tool to improve nitrification by avoiding the occurrence of severely repetitive inhibitive conditions due to the presence of inhibitive/toxic aromatic compounds.

The Inclusion of the Food Microstructural Influence in Predictive Microbiology: State-of-the-Art

Predictive microbiology has steadily evolved into one of the most important tools to assess and control the microbiological safety of food products. Predictive models were traditionally developed based on experiments in liquid laboratory media, meaning that food microstructural effects were not represented in these models. Since food microstructure is known to exert a significant effect on microbial growth and inactivation dynamics, the applicability of predictive models is limited if food microstructure is not taken into account. Over the last 10-20 years, researchers, therefore, developed a variety of models that do include certain food microstructural influences. This review provides an overview of the most notable microstructure-including models which were developed over the years, both for microbial growth and inactivation.

The complex multicellular morphology of the food spoilage bacteria Brochothrix thermosphacta strains isolated from ground chicken

Herein we describe a highly structured, filamentous growth phenotype displayed by an isolate of the food spoilage microorganism Brochothrix thermosphacta. The growth morphology of this B. thermosphacta strain (strain BII) was dependent on environmental factors such as the growth media, incubation temperatures, and the inoculum concentration. Inoculation of cultures in highly dilute suspensions resulted in the formation of isolated, tight aggregates resembling fungal growth in liquid media. This same strain also formed stable, mesh-like structures in 6-well tissue culture plates under specific growth conditions. The complex growth phenotype does not appear to be unique to strain BII but was common among B. thermosphacta strains isolated from chicken. Light and electron micrographs showed that the filaments of multiple BII cells can organize into complex, tertiary structures resembling multistranded cables. Time-lapse microscopy was employed to monitor the development of such aggregates over 18 h and revealed growth originating from short filaments into compact ball-like clusters that appeared fuzzy due to protruding filaments or cables. This report is the first to document this complex filamentous growth phenotype in a wild-type bacterial isolate of B. thermosphacta.

Case studies of packaging and processing solutions to improve meat quality and safety

A significant amount of the meat is wasted due to spoilage or safety risks. Active packaging systems have a great potential to reduce waste through chemical and microbial control of the product and/or the storage environment. Although commercial products are already available, active packaging is far from being fully developed. In contrast, passive packaging, such as modified atmosphere packaging (MAP) and vacuum packaging, have been fully implemented. Research conducted at the Danish Meat Research Institute (DMRI), demonstrates that it is possible to create new opportunities for the meat industry by modifying MAP or combining microwave treatment with vacuum packaging. Predictive shelf life models can be used to estimate the shelf life in MAP or vacuum under dynamic temperature conditions. Using the tri-gas guidelines, the industry can benefit from the increased eating quality, and the in-package decontamination process using vacuum packaging in combination with 5.8 GHz microwaves eliminates C. botulinum spores, resulting in increased food safety and an extended shelf life.

Predictive modelling of Lactobacillus casei KN291 survival in fermented soy beverage

The aim of the study was to construct and verify predictive growth and survival models of a potentially probiotic bacteria in fermented soy beverage. The research material included natural soy beverage (Polgrunt, Poland) and the strain of lactic acid bacteria (LAB) - Lactobacillus casei KN291. To construct predictive models for the growth and survival of L. casei KN291 bacteria in the fermented soy beverage we design an experiment which allowed the collection of CFU data. Fermented soy beverage samples were stored at various temperature conditions (5, 10, 15, and 20°C) for 28 days. On the basis of obtained data concerning the survival of L. casei KN291 bacteria in soy beverage at different temperature and time conditions, two non-linear models (r(2)= 0.68-0.93) and two surface models (r(2)=0.76-0.79) were constructed; these models described the behaviour of the bacteria in the product to a satisfactory extent. Verification of the surface models was carried out utilizing the validation data - at 7°C during 28 days. It was found that applied models were well fitted and charged with small systematic errors, which is evidenced by accuracy factor - Af, bias factor - Bf and mean squared error - MSE. The constructed microbiological growth and survival models of L. casei KN291 in fermented soy beverage enable the estimation of products shelf life period, which in this case is defined by the requirement for the level of the bacteria to be above 10(6) CFU/cm(3). The constructed models may be useful as a tool for the manufacture of probiotic foods to estimate of their shelf life period.

Prediction of Listeria innocua survival in fully cooked chicken breast products during postpackage thermal treatment

The effectiveness of postpackage hot water thermal treatment on survival of Listeria innocua in fully cooked chicken breast products was investigated at 60, 70, 80, and 90°C. Primary models based on log-linear and Weibull models were used to fit bacterial survival curves at different temperatures. The prediction plot and fit statistics indicated that the Weibull model provided a better fit than the log-linear model and was selected as the primary model. A secondary model based on linear regression was developed to describe the effect of temperature on the kinetic parameters of Listeria innocua survival derived from the Weibull model. The root mean square error and coefficients of determination indicated a good fit of the secondary model. The models were validated by independent data from pilot plant tests, and the values of bias factor and accuracy factor fell into the acceptable range. The models developed in this study can assist poultry producers and risk managers in designing appropriate thermal treatment regimens to minimize the risk associated with Listeria in ready-to-eat poultry products.

Effect of pressure-induced changes in the ionization equilibria of buffers on inactivation of Escherichia coli and Staphylococcus aureus by high hydrostatic pressure

Survival rates of Escherichia coli and Staphylococcus aureus after high-pressure treatment in buffers that had large or small reaction volumes (ΔV°), and which therefore underwent large or small changes in pH under pressure, were compared. At a low buffer concentration of 0.005 M, survival was, as expected, better in MOPS (morpholinepropanesulfonic acid), HEPES, and Tris, whose ΔV° values are approximately 5.0 to 7.0 cm(3) mol(-1), than in phosphate or dimethyl glutarate (DMG), whose ΔV° values are about -25 cm(3) mol(-1). However, at a concentration of 0.1 M, survival was unexpectedly better in phosphate and DMG than in MOPS, HEPES, or Tris. This was because the baroprotective effect of phosphate and DMG increased much more rapidly with increasing concentration than it did with MOPS, HEPES, or Tris. Further comparisons of survival in solutions of salts expected to cause large electrostriction effects (Na2SO4 and CaCl2) and those causing lower electrostriction (NaCl and KCl) were made. The salts with divalent ions were protective at much lower concentrations than salts with monovalent ions. Buffers and salts both protected against transient membrane disruption in E. coli, but the molar concentrations necessary for membrane protection were much lower for phosphate and Na2SO4 than for HEPES and NaCl. Possible protective mechanisms discussed include effects of electrolytes on water compressibility and kosmotropic and specific ion effects. The results of this systematic study will be of considerable practical significance in studies of pressure inactivation of microbes under defined conditions but also raise important fundamental questions regarding the mechanisms of baroprotection by ionic solutes.

Effect of temperature, pH, and NaCl on the inactivation kinetics of murine norovirus

We investigated the resistance of murine norovirus (MNV) and coliphage MS2, a culturable human norovirus surrogate, to temperature, salt, and pH. Virus inactivation was measured by plaque, real-time TaqMan reverse transcription (RT) PCR, and long-template RT-PCR assays. Both MNV and MS2 were rapidly inactivated at temperatures above 60°C. Similarly, MNV tolerated low salt concentrations (0.3% NaCl) to a greater degree than high salt concentrations (3.3 to 6.3% NaCl). MNV was relatively resistant to strong acidic conditions (pH 2) and was more tolerant of slightly acidic (pH 4) or neutral (pH 7) conditions. In contrast, MS2 was resistant to high salinity. Overall, temperature had a greater effect on infectivity than salt or low pH. Additionally, temperature and low pH had a synergistic effect on MNV infectivity. Both real-time and long-template RT-PCR assays significantly underestimated the inactivation by temperature, salt, and pH. The inactivation kinetics of both MNV and MS2 under various environmental conditions gave a good fit by the Weibull model (R² > 0.9). This study suggests both the capacity of infectious human norovirus to persist in the face of various environmental conditions and its sensitivity to high temperatures, which may provide a mechanism of protection against this virus.

A predictive model for the inactivation of Listeria innocua in cooked poultry products during postpackage pasteurization

Contamination of Listeria monocytogenes in ready-to-eat poultry products poses potential risk of listeriosis to the public. To control the level of Listeria contamination, attention has been focused on the postpackage pasteurization of fully cooked poultry products. In this study, we sought to develop a model to predict the thermal inactivation of L. monocytogenes in chicken drumettes during postpackage hot water pasteurization. Fully cooked chicken drumettes were inoculated with Listeria innocua as a surrogate microorganism for Listeria monocytogenes, vacuum packaged, and treated in hot water baths at 60, 70, 80, and 90°C for different heating times. Experimental results showed that a 7-log CFU/g reduction of L. innocua occurred at 54, 28, 18, and 10 min at 60, 70, 80, and 90°C, respectively. The Weibull model was used to fit the survival curves of L. innocua at each heating temperature. The root mean square errors and residual plots indicated good agreements between the predicted and observed values. The predictive model was further validated by predicting a new data set generated in the pilot-plant tests. Model performance was evaluated by the acceptable prediction zone method, and the results indicated that the percentages of acceptable prediction errors were 100, 100, 82.4, and 87.5% at 60, 70, 80 and 90°C, respectively, which were all greater than the threshold acceptable value of 70% , indicating good performance of the model. The developed predictive model can be used as a tool to predict thermal inactivation behaviors of L. monocytogenes in ready-to-eat chicken drumettes products.

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.

Stress-adaptive responses by heat under the microscope of predictive microbiology

AIMS

In previous studies the microbial kinetics of Escherichia coli K12 have been evaluated under static and dynamic conditions (Valdramidis et al. 2005, 2006). An acquired microbial thermotolerance following heating rates lower than 0.82 degrees C min(-1) for the studied micro-organism was observed. Quantification of this induced physiological phenomenon and incorporation, as a model building block, in a general microbial inactivation model is the main outcome of this work.

METHODS AND RESULTS

The microbial inactivation rate observed (k(obs)) under time-varying temperature conditions is studied and expressed as a function of the heating rate (dT/ dt). Hereto, a model building block related to the microbial physiology (k(phys)) under stress conditions is developed. Evaluation of the performance of the developed mathematical approach depicts that physiological adaptation is an essential issue to be considered when modelling microbial inactivation.

CONCLUSIONS

Consideration, at a mathematical level, of microbial responses resulting in physiological adaptations contribute to the reliable quantification of the safety risks during food processing.

SIGNIFICANCE AND IMPACT OF THE STUDY

By taking into account the physiological adaptation, the microbiological evolution during heat processing can be accurately assessed, and overly conservative or fail dangerous food processing designs can be avoided.

Effects of cell surface loading and phase of growth in cold atmospheric gas plasma inactivation of Escherichia coli K12

AIMS

To determine the effects of surface cell concentration and phase of growth on the inactivation of Escherichia coli cells using an atmospheric nonthermal plasma.

METHODS AND RESULTS

Cells of E. coli K12 were deposited onto the surface of membrane filters and exposed to the plume from a cold atmospheric gas plasma. Scanning electron microscopy revealed severe loss in structural integrity of plasma-treated cells, and optical emission spectra indicated that inactivation was brought about by reactive plasma species. The survival of E. coli cells was found to depend on the cell surface density: as the surface density increased from 10(7) to 10(11) CFU cm(-2), the rate constant in the Baranyi inactivation model decreased from 19.59 to 1.03 min(-1). Cells harvested from mid-exponential, late exponential and stationary phases of growth displayed differences in their resistances to the effects of the plasma however, exponential phase cells were not more susceptible than those from the stationary phase.

CONCLUSIONS

High surface concentrations of cells affects the penetration of plasma species and treatment effectiveness. The physiological state of cells, as determined by phase of growth, affects their resistance to plasma inactivation.

SIGNIFICANCE AND IMPACT OF THE STUDY

In designing inactivation treatments, surface concentration and cell physiology need to be taken into account.

Modelling the effect of high pressure on the inactivation kinetics of a pressure-resistant strain of Pediococcus damnosus in phosphate buffer and gilt-head seabream (Sparus aurata)

AIMS

The aim of this research was to: (i) determine the inactivation pattern of a pressure-resistant strain of Pediococcus damnosus by high hydrostatic pressure in phosphate buffer (pH 6.7) and gilt-head seabream using the linear, biphasic and Weibull models; and (ii) validate the applicability of the Weibull model to predict survival curves at other experimental pressure levels.

METHODS AND RESULTS

A pressure-resistant strain of P. damnosus was exposed to a range of pressures (500, 550, 600 and 650 MPa) in phosphate buffer (pH 6.7) and gilt-head seabream for up to 8 min at ambient temperature (23 degrees C). Inactivation kinetics were described by the linear, biphasic and Weibull models. Increasing the magnitude of the pressure applied resulted in increasing levels of inactivation. Pronounced tailing effect was observed at pressures over 600 MPa. The Weibull and biphasic models consistently produced better fit than the linear model as inferred by the values of the root mean squared error, coefficient of determination (R2) and accuracy factor (A(f)). The scale factor (b) of the Weibull model was linearly correlated with pressure (P) treatment in the whole pressure range. Substituting the b parameter in the initial Weibull function and calculating the shape factor (n) by linear interpolation, high pressure (P) was directly incorporated into the model providing reasonable predictions of the survival curves at 570 and 630 MPa. Comparison between the survival curves in phosphate buffer and gilt-head seabream showed a clear protective effect of the food matrix on the resistance of the micro-organism, especially at 500 and 550 MPa.

CONCLUSIONS

The Weibull and biphasic models were more flexible to describe the survival curves of P. damnosus in the experimental pressure range, taking also into account the tailing effect that could not be included in the linear model. The Weibull model could also give reasonable predictions of the survival curves at other experimental pressures in both pressure menstrua. As the food matrix has a protective effect in microbial inactivation, the development of accurate mathematical models should be done directly on real food to avoid under- or over-processing times.

SIGNIFICANCE AND IMPACT OF THE STUDY

The development of accurate models to describe the survival curves of micro-organisms under high hydrostatic pressure treatment would be very important to the food industry for process optimisation, food safety and extension of the applicability of high pressure processing.

Quantifying nonthermal inactivation of Listeria monocytogenes in European fermented sausages using bacteriocinogenic lactic acid bacteria or their bacteriocins: a case study for risk assessment

Listeria monocytogenes NCTC10527 was examined with respect to its nonthermal inactivation kinetics in fermented sausages from four European countries: Serbia-Montenegro, Hungary, Croatia, and Bosnia-Herzegovina. The goal was to quantify the effect of fermentation and ripening conditions on L. monocytogenes with the simultaneous presence or absence of bacteriocin-producing lactic acid bacteria (i.e., Lactobacillus sakei). Different models were used to fit the experimental data and to calculate the kinetic parameters. The best model was chosen based on statistical comparisons. The Baranyi model was selected because it fitted the data better in most (73%) of the cases. The results from the challenge experiments and the subsequent statistical analysis indicated that relative to the control condition the addition of L. sakei strains reduced the time required for a 4-log reduction of L. monocytogenes (t(4D)). In contrast, the addition of the bacteriocins mesenterocin Y and sakacin P decreased the t(4D) values for only the Serbian product. A case study for risk assessment also was conducted. The data of initial population and t(4D) collected from all countries were described by a single distribution function. Storage temperature, packaging method, pH, and water activity of the final products were used to calculate the inactivation of L. monocytogenes that might occur during storage of the final product (U.S. Department of Agriculture Pathogen Modeling Program version 7.0). Simulation results indicated that the addition of L. sakei strains significantly decreased the simulated L. monocytogenes concentration of ready-to-eat fermented sausages at the time of consumption.

Quantification of the effects of salt stress and physiological state on thermotolerance of Bacillus cereus ATCC 10987 and ATCC 14579

The food-borne pathogen Bacillus cereus can acquire enhanced thermal resistance through multiple mechanisms. Two Bacillus cereus strains, ATCC 10987 and ATCC 14579, were used to quantify the effects of salt stress and physiological state on thermotolerance. Cultures were exposed to increasing concentrations of sodium chloride for 30 min, after which their thermotolerance was assessed at 50 degrees C. Linear and nonlinear microbial survival models, which cover a wide range of known inactivation curvatures for vegetative cells, were fitted to the inactivation data and evaluated. Based on statistical indices and model characteristics, biphasic models with a shoulder were selected and used for quantification. Each model parameter reflected a survival characteristic, and both models were flexible, allowing a reduction of parameters when certain phenomena were not present. Both strains showed enhanced thermotolerance after preexposure to (non)lethal salt stress conditions in the exponential phase. The maximum adaptive stress response due to salt preexposure demonstrated for exponential-phase cells was comparable to the effect of physiological state on thermotolerance in both strains. However, the adaptive salt stress response was less pronounced for transition- and stationary-phase cells. The distinct tailing of strain ATCC 10987 was attributed to the presence of a subpopulation of spores. The existence of a stable heat-resistant subpopulation of vegetative cells could not be demonstrated for either of the strains. Quantification of the adaptive stress response might be instrumental in understanding adaptation mechanisms and will allow the food industry to develop more accurate and reliable stress-integrated predictive modeling to optimize minimal processing conditions.

Modelling Yersinia enterocolitica inactivation in coculture experiments with Lactobacillus sakei as based on pH and lactic acid profiles

In food processing and preservation technology, models describing microbial proliferation in food products are a helpful tool to predict the microbial food safety and shelf life. In general, the available models consider microorganisms in pure culture. Thus, microbial interactions are ignored, which may lead to a discrepancy between model predictions and the actual microbial evolution, particularly for fermented and minimally processed food products in which a background flora is often present. In this study, the lactic acid mediated negative microbial interaction between the lactic acid bacterium Lactobacillus sakei and the psychrotrophic food pathogen Yersinia enterocolitica was examined. A model describing the lactic acid induced inhibition (i.e., early induction of the stationary phase) of the pathogen [Vereecken, K.M., Devlieghere, F., Bockstaele, A., Debevere, J., Van Impe, J.F., 2003. A model for lactic acid induced inhibition of Yersinia enterocolitica in mono- and coculture with Lactobacillus sakei. Food Microbiology 20, 701-713.] was extended to describe the subsequent inactivation (i.e., decrease of the cell concentration to values below the detection limit). In the development of a suitable model structure to describe the inactivation process, critical points in the variation of the specific evolution rate mu [1/h] with the dynamic (time-varying) pH and undissociated lactic acid profiles were taken into account. Thus, biological knowledge, namely, both pH and undissociated lactic acid have an influence on the microbial evolution, was incorporated. The extended model was carefully validated on new data. As a result, the newly developed model is able to accurately predict the growth, inhibition and subsequent inactivation of Y. enterocolitica in coculture as based on the dynamic pH and lactic acid profiles of the medium.

On modeling and simulating transitions between microbial growth and inactivation or vice versa

Resumed growth of the survivors of a heat or chemical treatment after cooling or a disinfectant dissipation is not an uncommon phenomenon. Similarly, the inverse, the onset of mortality in a growing microbial population as a result of exposure to increasing temperature or concentration of an antimicrobial agent, is also a familiar scenario. Provided that in either regime, the organism has no time to adapt biologically, the continuous transition from growth to inactivation or vice versa can be simulated with conventional growth and inactivation models, whose rate constant is allowed to change sign. Where both the growth and inactivation follow first-order kinetics, the sign change has no effect on the model equation's solutions. The same applies when the growth and inactivation patterns are described by a rate model, like the differential logistic equation or its various variants. However, determination of such models' coefficients from experimental isothermal growth and inactivation data can be difficult for technical reasons, unless the model can be integrated analytically. If not, or when the model itself is unknown a priori, then the rate equation would have to be derived from the fit of empirical models like the Weibull, modified versions of the logistic function and the like. But this may create a new kind of problem as a result of that the log and certain power operations cannot be used for negative numbers. For certain models at least, the problem can be solved through modification of the procedure by which the rate equation is solved numerically. This is demonstrated in simulated transitions between growth and inactivation and between inactivation and growth based on the log linear and Weibullian-power law models and three logistic patterns based on a shifted logistic function, the Baranyi-Roberts model and a shifted arctan model.

Development of a structured model for batch cultures of lactic acid bacteria

A combined stochastic-deterministic model able to predict the growth curve of microorganisms, from inoculation to death, is presented. The proposed model is based on the assumption that microorganisms can experience two different physiological states: non-proliferating and proliferating. The former being the physiological state of the cells right after their inoculation into the new extracellular environment; the latter the state of microorganisms after adaptation to the new medium. To validate the model, a Lactobacillus bulgaricus strain was tested in a medium at pH 4.6 at two different temperatures (42 degrees C and 35 degrees C). Curves representing the bacterial growth cycle were satisfactorily fitted by means of the proposed model. Moreover, due to the mechanistic structure of the proposed model, valuable quantitative information on the following was obtained: rate of conversion of non-proliferating cells into proliferating cells, growth and death rate of proliferating cells, and rate of nutrient consumption.

Physiological and mathematical aspects in setting criteria for decontamination of foods by physical means

In heat processing, microbial inactivation is traditionally described as log-linear. As a general rule, the relation between rate of inactivation and temperature is also described as a log-linear relation. The model is also sometimes applied in pressure and in pulsed electric field (PEF) processing. The model has proven its value by the excellent safety record of the last 80 years, but there are many deviations from log-linearity. This could lead to either over-processing or under-processing resulting in safety problems or, more likely, spoilage problems. As there is a need for minimal processing, accurate information of the inactivation kinetics is badly needed. To predict inactivation more precisely, models have been developed that can cope with deviations of linearity. As extremely low probabilities of survival must be predicted, extrapolation is almost always necessary. However, extrapolation is hardly possible without knowledge of the nature of nonlinearity. Therefore, knowledge of the physiology of inactivation is necessary. This paper discusses the physiology of denaturation by heat, high pressure and pulse electric field. After discussion of the physiological aspects, the various aspects of the development of inactivation models will be addressed. Both general and more specific aspects are discussed such as choice of test strains, effect of the culture conditions, conditions during processing and recovery conditions and mathematical modelling of inactivation. In addition to lethal inactivation, attention will be paid to sublethal inactivation because of its relevance to food preservation. Finally, the principles of quantitative microbiological risk assessment are briefly mentioned to show how appropriate inactivation criteria can be set.

Application of recurrent neural network to predict bacterial growth in dynamic conditions

A combination of a factorial design and two central composite designs was used to assess quantitatively the effects of acid pH (5.6-7.0) or alkaline pH (7.0-9.5) and NaCl (0-8%) variations on the growth of Listeria monocytogenes in a meat broth, at 20 degrees C and lower temperature 10 degrees C. Two principal phenomena were observed when bacteria were submitted to abrupt change of pH and a(w) during growth, whatever the growth temperature: (i) large environmental variations induced a lag phase following the fluctuation, and (ii) the growth continued with a generation time value different from that observed before the change or that associated to the new environment. A dynamic model, based on recurrent neural network (RNN), was developed to describe the growth of L. monocytogenes as a function of temperature and fluctuating conditions of acid pH, alkaline pH and concentration of NaCl. The results showed that the neural network model can be used to represent the complex effects of environmental variable conditions on the microorganism behaviour.

On calculating sterility in thermal preservation methods: application of the Weibull frequency distribution model

A simple and parsimonious model which originated from the Weibull frequency distribution was proposed to describe nonlinear survival curves of spores. This model was suitable for downward concavity curves (Bacillus cereus and Bacillus pumilus), as well as for upward concavity curves (Clostridium botulinum). It was shown that traditional F values calculated from this new model were no longer additive, to such an extent that a heat treatment should be better characterized by the obtained decimal reduction of spores. A modified Bigelow method was then proposed to assess this decade reduction or to optimize the heat treatment for a target reduction ratio.

Structural model requirements to describe microbial inactivation during a mild heat treatment

The classical concept of D and z values, established for sterilisation processes, is unable to deal with the typical non-loglinear behaviour of survivor curves occurring during the mild heat treatment of sous vide or cook-chill food products. Structural model requirements are formulated, eliminating immediately some candidate model types. Promising modelling approaches are thoroughly analysed and, if applicable, adapted to the specific needs: two models developed by Casolari (1988), the inactivation model of Sapru et al. (1992), the model of Whiting (1993), the Baranyi and Roberts growth model (1994), the model of Chiruta et al. (1997), the model of Daughtry et al. (1997) and the model of Xiong et al. (1999). A range of experimental data of Bacillus cereus, Yersinia enterocolitica, Escherichia coli O157:H7, Listeria monocytogenes and Lactobacillus sake are used to illustrate the different models' performances. Moreover, a novel modelling approach is developed, fulfilling all formulated structural model requirements, and based on a careful analysis of literature knowledge of the shoulder and tailing phenomenon. Although a thorough insight in the occurrence of shoulders and tails is still lacking from a biochemical point of view, this newly developed model incorporates the possibility of a straightforward interpretation within this framework.

A prototype model structure for mixed microbial populations in homogeneous food products

An important factor which has not been included in many models in the field of predictive microbiology is the influence of a background of microflora in a food product. It is however generally known that the growth of a microorganism as a pure culture can be substantially different from its growth in a mixed culture, due to microbial interactions. Because of the importance of these interactions and the lack of suitable modeling techniques in the field of predictive microbiology to describe them, the potential of models in other research fields-namely ecology-to deal with interactions is explored in previous work of the authors. However, a model structure for microbial growth in food products cannot simply be copied from those elaborated in ecology. The structure of a predictive growth model is indeed typical, primarily due to the explicit modeling of a lag phase. The current paper proposes a prototype model structure for growth of mixed microbial populations in homogeneous food products. The model is able to describe a lag phase and reduces to a classical predictive growth model in the special case of single-species growth.

Predictive food microbiology for the meat industry: a review

Predictive food microbiology (PFM) is an emerging multidisciplinary area of food microbiology. It encompasses such disciplines as mathematics, microbiology, engineering and chemistry to develop and apply mathematical models to predict the responses of microorganisms to specified environmental variables. This paper provides a critical review on the development of mathematical modelling with emphasis on modelling techniques, descriptions, classifications and their recent advances. It is concluded that the role and accuracy of predictive food microbiology will increase as understanding of the complex interactions between microorganisms and food becomes clearer. However the reliance of food microbiology on laboratory techniques and skilled personnel to determine process and food safety is still necessary.

Visualization and modelling of the thermal inactivation of bacteria in a model food

A large number of incidents of food poisoning have been linked to undercooked meat products. The use of mathematical modelling to describe heat transfer within foods, combined with data describing bacterial thermal inactivation, may prove useful in developing safer food products while minimizing thermal overprocessing. To examine this approach, cylindrical agar blocks containing immobilized bacteria (Salmonella typhimurium and Brochothrix thermosphacta) were used as a model system in this study. The agar cylinders were subjected to external conduction heating by immersion in a water bath. They were then incubated, sliced open, and examined by image analysis techniques for regions of no bacterial growth. A finite-difference scheme was used to model thermal conduction and the consequent bacterial inactivation. Bacterial inactivation rates were modelled with values for the time required to reduce bacterial number by 90% (D) and the temperature increase required to reduce D by 90% taken from the literature. Model simulation results agreed well with experimental results for both bacteria, demonstrating the utility of the technique.

Variation in resistance of natural isolates of Escherichia coli O157 to high hydrostatic pressure, mild heat, and other stresses

Strains of Escherichia coli O157 isolated from patients with clinical cases of food-borne illness and other sources exhibited wide differences in resistance to high hydrostatic pressure. The most pressure-resistant strains were also more resistant to mild heat than other strains. Strain C9490, a representative pressure-resistant strain, was also more resistant to acid, oxidative, and osmotic stresses than the pressure-sensitive strain NCTC 12079. Most of these differences in resistance were observed only in stationary-phase cells, the only exception being acid resistance, where differences were also apparent in the exponential phase. Membrane damage in pressure-treated cells was revealed by increased uptake of the fluorescent dyes ethidium bromide and propidium iodide. When strains were exposed to the same pressure for different lengths of time, the pressure-sensitive strains took up stain sooner than the more resistant strain, which suggested that the differences in resistance may be related to susceptibility to membrane damage. Our results emphasize the importance of including stress-resistant strains of E. coli O157 when the efficacy of a novel or mild food preservation treatment is tested.

Model of the influence of time and mild temperature on Listeria monocytogenes nonlinear survival curves

Heat treatment has long been regarded as one of the most widely used and most effective means of destroying pathogens in food. Up to now the linear relationship between the death rate and the temperature has been used when choosing the best heat treatment to apply. However, the information given by this linear relationship is no longer sufficient when nonlinear survival curves are observed. Consequently, the agri-food industry needs a tool to choose the best mild heat treatment to apply in the case of nonlinear survival curves. This study deals with the temperature-induced death of Listeria monocytogenes CIP 7831 in the stationary phase of growth. Eleven temperatures were tested. With the proposed primary and secondary models good fits of our data were obtained. A model describing both the effect of the duration of treatment and the temperature on the logarithm of the number of survivors was then built. A clear increase in the precision of the estimation of the parameters was obtained with this model. Moreover, with this model a new graphical strategy to choose a mild heat increase regarding a maximal survivor number has been proposed.

A model describing the relationship between lag time and mild temperature increase duration

When a bacterial population undergoes an unfavourable increase in temperature for a given duration, called stress duration, a death phase followed by a lag and a growth phase are observed. The lag phase is actually of great interest in regard to foodstuff safety in choosing a suitable protocol for the detection of microorganisms which have undergone a mild heat treatment. The extension of lag time with the severity of the increase in temperature has been highlighted by previous papers. Our experimental results concerning Listeria monocytogenes and Escherichia coli revealed that a two phase relationship between lag time and stress duration is observed for a specific increase in temperature. The first phase consists of an increase in lag time up to a peak; the second one consists of a decrease from this peak to a steady threshold. The mathematical model presented, describing the relationship between lag time and stress duration was empirically built from our experimental data concerning L. monocytogenes and E. coli. The fit evaluation carried out led us to consider this model as a good description of the relationship studied. The potential contribution of our model in heat treatment optimization is discussed.