The boundary for growth of Zygosaccharomyces bailii in acidified products described by models for time to growth and probability of growth

Effects of Lactic Acid and Salt on Enterotoxin A Production and Growth of Staphylococcus aureus

Food poisoning caused by Staphylococcus aureus is responsible for staphylococcal enterotoxin (SE) produced in foods. Staphylococcal food poisoning is mostly caused by staphylococcal enterotoxin type A (SEA) among SEs. Growth/no growth for S. aureus under various environmental conditions was well studied with a logistic regression model so far. Recently we successfully described the boundaries of SEA production and growth of S. aureus in broth at various temperatures and salt concentrations with the model. In this study, the effects of lactic acid and salt on SEA production and growth of S. aureus was quantitatively studied. Consequently the boundaries of SEA production and growth of S. aureus cocktail in broth at various combinations of salt concentrations and pH values that were adjusted with lactic acid were successfully described with a logistic regression model. Here the cocktail was incubated in stationary culture at 30 °C and 10 °C. The maximum toxin production and cell growth of the cocktail were observed both at 5% salt in the pH range from 4.5 to 7.0. Also, the characteristics of individual strains of the cocktail in SEA production and growth at 30 °C and 10 °C were found to be specific to the strains. The present study revealed the effect of lactic acid and salt on SEA production and growth of S. aureus as well as the variety of SEA production and growth of S. aureus strains. These results would become useful information in food industry to prevent staphylococcal food poisoning. PRACTICAL APPLICATION: Boundaries of enterotoxin A production/no production and growth/no growth of staphylococcal cocktail at various combinations of pHs adjusted with lactic acid and salt concentrations were well described with a logistic regression model. The maximum toxin production and cell growth were observed both at 5% salt in the pH range from 4.5 to 7.0. A variety of the toxin production and cell growth were observed in terms of pH and salt concentration among individual strains of the cocktail.

Description of Aspergillus flavus growth under the influence of different factors (water activity, incubation temperature, protein and fat concentration, pH, and cinnamon essential oil concentration) by kinetic, probability of growth, and time-to-detection models

A Box-Behnken design was used to determine the effect of protein concentration (0, 5, or 10g of casein/100g), fat (0, 3, or 6g of corn oil/100g), a_w (0.900, 0.945, or 0.990), pH (3.5, 5.0, or 6.5), concentration of cinnamon essential oil (CEO, 0, 200, or 400μL/kg) and incubation temperature (15, 25, or 35°C) on the growth of Aspergillus flavus during 50days of incubation. Mold response under the evaluated conditions was modeled by the modified Gompertz equation, logistic regression, and time-to-detection model. The obtained polynomial regression models allow the significant coefficients (p<0.05) for linear, quadratic and interaction effects for the Gompertz equation's parameters to be identified, which adequately described (R²>0.967) the studied mold responses. After 50days of incubation, every tested model system was classified according to the observed response as 1 (growth) or 0 (no growth), then a binary logistic regression was utilized to model A. flavus growth interface, allowing to predict the probability of mold growth under selected combinations of tested factors. The time-to-detection model was utilized to estimate the time at which A. flavus visible growth begins. Water activity, temperature, and CEO concentration were the most important factors affecting fungal growth. It was observed that there is a range of possible combinations that may induce growth, such that incubation conditions and the amount of essential oil necessary for fungal growth inhibition strongly depend on protein and fat concentrations as well as on the pH of studied model systems. The probabilistic model and the time-to-detection models constitute another option to determine appropriate storage/processing conditions and accurately predict the probability and/or the time at which A. flavus growth occurs.

On the critical evaluation of growth/no growth assessment of Zygosaccharomyces bailii with optical density measurements: liquid versus structured media

Growth/no growth (G/NG) studies that include the effect of medium structure have typically been performed for (pathogenic) bacteria and on the basis of gelatin/agar as a gelling agent. In this study, the growth potential of the spoilage yeast Zygosaccharomyces bailii was investigated in two model systems that resemble the macroscopic physicochemical and rheological properties of acidic sauces. In a Carbopol model system, the effect of pH (3.5-4.5), glycerol concentration (17-32%), acetic acid concentration (1.5-2.0%) and medium structure (3 levels) was investigated. In xanthan gum, the behavior of the yeast was studied at different levels of pH (3.5-4.5), NaCl concentration (0.5-13.5%), acetic acid concentration (0-2.0%) and medium structure (2 levels). Rheologically, viscoelastic moduli failed to discriminate between different forms of microbial growth, whereas yield stress data appeared to provide a better indication. In general, G/NG results revealed an unexpected increase of growth probability as a function of medium structure, both at 22 and 30 °C. Whether this behavior is the result of an underlying growth-promoting mechanism could not be explained from a macroscopic point of view (e.g., macrorheology, a(w)), but may be more related to the local microscopic properties of the gels. In a second part of this study, the potential use and information content of optical density measurements for G/NG data collection in structured media were critically evaluated and confronted with their practical relevance to the food industry.

Modeling the Efficacy of Triplet Antimicrobial Combinations: Yeast Suppression by Lauric Arginate, Cinnamic Acid, and Sodium Benzoate or Potassium Sorbate as a Case Study

The growth of four spoilage yeasts, Saccharomyces cerevisiae, Zygosaccharomyces bailii, Brettanomyces bruxellensis, and Brettanomyces naardenensis, was inhibited with three-agent (triplet) combinations of lauric arginate, cinnamic acid, and sodium benzoate or potassium sorbate. The inhibition efficacy was determined by monitoring the optical density of yeast cultures grown in microtiter plates for 7 days. The relationship between the optical density and the sodium benzoate and potassium sorbate concentrations followed a single-term exponential decay model. The critical effective concentration was defined as the concentration at which the optical density was 0.05, which became an efficacy criterion for the mixtures. Critical concentrations of sodium benzoate or potassium sorbate as a function of the lauric arginate and cinnamic acid concentrations were then fitted with an empirical model that mapped three-agent combinations of equal efficacy. The contours of this function are presented in tabulated form and as two- and three-dimensional plots. Triplet combinations were highly effective against all four spoilage yeasts at three practical pH levels, especially at pH 3.0. The triplet combinations were particularly effective for inhibiting growth of Z. bailii, and combinations containing potassium sorbate had synergistic activities. The equal efficacy concentration model also allowed tabulation of the cost of the various combinations of agents and identification of those most economically feasible.

Modelling time to growth of Escherichia coli as a function of water activity and undissociated lactic acid

AIMS

To model the effect of water activity (a(w)) and concentration of undissociated lactic acid (HLac) on the time to growth (TTG) and the growth/no growth boundary of acid-adapted generic Escherichia coli, used as model organisms for Shiga toxin-producing E. coli (STEC).

METHODS AND RESULTS

For each of two E. coli strains, the TTG in brain heart infusion broth at 27 degrees C was estimated at 30 combinations of a(w) (range 0.945-0.995) and concentration of HLac (range 0-6.9 mol m(-3)) by using an automated turbidity reader. Survival analysis was used to develop a model predicting the TTG and the growth/no growth boundary.

CONCLUSIONS

The present model can be used to predict the TTG and to indicate the growth/no growth boundary of acid-adapted E. coli strains as a function of a(w) and concentration of HLac.

SIGNIFICANCE AND IMPACT OF THE STUDY

Fermented food products have been implicated as sources of STEC in several outbreaks. The study results are relevant for modelling of growth of STEC in fermented food and can be used in microbiological risk assessments or in the design and validation of food-production processes.

Growth/no growth models describing the influence of pH, lactic and acetic acid on lactic acid bacteria developed to determine the stability of acidified sauces

Growth/no growth models were developed for two spoilage bacteria typical for acidified sauces, L. plantarum and L. fructivorans. Influencing factors embedded in the model are also those typically encountered in these acidified sauces. The pH was varied between 3.0 and 5.0 (5 levels), and the acetic and lactic acid concentration ranged from 0 to 3% (6 levels). Modified MRS broth was inoculated at a high inoculation level (10(6) CFU/ml), incubated at 30 degrees C and growth was assessed by optical density measurements. All combinations of environmental conditions were tested in twelvefold yielding precise values for the probability of growth. Data were modelled by means of ordinary logistic regression. A comparison was made between a model containing the total acid concentrations as explanatory variables, on the one hand, and a model differentiating between the dissociated and undissociated concentrations, on the other hand. Results showed that (i) L. plantarum and L. fructivorans behave differently, resulting in a clearly distinct growth/no growth interface, (ii) there was no great difference between the established models with different explanatory variables, (iii) in some cases, growth/no growth boundaries at very low probabilities (which are more practical in industry) show illogical behaviour. The results of this study were also compared with the CIMSCEE code, which is often used by food producers to determine the stability of their acidified food products.

Antimicrobial activity of aroma compounds against Saccharomyces cerevisiae and improvement of microbiological stability of soft drinks as assessed by logistic regression

The combined effects of a mild heat treatment (55 degrees C) and the presence of three aroma compounds [citron essential oil, citral, and (E)-2-hexenal] on the spoilage of noncarbonated beverages inoculated with different amounts of a Saccharomyces cerevisiae strain were evaluated. The results, expressed as growth/no growth, were elaborated using a logistic regression in order to assess the probability of beverage spoilage as a function of thermal treatment length, concentration of flavoring agents, and yeast inoculum. The logit models obtained for the three substances were extremely precise. The thermal treatment alone, even if prolonged for 20 min, was not able to prevent yeast growth. However, the presence of increasing concentrations of aroma compounds improved the stability of the products. The inhibiting effect of the compounds was enhanced by a prolonged thermal treatment. In fact, it influenced the vapor pressure of the molecules, which can easily interact within microbial membranes when they are in gaseous form. (E)-2-Hexenal showed a threshold level, related to initial inoculum and thermal treatment length, over which yeast growth was rapidly inhibited. Concentrations over 100 ppm of citral and thermal treatment longer than 16 min allowed a 90% probability of stability for bottles inoculated with 10(5) CFU/bottle. Citron gave the most interesting responses: beverages with 500 ppm of essential oil needed only 3 min of treatment to prevent yeast growth. In this framework, the logistic regression proved to be an important tool to study alternative hurdle strategies for the stabilization of noncarbonated beverages.

Modelling of the growth–no growth interface of Issatchenkia occidentalis, an olive spoiling yeast, as a function of the culture media, NaCl, citric and sorbic acid concentrations: Study of its inactivation in the no growth region

A global logistic model incorporating a dummy variable for the growth medium (laboratory media or table olives brine) was used for the estimation of the growth-no growth interface of Issatchenkia occidentalis as a function of NaCl, citric and sorbic acid concentrations. The model permitted the deduction of the region where the combination of citric and sorbic acids in laboratory media (above 0.3% and 0.03% wt/vol, respectively) and brine (above 0.1% and 0.03% wt/vol), at 5% NaCl, inhibited the growth of the yeast. Subsequently, the model was validated in laboratory media within the no growth region by a response surface D-optimal design. Inactivation concentrations of sorbic acid produced a progressive loss of viability in I. occidentalis that followed a first order kinetic or downward concave inactivation curves, depending on environmental variables. These curves were properly described by a (primary) model deduced from the Weibull distribution, whose parameters, first decimal reduction time (D(beta)) and shape (beta), were expressed as a function of sorbic acid concentrations (secondary model). At 5% NaCl and within the experimental region checked, an increase of 0.010% and 0.008% sorbic acid reduced D(beta) in 10 h and decrease beta by 10%. Finally, the model was also validated in real "seasoned" table olives packing reporting a complete inactivation of the yeasts' population.

Use of logistic regression with dummy variables for modeling the growth-no growth limits of Saccharomyces cerevisiae IGAL01 as a function of sodium chloride, acid type, and potassium sorbate concentration according to growth media

A global logistic model was used to study the effects of both quantitative variables (NaCl, acid, and potassium sorbate concentrations) and dummy variables (laboratory medium or brine, and citric, lactic, or acetic acids) on growth of Saccharomyces cerevisiae IGAL01. The deduced equations, with the significant coefficients selected by a backward stepwise procedure, allowed estimations of the simultaneous comparison of behaviors of levels of the qualitative variables as a function of the quantitative variables and the development of the growth-no growth limits according to laboratory medium or brine and the different types of acidifying agents. The S. cerevisiae growth region in yeast malt glucose peptone broth was always wider than that in brine, in which this yeast was inhibited by 0.03% potassium sorbate and 6% NaCl, when the acid concentration (regardless of type) was 0.2 to 0.3%. These results demonstrate the applicability of such model designs to include qualitative variables in investigations related to the development of growth-no growth limits.

Salt, alone or in combination with sucrose, can improve the survival of Escherichia coli O157 (SERL 2) in model acidic sauces

The commercial production of microbiologically safe and stable sauces containing acetic acid is guided by the Comité des Industries des Mayonnaises et Sauces Condimentaires de la Communauté Economique Européenne's (CIMSCEE) code. The CIMSCEE safety value is calculated using a linear regression equation combining weighted contributions of pH and aqueous-phase concentrations of undissociated acetic acid, NaCl, and sugars. By implication, the CIMSCEE safety equation predicts that increasing concentrations of hurdles will always increase inactivation of the target pathogen. In this study, the time to achieve a 3-log10 reduction of an acid-resistant, acid-adapted, Shiga toxin-producing Escherichia coli (STEC) O157 isolate was determined experimentally for 81 formulations at various pHs and acetic acid, NaCl, and sucrose concentrations in a broth model. The combinations were intended to simulate the aqueous phase of acidic sauces and dressings. Experimental data were fitted to the log logistic model to estimate the time to 3-log10 reduction (t3D). Comparison of fitted t3D estimates with CIMSCEE values showed agreement in predicting safety (as defined by CIMSCEE) for the majority of formulations. However, CIMSCEE safety predictions were "fail dangerous" for 13 of 81 formulations. Among these formulations and others, the observed E. coli t3D initially increased and then decreased with increasing osmolalities (NaCl and sucrose). Relative protection increased with exposure time where the protective effect of NaCl predominated. While commercial acidic sauces are not considered high-risk vehicles for STEC, interactions among hurdles that decrease their combined effectiveness are deserving of further investigation because they may reveal mechanisms of broader relevance in the inactivation of pathogens in foods.

Relationship between time-to-detection (TTD) and the biological parameters of Pichia anomala IG02; modelling of TTD as a function of temperature, NaCl concentration, and pH and quantification of their effects

The time to detection (TTD) for Pichia anomala IG02 was defined, for inoculum sizes lower than 6 log(10)cfu/ml, as the time elapsed from inoculation to the moment at which an OD of 0.12 was reached. In other cases, TTD can be estimated by interpolation within the time elapsed from the previous readings below OD=0.12 and the next above it. A linear relationship, which depended on the inoculum size, between lnTTD with ln lambda and ln mu(m) was found. These relationships can be used to estimate the biological parameters of cultures with low inoculum levels. In addition, TTD for P. anomala IG02 could be modelled as a function of environmental conditions. The model can also be applied to lambda and mu(m) through their relationships with TTD. The effects of temperature, NaCl content and pH were quantified by the generalized z-values. An increase of 5.97 in NaCl concentration, a decrease of 1.97 units of pH, or a decrease of 6.08 degrees C doubled the TTD or caused a 2.53-fold increase in lambda and a 2.56-fold decrease in the mu(m).

Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes

AIMS

The effect of temperature (2-30 degrees C), pH (4.8-7.4) and water activity (0.946-0.995) on the relationship between optical density (OD) at 600 nm and the plate count (CFU ml(-1)) was investigated for Listeria monocytogenes.

METHODS AND RESULTS

Calibration curves, relating OD with plate counts, were collected by measuring the OD of consecutive one-half dilution series, before determining the cell density by classic plate count methods. The calibration curves were observed to be shifting in a parallel way, with increasing stress levels. Especially pH influenced the curve in a great extent, while the other variables were showing more synergetic effects. The reason for the shift was investigated by a microscopic viability test, showing a viability decrease with increasing stress levels, causing the shift of the calibration curve. In a last step a model was made describing the effect of environmental factors on the calibration curve, with different data transformations being tested. A polynomial equation was fitted to the data, taking into account a set of constraints to incorporate microbiological knowledge in the black box model. Hence, illogical interpolation results and overfitting of the data could be avoided.

CONCLUSIONS

Different stress factors are affecting the relationship between the OD and the cell count of L. monocytogenes by lowering the cell viability. These effects could be modelled using a constrained polynomial model.

SIGNIFICANCE AND IMPACT OF THE STUDY

The observed phenomena are important when calculating growth parameters, like growth rate and lag phase, based on OD data.

Modeling the growth boundary of Listeria monocytogenes in ready-to-eat cooked meat products as a function of the product salt, moisture, potassium lactate, and sodium diacetate concentrations

A central composite response surface design was used to determine the time to growth of Listeria monocytogenes as a function of four continuous variables: added sodium chloride (0.8 to 3.6%), sodium diacetate (0 to 0.2%), potassium lactate syrup (60% [wt/wt]; 0.25 to 9.25%), and finished-product moisture (45.5 to 83.5%) in ready-to-eat cured meat products. The design was repeated for ready-to-eat uncured meat products giving a fifth categorical variable for cure status. Products were stored at 4 degrees C. The results were modeled using a generalized regression approach. All five main effects, six two-factor interactions, and two quadratic terms were statistically significant. The model was used to show the boundary between growth and no-growth conditions at 4 degrees C using contour plots of time to growth. It was validated using independent challenge studies of cured and uncured products. Generally, the model predicted well, particularly for cured products, where it will be useful for establishing conditions that prevent the growth of L. monocytogenes. For uncured products, there was good agreement overall between predicted and observed times to growth, but the model is less thoroughly validated than for cured products. The model should initially only be used for screening of formulations likely to prevent growth of Listeria monocytogenes in uncured products, with recommendations subject to confirmation by challenge studies.

Application of elements of microbiological risk assessment in the food industry via a tiered approach

Food safety control is a matter for concern for all parts of the food supply chain, including governments that develop food safety policy, food industries that must control potential hazards, and consumers who need to keep to the intended use of the food. In the future, food safety policy may be set using the framework of risk analysis, part of which is the development of (inter)national microbiological risk assessment (MRA) studies. MRA studies increase our understanding of the impact of risk management interventions and of the relationships among subsequent parts of food supply chains with regard to the safety of the food when it reaches the consumer. Application of aspects of MRA in the development of new food concepts has potential benefits for the food industry. A tiered approach to applying MRA can best realize these benefits. The tiered MRA approach involves calculation of microbial fate for a product and process design on the basis of experimental data (e.g., monitoring data on prevalence) and predictive microbiological models. Calculations on new product formulations and novel processing technologies provide improved understanding of microbial fate beyond currently known boundaries, which enables identification of new opportunities in process design. The outcome of the tiered approach focuses on developing benchmarks of potential consumer exposure to hazards associated with new products by comparison with exposure associated with products that are already on the market and have a safe history of use. The tiered prototype is a tool to be used by experienced microbiologists as a basis for advice to product developers and can help to make safety assurance for new food concepts transparent to food inspection services.

Effect of chemicals on the microbial evolution in foods

In contrast with most chemical hazardous compounds, the concentration of food pathogens changes during processing, storage, and meal preparation, making it difficult to estimate the number of microorganisms or the concentration of their toxins at the moment of ingestion by the consumer. These changes are attributed to microbial proliferation, survival, and/or inactivation and must be considered when exposure to a microbial hazard is assessed. The number of microorganisms can also change as a result of physical removal, mixing of food ingredients, partitioning of a food product, or cross-contamination (M. J. Nauta. 2002. Int. J. Food Microbiol. 73:297-304). Predictive microbiology, i.e., relating these microbial evolutionary patterns to environmental conditions, can therefore be considered a useful tool for microbial risk assessment, especially in the exposure assessment step. During the early development of the field (late 1980s and early 1990s), almost all research was focused on the modeling of microbial growth over time and the influence of temperature on this growth. Later, modeling of the influence of other intrinsic and extrinsic parameters garnered attention. Recently, more attention has been given to modeling of the effects of chemicals on microbial inactivation and survival. This article is an overview of different applied strategies for modeling the effect of chemical compounds on microbial populations. Various approaches for modeling chemical growth inhibition, the growth-no growth interface, and microbial inactivation by chemicals are reviewed.

Modeling yeast spoilage in cold-filled ready-to-drink beverages with Saccharomyces cerevisiae, Zygosaccharomyces bailii, and Candida lipolytica

Mathematical models were developed to predict the probability of yeast spoilage of cold-filled ready-to-drink beverages as a function of beverage formulation. A Box-Behnken experimental design included five variables, each at three levels: pH (2.8, 3.3, and 3.8), titratable acidity (0.20, 0.40, and 0.60%), sugar content (8.0, 12.0, and 16.0 degrees Brix), sodium benzoate concentration (100, 225, and 350 ppm), and potassium sorbate concentration (100, 225, and 350 ppm). Duplicate samples were inoculated with a yeast cocktail (100 microl/50 ml) consisting of equal proportions of Saccharomyces cerevisiae, Zygosaccharomyces bailii, and Candida lipolytica (approximately 5.0 x 10(4) CFU/ml each). The inoculated samples were plated on malt extract agar after 0, 1, 2, 4, 6, and 8 weeks. Logistic regression was used to create the predictive models. The pH and sodium benzoate and potassium sorbate concentrations were found to be significant factors controlling the probability of yeast growth. Interaction terms for pH and each preservative were also significant in the predictive model. Neither the titratable acidity nor the sugar content of the model beverages was a significant predictor of yeast growth in the ranges tested.

Growth pH does not affect the initial physiological state parameter (pO) of Listeria monocytogenes

It has proven difficult to develop adequate mathematical models for the lag phase (lambda) which characterizes the adaptation period prior to the initiation of exponential growth by microorganisms. This is due, in part, to our incomplete understanding of the nature of the initial physiological state of cells (defined as h0 or p0 depending on the model), and changes taking place during adaptation. The objectives of the present study were to characterize p0 using data from growth of Listeria monocytogenes in an automated turbidimetric instrument (Bioscreen), and to determine the influence of limiting growth pH. A model was developed for individual cells which combined a continuous adaptation phase (defined by p0) with a discrete step marking the transition to a continuous exponential growth phase (the CDC model). Parameters of the new model were: p0; the specific growth rate (mu); the initial cell number (N0); and the maximum cell density (Nmax). Progressive reduction of the growth pH in the Bioscreen to 4.7 decreased the p. It was noted that the regression lines for all trials at all pH values appeared to have a common x-intercept (20.086+/-1.092), and it was deduced that, when the Bioscreen detection limit (15.07 In cfu well(-1)) was subtracted, the resulting value represented the "true" value for the initial physiological state of the cells.

A probability of growth model for Escherichia coli O157:H7 as a function of temperature, pH, acetic acid, and salt

Data accumulated on the growth of Escherichia coli O157:H7 in tryptic soy broth (TSB) were used to develop a logistic regression model describing the growth-no growth interface as a function of temperature, pH, salt, sucrose, and acetic acid. A fractional factorial design with five factors was used at the following levels: temperature (10 to 30 degrees C), acetic acid (0 to 4%), salt (0.5 to 16.5%), sucrose (0 to 8%), and pH (3.5 to 6.0). A total of 1,820 treatment combinations were used to create the model, which correctly predicted 1,802 (99%) of the points, with 10 false positives and 8 false negatives. Concordance was 99.9%, discordance was 0.1%, and the maximum rescaled R2 value was 0.927. Acetic acid was the factor having the most influence on the growth-no growth interface; addition of as little as 0.5% resulted in an increase in the observed minimum pH for growth from 4.0 to 5.5. Increasing the salt concentration also had a significant effect on the interface; at all acetic acid concentrations, increasing salt increased the minimum temperature at which growth was observed. Using two literature data sets (26 conditions), the logistic model failed to predict growth in only one case. The results of this study suggest that the logistic regression model can be used to make conservative predictions of the growth-no growth interface of E. coli O157:H7.