Probabilistic modeling of Saccharomyces cerevisiae inhibition under the effects of water activity, pH, and potassium sorbate concentration

Determination of bioremediation properties of soil-borne Bacillus sp. 5O5Y11 and its effect on the development of Zea mays in the presence of copper

Today, industrial activities lead to the accumulation of heavy metals in the soil, water, and air due to mine deposits and operations, fertilizers, and drugs used in agriculture, and urban wastes. Using microorganism bioremediation of metals is an important technique in solving these problems. Herein, a rhizoid bacterium isolated from orchids that grow in Ovit plateau was defined as Bacillus sp. 5O5Y11 by conventional and molecular methods and the bioremediation properties of strain were investigated. It was capable of growth at high salt (10-15%) concentration, wide temperature (10-45 °C) and pH range (pH 4.5-8.0), and was observed to have strong lecithinase, gelatinase activity, and nitrate reduction. When the plant growth-promoting properties of this strain were examined, strong siderophore and ammonium production were observed in in vitro conditions. Bacillus sp. 5O5Y11 was found to have high tolerance to a group of heavy metals [iron (Fe), copper (Cu), lead (Pb), silver (Ag), zinc (Zn)]. Minimum inhibition concentration (MIC) and minimum bactericidal concentration (MBC) values of copper metal on Bacillus sp. 5O5Y11 were determined as 12.5 mM and 50 mM, respectively. The effectiveness of this bacterium on the germination and growth of maize plant in the presence and absence of copper were investigated. These results suggest that Bacillus sp. 5O5Y11 is a microorganism, which has potential in metal bioremediation and plant growth promotion.

Probabilistic Models to Predict the Growth Initiation Time for Pseudomonas spp. in Processed Meats Formulated with NaCl and NaNO2

This study developed probabilistic models to determine the initiation time of growth of Pseudomonas spp. in combinations with NaNO2 and NaCl concentrations during storage at different temperatures. The combination of 8 NaCl concentrations (0, 0.25, 0.5, 0.75, 1, 1.25, 1.5, and 1.75%) and 9 NaNO2 concentrations (0, 15, 30, 45, 60, 75, 90, 105, and 120 ppm) were prepared in a nutrient broth. The medium was placed in the wells of 96-well microtiter plates, followed by inoculation of a five-strain mixture of Pseudomonas in each well. All microtiter plates were incubated at 4, 7, 10, 12, and 15℃ for 528, 504, 504, 360 and 144 h, respectively. Growth (growth initiation; GI) or no growth was then determined by turbidity every 24 h. These growth response data were analyzed by a logistic regression to produce growth/no growth interface of Pseudomonas spp. and to calculate GI time. NaCl and NaNO2 were significantly effective (p<0.05) on inhibiting Pseudomonas spp. growth when stored at 4-12℃. The developed model showed that at lower NaCl concentration, higher NaNO2 level was required to inhibit Pseudomonas growth at 4-12℃. However, at 15℃, there was no significant effect of NaCl and NaNO2. The model overestimated GI times by 58.2±17.5 to 79.4±11%. These results indicate that the probabilistic models developed in this study should be useful in calculating the GI times of Pseudomonas spp. in combination with NaCl and NaNO2 concentrations, considering the over-prediction percentage.

Modelling the effect of temperature and water activity on the growth rate and growth/no growth interface of Byssochlamys fulva and Byssochlamys nivea

The purpose of the present study was to apply a modelling approach to define the growth rate and growth/no growth interface of Byssochlamys fulva and Byssochlamys nivea on a synthetic medium as a function of temperature and water activity. Both fungal species were grown on malt extract agar at different temperatures (10, 15, 20, 25, 30, 35, 40 and 45 degrees C) and a(w) levels (0.88, 0.90, 0.92, 0.94, 0.96 and 0.99) for a period of 30 days. Growth responses were evaluated over time in terms of colony diameter changes. Growth data were fitted to the primary model of Baranyi and the resulting growth rates were further modeled as a function of temperature and water activity using the cardinal model with inflection (CMI) (Rosso et al., 1993). A logistic regression quadratic polynomial model was also employed to predict the probability of growth over storage time. Estimated parameters for minimum, maximum and optimum temperatures for growth were 9.1 degrees C, 46.4 degrees C and 32.1 degrees C for B. fulva and 10.5 degrees C, 43.2 degrees C and 32.1 degrees C for B. nivea. The respective values for a(w) were 0.893, 0.993 and 0.985 for B. fulva and 0.892, 0.992 and 0.984 for B. nivea. No growth was observed at 0.88 a(w) regardless of temperature for both species, whereas B. nivea ascospores could not grow at 10 and 45 degrees C irrespective of a(w). Regarding growth boundaries, the degree of agreement between predictions and observations was >98% concordant for both species. The erroneously predicted growth cases were 1.4-4.2% false positive and 2.1-3.5% false negative for B. nivea and B. fulva, respectively. The developed logistic model was validated with two literature data sets as well as with data from independent experiments carried out on fruit juices. Validation results showed that agreement with literature data for growth was 25 out of 36 (69.4%) cases, whereas validation on fruit juice data failed in only 6 cases (5 false positives and 1 false negative) out of 128 cases.

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.

Colletotrichum gloeosporioides growth-no-growth interface after selected microwave treatments

To study microwave heating for potential postharvest treatments against anthracnose disease, Colletotrichum gloeosporioides growth-no-growth response after selected microwave treatments (2,450 MHz) was fitted by using a logistic regression model. Evaluated variables were power level, exposure time, presence or absence of water in the medium during treatment, and incubation-observation time. Depending on the setting, the applied power ranged from 77.2 to 435.6 W. For the experiments on dry medium (mold spores over filter paper), exposure times were 1, 2, 3, or 4 min, whereas spores dispersed in potato dextrose agar, a wet medium, had exposure times of 3, 6, or 9 s. Growth (response = 1) or no growth (response = 0) was observed after two different incubation-observation times (4 or 10 days). As expected, high power levels and long exposure times resulted in complete inhibition of C. gloeosporioides spore germination. In a number of cases (such as low power levels and short treatment times), only a delay in mold growth was observed. Scanning electron micrographs showed signs of mycelia dehydration and structural collapse in the spores of the studied mold. Cell damage was attributed to heating during microwave exposure. Reduced logistic models included variables and interactions that significantly (P < 0.05) affected mold growth, and were able to predict the growth-no-growth response in at least 83% of the experimental conditions. Microwave treatments (4 min at any of the studied power levels in dry medium, and 9 s at power levels of 30% or more for wet medium) proved effective in the inhibition of C. gloeosporioides in model systems. These no-growth conditions will be tested further on fresh fruits in order to develop feasible postharvest microwave treatments.

Use of a D-optimal design with constrains to quantify the effects of the mixture of sodium, potassium, calcium and magnesium chloride salts on the growth parameters of Saccharomyces cerevisiae

The combined effect of NaCl, KCl, CaCl(2), and MgCl(2) on the water activity (a (w)) and the growth parameters of Saccharomyces cerevisiae was studied by means of a D-optimal mixture design with constrains (total salt concentrations < or = 9.0%, w/v). The a (w) was linearly related to the concentrations of the diverse salts; its decrease, by similar concentrations of salts, followed the order NaCl > CaCl(2) > KCl > MgCl(2), regardless of the reference concentrations used (total absence of salts or 5% NaCl). The equations that expressed the maximum specific growth (mu (max)), lag phase duration (lambda), and maximum population reached (N (max)) showed that the values of these parameters depended on linear effects and two-way interactions of the studied chloride salts. The mu (max) decreased as NaCl and CaCl(2) increased (regardless of the presence or not of previous NaCl); however, in the presence of a 5% NaCl, a further addition of KCl and MgCl(2) markedly increased mu (max). The lambda was mainly affected by MgCl(2) and the interactions NaCl x CaCl(2) and CaCl(2) x MgCl(2). The further addition of NaCl and CaCl(2) to a 5% NaCl medium increased the lag phase while KCl and MgCl(2) had negligible or slightly negative effect, respectively. N (max) was mainly affected by MgCl(2) and its interactions with NaCl, KCl, and CaCl(2); MgCl(2) stimulated N (max) in the presence of 5% NaCl while KCl, NaCl, and CaCl(2) had a progressive decreasing effect. These results can be of interest for the fermentation and preservation of vegetable products, and foods in general, in which this yeast could be present.

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.

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).

Predicting noncompliant levels of ochratoxin A in cereal grain from Penicillium verrucosum counts

AIMS

To model the probability of exceeding the European legislative limit of 5 microg ochratoxin A (OTA) per kilogram grain in relation to Penicillium verrucosum levels and storage conditions, and to evaluate the possibilities of using P. verrucosum colony counts for predicting noncompliant OTA levels.

METHODS AND RESULTS

Cereal samples were inoculated with P. verrucosum spores and stored for up to 9 months at temperatures and water activities ranging from 10-25 degrees C and aw 0.77-0.95. A logistic regression analysis showed that the probability of exceeding 5 microg OTA kg(-1) grain was related to colony counts of P. verrucosum and water activity. The sensitivity and specificity of various P. verrucosum count thresholds for predicting noncompliant OTA levels were estimated, using data from the storage trial and natural cereal samples.

CONCLUSION

The risk of exceeding 5 microg OTA kg(-1) grain increased with increasing levels of P. verrucosum, and with increasing water activities. A threshold of 1000 CFU P. verrucosum per gram grain is suggested to predict whether or not the legislative limit is exceeded.

SIGNIFICANCE AND IMPACT OF THE STUDY

This study has provided a tool to evaluate the levels of P. verrucosum in grain in relation to OTA levels. Hence, mycological analyses can be used to identify cereal samples with high risk of containing OTA levels above the legislative limit.

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.

A probabilistic neural network approach for modeling and classification of bacterial growth/no-growth data

In this paper, we propose to use probabilistic neural networks (PNNs) for classification of bacterial growth/no-growth data and modeling the probability of growth. The PNN approach combines both Bayes theorem of conditional probability and Parzen's method for estimating the probability density functions of the random variables. Unlike other neural network training paradigms, PNNs are characterized by high training speed and their ability to produce confidence levels for their classification decision. As a practical application of the proposed approach, PNNs were investigated for their ability in classification of growth/no-growth state of a pathogenic Escherichia coli R31 in response to temperature and water activity. A comparison with the most frequently used traditional statistical method based on logistic regression and multilayer feedforward artificial neural network (MFANN) trained by error backpropagation was also carried out. The PNN-based models were found to outperform linear and nonlinear logistic regression and MFANN in both the classification accuracy and ease by which PNN-based models are developed.

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.

Comparison of logistic regression and linear regression in modeling percentage data

Percentage is widely used to describe different results in food microbiology, e.g., probability of microbial growth, percent inactivated, and percent of positive samples. Four sets of percentage data, percent-growth-positive, germination extent, probability for one cell to grow, and maximum fraction of positive tubes, were obtained from our own experiments and the literature. These data were modeled using linear and logistic regression. Five methods were used to compare the goodness of fit of the two models: percentage of predictions closer to observations, range of the differences (predicted value minus observed value), deviation of the model, linear regression between the observed and predicted values, and bias and accuracy factors. Logistic regression was a better predictor of at least 78% of the observations in all four data sets. In all cases, the deviation of logistic models was much smaller. The linear correlation between observations and logistic predictions was always stronger. Validation (accomplished using part of one data set) also demonstrated that the logistic model was more accurate in predicting new data points. Bias and accuracy factors were found to be less informative when evaluating models developed for percentage data, since neither of these indices can compare predictions at zero. Model simplification for the logistic model was demonstrated with one data set. The simplified model was as powerful in making predictions as the full linear model, and it also gave clearer insight in determining the key experimental factors.