New models for the time dependent toxicity of individual and combined toxicants.

Time-dependent toxicity data of specific toxicants observed against A. fischeri were analysed using a single time-dependent Weibull cumulative distribution function (CDF). For binary mixtures the individual Weibull parameters provided the marginals for a bivariate copula model, characterised by a single extra parameter, the interaction exponent, θ. The copula model unites both the dose addition (DA, Loewe additivity) and dose independence (DI, Bliss independence) hypotheses of combinations into a single explicit equation and returns both hypotheses as special cases. The model predicts the linear isoboles from sham (like against like) experiments and the linear, concave, convex and mixed concave-convex isoboles from true binary mixtures. Systems are defined as being independent when θ = 1, additive when min(n 1, n 2) ≤ θ ≤ max(n 1, n 2), antagonistic when θ < min(n 1, n 2) and synergistic when θ > max(n 1, n 2), where n i are the individual dose (concentration) exponents. More complex mixtures were analysed by developing n-dimensional copulas: two ternary systems were analysed using a ternary copula that returned the three bivariate marginals and the three individual marginals of the mixture. The general model can also be used for time-independent studies by simply removing the time dependency. Research into combined effects has often assumed that if both the parameters for all the individual components in a mixture and the model for combinations were known then the additive effect of the whole could be predicted. This hypothesis has been shown to be false because without knowing how the components in a mixture interact the predictions from the standard DI or DA models provide only an initial, best guess, analysis.

Assessing the survival of Listeria monocytogenes in a domestic freezer by analyzing subsequent growth at 30°C using a novel reference method.

Listeria monocytogenes is a serious pathogen capable of extensive survival under frozen storage. Using optical density and multiple initial inocula in multiple identically prepared microtiter plates, the effect of storage time at -22°C on the subsequent growth at 30°C of the organism when defrosted was studied using a technique that compared the growth (through time to detection) of a test plate (previously frozen) with that of an identically prepared control plate, analyzed at the start of the experiment. Experiments were carried out using tryptic soy broth (TSB) or TSB supplemented with 3% salt. Plates were stored and frozen for up to 6 months (10 days, 20 days, 2 months, and 6 months). As storage time increased, there was only a small relative increase in the lag and the variance in the time to detection observed. When compared with storage in 3% salt TSB, which reduced the specific growth rate relative to growth in standard TSB, there were only marginally greater increases in lag and data variance. After 6 months storage in 3% salt TSB, there were some indications of inactivation (observed as small reductions of the initial optical density (equal to 1 × 10(9) CFU/ml) equivalent to a 50% inactivation. The method and the analyses suggest that this technique could allow easy examination of the effect of frozen storage on given cultures, with respect to the effects of pH, water activity, and also the effect of preservatives commonly used as extra hurdles in foods.

A generic model for spoilage of acidic emulsified foods: combining physicochemical data, diversity and levels of specific spoilage organisms.

The spoilage pattern of three emulsified, vegetable-based spreads of low pH (3.90-4.15) adjusted with acetic acid was characterized by correlating the growth of spoilage flora with the organoleptic and physicochemical changes, as well as the changes in the species composition of the dominant microflora during storage under isothermal conditions. In a further step, a generic (hereafter called 'unified') model was developed to describe the maximum specific growth rate of the specific spoilage organisms (SSOs) in all acetic acid acidified products, including literature data and additional in-house data from similar products, as a function of the storage temperature, pH (3.61-4.25) and initial concentration of the undissociated acetic acid in each product. The predictions of the unified model were compared with those of product-specific models, with temperature as the sole predictor variable. Two independent batches of commercially prepared pepper- (PS), fava beans- (FS) and eggplant-based (ES) spreads were stored at 4, 7, 10, 12, 15, 18, 20 and 25°C. The growth of lactic acid bacteria (SSOs; LAB) was correlated with changes in pH, titratable acidity and organic acids concentration, as well as sensory characteristics, in order to define the shelf-life of the products. Isolates from each spread and storage temperature were grouped with SDS-PAGE and were identified with 16S rRNA, determining the association between spoilage and species diversity. Product-specific models were developed using the square root model, while a polynomial and the Ratkowsky model were used for the development of the unified model. Products with lower pH and/or higher acetic acid content showed higher microbial stability. Lactobacillus plantarum or Lactobacillus brevis dominated the LAB association in all three spreads, although their relative percentage at the beginning of storage varied significantly. These facultative or obligate hetero-fermentative bacteria increased lactic acid and, sporadically, acetic acid levels in the spreads. The developed models were validated under real chill chain conditions and showed very good agreement with the observed data in PS and FS. The spoilage perception patterns of the different products were similar and thus, the proposed unified model may provide accurate predictions for the spoilage of a wide variety of acetic acid-acidified spreads, regardless of differences in the formulation (e.g., raw materials) and the manufacturing procedure.

Rapid throughput analysis of filamentous fungal growth using turbidimetric measurements with the Bioscreen C: a tool for screening antifungal compounds.

A rapid method for screening antifungal compounds and performing ecophysiological studies with filamentous fungi has been developed by the use of specific semi-solid media and spectrophotometric/turbidimetric measurements using the Bioscreen C with 2×100 microtitre well plates. The medium composition and preparation, inoculum size, medium volumes, and incubation parameters for measuring initial germination and growth dynamics have been optimised. These have been applied to assess the effectiveness of 18 concentrations of propyl propane thiosulfinate (PTS) against Aspergillus flavus in YES medium under different environmental regimes. Minimum inhibitory concentrations (MIC), and non-inhibitory concentration (NIC) values, and a newly developed MIC(50), have been calculated for the efficacy of these concentrations of PTS under four different environmental conditions (0.995 and 0.95 water activity (a(w)); 20 and 25°C) over 7d periods with automated measurements every 20 min. Data were modelled using the Lambert-Pearson Model, a mathematical modelling approach previously used for bacterial inhibition. Results have been compared with traditional growth rate data and Lethal Dose(50) (LD(50)) values. This approach could have major implications for rapid screening assays for growth and secondary metabolite production by filamentous organisms and has major advantages in terms of time reduction, culture medium volumes required, measurement and the ability to integrate and model key parameters for comparing efficacy.

Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel.

This study describes a method to obtain parameter confidence intervals from the fitting of non-linear functions to experimental data, using the SOLVER and Analysis ToolPaK Add-In of the Microsoft Excel spreadsheet. Previously we have shown that Excel can fit complex multiple functions to biological data, obtaining values equivalent to those returned by more specialized statistical or mathematical software. However, a disadvantage of using the Excel method was the inability to return confidence intervals for the computed parameters or the correlations between them. Using a simple Monte-Carlo procedure within the Excel spreadsheet (without recourse to programming), SOLVER can provide parameter estimates (up to 200 at a time) for multiple 'virtual' data sets, from which the required confidence intervals and correlation coefficients can be obtained. The general utility of the method is exemplified by applying it to the analysis of the growth of Listeria monocytogenes, the growth inhibition of Pseudomonas aeruginosa by chlorhexidine and the further analysis of the electrophysiological data from the compound action potential of the rodent optic nerve.

Limiting mycotoxins in stored wheat.

The quality of harvested wheat grain can deteriorate markedly during the post-harvest management stages. Biotic factors, such as grain type and ripeness, coupled with the prevailing abiotic factors, such as water content and temperature, and also preservative concentration will influence the safe storage life and the level of contamination with mycotoxins. These mycotoxins include deoxynivalenol (DON) produced pre-harvest and zearalenone (ZEA) produced post-harvest by Fusarium graminearum and Fusarium poae, respectively, ochratoxin (OTA) produced by Penicillium verrucosum post-harvest in cool damp northern European climates, and perhaps T-2 and HT-2 toxins produced by Fusarium langsethiae. This review presents recent data on the relationship between dry matter losses caused by F. graminearum under different environmental regimes (water activities, temperatures) and the level of contamination with DON. This is important as poor post-harvest drying and storage management may exacerbate DON contamination already present pre-harvest. It is thus critical to relate the environmental factors in stored wheat grain during storage, especially of intergranular relative humidity (RH) and temperature, to safe storage periods without spoilage or risk from increased DON contamination. The growth/no growth and DON/no DON (F. graminearum) and OTA/no toxin production (P. verrucosum) have been used to build a model with a simple interface to link temperature and RH values to the potential risk level which may allow growth or toxin production. This paper also considers the use of modified atmospheres, preservatives and biocontrol to minimise DON and OTA in moist wheat grain. These approaches together with clear monitoring criteria and hygiene could contribute to better post-harvest management of stored temperate cereals and ensure that mycotoxin contamination is minimised during this key phase in the food/feed chain.

Quantification of hurdles: predicting the combination of effects -- Interaction vs. non-interaction.

Combination of disparate as well as related antimicrobial effects constitutes the concept of hurdle technology. Quantification of combined effects, including claims of synergy, can be accomplished using surface response modelling, as is frequently done and reported. The Gamma hypothesis, however, states that the relative effects of different antimicrobial factors combine independently. Studies performed using time to detection have shown that the Gamma hypothesis is an adequate foundation for the analysis of multi-factor environmental stresses placed on microorganisms, including pH, weak acids and temperature. Data from the combined action of Na acetate and pH on Aeromonas hydrophila, Na acetate/pH , K sorbate/pH and combined Na acetate/K sorbate at pH 6.5, 6.0 and 5.5 on Escherichia coli and the combined action of Na acetate/pH and temperature on Enterobacter sakazakii were examined using nominal logistic modelling, response surface modelling (RS) and by using a Gamma model. The Gamma model can be used in a predictive manner unlike the RS models and the parameters of the RS models can be approximated from the fit of the Gamma model to the observed data. The expansion of the Gamma model explains the occurrence of the statistically significant cross terms of the RS polynomials. The emphasis within the literature of seeking interactions or synergies between environmental factors should be replaced with one emphasising the falsification of the Gamma approach. This can be done by examining the relative ratios of the gamma factors when in combination, but this also requires the use of appropriate functions to do this.

Application of predictive modelling techniques in industry: from food design up to risk assessment.

In this communication, examples of applications of predictive microbiology in industrial contexts (i.e. Nestlé and Unilever) are presented which cover a range of applications in food safety from formulation and process design to consumer safety risk assessment. A tailor-made, private expert system, developed to support safe product/process design assessment is introduced as an example of how predictive models can be deployed for use by non-experts. Its use in conjunction with other tools and software available in the public domain is discussed. Specific applications of predictive microbiology techniques are presented relating to investigations of either growth or limits to growth with respect to product formulation or process conditions. An example of a probabilistic exposure assessment model for chilled food application is provided and its potential added value as a food safety management tool in an industrial context is weighed against its disadvantages. The role of predictive microbiology in the suite of tools available to food industry and some of its advantages and constraints are discussed.

An explanation for the effect of inoculum size on MIC and the growth/no growth interface.

The inoculum effect (IE) is the phenomenon observed where changes in the inoculum size used in an experiment alters the outcome with respect to, for example, the minimum inhibitory concentration of an antimicrobial or the growth/no growth boundary for a given set of environmental conditions. Various hypotheses exist as to the cause of the IE such as population heterogeneity and quorum sensing, as well as the null hypothesis - that it is artefactual. Time to detection experiments (TTD) were carried out on different initial inoculum sizes of several bacterial species (Aeromonas hydrophila, Enterobacter sakazakii, Salmonella Poona, Escherichia coli and Listeria innocua) when challenged with different pH and with combined pH and sodium acetate. Data were modelled using a modification to a Gamma model (Lambert and Bidlas 2007, Int. J. Food Microbiology 115, 204-213), taking into account the inoculum size dependency on the TTD obtained under ideal conditions. The model suggests that changes in minimum inhibitory concentration (MIC) or in the growth-no growth boundary with respect to inoculum size are due to using a smaller or larger inoculum (i.e. is directly related to microbial number) and is not due to other, suggested, phenomena. The model used further suggests that the effect of a changing inoculum size can be modelled independently of any other factor, which implies that a simple 1 to 2-day experiment measuring the TTD of various initial inocula can be used as an adjunct to currently available models.

Comparing the antimicrobial effectiveness of NaCl and KCl with a view to salt/sodium replacement.

A study using a small range of pathogenic bacterial species (Aeromonas hydrophila, Enterobacter sakazakii, Shigella flexneri, Yersinia enterocolitica and 3 strains of Staphylococcus aureus) has shown that potassium chloride has an equivalent antimicrobial effect on these organisms when calculated on a molar basis. Combined NaCl and KCl experiments were carried out and data was analysed using a modification to the Lambert and Lambert [Lambert, R.J.W., and Lambert, R., 2003. A model for the efficacy of combined inhibitors. Journal of Applied Microbiology 95, 734-743.] model for combined inhibitors and showed that in combination KCl is a direct 1:1 molar replacement for the antimicrobial effect of common salt. If this is a general finding then, where salt is used to help preserve a product, partial or complete replacement by KCl is possible.

Gamma study of pH, nitrite, and salt inhibition of Aeromonas hydrophila.

The gamma hypothesis states that there are no interactions between antimicrobial environmental factors. The time to growth of Aeromonas hydrophila challenged with pH, NaNO(2), and salt combinations at 30 degrees C was investigated. Data were examined using a model based on the gamma hypothesis (the gamma model), which takes into account variance-stabilizing transformations and which gives biologically relevant parameters. At high concentrations of NaNO(2) and at pHs of >6.0, the antimicrobial action of the nitrite ion has a strong influence (MIC = 2,033 mg liter(-1)), whereas at pHs of <6, nitrous acid is dominant (MIC = 1.5 mg liter(-1)). This change is not due to a "synergy" between pH and the nitrite ion but is due to the shift in the equilibrium concentrations of nitrous acid and nitrite in solution caused by pH. In combination with salt, the parameters found for the action of Na nitrite were identical to those found when it was examined in isolation. Therefore, pH, NaNO(2), and salt act independently on the growth of A. hydrophila. By expanding the gamma model with a cardinal temperature model, the results of fitting the model of Palumbo et al. (J. Food Prot. 54:429-435, 1994) to randomly produced environmental conditions could be reproduced, suggesting that temperature also has an independent effect.

A study of the Gamma hypothesis: predictive modelling of the growth and inhibition of Enterobacter sakazakii.

Although the temperature growth profile of the opportunistic pathogen Enterobacter sakazakii is known, few other environmental factors affecting growth have been analysed. Using a model based on the Gamma hypothesis--that antimicrobial factors in mixtures exert independent effects--a range of weak acids (lactic, acetic, propionic, citric, sorbic and benzoic), pH, salt and temperature and some of their combinations were examined. The weak acids examined inhibited principally with the acid-form of the weak acid, however, benzoic, sorbic and propionic acids also displayed an inhibitory contribution from their respective anionic forms. In all cases pH could be considered an independent inhibiting factor. The minimum pH and maximum salt concentration for growth were calculated to be 3.89 and 9.1% respectively. In combination, there was no suggestion of any interactive effect between them. Studies performed on combinations of Na acetate/pH between 25 and 41 degrees C showed that temperature did not affect the relative inhibitory effects of the weak acid/pH mixtures. The results of this study support the Gamma hypothesis suggesting that there are no synergistic interactions between inhibitory factors and that growth can be predicted from a library of known effects. More importantly to the food industry, the results can be used to design good quality shelf-life challenge tests by reducing the number of studies required.

An investigation of the Gamma hypothesis: a predictive modelling study of the effect of combined inhibitors (salt, pH and weak acids) on the growth of Aeromonas hydrophila.

The Gamma hypothesis, that multiple inhibitory factors combine independently, is the underlying hypothesis for the quantification of the Hurdle concept used in food manufacture. The literature, however, is confused as to whether interactive effects exist and under which circumstances they occur, if at all. Using the method of time to detection (TTD), the inhibitory effect of pH, salt and specific weak acids (acetic, propionic, sorbic and benzoic) and combinations of these with respect to the growth of Aeromonas hydrophila (ATCC 7966) were analysed. A model based on the relative rate to detection described all combinations analysed as having independent effects on the TTD. No synergistic interactions were found between pH and salt, between pH and individual weak acids or between combinations of weak acids and pH for any of the systems under study. This study supports the validity of the Gamma concept -- that individual environmental effects act independently and should, in turn, facilitate attempts to model the growth of other microorganisms under a variety of conditions.