Efstathios Z. Panagou, Laboratory of Microbiology and Biotechnology of Foods, Department of Food Science and Technology, Agricultural University of Athens, 75 Iera Odos str., Athens, GR-118 55, Greece. E-mail: firstname.lastname@example.org
Aims: To develop descriptive models for the combined effect of temperature (10–40°C) and water activity (0·850–0·980) on the growth of two ochratoxin A producing strains of Aspergillus carbonarius from Greek wine grapes on a synthetic grape juice medium.
Methods and Results: Fungal growth was measured as changes in colony diameter on a daily basis. The maximum specific colony growth rates (μmax) were determined by fitting the primary model of Baranyi describing the change in colony diameter (mm) with respect to time (days). Secondary models, relating μmax with temperature and aw were developed and comparatively evaluated based on polynomial, Parra, Miles, Davey and Rosso equations. No growth was observed at 0·850 aw (water activity) regardless of temperature, as well as at marginal temperature levels assayed (10 and 40°C) regardless of water activity. The data set was fitted successfully in all models as indicated by the values of regression coefficients and root mean square error. Models with biological interpretable parameters were highly rated compared with the polynomial model, providing realistic cardinal values for temperature and aw. The optimum values for growth were found in the range 0·960–0·970 aw and 34–35°C respectively for both strains. The developed models were validated on independently derived data from the literature and presented reasonably good predictions as inferred by graphical plots and statistical indices (bias and accuracy factors).
Conclusions: The effect of temperature and aw on the growth of A. carbonarius strains could be satisfactorily predicted under the current experimental conditions, and the proposed models could serve as a tool for this purpose.
Significance and Impact of the Study: The results could be successfully employed as an empirical approach in the development and prediction of risk models of contamination of grapes and grape products by A. carbonarius.
In the case of A. carbonarius, there are several published studies reporting the effect of temperature and aw on fungal growth using modelling approaches (Bellíet al. 2004b, 2005; Mitchell et al. 2004; Magan and Aldred 2005; Pardo et al. 2005). However, these studies are focused almost exclusively on secondary polynomial model development producing response surface contour plots. In addition, these models were used for fitting the experimental data and defining optimum conditions for germination and growth, whereas no attempt was made to validate them with independently derived data and assess their prediction capability.
The aim of this work was to (i) develop and evaluate comparative empirical models, including models with biological meaningless parameters and cardinal models, in an attempt to describe the effect of temperature and water activity on the growth rate of two ochratoxigenic A. carbonarius strains on a synthetic grape nutrient medium and (ii) to validate the developed models with independent data from the literature.
Materials and methods
Fungal isolate and growth medium
This study was carried out on two ochratoxigenic isolates of A. carbonarius from wine grapes in Greece. The isolates were deposited in the mycological collection of the Faculty of Biology of the University of Athens as A. carbonarius ATHUM 5659 and A. carbonarius ATHUM 5660. Both strains were initially tested for OTA production capability on CYA medium, using the method developed by Bragulat et al. (2001), showing mycotoxin potential >8 μg g−1 substrate. A synthetic nutrient medium (SNM), similar to grape composition between véraison and ripeness was used in this study, with the following composition: d(+) glucose, 70 g; d(−) fructose, 30 g; l(−) tartaric acid, 7 g; l(−) malic acid, 10 g; (NH4)2HPO4, 0·67 g; KH2PO4, 0·67 g; MgSO4·7H2O, 1·5 g; NaCl, 0·15 g; CuCl2, 0·0015 g; FeSO4·7H2O, 0·021 g; ZnSO4·7H2O, 0·0075 g; (+)Catechin hydrate, 0·05 g; agar, 25 g; distilled water, c. 1000 ml. The pH of the medium was adjusted to 3·5 with KOH (2 mol l−1). The aw of the unmodified medium was 0·980, measured by a Novasina Thermoconstander RTD 33 (Novasina AG, Zürich, Switzerland) water activity meter at 20°C, and it was used as the control treatment. The water activity of the SNM growth medium was modified to 0·850, 0·900, 0·930 and 0·960 aw by adding different amounts of glycerol (Mitchell et al. 2004).
Inoculation and incubation conditions
Fungi were grown on SNM medium for 10 days at 25°C to obtain sporulating cultures. Spore suspensions were obtained by flooding the plates with 15 ml sterile phosphate buffer solution (pH 7·0) containing 0·1% of a wetting agent (Tween 80; Merck, Darmstadt, Germany) and gently scraping the surface of the medium with a sterile spatula. After filtering through sterile medical tissue (Aseptica, Athens, Greece), the final concentration of spores was assessed by a Neubauer counting chamber (Brand, Wertheim, Germany) and adjusted to 106 spores per ml. A 5 μl volume of spore suspension was inoculated in the centre of 90 mm Petri dishes containing 20 ml solidified SNM growth medium. The inoculated plates were sealed with parafilm, wrapped in polyethylene bags to avoid desiccation and incubated at seven different temperatures from 10 to 40°C (at 5°C intervals). The effect of temperature and water activity on fungal growth was examined by means of a full factorial design. For each strain, aw/temperature combinations were carried out in triplicate and the whole experiment was repeated twice (n =6).
Fungal growth measurement and model development
Fungal growth was established by diametric measurements (expressed in mm) at right angles to each other on a daily basis. The mean value of the two diameters was used in the modelling. Measurements were carried out for a maximum of 50 days or until Petri dishes were completely colonized. A standard two-step approach was followed to develop a model for the influence of temperature and aw on fungal growth. First, estimates of the maximum specific colony growth rates (μmax) were obtained by applying Baranyi’s primary model (Baranyi et al. 1993; Baranyi and Roberts 1994). An explicit version of the model is the following:
where t is time, y0 is the initial colony diameter, ymax is the maximal colony diameter, μmax is the maximum specific colony growth rate (mm day−1), m is a curvature parameter and A(t) is a delayed time variable (lag phase).
The average estimates of μmax were then fitted to secondary models to describe the single and combined effects of temperature and water activity on fungal growth.
A quadratic response surface model was the first model used. The following transformation of water activity was applied, as introduced by Gibson et al. (1994):
Therefore, the quadratic expression of the natural logarithm of maximum colony growth rate had the following form:
where a0…a5 are design parameters estimated by nonlinear regression. The natural logarithm transformation was introduced to stabilize the variance of the fitted values for growth rate (Gibson and Hocking 1997).
The extended combined model proposed by Parra and Magan (2004), based on the Gibson-type aw dependence [eqn (2)] and the Ratkowsky-type temperature dependence on growth rate, was the second modelling approach to study the effect of temperature and aw on the growth of A. carbonarius. The model has the general form:
where μmax is the maximum specific growth rate (mm day−1) and a0…a4 are regression coefficients.
The model of Miles et al. (1997) was the third approach followed to study the effect of the entire biokinetic range of temperatures and aw levels on the growth of the fungus. The model is based on the following equation:
where b, c and d are coefficients to be fitted and Tmin, Tmax, aw min, aw max are the minimum and maximum values of temperature and water activity, respectively, beyond which growth is not possible.
The linear Arrhenius–Davey equation (Davey 1989) was the forth model tested, based on the following equation:
where T is absolute temperature (°K), aw is water activity and a0…a4 are coefficients to be determined.
The terms Tmin, Tmax, aw min, aw max correspond to the values of temperature and water activity, respectively, below and above which no growth occurs. Additionally, Topt and aw opt are the values of temperature and water activity at which μmax is equal to its optimal value (μopt).
The in-house programme DMFit (Institute of Food Research, Norwich, UK) was used to fit the growth curves and estimate the maximum specific colony growth rate (μmax). Non-linear regression was carried out using the Quasi-Newton algorithm of the NLIN procedure of Statistica release 6.0 (Statsoft Inc., Tulsa, OK, USA) to fit the secondary growth models. The indices used for statistical comparison of models were the regression coefficient (R2) and the root mean squared error (RMSE).
The developed models were validated with independent data from the literature (Mitchell et al. 2004; Bellíet al. 2005) for 16 strains of A. carbonarius grown at different aw and temperature regimes on the same synthetic grape juice medium (SNM). More specifically, growth data from Bellíet al. (2005) refer to eight isolates of A. carbonarius from four European countries within a temperature/aw range from 15–37°C and 0·900–0·990 respectively. In the case of Mitchell et al. (2004), experimental data come from eight strains of the fungus from three European countries and Israel in a temperature/aw range from 10–40°C and 0·850–0·987 respectively. The selected data for validation were all within the range of experimental conditions (temperature, aw) used for the development of the models in order to avoid any extrapolation. The prediction capability of the models was evaluated using graphical plots as well as the bias (Bf) and accuracy (Af) factors (Ross 1996).
The growth curves based on colony diameter changes were typical of fungal growth presenting a straight line after a short lag period. The colony growth rate was calculated with the Baranyi primary model as the slope of the linear segment of each growth curve. No significant differences were observed in the growth rates of the two strains (data not shown) for each temperature/aw treatment and for this reason all models were developed on the joint data from both strains. Parameter estimation for eqns (3) and (4) was based on the transformation of aw to bw. However, for easier comparison, all graphs are presented in aw terms. No growth was observed at 10 and 40°C in the time frame of the experiments, regardless of aw treatment. In addition, no growth was evident at aw values equal to 0·850 at all experimental temperatures. The response of the fungus to the environmental variables examined was quantified with five different models. Initially, the natural logarithm of the maximum specific colony growth rate (ln μmax) was modelled vs temperature and bw with a quadratic response surface model [eqn (3); Fig. 1; Table 1]. From the generated response surface it is evident that the maximum specific colony growth rates form parabolic curves with relatively parallel positions, implying that the environmental factors act independently and result additive effects. Curvature is observed in the optimal/super-optimal region for temperature, i.e. at 25–35°C. It is more intense at lower aw values over the whole range of temperature, but as aw moves to optimal/super-optimal values curvature is greatly reduced. Growth rates presented a peak at 35°C for all aw levels tested. The maximum specific colony growth rate was obtained at 35°C and 0·960 aw. The second model tested was the extended combined model proposed by Parra and Magan [eqn (4); Fig. 2; Table 1]. The strain was characterized by a sharp decrease in colony growth rate from aw,opt to aw,max and from a slower decrease from aw,opt to aw,min. The aw for optimal growth rate was c. 0·960–0·970 at all temperatures tested. The parallel position of temperature curves indicates that this factor had little effect on fungal growth, as it is also exemplified in Table 1 where temperature coefficients (a3, a4) were either nonsignificant or had low value. The third model was an extended square root-type model proposed by Miles et al. (1997) in which the relative effect of temperature and aw was modelled vs the square root of the maximum specific colony growth rate () [eqn (5); Fig. 3; Table 1]. This model has the advantage to provide parameter estimates (cardinal parameters) with biological meaning, such as minimal temperature for growth (Tmin), maximum temperature for growth (Tmax), minimal aw for growth (aw,min) and maximum aw for growth (aw,max) (Table 1). Based on this model the aw,opt for growth was found to be at c. 0·970 for all incubation temperatures (Fig. 4) whereas the minimal and maximum aw for growth were 0·860 and 0·990 respectively. However, this model provided a rather unrealistic temperature estimate for minimal growth (Tmin), −0·15, and a higher maximum growth temperature (Tmax) for A. carbonarious, c. 43°C (Table 1). Fitting results obtained by the modified (linear) version of the Arrhenius equation proposed by Davey (1989) [eqn (6)] are presented in Fig. 4 and Table 1 respectively. However, a weak point of this model is the lack of physiological interpretation for the significance of the values of the estimated regression parameters. The aw for optimum growth was 0·960 regardless of incubation temperature (Fig. 4). Besides, the parameters 1/T and 1/T2 were not statistically significant (Table 1) indicating that fungal growth was influenced primarily by water activity and to a much lesser extend by incubation temperature. Finally, the complete model of Rosso gave a good quality fit for the data set providing cardinal values of environmental factors (minimal, maximum and optimal values) [eqn (7); Fig. 5; Table 1]. The estimates for aw,min, aw,max and Tmax were comparable with the values of eqn (5) (Miles model) although the latter model gave a slightly higher estimate of aw,min for growth. Additionally, the Rosso-type model provided estimates for optimum values of growth rate, temperature and water activity (Table 1), but again an unrealistic estimate for Tmin was predicted. As far as the statistical evaluation is concerned, all models exhibited reasonably good fit to experimental data in terms of R2 and RMSE. The highest RMSE values were observed in the Rosso-type model. This is associated with the transformation of maximum specific colony growth rates used in the other four models (either ln or square root), in contrast to the untransformed values introduced to the Rosso model.
Table 1. Parameter estimation and performance statistics of the coefficients of the models for the μmax of two Aspergillus carbonarius strains
*Not significant at P <0·05.
−2·411 ± 0·167
0·140 ± 0·063
−0·003 ± 0·001
18·263 ± 5·973
−70·311 ± 14·726
0·374 ± 0·104
−2·657 ± 1·157
26·784 ± 9·986
−70·311 ± 21·714
0·072 ± 0·012
−0·139 ± 0·130*
0·318 ± 0·054
0·293 ± 0·072
50·00 ± 11·85
0·864 ± 0·043
0·999 ± 0·027
−0·81 ± 0·14*
42·08 ± 4·32
−233·713 ± 104·469
537·610 ± 196·829
−279·449 ± 104·723
−6931·21 ± 2898·92*
−46·561 ± 43·11·105*
7·95 ± 0·60
0·826 ± 0·037
0·999 ± 0·029
0·962 ± 0·004
−0·08 ± 6·48*
40·54 ± 13·04
34·20 ± 2·63
The graphical comparisons of the observed growth rates of 16 A. carbonarius strains from independent literature data vs the predicted growth rates by the five developed models is presented in Fig. 6. To facilitate the graphical interpretation of results, only the average values of growth rates obtained at the same temperature and aw levels for all strains are presented. The performance of validation in terms of calculated bias (Bf) and accuracy (Af) factors is shown in Table 2. The calculated Bf values were >1, indicating that, in general, the models predicted higher maximum specific colony growth rates than observed. Moreover, the values of Af indicated that all models predicted colony growth rates with approximately the same deviation from the observed growth rates.
Table 2. Validation indices (bias and accuracy factors) for the performance of the developed models on independently derived data from the literature (Mitchell et al. 2004; Bellíet al. 2005)
Aspergillus carbonarius is a rather fast growing fungus with a reported temperature range for growth from 10 to 40°C (Esteban et al. 2004) and optimum aw at 0·980–0·990 (Magan and Aldred 2005; Battilani et al. 2006b). In this study, no growth was observed at marginal conditions of aw (0·850) and temperatures (10 and 40°C) assayed in the time scale of the experiment. These results are comparable with Mitchell et al. (2004), who reported no growth of eight A. carbonarius strains from Portugal, Israel, Italy and Greece at 0·880 aw. The same authors reported no growth of any strain at 10°C, whereas in another study (Bellíet al. 2004b) minimum growth rates were observed at this temperature.
The effect of temperature and water activity on fungal growth was quantified by two different types of models. One was based on equations with dimensionless (biologically meaningless) parameters [eqns (3), (4) and (6)] and the other on models with cardinal values [eqns (5) and (7)]. A quadratic polynomial model was selected as a classical modelling approach for fungi (Gibson et al. 1994; Valík et al. 1999; Valík and Piecková 2001; Pardo et al. 2005) and exhibited good performance in terms of R2 and RMSE (Table 1; Fig. 1) predicting optimal conditions for growth at 35°C and 0·960 aw. These results are consistent with previous published works (Mitchell et al. 2003; Leong et al. 2004) reporting optimal temperatures for A. carbonarius between 25 and 35°C, whereas other authors reported lower optimal temperature for growth at 30°C (Battilani et al. 2006b). The aw,opt value predicted by the polynomial model agrees with previous findings (Mitchell et al. 2003, 2004) who reported optimum growth rates at intermediate aw levels. The extended combined model of Parra and Magan (2004) was the second model selected. It combines the parabolic relationship between the natural logarithm of growth rate and aw developed by Gibson et al. (1994), with the square root model showing the relationship between temperature and bacterial growth developed by Ratkowsky et al. (1983). The model also presented satisfactory performance as inferred by the relevant statistical indices of R2 and RMSE (Table 1; Fig. 2). The linear Arrhenius–Davey model is an expansion of the original Arrhenius model introduced by Davey (1989) to model the effect of incubation temperature on microbial growth. This model which is widely applied to bacterial growth (Ross and Dalgaard 2004) was selected to determine how well it could describe fungal growth. The model presented satisfactory fitting to the current data (Table 1; Fig. 4) suggesting that this approach could also be expanded to account for fungal growth. The aw, opt was similar to the value predicted by the previous two models. In the last two models the estimated parameters for temperature were not significant (Table 1), confirming thus previous findings that aw has a larger effect on fungal growth than temperature (Holmquist et al. 1983; Sautour et al. 2002; Samapundo et al. 2005). However, closer inspection of Figs 2 and 4 showed that the parabolic curves did not follow adequately the trend of experimental data points for temperature and could not thus sufficiently describe the variance of μmax despite the reasonably good performance of these models in terms of R2 and RMSE. Consequently, it appears that the models of Davey [eqn (6)] and Parra and Magan [eqn (4)] could not describe successfully the trend of temperature although it was evident by the data.
As a second modelling approach models with cardinal values were selected. One of the advantages of these models is that they enable easy assessment of initial parameter values and hence, facilitate the convergence procedure. An expanded square root-type model taking into account the entire biokinetic ranges of temperature and water activity was initially tested (Table 1; Fig. 3). The model performed well with the data set and gave realistic estimates for aw, min and aw, max which are in line with published values (Mitchell et al. 2003, 2004; Magan and Aldred 2005). However, the model gave an unrealistic value for Tmin and a slightly higher value for Tmax than the reported growth range, 10–40°C (Esteban et al. 2004). Finally, the complete model of Rosso et al. (1995) provided additionally estimates of the optimum values for temperature (Topt) and aw (aw, opt) for growth as well as an estimate for the optimum growth rate (μopt) (Table 1; Fig. 5). These values are in comparable with previous authors (Magan and Aldred 2005) who reported an optimum radial extension of c. 10 mm day−1 at 30–35°C and 0·990–0·930 aw. The unrealistic Tmin values in both Miles and Rosso models were possibly due to the exclusion of no growth cases from the data set, in an effort to make the dependent variable (μmax) fully comparable between different models, as a zero value for growth would make the ln transformation impossible.
Validation of the developed models with independent data from the literature (Mitchell et al. 2004; Bellíet al. 2005) showed reasonably good correlation among observed and predicted colony growth rates (Table 2; Fig. 6). However, the distribution of the majority of data points above the diagonal line indicated that all models overestimated fungal growth rates, i.e. the predicted values were higher that the observed. The difference was more intense at higher (35°C) than at lower temperatures (15°C). There were two potential limitations in the validation of the models with literature data. One was due to inherent differences in the observed growth rates among the different strains of A. carbonarius reported by the above authors, as there was variation in the growth rates of various strains between countries and also within the same country. The second was related to the concentration of spore suspension used as inoculum. Although the initial stock solution of fungal spores was the same in all works (c. 105–106 spores per ml), SNM Petri plates were inoculated with 5 μl of spore suspension in the case of Mitchell et al. (2004) whereas in Bellíet al. (2005) plates were needle inoculated.
In conclusion, the results of this study showed that under the current experimental conditions, the combined effect of temperature and water activity on the growth responses of A. carbonarius could be satisfactorily predicted, and the examined models could serve as tools for this purpose. Models with biological interpretable parameters (Miles and Rosso) presented good overall performance and may contribute to the literature with cardinal temperatures and aw values to determine the conditions for germination and growth of A. carbonarius. However, to build better models, a database is necessary with information from a wide range of strains from different climatic conditions and countries. In addition a common experimentation protocol is necessary among the different research groups for the harmonization of model development and validation.
This work was supported by the project ‘Presence of ochratoxin A in Greek wines and study on the conditions that influence its production’ financed by the General Secretariat for Research and Technology of the Greek Ministry for Development. In addition, Mr P. Natskoulis would like to thank the Cranfield Health, Cranfield University for supporting this research as part of his PhD thesis.