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N. Magan, Applied Mycology Group, Institute of BioScience and Technology, Cranfield University, Silsoe, Bedford MK45 4DT, UK (e-mail: firstname.lastname@example.org).
Aims: To develop a model for the combined effect of water activity (aw) and temperature on growth of strains of Aspergillus niger, and comparison with data on food spoilage moulds in the literature.
Methods and Results: An extended combined model describing the growth of two strains of A. niger, as a function of temperature (25–30°C) and aw (0·90–0·99) was developed. The growth rate (μ) was expressed as the increase in colony radial growth per unit of time. This extends the previous square root model showing the relationship between temperature and bacterial growth rate developed by Ratkowsky et al. (1983) and the parabolic relationship between the logarithm of the growth rate and aw developed by Gibson et al. (1994). A good correlation between the experimental data and the model predictions was obtained, with regression coefficients (r2) > 0·99. In addition, the use of this model allowed predictions of the cardinal aw levels: aw(min), and aw(opt). The estimation of the minimum aw levels (aw(min)) was in accordance with data in the literature for similar and a range of other Aspergillus and related species, regardless of the solutes used for aw modification. The estimation of the optimal aw (aw(opt)) and the optimal growth rate (μopt) were in good agreement with the experimental results and data from the literature.
Conclusions: This approach enables accurate prediction of the combined effects of environmental factors on growth of spoilage fungi for rapid prediction of cardinal limits using surface response curves.
Significance and Impact of the Study: This approach is a rapid method for predicting optimal and marginal conditions for growth of a wide range of spoilage micro-organisms in relation to interacting environmental conditions and will have applications for improving shelf-life of intermediate moisture foods.
In the last two decades, predictive food microbiology has included the development of models capable of describing the growth of pathogenic bacteria (Buchanan and Phillips 1990). However, predictive modelling of filamentous fungal growth has not received the same attention (Gibson et al. 1994; Gibson and Hocking 1997). Two of the most important environmental parameters that determine the ability of moulds to grow on foods are water activity (aw) and temperature (T) (Scott 1957). An empirical approach to modelling the effects of aw on mould growth was used by Gibson et al. (1994) who found that the logarithm of the fungal growth rate (μ, measured as the increase in colony radial growth per unit of time) showed a parabolic relationship with the square root of bw. The bw was defined as the difference between the aw of pure water (1) and that of a set aw for a specific growth kinetic. They investigated the appropriateness of models that were previously used to predict bacterial growth for the interpretation of mould growth data.
Much work has been directed towards the development of models for bacterial growth as a function of temperature and aw (McMeekin et al. 1987; Zwietering et al. 1994; Rosso et al. 1995). The temperature dependence of the specific growth rate of bacteria may be modelled by means of the square root model (Ratkowsky et al. 1983) with the cardinal parameters (e.g. the minimal temperature for growth, Tmin and the maximum temperature for growth, Tmax).
Cuppers et al. (1997) successfully combined the models of Rosso et al. (1995) and Ratkowsky et al. (1983) to describe the combined effects of temperature and NaCl on the growth rate of some food spoilage moulds. The four moulds used, Penicillium chrysogenum, Cladosporium cladosporioides, Aspergillus flavus and Alternaria alternata, were inoculated at the optimum temperature for growth and at pH close to optimum.
The main objective of this work was to develop a combined model based on the Gibson-type aw dependence and the Ratkowsky-type temperature dependence model on growth rate that could be used to describe the effect of interacting conditions of aw and temperature for the first time. This was then used to estimate the cardinal aw levels (aw(min), aw(max), aw(opt)) under different temperatures for two strains of A. niger. Correlations with literature data were made for a wide range of Aspergillus and Eurotium species.
Materials and methods
Two strains of A. niger (L11, AB4·1; van Hartingsveldt et al. 1987) containing the full-length hen egg white lysozyme cDNA under the control of the A. niger. var. awamori glucoamylase promoter were used in this study (Archer et al. 1990).
Media preparation, incubation and growth rate assessment
The water activity of 4·8% malt extract agar (MEA) (Oxoid) was modified with calculated amounts of the non-ionic solute glycerol 0·99–0·90 aw. A Novasina Humidat-IC-II (Pfaffikon, Switzerland) was used to check the aw levels obtained and found to be within 0·005 of the desired aw level.
Actively growing 8-day-old colonies of A. niger L11 and B1 on MEA were used to prepare a spore suspension (1·8 × 107 spores ml−1 ± 2%). Fungal spore suspensions were prepared in a solution of Tween-80 (100 μl l−1). Petri plates with glycerol-modified MEA were inoculated with 5 μl of the spores suspension and incubated at 25, 30 and 35°C.
Assessment of hyphal growth rate
The radial mycelial growth of each plate was measured in two directions at right angles to each other. Measurements were recorded on alternate days during the growth until the Petri plates were completely colonized. Radial mycelial growth vs. time was plotted and radial growth rates (μ, mm day−1) were evaluated from the slopes by linear regression (Baxter et al. 1998; Aldred et al. 1999).
Experimental design and data treatment
A fully randomized factorial design run in quadruplicate was used to generate the growth rate of the A. niger strains L11 and B1 at three temperatures and five aw levels modified with glycerol. In all cases a linear regression of the increase in radial extension against time was used to obtain the growth rates under each set of treatment conditions.
Previously, square root-type models (Ratkowsky et al. 1983) to describe the effect of temperature used cardinal parameters (e.g. the minimal temperature for growth, Tmin and the maximum temperature for growth, Tmax) has been used:
where μ = growth rate (mm day−1), T = temperature, Tmin = theoretical minimal temperature, Tmax = theoretical maximal temperature were b and c are design parameters.
Gibson et al. (1994) found that the logarithm of fungal growth rate (μ, measured as the increase in colony radial growth per unit of time) showed a parabolic relationship with the square root of
The proposed model is derived from eqns (1) and (3) and have the general form of
where μ = growth rate (mm day−1), b0, b1, b2, b3 and b4 are design parameters, aw = water activity and T = temperature (°C). The regressed parameters were found by nonlinear estimation with Hooke-Jeeves and the quasi-Newton method of Statistica v6.0 [StatSoft, Inc. (1984–2001), Tulsa, OK, USA] and simulated data and uncertainty of the parameters were evaluated with Crystal Ball 2000 v5.2 [Decisioneering, Inc. (1988–2002), Denver, CO, USA).
The growth data modelled in this work comprised the growth curves of two strains of A. niger L11 and B1 at five aw and three temperatures. Mycelial extension of colonies vs time almost invariably showed a straight line, after an initial lag period. The growth rate (μ) in mm per day, was calculated as the slope of a regression line through these points. The growth rate (μ) under the conditions of aw and temperatures recorded (data presented elsewhere) were used as inputs to calculate the design parameters of eqn (4).
The mean logarithm of growth rate [ln(μ)] and standard deviation were found to be higher and lower, respectively, for L11 than for B1 (Table 1). A lower variability of the dispersed data of L11 could increase the robustness of the model for strain L11. Estimates of eqn (4) and approximate standard errors are presented in the Table 2 for the strains L11 and B1 respectively. In both models there were no significant differences of the design parameters obtained in the four replicates.
Table 1. Standard deviation of the model of the data for Aspergillus niger strains L11 and B1
Table 2. Parameter estimation for eqn (4), their asymptotic standard errors and performance statistics for (a) A. niger strain L11 and (b) strain B1
−1·26 × 10−4
±8·25 × 10−7
±2·13 × 10−7
1·33 × 10−1
±2·76 × 10−3
2·47 × 10−4
±2·02 × 10−5
±5·21 × 10−6
Figures 1 and 2 shows the experimental data and the fitted data based on the model. The two strains of A. niger L11 and B1 are characterized by a sharp decrease in the radial growth rate from aw(opt) to aw(max), and from aw(opt) to ca 0·92 aw and from this aw slow decrease in the growth rate until aw(min). The aw for optimal growth rate (aw(opt)) was calculated to be 0·97 for both L11 and B1 and the minimum aw (aw(min)) 0·84 and 0·82 at 25°C, respectively. No differences were found in the optimal aw (aw(opt)) at 30 and 35°C. However minimum aw (aw(min)) at 35°C for B1 was 0·80.
A computer-simulated growth rate logarithm [ln(μ)] of L11 was plotted against aw at 25, 30 and 35°C to confirm the certainty of the simulated design parameters b0, b1, b2, b3, b4 and b5, assuming a normal distribution under a 95% variation of the parameters (Fig. 3). Robust model outputs growth rates [ln(μ)] were obtained for strain L11 at all temperatures at 50% variation of the design parameters. The logarithm of the growth rate at 25°C and 30°C showed very robust forecasts of the equation under all the distribution of the design parameters. The most stable design parameter was found between 0·99 and 0·97 aw. Moreover a reduction of aw increased the uncertainty of the model at 25 and 35°C for strain L11 and B1 (data not presented). A variation of the design parameters above 50% of the distribution in the 95% lead to a instability of the model and divergence of the results at 35°C. This result shows the high certainty of the parameters at high temperatures.
Fig. 4 shows the generated surface of the modelled and experimental data (o) of aw and temperature on growth rate expressed as logarithm [ln (μ, (mm day−1))] for A. niger strain L11 and B1 (r2 = 0·99). The surface generated by the model and the experimental data summarizes all the interactions previously described. The surfaces show greater sensitivity of the A. niger L11 to the higher temperatures under optimal aw (aw(opt)) conditions.
Comparisons with published data
Published reports of optimal aw values for several species of Aspergillus have been obtained at temperatures of between 15 and 37°C, using a variety of humectants, over the range 0·85–0·995 aw. The values predicted from the present model are that a aw of 0·97 is optimum for growth, which is in good agreement with the published data obtained at 25, 30 and 35°C with several species of the genus Aspergillus, which was frequently shown to be at 0·96–995 aw range depending on humectant used (Fig. 5).
A forecasted value of 33°C as an optimum for growth was found at the 95% confidence level. This would also be partially influenced by the range of humectants and species used in the literature. At >35 and <25°C, which are the limits of the model, again gave good agreement with published work. Discrepancies were found of the forecasted and reported values at 20°C (Wheeler et al. 1988). However, they used glucose/fructose as the humectant. More information on growth rates at this temperature is needed to obtain more accurate optimal aw ranges at this temperature.
The model gave a good prediction of minimal aw levels for growth in relation to a range of temperatures between 25 and 35°C (Fig. 9). An extrapolation of the model produced a good estimated of aw(min) at 15 (Marin et al. 1998) and 20°C (Wheeler et al. 1988). At 37°C the predicted value falls on the mean of the reported values (Marin et al. 1998). The best agreement of minimal water activity was obtained with species of A. flavus, A. niger, A. ochraceus and A. parasitucus at 25°C. Moreover good agreement was found with A. candidus, A. nidulans, A. versicolor at 30°C and Eurotium repens at 35°C (Fig. 10).
In the present work the model has been investigated as a tool for the interpretation of fungal growth rate data. Within the experimental boundary limits of temperature and aw the model produced is able to predict accurately the colony radial growth rates (mm day−1) and at the margins of the model it produces good forecast values. This type of model will assist in predicting conditions over which growth in food matrices may be a problem and also may assist in developing prevention strategies in food production processes. However, it also has applications as a bioprocess tool to assess the aw and temperature conditions to achieve a specific growth rate according to the operational parameters in biotechnological applications. Potential exists to extend the model application to wider range of different humectants with different properties such as ionic solutes. Although data regarding the effect of aw on mould growth is available, comparisons of results between investigators is often difficult because of differences in methodology or isolates used. Standardization of methodology across combinations of factors affecting growth can help to produce models to describe growth under any combination of conditions within the range tested.
We are grateful to the National Council of Science and Technology (CONACYT) of Mexico for financial support and to Prof. D.B. Archer for the strains.