Modelling the combined effect of temperature, pH and aw on the growth rate of Monascus ruber, a heat-resistant fungus isolated from green table olives


P.N. Skandamis, Agricultural University of Athens, Department of Food Science and Technology, Laboratory of Microbiology and Biotechnology of Foods, Iera Odos 75, Athens, Greece, GR-11855 (e-mail:


Aims: Growth modes predicting the effect of pH (3·5–5·0), NaCl (2–10%), i.e. aw (0·937–0·970) and temperature (20–40°C) on the colony growth rate of Monascus ruber, a fungus isolated from thermally-processed olives of the Conservolea variety, were developed on a solid culture medium.

Methods and Results: Fungal growth was measured as colony diameter on a daily basis. The primary predictive model of Baranyi was used to fit the growth data and estimate the maximum specific growth rates. Combined secondary predictive models were developed and comparatively evaluated based on polynomial, Davey, gamma concept and Rosso equations. The data-set was fitted successfully in all models. However, models with biological interpretable parameters (gamma concept and Rosso equation) were highly rated compared with the polynomial equation and Davey model and gave realistic cardinal pHs, temperatures and aw.

Conclusions: The combined effect of temperature, pH and aw on growth responses of M. ruber could be satisfactorily predicted under the current experimental conditions, and the models examined could serve as tools for this purpose.

Significance and Impact of the Study: The results can be successfully employed by the industry to predict the extent of fungal growth on table olives.


Monascus is an ascomycetous fungus traditionally used for the production of food coloring, fermented foods and beverages in southern China, Taiwan, Japan, Thailand, Indonesia and the Philippines (Martínková and Patáková 1999). Members of the genus can commonly survive heat treatments and grow under reduced oxygen levels, resulting in food spoilage. Monascus ruber‘anamorph Basipetospora rubra (Cole and Kendrick 1968)’ is the most widespread species of the genus in Europe, where it is especially common in silage and deteriorating grain (Hawksworth and Pitt 1983). In Greece, the fungus has been isolated from the brine of thermally-processed green olives of the Conservolea variety and may result in economically significant spoilage losses. Spoilage may result from the development of a mycelial mat on the surface of the olives, and from a softening of the fruits and changes in the pH of the final product. Temperature, pH and NaCl are generally regarded as the principal controlling factors during fermentation and subsequent storage of table olives. A combination of these factors could effectively control the growth of the fungus during storage.

Predictive modelling has been extensively used mainly to predict bacterial growth as a function of environmental factors such as temperature, pH and aw (McMeekin et al. 1987; Davey 1994; Zwietering et al. 1994; Rosso et al. 1995). However, model development of filamentous fungal growth has not received the same level of attention as that of bacterial growth. A few studies concerning fungal growth have dealt with the predictive modelling approach (Gibson et al. 1994; Cuppers et al. 1997; Valík et al. 1999; Membré and Kubaczka 2000). To the best of our knowledge, fewer studies have been carried out to model the growth of heat-resistant fungi (Valík and Piecková 2001).

The aim of the present work was to develop and evaluate comparatively empirical models, including models with biological meaningless parameters and cardinal models (Rosso and Robinson 2001), in an attempt to describe the effect of temperature, salt concentration and pH on the growth of M. ruber ascospores.

Materials and methods

Fungus and preparation of ascospore suspension

The fungus used in this study was isolated in this Institute from the brine of thermally-processed table olives of Conservolea variety and was identified as Monascus ruber according to the method of Hawksworth and Pitt (1983). The fungus was routinely grown on malt extract agar plates (MEA; Merck, Darmstadt, Germany) at 30°C for 1 month. All plates were wrapped in plastic bags to avoid dessication of the growth medium due to prolonged incubation. Ascospores were prepared by flooding the plates with 20 ml sterile phosphate buffer solution (pH 7·0) and gently scraping the surface of the medium with a sterile spatula. The suspension was subjected to sonification as described by Kotzekidou (1997) in order to disrupt asci and liberate ascospores. After sonification, the suspension was heat-treated at 75°C for 30 min to break ascospore dormancy and destroy any remaining conidia and mycelial fragments. Finally, the suspension was filtered through sterile medical tissue, collected in a sterile test tube and stored at 4°C. Ascospore density was determined by the use of a counting chamber at 400 × magnification (Nikon Labophot-2 microscope, Osaka, Japan) and was found to be about 105 ascospores ml−1.

Growth media and incubation conditions

The standard growth medium used in all experiments was malt extract agar. The medium was adjusted by adding NaCl (Merck) in concentrations of 2%, 4%, 6%, 8% and 10% (w/v) with corresponding water activity (aw) levels of 0·970, 0·957, 0·943, 0·937 and 0·919, respectively. Water activity was measured using a Novasina Thermoconstander RTD 33 (Novasina AG, Zürich, Switzerland) at 20°C. The pH of the medium was adjusted using either 0·1 N HCl or NaOH to obtain pH values of 3·5, 4·0, 4·5 and 5·0.

A 10 µl volume of ascospore suspension was inoculated in the centre of 90 mm Petri dishes containing 20 ml solidified growth medium. The inoculated Petri dishes were incubated at 20, 25, 30, 35 and 40°C in high precision (± 0·2°C) incubators. The effect of different temperatures, NaCl and pH levels on fungal growth was examined by means of a full factorial experiment. One hundred experiments (five temperatures × five NaCl concentrations × four pH levels) were prepared in all. Each experiment was repeated five times. The range of experimental conditions was chosen to be within the limits of the brine environment. However, some combinations were extended to study the effect of higher temperatures, pH and NaCl levels on fungal growth.

Model development

Fungal growth was established by diameter measurements (expressed in mm) at right angles on a daily basis. The average value of the two diameters was used in modelling. A standard two-stage method was applied to obtain a model for the influence of temperature, pH and NaCl on growth of M. ruber ascospores. First, estimates of the maximum colony growth rates (µmax) were obtained by applying Baranyi's model (Baranyi et al. 1993). The average estimates of µmax were then fitted to secondary models to describe the single and combined effects of temperature, pH and NaCl on fungal growth. The models examined were mathematically and statistically evaluated.

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:


The coefficients a1a10 were estimated by linear regression.

An extended Davey (linear Arrhenius) model (Davey 1989) was the second approach to be tested based on the following equation:


where ln µmax is the natural logarithm of the maximum colony growth rate and a1a7 are coefficients to be estimated by nonlinear regression.

Models based on combinations of the gamma concept (Zwietering et al. 1996) and Rosso model (Rosso et al. 1995) were also tested. The complete model of Zwietering et al. (1996) for the relative effect of temperature, aw and pH has the general form: (4)


The relative effect of one variable can then be described by the gamma-factor of that variable:


where pHopt and Topt are the respective pH and temperature at which the µmax is optimal, Tmin is the temperature below which no growth occurs and µopt (days−1) is the µmax at optimum conditions (pHopt, Topt).

The gamma factor of temperature in Equation 4 was replaced by the extended square root model (8) to include the super-optimal temperature:


where Tmax is the temperature beyond which no growth occurs and c (degrees Celsius) is a regression coefficient. Equation 4 was fitted to the data-set, with Equations 6 to 8 as multiplicative terms.

The Rosso equation (Rosso et al. 1995; Rosso and Robinson 2001) for the effect of pH and temperature, combined with the gamma factor for water activity (Equation 7), had the following form:


Finally, by replacing the term of water activity of Equation 9 with the corresponding term of aw in the Rosso general equation, we used the complete cardinal temperature, pH and water activity model (CTPAM) of Rosso:


The in-house programme DMFit (Institute of Food Research, Norwich, UK) was used to fit the growth curves. Non-linear regression was carried out using the NLIN procedure of Statistica software (Statsoft Inc., USA) to fit the secondary growth models. The indices used for statistical comparison of models were the regression coefficient and the root mean square error (RMSE), given by the following equation:


where RSS is the residual sum of squares and df are the degrees of freedom.


The growth curves based on colony diameters were typical of linear fungal growth after a short germination (lag) period and ranged from 5 to 7 days (results not shown). The estimated maximum colony growth rates for each combination of pH, temperature (T) and NaCl are presented in Table 1. Fungal growth decreased as the concentration of NaCl was increased gradually from 2 to 10%, where no growth was evident in all cases. With respect to the effect of pH, experimental values were found mainly in the optimum/super-optimum range and for this reason, no significant curvature of maximum colony growth rate due to pH was evident. Moreover, at concentrations of 2% NaCl, colony growth rates were almost invariant for the whole range of pH, with small peaks at pH values around 4·5–4·8. Higher concentrations of NaCl resulted in optimum pH values close to 3·5 and a drop of maximum colony growth rates as the pH increased to 5 (Fig. 1).

Table 1.  Maximun specific growth rates of Monascus ruber at various temperatures, pH values and aw
Temperature (°C)pHNaCl (%)awbwµmax (days−1)s.d.
203·520·9700·173 3·8510·245
204·020·9700·173 3·2320·345
204·520·9700·173 3·1100·541
205·020·9700·173 2·5210·444
253·520·9700·173 8·2080·353
254·020·9700·173 7·2890·731
254·520·9700·173 8·9890·320
255·020·9700·173 8·4760·650
404·020·9700·173 8·2990·210
405·020·9700·173 8·2500·572
203·540·9570·207 3·6400·175
204·040·9570·207 3·2380·032
204·540·9570·207 2·4550·275
205·040·9570·207 1·8760·077
253·540·9570·207 7·7570·232
254·040·9570·207 6·4820·232
254·540·9570·207 5·6830·078
255·040·9570·207 4·8690·187
304·540·9570·207 9·9780·620
305·040·9570·207 7·6950·056
355·040·9570·207 7·9060·155
405·040·9570·207 8·9870·454
203·560·9430·238 2·5550·246
204·060·9430·238 2·2160·062
204·560·9430·238 1·7260·068
253·560·9430·238 5·8090·301
254·060·9430·238 5·1240·178
254·560·9430·238 3·9730·216
255·060·9430·238 4·0090·378
303·560·9430·238 9·0160·395
304·060·9430·238 8·6640·163
304·560·9430·238 7·3860·204
305·060·9430·238 5·5380·269
353·560·9430·238 9·1020·217
354·060·9430·238 8·2130·095
Figure 1.

Quadratic response surfaces predicting the effect of temperature, pH and NaCl concentration on the natural logarithm of maximum specific colony growth rate (ln rate) of Monascus ruber. (a) 2% NaCl; (b) 4% NaCl; (c) 6% NaCl; (d) 8% NaCl; 10% NaCl gave no growth in all cases

The response of the fungus to the environmental variables examined was quantified with four different models. Initially, the natural logarithm of maximum colony growth rate (ln µmax) was modelled vs pH, temperature and bw with a quadratic response surface model (Equation 2). From the response surfaces in Fig. 1, it is evident that the data for maximum colony growth rates for the range of experimental conditions examined form parabolic curves with relatively parallel positions, implying that the experimental factors act independently and pose additive effects. Curvature is observed in the optimal/super-optimal region, i.e. at 35 and 40°C, whereas the effect of lower temperatures (20–30°C) tends to be linear. The second model was the modified (linear) version of the Arrhenius model as proposed by Davey (1989) (Equation 3; Fig. 2). To date, use of this model has been restricted to bacterial growth, and good results have been obtained for the combined effect of either temperature and water activity, or of temperature and pH, on spoilage bacteria. In the present study, good fitting was obtained only when the transformation of aw proposed by Gibson (Equation 1) was used (Table 2). Three models were examined in the trials of models with biological meaningful parameters. The first was the complete model of Zwietering et al. (1996) (Equation 4), in which the relative effect of pH and water activity is given by Equations 6 and 7, respectively, whereas the temperature effect is expressed via the extended square root model of Ratkowsky et al. (1983) (Equation 8). The latter substitution was made for temperature only, since no successful run was obtained when the extended square root terms for pH and aw were tested. The substitution of temperature terms increased the percentage of the explained variance from 60·1% to 86·4% and enabled realistic estimates. In particular, the model estimated a minimum aw of 0·90 and a pH growth range from 1·37 to 6·5 (pHmin and pHmax, respectively) with optimum pH value 2·99, whereas the temperature minimum and maximum values were 14·39 and 50·93°C, respectively. However, no confidence limits for parameters could be estimated, implying the occurrence of structural correlation between parameters.

Figure 2.

Fitted curves of the Davey model (Equation 3) describing the temperature dependence of µmax of Monascus ruber at different pH and NaCl concentrations. (●) pH 3·5; (▪) 4·0; (▴) 4·5; (▾) 5·0. (a) 2% NaCl; (b) 4% NaCl; (c) 6% NaCl; (d) 8% NaCl; 10% NaCl gave no growth in all cases

Table 2.  Estimated values and statistics of the coefficients of the models for the µmax of Monascus ruber at different conditions of temperature, pH and aw
Equation typeParameterEstimated valuetr2d.f.RMSE
  • Value ± standard error.

  • Correlation coefficient.

  • *

    Not significant at P < 0·05.

Polynomiala1− 10·03 ± 3·04 × 10−13·290·959660·189
a232·49 × 10−2 ± 5·26 × 10−26·17   
a356·47 ± 17·653·19   
a41·08 ± 0·871·21*   
a5− 67·59 × 10−4 ± 57·39 × 10−5− 11·77   
a6− 156·3 ± 36·86− 4·24   
a7− 12·82 × 10−2 ± 9·00 × 10−2− 1·42*   
a835·81 × 10−2 ± 12·57 × 10−22·84   
a915·6 × 10−3 ± 6·07 × 10−32·57   
a10− 2·94 × 10−1 ± 1·46− 2·01   
Daveya1− 590·50 × 101 ± 58·48− 10·090·949690·217
a256·51 × 10−2 ± 84·56 × 10−20·66*   
a3− 85·85 × 10−3 ± 99·86 × 10−3− 0·85*   
a453·80 ± 17·263·11   
a5− 151·5 ± 40·99− 3·69   
a636·13 × 104 ± 35·35 × 10310·22   
a7− 55·56 × 106 ± 53·67 × 105− 10·35   
Equation 9µopt(days−1)21·89 ± 0·8525·580·931681·321
aw,min0·906 ± 0·001698·53   
pHmin− 101·1 ± 50·61− 1·99*   
pHmax5·00 ± 0·02172·25   
pHopt4·81 ± 0·0854·90   
Tmax (°C)46·19 ± 2·0222·82   
Tmin (°C)14·61 ± 1·927·57   
Topt (°C)34·36 ± 0·4477·13   
Rossoµopt(days−1)16·06 ± 1·3511·890·922691·477
aw,min0·919 ± 0·115 × 10−37950·07   
aw,max1·078 ± 3·36 × 10−532060·6   
aw,opt0·998 ± 3·025 × 10−3330·19   
Tmax (°C)46·43 ± 1·8624·89   
Tmin (°C)14·91 ± 1·858·04   
Topt (°C)34·40 ± 0·4476·86    

The second model (Equation 9) derived from substitution of pH and temperature terms of the previous model with relevant terms proposed by Rosso et al. (1995) (Fig. 3). Determination of 95% confidence limits was possible for all parameters. The model estimated a similar growth range for water activity and temperature, including optimum values, whereas it provided a different and unrealistic pH growth range, with pHopt being unexpectedly close to pHmax and pHmin being completely without sense (Table 2). The former is probably associated with the short experimental range of pH, which contrasts with the wide range of pH optimal values (3·5–4·8) for M. ruber. Indeed, pH seemed to negligibly explain the variation of µmax, especially at low NaCl concentrations of 2% and in some cases, at 4% and 6%. This was evidenced both graphically and statistically by the lack of µmax curvature due to pH (Fig. 3) and the low t-values for the coefficients of pH terms (Table 2), respectively. Furthermore, step-wise regression (F-test) showed that removing terms of pH from Equation 9 does not change the goodness of fit significantly (P < 0·05; results not shown). Accordingly, in the third model, i.e. the complete model of Rosso et al. (1995) (Equation 12), no good fit was obtained unless pH was disregarded (Fig. 4). Doing this, convergence was completed with low number of iterations, resulting in estimation of similar cardinal temperatures and water activities as in the previous models (Table 2). As far as the statistical evaluation is concerned, the two cardinal models (Equations 9 and 11) indicated significantly higher RMSE values than those of the polynomial equation and Davey model (Table 2). This is probably associated with the use of ln transformation of maximum specific colony growth rates in the polynomial equation and Davey model, in contrast to the untransformed growth rates introduced in the other equations. However, the residual values seemed to be fairly randomly distributed regardless of transformation (Fig. 5).

Figure 3.

Fitted curves of Equation 9 describing the effect of temperature on µmax of Monascus ruber at different pH and NaCl concentrations. (•) pH 3·5; (▪) 4·0; (▴) 4·5; (▾) 5·0. (a) 2% NaCl; (b) 4% NaCl; (c) 6% NaCl; (d) 8% NaCl; 10% NaCl gave no growth in all cases

Figure 4.

Comparison of predicted µmax of Monascus ruber by the Rosso model (Equation 12) and observed values for the whole data-set

Figure 5.

Distribution plots of residuals for the Davey model (a) and Equation 9 (b). Line: expected normal distribution for the present residuals; Bars: residuals derived from fitting


Monascus is a rather fast-growing fungus. Indeed, in the majority of cases, fungal growth presented similar or even higher maximum colony growth rates compared with the most common food spoilage fungi, as reported by other workers (Gibson et al. 1994; Valík et al. 1999; Rosso and Robinson 2001). Since the fungus was isolated from table olives, it was considered important to investigate experimental conditions closer to the brine environment. Thus, the NaCl concentration ranged from 2 to 10%, which is commonly used by the Greek table olive industries. The temperature ranged from 20 to 40°C since in many cases, olives are stored in plastic barrels outdoors where temperatures of 35–40°C are very common, especially during the summer. Finally, the pH ranged from 3·5 to 5 because after a proper fermentation, pH values are expected to range between 3·8 and 4·5. The experimental data indicated an observed optimum temperature of 35°C. This observation is in agreement with Domsch et al. (1980) who reported an optimum temperature between 30 and 37°C for different isolates of Monascus sp.

Quantification of the observed results via predictive models was performed. The polynomial model was selected first as an empirical modelling approach for fungi (Gibson et al. 1994; Valík et al. 1999; Valík and Piecková 2001) and exhibited good performance in terms of R2 and RMSE (Table 2; Fig. 1). Apart from the typical polynomial models, the satisfactory fitting of the Davey model to the current data suggests that this approach can also be expanded to account for fungal growth under the combined effect of low pH and high values of NaCl, with temperature ranging from suboptimal to super-optimal values. However, despite the good quality of fit, the above models lack biological meaningful parameters compared with the classical models of Ratkowsky et al. (1983) and Zwietering et al. (1996), as well as their modified versions (Wijtzes et al. 1993; Membréet al. 1999). Furthermore, Rosso et al. (1995) introduced a cardinal model applicable to bacteria, yeasts and moulds (Rosso et al. 1995; Cuppers et al. 1997; Membréet al. 1999; Rosso and Robinson 2001). One of the advantages of these approaches is that they enable easy assessment of initial parameter values and hence, facilitate the convergence procedure. However, it needs to be noted that these models may not be applicable to a situation in which the cardinal values of one environmental factor depend on the other factor, as it is not the case in this work where, for example, the optimum temperature for growth is in the range 30–35°C regardless of pH and NaCl concentration (Figs 1–3). With respect to error estimations (a potential weak point of the gamma concept), the Rosso model is considered more appropriate due to the absence of structural correlation between parameters.

The choice of current models was mainly motivated by the lack of information on the applicability of such models in data-sets, where the combined effect of three rather than one or two factors is investigated, especially in the case of fungi. It was shown that under the current experimental conditions, the combined effect of temperature, pH and NaCl concentrations on growth responses of M. ruber could be satisfactorily predicted, and the examined models could serve as tools for this purpose. However, models with biological interpretable parameters were highly rated compared with the polynomial equation and the Davey model, although the latter may provide a better fit and the polynomial equation has been established as the most common approach for predicting fungal growth. Indeed, the cardinal models showed a similar overall performance, with an equal or even lower number of parameters than the polynomial and Davey model. However, due to the consistency of estimates with biological observations, Equations 9 and 12 may contribute to the literature with cardinal temperatures, pH and water activity values for a specific mould responsible for post-heat treatment fungal spoilage of such an important fermented food as olives. The study aimed to contribute to the research area for fungal growth by adding both growth data for a wide range of the most common ecological determinants, and alternative modelling approaches that will facilitate future decision support systems in food manufacturing processes.


This work was partly funded by the Greek Ministry for Development (PAVE-99BE-262), the EU programmes OLITEXT (FAIR-CT97-3053) and FAIR-CT97-9523. In addition, E.P. would like to thank the National Agricultural Research Foundation (NAGREF) of Greece for supporting this research as part of his PhD thesis.