Combined Effects of pH and Sugar on Growth Rate of Zygosaccharomyces rouxii, a Bakery Product Spoilage Yeast

Abstract

The effects of citric acid-modified pH (pH 2.5, 2.75, 3, 3.5, 4, 4.5, 5, and 5.5) and a 30% glucose–70% sucrose mixture (300, 400, 500, 600, 700, 800, 875, and 900 g/liter) on an osmophilic yeast, Zygosaccharomyces rouxii, were determined by using synthetic medium. One hundred experiments were carried out; 50-ml culture flasks were inoculated with 10³ CFU ml⁻¹ by using a collection strain and a wild-type strain cocktail. The biomass was measured by counting cell colonies, and growth curves were fitted by using a Baranyi equation. The growth rate decreased linearly with sugar concentration, while the effect of pH was nonlinear. Indeed, the optimal pH range was found to be pH 3.5 to 5, and pH 2.5 resulted in a 30% reduction in the growth rate. Finally, we evaluated the performance of two nonlinear predictive models developed previously to describe bacterial contamination. Equations derived from the Rosso and Ratkowsky models gave similar results; however, the model that included dimensionless terms based on the Ratkowsky equation was preferred because it contained fewer estimated parameters and also because biological interpretation of the results was easier.

Over the last 15 years, the predictive modelling approach has been developed in order to determine microbial growth as a function of temperature, pH, and water activity (a_w) (19). Predictive microbiology has been focused on pathogenic bacteria (3, 6, 15, 20, 21), yet food spoilage by yeasts or molds causes serious deterioration and produces visible growth on surfaces, off-odors, off-flavors, and slime. Yeasts and molds can be found in a wide variety of environments due to their capacity to utilize a variety of substrates and their tolerance of low pH values, low a_w values, and low temperatures (12). A few yeast or mold contamination studies have used the predictive modelling approach (4, 9).

With bakery products, a_w is the most important factor affecting the type and rate of spoilage. In most cases, an osmophilic yeast can grow in products at low pH values and/or in the presence of high sugar concentrations when competition with bacteria is restricted. Yeast spoilage is characterized by visible growth on the surfaces of products (white or cream patches) or by the production of gas, including bubbling in jams and fondants and expansion of flexible packaging (14). Foods that contain high sugar concentrations and thus have low a_w values are spoiled first by Zygosaccharomyces rouxii (7). In addition, Z. rouxii is able to grow at a wide range of pH values, such as pH 1.8 to 8.0 in the presence of high concentrations of glucose (28) or pH 1.5 to 10.5 in 12% glucose medium (25). In his well-documented review of spoilage yeast, Fleet (7) mentioned that a high sugar concentration may either increase or decrease the low-pH tolerance of yeast and emphasized that further study of these influences would be needed to clarify the discrepant observations that have been described. In this paper, we describe the combined effects of pH and high sugar concentrations on the Z. rouxii growth rate. To predict the influence of these factors, two nonlinear models were evaluated by using our data.

MATERIALS AND METHODS

Organism, culture medium, diluent, and enumeration procedures.

Two strains of Z. rouxii were used in a cocktail to introduce variability due to strains and therefore to facilitate validation of laboratory results in an industrial context. One strain was an osmotolerant collection strain (DSM 70540), and the other was a wild-type strain isolated at the ADRIANOR, Arras, France, from spoiled bakery products. The synthetic culture medium used was modified osmophilic yeast medium DSM 187 and contained 20 g of malt extract (Difco Laboratories, Detroit, Mich.) per liter and 5 g of yeast extract (Biokar, Beauvais, France) per liter; this medium was supplemented with glucose (Acros, Geel, Belgium) and sucrose (Merck, Darmstadt, Germany) as required by the experimental design. The pH was adjusted by adding citric acid (Prolabo, Paris, France). Experiments were carried out in 250-ml flasks containing 50 ml of medium, and the flasks were incubated at 25°C for up to 20 days.

As recommended by Abdul-Raouf et al. (1), biomass was measured by counting cell colonies on malt agar (medium DSM 186) containing (per liter) 3 g of malt extract, 3 g of yeast extract, 5 g of proteose peptone (Difco), 10 g of glucose, and 15 g of type E agar (Biokar) after appropriate dilution in 40% glucose–sterile water tubes to reduce the osmotic shock. Preliminary experiments performed in our laboratory showed that there was no difference between the number of CFU on plates containing malt agar supplemented with 50% glucose and the number of CFU on plates containing only malt agar.

Three colonies from a malt agar plate that had been stored at 4°C were transferred into culture medium that was supplemented with 165 g of glucose per liter and 385 g of sucrose per liter and adjusted to pH 4.5, and the preparation was incubated at 25°C for 15 h. Actually, to obtain reproducible results, we concluded on the basis of previous results obtained in our laboratory that exponential-phase cells were more appropriate. This primary culture was used to inoculate secondary cultures that were incubated under each of the experimental conditions. Each inoculum was adjusted to contain about 10³ CFU ml⁻¹ (50% collection strain cells and 50% wild-type strain cells).

Experimental design.

An initial complete factorial experiment was performed by using pH 2.5, 2.75, 3, 3.5, 4, 4.5, 5, and 5.5 and sugar concentrations of 300, 400, 500, 600, 700, and 800 g liter⁻¹. The final sugar concentration was obtained by mixing 30% glucose and 70% sucrose; for instance, 90 g of glucose per liter and 210 g of sucrose per liter were mixed to obtain a sugar concentration of 300 g liter⁻¹. The corresponding sugar and a_w levels were as follows: 300 g liter⁻¹ and 0.957 a_w; 400 g liter⁻¹ and 0.946 a_w; 500 g liter⁻¹ and 0.923 a_w; 600 g liter⁻¹ and 0.904 a_w; 700 g liter⁻¹ and 0.880 a_w; 800 g liter⁻¹ and 0.843 a_w; and 950 g liter⁻¹ and 0.788 a_w (Awx-3001, Ebro, Germany). Duplicate growth curves were generated for each of the experimental treatments. Then, to determine the relevance of maximal sugar concentrations as estimated by modelling, a second data set was obtained by using a factorial design in which we combined sugar concentrations of 875 and 950 g liter⁻¹ with pH 3, 3.5, 4, 4.5, 5, and 5.5. No replicates were used in the latter experiment.

Curve fitting.

Using the experimental designs, we generated 100 growth curves (96 treatments from the first experimental design, 12 treatments from the second experimental design, and 8 treatments randomly missing data). The change in the natural logarithm of the biomass (CFU per milliliter) versus time was described with the logistic curve modified by Baranyi et al. (2, 13) as equations 1 and 2:

1

2

where t is time, ln N₀ is the inoculum size, L is the lag phase, μ is the specific growth rate, and ln N_max is the maximal population density.

The specific growth rate was then studied as a response in a second modelling step. The effects of sugar concentration (S) and pH were analyzed by comparing two nonlinear models. First, based on the square root model (18, 26) (equation 3), since sugar had a linear effect on the growth rate in the concentration range which we used (Fig. 1), a model that included dimensionless multiplicative terms was developed (equation 4):

3

4

where pH_min and pH_max are representative minimal and maximal pH values, respectively, S_max is the maximal sugar concentration when growth is observed, and Cst and c are estimated parameters. Hence, experimental data could be fitted to equation 4 by performing nonlinear regression with estimated values for four parameters.

FIG. 1.

Linear relationship between specific growth rate (μ) and sugar concentration. Experimental data were obtained at 25°C and pH 3.5 to 5.

Second, the Rosso equation for pH effect (27) was used, and since we assumed that the sugar effect was linear, the data set was fitted by using equation 5:

5

where μ_opt is the growth rate under optimum conditions and pH_opt is the optimal pH. This model contained five estimated parameters.

Nonlinear regression was computed by using S-plus software (AT&T Bell Laboratories, Murray Hill, N.J.), and the parameters of the regression were estimated by the maximum-likelihood method (11).

RESULTS AND DISCUSSION

Kinetic profiles.

Kinetic profiles were determined for up to 500 h (20 days). The maximal cell density was estimated to be up to 10⁸ CFU ml⁻¹, whatever the combination of experimental conditions used. No lag phase was observed at pH 2.5 to 5.5 and at sugar concentrations ranging from 300 to 950 g liter⁻¹. On the other hand, additional experiments were performed at pH 2 (data not shown), and in this case, no growth was observed after 30 days. Kinetic profiles were successfully fitted by using the function of Baranyi et al. (Fig. 2). This model was preferred to the Gompertz equation, which is widely used in predictive microbiology studies, because systematic overestimates of the maximum specific growth rate have been obtained previously with the Gompertz function (5, 23). Moreover, the model of Baranyi et al. has recently given satisfactory results (8, 17, 22).

FIG. 2.

Growth kinetics of Z. rouxii in synthetic medium at 25°C in the presence of high sugar concentrations. The symbols indicate observed values, and the lines are Baranyi fitting curves.

Effects of sugar and pH.

The specific growth rate at 25°C changed as a function of the pH and sugar concentration, but these two factors had different effects. In fact, increasing the sugar concentration from 300 to 800 g liter⁻¹ resulted in a linear reduction in the specific growth rate (Fig. 1), and the growth rate at high concentrations, such as 875 and 950 g liter⁻¹, was very low (the specific growth rate was less than 0.05 h⁻¹ [i.e., the generation time was up to 14 days] in the presence of 875 g liter⁻¹).

We used a mixture of glucose and sucrose because this mixture is widely used as an a_w-reducing agent in foods with intermediate levels of moisture. Adding glucose diminishes the perception of a sweet taste and increases the sucrose solubility (10). There are many foods that contain 40 to 70% sugar, including syrups, molasses, fruit juice concentrates, jams, jellies, and confectionery products like fillings, and they can be contaminated by yeast if they are inadequately processed and stored (7). Using glucose as the only sugar, Praphailong and Fleet (24) concluded that 700 g liter⁻¹ was the maximal sugar concentration in which Z. rouxii proliferated, while this yeast has been reported to grow at low a_w levels, such as 0.65 (14, 28), a value consistent with our results since 950 g liter⁻¹ in our culture medium equalled an a_w value of 0.79. Z. rouxii growth was affected greatly by the sugar concentration, but its activity was not completely inhibited; the preservative effect of sucrose and glucose does not seem to be strong enough to eliminate osmophilic yeast proliferation.

Foods such as bakery products have pH values that range from 3 to 5; therefore, it seemed important to focus on the pH effects at relatively low pH values. Moreover, to extend the predictive microbiology approach initially developed for food-borne pathogenic bacteria to yeasts or molds, the validity of models had to be tested at low pH values. On the other hand, during contamination of food, the pH varies as microbial proliferation occurs; thus, to mimic the microbial behavior in food during processing or storage in this study, the pH was adjusted only initially. The optimum pH range for the cocktail containing the two Z. rouxii stains when citric acid was the preservative agent was 3.5 to 5 (Fig. 3), which is in agreement with the pH range reported previously (25, 28). A pH of 2.5 resulted in a 30% reduction in the growth rate, and no growth occurred at pH 2 at any sugar concentration. This is a minimal value that is higher than the values generally reported. For instance, Restaino et al. (25) found that pH 1.5 was the minimal pH for growth in a culture medium modified by adding HCl. Undissociated organic acids are known to be efficient microbial activity inhibitors, and they are frequently employed as preservative agents in the food industry. Moreover, citric acid is one of the pH-reducing agents commonly used in bakery products or in foods with intermediate levels of moisture.

FIG. 3.

Effect of pH on the specific growth rate (μ) at 25°C for various sugar concentrations. The symbols indicate observed values, and the lines are nonlinear model curves. (a) Ratkowsky-derived model (equation 4). (b) Rosso-derived model (equation 5). Symbols: ⧫, 300 g of sugar liter⁻¹; □, 400 g of sugar liter⁻¹; ▴, 500 g of sugar liter⁻¹; ■, 600 g of sugar liter⁻¹; ▵, 700 g of sugar liter⁻¹; ●, 800 g of sugar liter⁻¹; ×, 875 g of sugar liter⁻¹; ○, 950 g of sugar liter⁻¹.

Evaluation of two nonlinear models.

The data set was used with two models (Fig. 3). The first model was based on the square root model that was initially developed by Ratkowsky (equation 3) and was modified by introducing dimensionless expressions for the sugar and pH factors (equation 4). The second model was the Rosso equation for pH effect (27) combined with a linear expression for the sugar concentration effect (equation 5). These two mathematical expressions were chosen because they gave accurate modelling results in studies of pathogenic bacteria (16, 27, 29) and also because they have recently been applied to food contamination by molds (4). Moreover, both have dimensionless expressions to quantify factor effects and relatively interpretable parameters, which is a convenient way of obtaining the initial values in the numerical process of nonlinear regression resolution. From a statistical point of view, a model has to be without bias, and the residual error is assumed to have a homogeneous variance in the whole experimental design. Both the modified Ratkowsky model (equation 4) and the Rosso model (equation 5) produced satisfactory results (Fig. 4). The graphical conclusion was completed by comparing the statistical criteria listed in Table 1. The residual mean square is very often used as the standard for comparing the fit of models; however, since nonlinear regression was performed with the maximum-likelihood method, this criterion is also discussed below. Again, both models seemed to fit data collected during growth of Z. rouxii in synthetic medium in the presence of various high sugar concentrations and at various pH values. On the other hand, in this study the minimal and maximal pH values and the maximal sugar concentration were considered estimated parameters; therefore, the values obtained with the two models are not similar. Nevertheless, it was possible to compare previously reported values for growth rates under minimal and maximal pH conditions and in the presence of the maximal sugar concentration when growth was observed with values estimated by the two models. The findings were then used as an indicator of the modelling relevance even if the pH was not maintained at a constant value along the kinetic line. The estimated maximal sugar concentrations obtained with the two models were very similar and were consistent with biological observations. In fact, a plot of the specific growth rate versus sugar concentration (Fig. 1) indicated that the maximum sugar concentration was about 1,000 g liter⁻¹, a value included in both 95% confidence intervals (Table 1). In contrast, the maximal pH estimated with the Rosso-derived model (pH 15) did not appear to be realistic, and this model did not seem to be particularly well-adapted to our data. This was probably due to the shape of the specific growth rate-versus-pH curve (Fig. 3). Indeed, the broad range of optimal pH values (pH 3.5 to 5) combined with an experimental design that did not result in data at high pH values prevented the maximal pH from being properly estimated. However, results given by the Ratkowsky-derived model were more consistent with biological observations (the maximal pH was estimated to be 10.4, and the 95% confidence limits were pH 8.5 to 12.4). Finally, the minimal pH estimates given by both models (Table 1) are reasonable since no growth was observed at pH 2 in the presence of any sugar concentration.

FIG. 4.

Histograms of residual values. (a) Ratkowsky-derived model (equation 4). (b) Rosso-derived model (equation 5).

TABLE 1.

Modelling the effect of pH and sugar concentration on the specific growth rate by using two nonlinear equations: estimated values and statistical criteria

Model	Estimated Cst or optimal specific growth rate (h−1)	Estimated minimal pH	Estimated maximal pH	Estimated optimal pH	Estimated maximal sugar concn (g liter−1)	No. of observations	No. of parameters	−2 log (likelihood)/n	Sum of squared residuals	Residual mean squarea
Ratkowsky (equation 4)	1.4 (1.2–1.6)b	1.9 (1.7–2.1)	10.4 (8.5–12.4)		980 (951–1,008)	100	4	−4.19	0.0885	0.00092
Rosso (equation 5)	0.48 (0.46–0.51)	2.3 (2.1–2.5)	15.1 (4.5–25.6)	4.0 (3.7–4.3)	981 (952–1,009)	100	5	−4.24	0.0847	0.00089

^aCalculated as follows: sum of squared residuals/(number of observations − number of parameters). 

^bThe values in parentheses are 95% confidence intervals based on the quantiles of the asymptotic normal distribution. 

In conclusion, the Rosso model developed for bacterial contamination cannot be transferred perfectly to yeast spoilage, perhaps due to yeast behavior at different pH values. The ability of Z. rouxii to grow at low pH values and the optimal pH of less than 6 led to a shape for the pH curve that was very different from the shape of the pH bacterial response curve. However, use of the Ratkowsky-derived model (equation 4), which included dimensionless terms to describe the sugar concentration and pH and contained four estimated parameters (Cst, maximal sugar concentration, minimal pH, and maximal pH) resulted in a satisfactory fit of the curve to the data (the standard deviation was estimated to be 0.03 h⁻¹, and the coefficient of variation was estimated to be 18%). The mathematical expression with multiplicative terms implies that there is no interaction between citric acid-modified pH and high sugar concentration, as illustrated in Fig. 5. For instance, in the presence of 60% sugar yeast proliferation was one-half as great as yeast proliferation in the presence of 30% sugar whatever the pH. Thus, our data contribute to the knowledge concerning pH and sugar effects, as Fleet emphasized that more information concerning the effects of high sugar concentrations on yeast preservative acid tolerance was needed (7).

FIG. 5.

Effects of sugar and pH on the specific growth rate (μ) at 25°C, as determined with the Ratkowsky-derived model (equation 4).

In this study, we demonstrated that Z. rouxii, an osmophilic organism, can adapt to high sugar concentrations and grow instantaneously at the time of contamination. To mimic the yeast proliferation growth rate during bakery product contamination, a predictive model adapted from the Ratkowsky equation gave satisfactory results. Until now, predictive microbiology strategies have been developed mainly for pathogenic bacteria. Recently, Cuppers et al. (4) described food spoilage molds. In a similar way, this study of osmophilic yeast behavior should allow predictive modelling to be extended to other areas of food microbiology.