Introduction

Traditionally, kefir has been prepared by fermenting fresh milk with kefir grains, a symbiotic culture starter containing a spectrum of lactic acid bacteria, yeasts, and acetic acid bacteria in the form of small, yellowish-white, irregularly shaped grains that increase in size during the fermentation process. These grains are able to use lactose; thus, whey rich in lactose can be applied as a culture medium. Considering their potential applications, to the best of our knowledge, no successful attempt has been made to optimize the propagation of kefir grains in whey. This study was based on the belief that by using statistical techniques for optimization, further increases in biomass could be attained. Thus, the main objective of this research was to investigate the individual and the interactive effects of the various concentrations of whey lactose, yeast extract, pH, and temperature on kefir grain biomass increase.

Materials and Methods

Starter Culture and Fermentation Medium

Fresh kefir grains, used as the starter culture in this study, were obtained from a household (Tehran, Iran). The grains were kept in skimmed milk at room temperature (25 ± 1 °C) for short periods, and the medium was exchanged for fresh skimmed milk daily to maintain the grains’ viability. In order to increase the kefir grain biomass, the grains were activated (Tramšek and Goršek 2007). Cheese whey was obtained from Sahar Company (Ghazvin, Iran) and deproteinazed, as described in a previous study (Khodaiyan et al. 2008). The liquid was diluted or concentrated as necessary. Whey lactose was determined by using the HPLC (Shimadzu, Model UV-3100, Kyoto, Japan) according to the method of Jeon et al. (1984).

Fermentation Experiments

To further enhance kefir grain propagation, a number of different sources (yeast extract, peptone, malt extract, ammonium nitrate, ammonium chloride, ammonium sulfate, and urea at a concentration of 1%, w/v; Merck, Darmstadt, Germany) were added to the cheese whey in Erlenmeyer flasks, while other factors were kept constant. After choosing that, the flasks were inoculated with 1.5% (w/v) kefir grain and incubated at specific pH and incubation temperatures (20, 25, or 30 according to the matrix design) without shaking for 120 h. Temperature fluctuations in the culture liquid were reduced by wrapping flasks with aluminum foil. All the experiments were performed in triplicate.

Determination of Wet Weight of Kefir Grains

After incubation, the kefir grains were separated from the fermented culture medium with a household sieve, washed with cold water, dried on the filter paper, and weighed on an electronic balance (AND series HR-200, USA) with a precision of 0.0001 g. The results were expressed as mean ± SD.

Experimental Design and Statistical Analysis

A total of 31 experimental runs with combinations of concentrations of whey lactose, yeast extract, pH, and temperature were conducted by central composite design. Analysis of variance (ANOVA) and graphical representations of the data were calculated and analyzed using the Design Expert statistical software package (trial version 7.1.6, Stat-Ease Inc., Minneapolis, USA).

The results of the experimental design were fitted by a second-order polynomial equation in order to correlate the response to the independent variables:

$$ Y = {C_{{k0}}} + \sum\limits_{{i = 1}}^4 {{C_{{ki}}}{x_i} + \sum\limits_{{i = 1}}^4 {{C_{{kii}}}x_i^2 + \sum\limits_{{i < j = 2}}^4 {{C_{{kij}}}{x_i}{x_j}} } } $$
(1)

where Y stands for the percentage of kefir grain biomass increase; C k0,C ki ,C kii , and C kij represent regression coefficients; and x i and x j are the coded independent factors. The quality of the fit of the polynomial model was expressed by the coefficients of determination R 2 and R 2adj . Adequate precision compares the range of the predicted values at the design points to the average prediction error.

Kefir Grain Composition

The grains’ water content was determined by drying them at 100 °C to constant weight. Polysaccharide content was measured by the phenol–sulfuric acid method (Dubois et al. 1956). Protein content was determined by the Kjeldahl method (AOAC 1990).

Results and Discussion

Screening of Nitrogen Sources

The results of kefir grain biomass as results of using different nitrogen sources were 55.22%, 31.44%, 45.88%, 19.11%, 7.22%, 6%, and 25% for yeast extract, peptone, malt extract, ammonium nitrate, ammonium chloride, ammonium sulfate, and urea, respectively. On the basis of that, yeast extract was chosen as a significant nitrogen source.

Mathematical Modeling

Table 1 shows the design matrix for these factors in the experimental runs. ANOVA analysis (Table 2) was performed to check the adequacy of the suggested models and identify the significant factors. A second-order polynomial model is shown in Eq. 2 in coded form:

$$ \begin{array}{*{20}{c}} {Y = {58}.{9}0 + {3}.{52}{X_{{1}}} + {4}.{43}{X_{{2}}} + {5}.{31}{X_{{3}}} - {7}.{35}{X_{{4}}} - {2}.{56}{X_{{2}}}{X_{{3}}}} \hfill \\ { - { 4}.{27}{X_{{2}}}{X_{{4}}} - {4}.{8}0X_3^2 - {7}.{77}X_4^2} \hfill \\ \end{array} $$
(2)

where Y is the experimental response and X 1, X 2, X 3, and X 4 correspond to the independent variables of whey lactose, yeast extract, pH, and temperature, respectively.

Table 1 Coded levels and actual values of the independent variables in central composite design and experimental results of kefir grain biomass increase
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Table 2 ANOVA analysis and statistical parameters of the model
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ANOVA

The F value of 1.77 for the lack of fit implies that it is not significant relative to the pure experimental error, suggesting that the model correlated well with the experimental values. Statistical parameters of the model are shown in Table 2. R 2, a measure of the goodness of fit of the model was 0.898. The adjusted R 2 value (0.851) also indicated the model’s goodness of fit. For the proposed model, the value of 18.78 for adequate precision indicates an adequate signal, suggesting that this model can be used to navigate the design space. Also, Table 2 shows a value of 1,759.34 for the predicted residual sum of squares, a measure of how a particular model fits each point in the design.

Model Adequacy Testing

Diagnostics

Figure 1 shows the residual and the influence plots for the experiments in this study. Figure 1a shows that the normal plot of residuals for response was normally distributed, as they lie approximately on a straight line and show no deviation of the variance. Figure 1b shows the studentized residuals versus predicted data points. The predicted and actual values also show relatively good agreement, as shown in Fig. 1c. Hence, no obvious patterns were found in the analysis of residuals.

Fig. 1
figure 1

Normal probability graph of internally studentized residuals (a), internally studentized residuals vs. predicted values plot (b), predicted versus actual plot (c), externally studentized residuals vs. run number (d), leverage vs. run number (e), difference of fits (DFFITS) vs. run number (f), difference in beta values (DFBETAS) vs. run number (g), and Cook’s distance vs. run number

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Influence Plots

Figure 1d shows that all the data points lay within the limits. Since all leverage values were less than 1 (Fig. 1e), there are no outliers or unexpected errors in the model. Difference of fits plot (Fig. 1f), a measure of the influence of each point on the predicted value, suggested two points (corresponding to runs 24 and 25) that influence the regression equation and the response very disproportionately. However, difference in beta values plot (Fig. 1g) showed no undue influence of any observation on any of the regression coefficients. Since the Cook’s distance values are in the determined range (shown with red line in Fig. 1h), there is no strong evidence of influential observations in these data.

Model Interpretation

Figure 2a, b contain the response surface and contour plot, showing the effect of pH and yeast extract concentration on the response at the fixed values of temperature and whey lactose concentration in their center values. The percentage grain weight increased when pH and yeast extract were increased to around 5.5 and 19 g/l, respectively, but decreased when they were increased past these levels. From the curves in Fig. 2c, d, which presents the interaction of yeast extract concentration and temperature, it is clear that maximum biomass increase was obtained at high yeast extract concentration and low temperature.

Fig. 2
figure 2

Three-dimensional (3D) response surface and contour plot for pH–yeast extract concentration (a and b; whey lactose = 60 g/l, temperature = 25 °C) and for temperature–yeast extract concentration (whey lactose = 60 g/l, pH = 5.5; c and d)

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Optimization and Model Validation

The analysis of the design indicated that optimal conditions for the highest kefir grain increase (76.13%) were lactose concentration of 88.4 g/l, yeast extract of 21.3 g/l, pH of 5.2, and temperature of 20 °C. The maximum grain produced experimentally was found to be 81.34%, which was clearly very close to the predicted value. Response surface methodology has been broadly discussed in the literature for optimizing different processes (Chopra et al. 2009; Tripathi and Mishra 2009). For example, Bitaraf et al. (2010) used this methodology to study the individual and interactive effects of inulin content, probiotic inoculum level, and incubation temperature on fermentation time and rheological properties of yogurt. Their results showed that the quadratic models are well adjusted to predict the experimental data. Comparison of this study’s optimization results with the literature on the enhancement of kefir grain biomass using other culture media revealed that this study’s results were considerably closer to experimental values than those in other investigations (Schoevers and Britz 2003; Goršek and Tramšek 2007). For example, in a study conducted by Schoevers and Britz (2003) that used kefir grains in different incubation times, the maximum biomass increase in a defined medium was around 52% (after 120 h incubation time), lower than this study’s results.

Kefir Grain Composition

The chemical composition of grains after seven subcultures in whey was 81.5% water, 8.6% polysaccharide, and 7.2% protein. These values did not differ from those obtained from grains grown in milk (Goršek and Tramšek 2007).

Conclusion

The study successfully optimized the enhancement of kefir grain biomass in cheese whey by using central composite design and response surface methodology. This indicates that cheese whey can be considered as a potential culture medium for different applications, such as propagation of kefir grains, a conclusion that has until this point been lacking in the literature.