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Modeling combined effects of temperature and pH on the growth of Zygosaccharomyces rouxii in soy sauce mash
JOURNAL OFFERMENTATION ANDBIOENGINEER~G Vol. 85, No. 6, 638-641. 1998
Modeling Combined Effects of Temperature and pH on the Growth of Zygosaccharomyces rouxii in Soy Sauce Mash MAKIO KOBAYASHI*
AND SATOMI
HAYASHI
Research Laboratory of Higashimaru Shoyu Co. Ltd., 100-3 Tominaga, Tatsuno, Hyogo 679-4193, Japan Received 4 December 1997/Accepted 27 February 1998 The growth of Zygosaccharomyces rouxii in soy sauce mash (shoyu moromi) was significantly affected by the pH, temperature, and nitrogen concentration. The effects of pH and temperature on the rate coefficient for growth of Z. rouxii were incorporated in the combined quadratic model form of Davey (Int. J. Food Microbial., 23: 295-303, 1994). The model gave a very high degree of goodness of fit between the predicted and observed values. From the results of regression analyses, it was estimated that pH had a 3-fold greater influence on the growth of Z. rouxii at a nitrogen concentration of 1.5% (w/v) than at 1.0% (w/v). [Key words: environmental factors, moromi, soy sauce (shoyu), temperature-pH effects, Zygosaccharomyces rouxiij Zygosaccharomyces rouxii is valuable for the development of aroma in the fermentation of soy sauce (shoyu) and miso paste (l-3). A starter (seed) culture of Z. rouxii is usually added to the immature moromi mash to promote ethanol fermentation as well as to produce other alcohol and ester compounds at desirable levels (4). During the fermentation period, protein contained in the raw materials is enzymatically digested and solubilized, resulting in an increasing total nitrogen (TN) concentration in the moromi juice. Over a fermentation period of 40d, the pH of the moromi mash gradually decreased from 6.5-7.0 to 5.2-5.5 due to degradation of the materials and lactic acid fermentation. The Z. rouxii is fermented in the lactic acid fermentation. The temperature of the moromi mash, initially about 15”C, gradually increases, and reaches about 25°C after 40 d. On an industrial scale, however, both the pH and temperature of the moromi mash are very variable, so it is difficult to maintain optimal conditions for yeast cultivation in each fermentation tank. Predictive microbiological modeling is becoming a powerful tool for assessment, prediction, and potential control in many food processing industries (5). Models that are able to predict the combined effects of environmental factors (e.g. temperature, pH, aw) on microorganisms are of great interest. A number of approaches have been used, including linear Arrhenius (6, 7), non-linear Arrhenius (8, 9), square root (10, ll), and polynomial forms (12, 13). Among these, the linear Arrhenius model of Davey (7) has been demonstrated to have several advantages: wide application to the growth phase, simplicity, and ease of use. Based on its successful applications, Davey (14) has suggested the following as a generalized model form: lnk=Co+C1~~+CC2~~z+C31/Z+CC4~~z
which factors play a major role in controlling the proliferation of the yeast, this model was used in the present study to examine the combined effects of temperature and pH on the specific growth rate of Z. rouxii in two types of moromi juice media. Zygosaccharomyces rouxii AM-105 was used. The soy sauce medium was that reported by Hamada et al. (15), containing 360 ml of soy sauce and 75 g of glucose per liter (final NaCl concentration, 9% w/v). Chemical analysis of the soy sauce used in the study showed the following contents: TN, 1.5-1.8x w/v; reducing sugar, 3-5% w/v; ethanol, 2-3% w/v; organic acids (80% lactic acid), 2% w/v; NaCl, 18% w/v; trace amounts of minerals; the pH was 4.75-4.95. For the basal culture, Z. rouxii was grown in 100 ml of soy sauce medium in 500ml shaking flasks for 3 d at 30°C as described (15). To examine the growth of Z. rouxii in the moromi mash conditions, two types of moromi juice media, as described by Kanbe and Uchida (16), were used. The two media were prepared as follows: a low-TN medium filtrate from 20-d moromi mash (TN, 1.0% w/v; NaCl, 17% w/v; reducing sugar, 6% w/v), and a high-TN medium filtrate from 40-d moromi mash (TN, 1.5% w/v; NaCl, 17% w/v; reducing sugar, 8% w/v). Factorial design was used to assess the effects of temperature (15, 18, 20, and 23°C) and initial pH (5.2, 5.4, 5.6, and 5.8) in the low TN medium (1.0% w/v), and temperature (23, 25, 27, and 30°C) and initial pH (5.0, 5.2, 5.4, and 5.6) in the high TN medium (1.5% w/v), respectively, on the growth of Z. rouxii. The initial pH was adjusted using 1 M NaOH or 1 M HCl. The number of replicate cultures tested for each variable combination is given in Fig. 1. Basal yeast cultures were inoculated into 100 ml of moromi juice medium in 300-ml flasks at a concentration of lo5 cells/ml. The flasks were then incubated statically for 7 d in triplicate. Cell growth was determined by either counting the cell number with a hemacytometer, or by measuring the optical density (OD) at 660 nm, as described by Tomita (17). The rate coefficient for growth (k) represented as the specific growth rate was calculated from the changes in cell density. Thus, the specific growth rate was calculated from the linear part of a plot of ODe6,, against time on a semilogarithmic scale.
(1)
where k is the rate coefficient for growth, Co to C4 are the coefficients to be estimated, and Vi and V, are environmental factors, respectively-including the reciprocal of the absolute temperature, pH, and a,. To elucidate the effects of certain conditions in the moromi mash on the growth of Z. rouxii as well as to determine * Corresponding author. 638
VOL. 85,
1998
NOTES
d-r),
k=ln
'i 3 al H =
1
0.6
h = 0 r
0.6
i+ 0.4 t% I
I
/
I
15
20
26
30
-I
Temperature (“C) FIG. 1. Specific growth rate of 2. rouxii under moromi mash conditions. TN concentrations: unfilled symbols, TN= 1.0% (w/v); filled symbols, TN= 1.5% (w/v). Symbols (pH): 0, 5.2; 0, 5.4; a, 5.6; 0, 5.8; n , 5.0; 0, 5.2; A, 5.4; +, 5.6.
Modeling for growth For from Eq. 1 is given by (18):
temperature,
the
In k=Co+CI/T+Cz/T2
model
(2)
For combined temperature and pH, the model from Eq. 1 is therefore given by (19): In k=C0+C1/T+C2/TZ+C~pH+C~pH2
(3)
where k is expressed in d I, T is the absolute temperature, and C0 to Cd are the coefficients to be estimated. Equations 2 and 3 show a quadratic dependence of the rate coefficient for growth. The regressions were conveniently and simply carried out on a Personal Computer (Power Macintosh 8500/132) using LINEST (Microsoft Excel, ver. 5.0). The criterion for the “goodness of fit” of the model was the percent variance (%I’) as described by Davey (7, 14, 19). The % V is obtained from: %v=1-{(l-rZ)(n-I)/@-N-l)}
(4)
where r2 is the multiple regression coefficient, n is number of observations in the data set, and N is number of terms in the model. For Eq. 3, the number of terms is N=4 (namely, l/T, l/p, pH, and pHZ). An alternative measure of the goodness of fit, the mean square error (MSE), proposed by Adair et al. (20), Little et al. (21) and Vivier et al. (22), is given by: MSE = 1 {(ohs ~ pred)2/nj
(5)
where n is number of observations in the data set, “obs” is observed value of the growth rate, and “pred” is predicted value. The relationship between k (i.e. specific growth rate, TABLE 1. Equationa In k=Coi
and the generation
C,/T+CZ/F
Ink=Co+CI/T+Cz/T-+C3pH+C4pH2
time (g, d) is:
2/g
(6)
Figure 1 shows the specific Growth of Z. rouxii growth rate of Z. rouxii under the moromi mash conditions using the two types of moromi juice media. The growth of Z. rouxii was dependent on temperature, and markedly affected by pH in the high TN (1.5% w/v) medium, but not in the low TN (1.0% w/v) one. The values of the model coefficients (C, to C.,) obtained from regression analyses of the graphical data of Fig. 1 for 2. rouxii are presented in Table 1. The coefficients of the model were all significant. From Eq. 2, in the 1.0% (w/v) TN medium, the rate coefficients are obtained by substituting the coefficients from Table 1. Thus, the rate model for growth under a low TN is: Ink=
~ 1431.517+8.4637 - 12.5102 x 107/Tz
x 105/T (7)
where k is expressed in d I. Substitution of T=290 K gives k=0.584d-‘. From Eq. 6, this corresponds to a generation time of g=1.187 d. Since Eq. 7 showed a good fit (i.e. a very high % V and very low MSE), it was evident that temperature is the sole influencing factor in the low TN medium (1.0% w/v). In contrast, in the 1.5% (w/v) TN medium, Eq. 2 was not applicable for predicting the growth of 2. rouxii. Therefore, we assessed the combined temperaturepH as the influencing factors using Eq. 3. From Eq. 3, in the 1.5% (w/v) TN medium, the rate coefficients are obtained by substituting the coefficients from Table 1. Thus, the rate model for growth under a high TN is: Ink= - 1743.256+ 10.3111 x 1O5/T - 15.4925 x 107/72+ 10.78 pH- 1.05 pHZ
(8)
where k is expressed in d I. Substitution of T=300 K and pH=5.5 gives k=0.919dp1. From Eq. 6, this corresponds to a generation time of g=O.754 d. A comparison of the model predictions of the rate coefficient for growth against the observed values at each temperature and pH is shown in Fig. 2. From the magnitudes of the values of the % V (and very low MSEs) in Table 1 and the comparison in Fig. 2, it is evident that the model provides a high degree of accuracy of prediction against the observed data. Although, in common with various other microbiological models, the model presented here has no theoretical foundation (19), the quadratic term would act as a “modulator” on the simpler Arrhenius model. Furthermore, the first derivative of the quadratic form of the model indicates a maximum rate of growth at values of Tmax= --2C2/C, and pH,, = - C3/2C, (19). The predicted values for temperature and pH are T,, ~295.6 (K) in the low-TN condition using Eq. 7, and T,,,,=300.5 (K) and pH,,,=5.13 in the
Fit of the model for the rate coefficient
TN
CO
c, x 10-5
Cl x IO-7
l.Ob
-1431.517 - 1715.645 - 1422.204 - 1743.256
8.4437 10.3111 8.4637 10.3111
-12.5102 -15.4925 - 12.5102 - 15.4925
1.Y l.Ob 1.5’
639
a Tin degrees absolute; k in d -I. b Prepared from 20-d moromi mash. Range: T (“C), 15-23; pH, 5.2-5.8; n= 16. c Prepared from 40-d moromi mash. Range: T (“C), 23-30; pH, 5.0-5.6; n= 16.
c3
-3.54 10.78
G
0.335 - 1.050
r?
o6 V
(MSE)
0.97 0.62 0.98 0.84
96.7 55.9 97.2 78.6
(0.002) (0.011) (0.001) (0.004)
640
KOBAYASHI AND HAYASHI
J.
FERMENT. BIOENG.,
: multiple regression coefficient, : number of observations in the data set, :: : number of terms in the model, MSE : mean square error, obs : observed value of the growth rate, d--i pred : predicted value of the growth rate, d-l : generation time, d g r2
We are grateful to Dr. Kohei Ushio and Dr. Yasunobu Tsuji (Research Laboratory of Higashimaru Shoyu Co. Ltd.) for their critical reading of the manuscript and helpful discussion. REFERENCES
Oa20,
.2
Predicted growth rate (d-1) FIG. 2. Comparison of observed and predicted growth rates of Z. rouxii in moromi mash. Equation 1 was used for TN = 1.O% (w/v) and Eq. 8 for TN=l.S% (w/v). TN concentrations: unfilled symbols, TN= 1.0% (w/v); filled symbols, TN= 1.5% (w/v).
high-TN condition using Eq. 8, respectively. Comparing the coefficients of Eq. 3 between the 1.0 and 1.5% (w/v) TN media in Table 1, the ratios of temperature (C, and C,) are 1.5%/1.0% TN (w/v)= 1, while the ratios of pH (C, and C4) are 1.5%/1.0x TN (w/v)=3. Therefore, it seems likely that in the moromi mash, pH had a 3-fold greater influence on the growth of 2. rouxii at a nitrogen concentration of 1.5% (w/v) than at 1.0% (w/v). In continuous culture of Z. rouxii, Hamada et al. (15) also reported the same effects of carbon and nitrogen concentrations on cell growth. Lactic acid produced by the salt-tolerant bacterium Tetragenococcus halophilus has a marked influence on pH in the moromi mash (2). Since T. halophilus is in antagonism to Z. rouxii in the mash, it is difficult to control the growth of the two microorganisms under the optimum conditions for each on an industrial scale, such as in a lOO-kl tank fermentor. The mathematical model proposed here was able to estimate the growth of Z. rouxii from two environmental factors, temperature and pH, under the moromi mash conditions. To investigate further the antagonism between T. halophilus and Z. rouxii in the moromi mash, we are now applying this mathematical model to assess the combined effects of environmental factors on the growth of each microorganism. Furthermore, predictive microbiological modeling will be widely applicable to the assessment, prediction, and potential control by environmental factors in many food industry processes, such as the production of soy sauce. NOMENCLATURE
k 2 c2 c3
c, VI v2
T V
: rate coefficient for growth (i.e. specific rate), d-l * coefficient in Eqs. 1, 2, and 3, *: coefficient in Eqs. 1, 2, and 3, : coefficient in Eqs. 1, 2, and 3, : coefficient in Eqs. 1 and 3, : coefficient in Eqs. 1 and 3, : environmental factor in Eq. 1, : environmental factor in Eq. 1, : absolute temperature, K : percent variance, %
growth
1. Onishi, H.: Osmophilic yeasts. Adv. Food Res., 12, 53-94 (1963). 2. Yokotsuka, T.: Some recent technological problems related to the quality of Japanese shoyu, p. 659-662. In Terui, G. (ed.), Fermentation technology today. Society of Fermentation Technology, Osaka (1972). 3. Sasaki, M.: Influence of sodium chloride on the levels of flavor compounds produced by shoyu yeast. J. Agric. Food Chem., 44, 32’73-3215 (1996). 4. Noda, Y., Iooue, H., Kusuda, H., Ohba, K., and Nakano, M.: Studies on the control of the fermentation of the soy sauce-mash. V. The additional effect of yeast and lactic acid bacterium in the industrial scale of soy sauce brewing. J. Jpn. Soy Sauce Res. Inst., 8, 108-l 16 (1982). (in Japanese) 5. Gould, G. W.: Predictive mathematical modelling of microbial growth and survival in foods. Food Sci. Technol. Today, 3, 89-92 (1989). 6. Davey, K. R., Lin, S. H., and Wood, D. G.: The effect of pH on continuous high-temperature/short time sterilization of liquid. Am. Inst. Chem. Eng. J., 24, 537-540 (1978). 7. Davey, K. R.: A predictive model for combined temperature and water activity on microbial growth during the growth phase. J. Appl. Bacterial., 67, 483-488 (1989). 8. Brounball. J. M.. Aoslow. P. A.. and Kilsbv. D. C.: Hazard analysis applied to microbial growth in foods:‘development of mathematical equations describing the effect of water activity. J. Appl. Bacterial., 55, 101-110 (1983). 9. Broughall, J. M. and Brown, C.: Hazard analysis applied to microbial growth in foods: development and application of three-dimensional models to predict bacterial growth. Food Microbial., 1, 13-22 (1984). 10. Ratkowsky, D.A., Lowry, R. K., McMeekin, T. A., Stokes, A. N., and Chandler, R. E.: Model for bacterial growth rate throughout the entire bio-kinetic temperature range. J. Bacteriol., 154, 1222-1226 (1983). Il. McMeekio, T. A., Chandler, R. E., Doe, P. E., Garland, C. D., Olley, J., Putro, S., and Ratkowsky, D. A.: Model for combined effect of temperature and salt concentration/water activity on the growth rate of Staphylococcus xylosus. J. Appl. Bacterial., 62, 543-550 (1987). 12. Roberts, T. A. and Gibson, A.M.: Chemical methods for controlling Clostridium botulinurn in processed meats. Food TechnoLbO, 163-171 (1986). 13. Thaver. D. W.. Muller. W. S.. Buchanan. R. L.. and Phillins. J. G-z Effect of NaCl,’ pH, temperature,’ and atmosphere bn growth of Salmonella typhimurium in glucose-mineral salts medium. Appl. Environ. Microbial., 53, 1311-1315 (1987). 14. Davey, K.R.: Linear Arrhenius models for bacterial growth and death and vitamin denaturations. J. Ind. Microbial., 12, 172-179 (1993). 15. Hamada, T., Fukushima, Y., Hashiba, H., and Motai, H.: Improved production of viable cells of the salt-tolerant yeast Zygosaccharomyces rouxii by continuous culture. APP~. Microbial. Biotechnol., 36, 388-393 (1991). 16. Kanbe, C. and Uchida, K.: Reducing activity of soy pediococci (Pediococcus halophilus) and oxidation-reduction potentials of soy sauce mash. Nippon Nogeikagaku Kaishi, 68, 487-490 (1984). (in Japanese)
VOL. 85, 1998 17. Tomita, M.: Characterization of an osmo-tolerant yeast for tniso making. J. Ferment. Technol., 54, 287-291 (1976). (in Japanese) 18. Davey, K. R.: Application of the Davey (linear Arrhenius) predictive model to the lag phase of microbial growth. J. Appl. Bacterial., 70, 253-257 (1991). _ 19. Davey, K. R.: Modelling the combined effect of temperature and pH on the rate coefficient for bacterial growth. Int. J. Food Microbial., 23, 295-303 (1994). 20. Adair, C., Kilsby, D. C., and Whittall, P. T.: Comparison of the Schoolfield (non-linear Arrhenius) model and the square
root model for predictive bacterial Microbial., 6, 7-17 (1989).
growth
NOTES
641
in foods.
Food
21 Little,
C. L., Adams, M. R., Anderson, W. A., and Cole, M. B.: Comparison of a quadratic response surface model and a square root model for predicting the growth rate of Yersinia
enterocoliticu. Lett. Appl. Microbial., 15. 63-68 (1992). _ 22. Vivier, D., Ratomahenina, R., Moulin, G., and Glazy, P.: Study of physiochemical factors limiting the growth of Kluyveromyces marxiunus. J. Ind. Microbial., 11, 157-161 (1993).
Modeling Combined Effects of Temperature and pH on the Growth of Zygosaccharomyces rouxii in Soy Sauce Mash MAKIO KOBAYASHI*
AND SATOMI
HAYASHI
Research Laboratory of Higashimaru Shoyu Co. Ltd., 100-3 Tominaga, Tatsuno, Hyogo 679-4193, Japan Received 4 December 1997/Accepted 27 February 1998 The growth of Zygosaccharomyces rouxii in soy sauce mash (shoyu moromi) was significantly affected by the pH, temperature, and nitrogen concentration. The effects of pH and temperature on the rate coefficient for growth of Z. rouxii were incorporated in the combined quadratic model form of Davey (Int. J. Food Microbial., 23: 295-303, 1994). The model gave a very high degree of goodness of fit between the predicted and observed values. From the results of regression analyses, it was estimated that pH had a 3-fold greater influence on the growth of Z. rouxii at a nitrogen concentration of 1.5% (w/v) than at 1.0% (w/v). [Key words: environmental factors, moromi, soy sauce (shoyu), temperature-pH effects, Zygosaccharomyces rouxiij Zygosaccharomyces rouxii is valuable for the development of aroma in the fermentation of soy sauce (shoyu) and miso paste (l-3). A starter (seed) culture of Z. rouxii is usually added to the immature moromi mash to promote ethanol fermentation as well as to produce other alcohol and ester compounds at desirable levels (4). During the fermentation period, protein contained in the raw materials is enzymatically digested and solubilized, resulting in an increasing total nitrogen (TN) concentration in the moromi juice. Over a fermentation period of 40d, the pH of the moromi mash gradually decreased from 6.5-7.0 to 5.2-5.5 due to degradation of the materials and lactic acid fermentation. The Z. rouxii is fermented in the lactic acid fermentation. The temperature of the moromi mash, initially about 15”C, gradually increases, and reaches about 25°C after 40 d. On an industrial scale, however, both the pH and temperature of the moromi mash are very variable, so it is difficult to maintain optimal conditions for yeast cultivation in each fermentation tank. Predictive microbiological modeling is becoming a powerful tool for assessment, prediction, and potential control in many food processing industries (5). Models that are able to predict the combined effects of environmental factors (e.g. temperature, pH, aw) on microorganisms are of great interest. A number of approaches have been used, including linear Arrhenius (6, 7), non-linear Arrhenius (8, 9), square root (10, ll), and polynomial forms (12, 13). Among these, the linear Arrhenius model of Davey (7) has been demonstrated to have several advantages: wide application to the growth phase, simplicity, and ease of use. Based on its successful applications, Davey (14) has suggested the following as a generalized model form: lnk=Co+C1~~+CC2~~z+C31/Z+CC4~~z
which factors play a major role in controlling the proliferation of the yeast, this model was used in the present study to examine the combined effects of temperature and pH on the specific growth rate of Z. rouxii in two types of moromi juice media. Zygosaccharomyces rouxii AM-105 was used. The soy sauce medium was that reported by Hamada et al. (15), containing 360 ml of soy sauce and 75 g of glucose per liter (final NaCl concentration, 9% w/v). Chemical analysis of the soy sauce used in the study showed the following contents: TN, 1.5-1.8x w/v; reducing sugar, 3-5% w/v; ethanol, 2-3% w/v; organic acids (80% lactic acid), 2% w/v; NaCl, 18% w/v; trace amounts of minerals; the pH was 4.75-4.95. For the basal culture, Z. rouxii was grown in 100 ml of soy sauce medium in 500ml shaking flasks for 3 d at 30°C as described (15). To examine the growth of Z. rouxii in the moromi mash conditions, two types of moromi juice media, as described by Kanbe and Uchida (16), were used. The two media were prepared as follows: a low-TN medium filtrate from 20-d moromi mash (TN, 1.0% w/v; NaCl, 17% w/v; reducing sugar, 6% w/v), and a high-TN medium filtrate from 40-d moromi mash (TN, 1.5% w/v; NaCl, 17% w/v; reducing sugar, 8% w/v). Factorial design was used to assess the effects of temperature (15, 18, 20, and 23°C) and initial pH (5.2, 5.4, 5.6, and 5.8) in the low TN medium (1.0% w/v), and temperature (23, 25, 27, and 30°C) and initial pH (5.0, 5.2, 5.4, and 5.6) in the high TN medium (1.5% w/v), respectively, on the growth of Z. rouxii. The initial pH was adjusted using 1 M NaOH or 1 M HCl. The number of replicate cultures tested for each variable combination is given in Fig. 1. Basal yeast cultures were inoculated into 100 ml of moromi juice medium in 300-ml flasks at a concentration of lo5 cells/ml. The flasks were then incubated statically for 7 d in triplicate. Cell growth was determined by either counting the cell number with a hemacytometer, or by measuring the optical density (OD) at 660 nm, as described by Tomita (17). The rate coefficient for growth (k) represented as the specific growth rate was calculated from the changes in cell density. Thus, the specific growth rate was calculated from the linear part of a plot of ODe6,, against time on a semilogarithmic scale.
(1)
where k is the rate coefficient for growth, Co to C4 are the coefficients to be estimated, and Vi and V, are environmental factors, respectively-including the reciprocal of the absolute temperature, pH, and a,. To elucidate the effects of certain conditions in the moromi mash on the growth of Z. rouxii as well as to determine * Corresponding author. 638
VOL. 85,
1998
NOTES
d-r),
k=ln
'i 3 al H =
1
0.6
h = 0 r
0.6
i+ 0.4 t% I
I
/
I
15
20
26
30
-I
Temperature (“C) FIG. 1. Specific growth rate of 2. rouxii under moromi mash conditions. TN concentrations: unfilled symbols, TN= 1.0% (w/v); filled symbols, TN= 1.5% (w/v). Symbols (pH): 0, 5.2; 0, 5.4; a, 5.6; 0, 5.8; n , 5.0; 0, 5.2; A, 5.4; +, 5.6.
Modeling for growth For from Eq. 1 is given by (18):
temperature,
the
In k=Co+CI/T+Cz/T2
model
(2)
For combined temperature and pH, the model from Eq. 1 is therefore given by (19): In k=C0+C1/T+C2/TZ+C~pH+C~pH2
(3)
where k is expressed in d I, T is the absolute temperature, and C0 to Cd are the coefficients to be estimated. Equations 2 and 3 show a quadratic dependence of the rate coefficient for growth. The regressions were conveniently and simply carried out on a Personal Computer (Power Macintosh 8500/132) using LINEST (Microsoft Excel, ver. 5.0). The criterion for the “goodness of fit” of the model was the percent variance (%I’) as described by Davey (7, 14, 19). The % V is obtained from: %v=1-{(l-rZ)(n-I)/@-N-l)}
(4)
where r2 is the multiple regression coefficient, n is number of observations in the data set, and N is number of terms in the model. For Eq. 3, the number of terms is N=4 (namely, l/T, l/p, pH, and pHZ). An alternative measure of the goodness of fit, the mean square error (MSE), proposed by Adair et al. (20), Little et al. (21) and Vivier et al. (22), is given by: MSE = 1 {(ohs ~ pred)2/nj
(5)
where n is number of observations in the data set, “obs” is observed value of the growth rate, and “pred” is predicted value. The relationship between k (i.e. specific growth rate, TABLE 1. Equationa In k=Coi
and the generation
C,/T+CZ/F
Ink=Co+CI/T+Cz/T-+C3pH+C4pH2
time (g, d) is:
2/g
(6)
Figure 1 shows the specific Growth of Z. rouxii growth rate of Z. rouxii under the moromi mash conditions using the two types of moromi juice media. The growth of Z. rouxii was dependent on temperature, and markedly affected by pH in the high TN (1.5% w/v) medium, but not in the low TN (1.0% w/v) one. The values of the model coefficients (C, to C.,) obtained from regression analyses of the graphical data of Fig. 1 for 2. rouxii are presented in Table 1. The coefficients of the model were all significant. From Eq. 2, in the 1.0% (w/v) TN medium, the rate coefficients are obtained by substituting the coefficients from Table 1. Thus, the rate model for growth under a low TN is: Ink=
~ 1431.517+8.4637 - 12.5102 x 107/Tz
x 105/T (7)
where k is expressed in d I. Substitution of T=290 K gives k=0.584d-‘. From Eq. 6, this corresponds to a generation time of g=1.187 d. Since Eq. 7 showed a good fit (i.e. a very high % V and very low MSE), it was evident that temperature is the sole influencing factor in the low TN medium (1.0% w/v). In contrast, in the 1.5% (w/v) TN medium, Eq. 2 was not applicable for predicting the growth of 2. rouxii. Therefore, we assessed the combined temperaturepH as the influencing factors using Eq. 3. From Eq. 3, in the 1.5% (w/v) TN medium, the rate coefficients are obtained by substituting the coefficients from Table 1. Thus, the rate model for growth under a high TN is: Ink= - 1743.256+ 10.3111 x 1O5/T - 15.4925 x 107/72+ 10.78 pH- 1.05 pHZ
(8)
where k is expressed in d I. Substitution of T=300 K and pH=5.5 gives k=0.919dp1. From Eq. 6, this corresponds to a generation time of g=O.754 d. A comparison of the model predictions of the rate coefficient for growth against the observed values at each temperature and pH is shown in Fig. 2. From the magnitudes of the values of the % V (and very low MSEs) in Table 1 and the comparison in Fig. 2, it is evident that the model provides a high degree of accuracy of prediction against the observed data. Although, in common with various other microbiological models, the model presented here has no theoretical foundation (19), the quadratic term would act as a “modulator” on the simpler Arrhenius model. Furthermore, the first derivative of the quadratic form of the model indicates a maximum rate of growth at values of Tmax= --2C2/C, and pH,, = - C3/2C, (19). The predicted values for temperature and pH are T,, ~295.6 (K) in the low-TN condition using Eq. 7, and T,,,,=300.5 (K) and pH,,,=5.13 in the
Fit of the model for the rate coefficient
TN
CO
c, x 10-5
Cl x IO-7
l.Ob
-1431.517 - 1715.645 - 1422.204 - 1743.256
8.4437 10.3111 8.4637 10.3111
-12.5102 -15.4925 - 12.5102 - 15.4925
1.Y l.Ob 1.5’
639
a Tin degrees absolute; k in d -I. b Prepared from 20-d moromi mash. Range: T (“C), 15-23; pH, 5.2-5.8; n= 16. c Prepared from 40-d moromi mash. Range: T (“C), 23-30; pH, 5.0-5.6; n= 16.
c3
-3.54 10.78
G
0.335 - 1.050
r?
o6 V
(MSE)
0.97 0.62 0.98 0.84
96.7 55.9 97.2 78.6
(0.002) (0.011) (0.001) (0.004)
640
KOBAYASHI AND HAYASHI
J.
FERMENT. BIOENG.,
: multiple regression coefficient, : number of observations in the data set, :: : number of terms in the model, MSE : mean square error, obs : observed value of the growth rate, d--i pred : predicted value of the growth rate, d-l : generation time, d g r2
We are grateful to Dr. Kohei Ushio and Dr. Yasunobu Tsuji (Research Laboratory of Higashimaru Shoyu Co. Ltd.) for their critical reading of the manuscript and helpful discussion. REFERENCES
Oa20,
.2
Predicted growth rate (d-1) FIG. 2. Comparison of observed and predicted growth rates of Z. rouxii in moromi mash. Equation 1 was used for TN = 1.O% (w/v) and Eq. 8 for TN=l.S% (w/v). TN concentrations: unfilled symbols, TN= 1.0% (w/v); filled symbols, TN= 1.5% (w/v).
high-TN condition using Eq. 8, respectively. Comparing the coefficients of Eq. 3 between the 1.0 and 1.5% (w/v) TN media in Table 1, the ratios of temperature (C, and C,) are 1.5%/1.0% TN (w/v)= 1, while the ratios of pH (C, and C4) are 1.5%/1.0x TN (w/v)=3. Therefore, it seems likely that in the moromi mash, pH had a 3-fold greater influence on the growth of 2. rouxii at a nitrogen concentration of 1.5% (w/v) than at 1.0% (w/v). In continuous culture of Z. rouxii, Hamada et al. (15) also reported the same effects of carbon and nitrogen concentrations on cell growth. Lactic acid produced by the salt-tolerant bacterium Tetragenococcus halophilus has a marked influence on pH in the moromi mash (2). Since T. halophilus is in antagonism to Z. rouxii in the mash, it is difficult to control the growth of the two microorganisms under the optimum conditions for each on an industrial scale, such as in a lOO-kl tank fermentor. The mathematical model proposed here was able to estimate the growth of Z. rouxii from two environmental factors, temperature and pH, under the moromi mash conditions. To investigate further the antagonism between T. halophilus and Z. rouxii in the moromi mash, we are now applying this mathematical model to assess the combined effects of environmental factors on the growth of each microorganism. Furthermore, predictive microbiological modeling will be widely applicable to the assessment, prediction, and potential control by environmental factors in many food industry processes, such as the production of soy sauce. NOMENCLATURE
k 2 c2 c3
c, VI v2
T V
: rate coefficient for growth (i.e. specific rate), d-l * coefficient in Eqs. 1, 2, and 3, *: coefficient in Eqs. 1, 2, and 3, : coefficient in Eqs. 1, 2, and 3, : coefficient in Eqs. 1 and 3, : coefficient in Eqs. 1 and 3, : environmental factor in Eq. 1, : environmental factor in Eq. 1, : absolute temperature, K : percent variance, %
growth
1. Onishi, H.: Osmophilic yeasts. Adv. Food Res., 12, 53-94 (1963). 2. Yokotsuka, T.: Some recent technological problems related to the quality of Japanese shoyu, p. 659-662. In Terui, G. (ed.), Fermentation technology today. Society of Fermentation Technology, Osaka (1972). 3. Sasaki, M.: Influence of sodium chloride on the levels of flavor compounds produced by shoyu yeast. J. Agric. Food Chem., 44, 32’73-3215 (1996). 4. Noda, Y., Iooue, H., Kusuda, H., Ohba, K., and Nakano, M.: Studies on the control of the fermentation of the soy sauce-mash. V. The additional effect of yeast and lactic acid bacterium in the industrial scale of soy sauce brewing. J. Jpn. Soy Sauce Res. Inst., 8, 108-l 16 (1982). (in Japanese) 5. Gould, G. W.: Predictive mathematical modelling of microbial growth and survival in foods. Food Sci. Technol. Today, 3, 89-92 (1989). 6. Davey, K. R., Lin, S. H., and Wood, D. G.: The effect of pH on continuous high-temperature/short time sterilization of liquid. Am. Inst. Chem. Eng. J., 24, 537-540 (1978). 7. Davey, K. R.: A predictive model for combined temperature and water activity on microbial growth during the growth phase. J. Appl. Bacterial., 67, 483-488 (1989). 8. Brounball. J. M.. Aoslow. P. A.. and Kilsbv. D. C.: Hazard analysis applied to microbial growth in foods:‘development of mathematical equations describing the effect of water activity. J. Appl. Bacterial., 55, 101-110 (1983). 9. Broughall, J. M. and Brown, C.: Hazard analysis applied to microbial growth in foods: development and application of three-dimensional models to predict bacterial growth. Food Microbial., 1, 13-22 (1984). 10. Ratkowsky, D.A., Lowry, R. K., McMeekin, T. A., Stokes, A. N., and Chandler, R. E.: Model for bacterial growth rate throughout the entire bio-kinetic temperature range. J. Bacteriol., 154, 1222-1226 (1983). Il. McMeekio, T. A., Chandler, R. E., Doe, P. E., Garland, C. D., Olley, J., Putro, S., and Ratkowsky, D. A.: Model for combined effect of temperature and salt concentration/water activity on the growth rate of Staphylococcus xylosus. J. Appl. Bacterial., 62, 543-550 (1987). 12. Roberts, T. A. and Gibson, A.M.: Chemical methods for controlling Clostridium botulinurn in processed meats. Food TechnoLbO, 163-171 (1986). 13. Thaver. D. W.. Muller. W. S.. Buchanan. R. L.. and Phillins. J. G-z Effect of NaCl,’ pH, temperature,’ and atmosphere bn growth of Salmonella typhimurium in glucose-mineral salts medium. Appl. Environ. Microbial., 53, 1311-1315 (1987). 14. Davey, K.R.: Linear Arrhenius models for bacterial growth and death and vitamin denaturations. J. Ind. Microbial., 12, 172-179 (1993). 15. Hamada, T., Fukushima, Y., Hashiba, H., and Motai, H.: Improved production of viable cells of the salt-tolerant yeast Zygosaccharomyces rouxii by continuous culture. APP~. Microbial. Biotechnol., 36, 388-393 (1991). 16. Kanbe, C. and Uchida, K.: Reducing activity of soy pediococci (Pediococcus halophilus) and oxidation-reduction potentials of soy sauce mash. Nippon Nogeikagaku Kaishi, 68, 487-490 (1984). (in Japanese)
VOL. 85, 1998 17. Tomita, M.: Characterization of an osmo-tolerant yeast for tniso making. J. Ferment. Technol., 54, 287-291 (1976). (in Japanese) 18. Davey, K. R.: Application of the Davey (linear Arrhenius) predictive model to the lag phase of microbial growth. J. Appl. Bacterial., 70, 253-257 (1991). _ 19. Davey, K. R.: Modelling the combined effect of temperature and pH on the rate coefficient for bacterial growth. Int. J. Food Microbial., 23, 295-303 (1994). 20. Adair, C., Kilsby, D. C., and Whittall, P. T.: Comparison of the Schoolfield (non-linear Arrhenius) model and the square
root model for predictive bacterial Microbial., 6, 7-17 (1989).
growth
NOTES
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in foods.
Food
21 Little,
C. L., Adams, M. R., Anderson, W. A., and Cole, M. B.: Comparison of a quadratic response surface model and a square root model for predicting the growth rate of Yersinia
enterocoliticu. Lett. Appl. Microbial., 15. 63-68 (1992). _ 22. Vivier, D., Ratomahenina, R., Moulin, G., and Glazy, P.: Study of physiochemical factors limiting the growth of Kluyveromyces marxiunus. J. Ind. Microbial., 11, 157-161 (1993).