Mixed culture growth kinetics of Streptococcus thermophilus and Lactobacillus bulgaricus

Mixed culture growth kinetics of Streptococcus thermophilus and

Lactobacillus bulgaricus T. Berkman, T. F. Bozoglu and M. ¢)zilgen

F o o d Engineering Department, Middle East Technical University, Ankara, Turkey

A simple microbiological technique was used to differentially enumerate growth of Streptococcus thermophilus and Lactobacillus bulgaricus in a mixed cuhure. The growth of the microorganisms in the mixed culture was satisfactorily simulated with a set of modified logistic equations. This simple model was valid for various initial biomass concentrations and their ratios. It did not need substrate or product data for simulation of biomass growth, which may simplify the calculations in fermenter design. It was shown that our model may also be regarded as a special case of a common mixed culture model: Volterra's competition analysis.

Keywords:Mixed culture; enumeration; kinetics; modeling

Introduction The growth of single strains of microorganisms has conveniently been simulated with the logistic equation J-3 as: " dt

izX

1

([)

where X is biomass concentration, Xmax is maximum attainable biomass concentration, t is time, and/z is the initial (maximum) specific growth rate. The term ( 1 X/Xmax) introduces the effect of approaching Xm, x. The term/x(1 - X/Xn~x) is the effective specific growth rate of the culture. In most fermentation processes, Xm~ is much larger than the initial biomass concentration X0. Therefore, the numerical value of the term (1 X/Xm,x) approaches 1 at the beginning of the cultivation, and thus the p a r a m e t e r / z represents the initial value of the effective specific growth rate. As X approaches X . . . . the term (1 - X/Xmax) approaches zero, implying that the culture is entering into the stationary

Address reprint requests to Dr. Ozilgen at the Food Engineering Department, Middle East Technical University, 06531 Ankara, Turkey Received 10 November 1988; revised 22 February 1989 138

Enzyme Microb. Technol., 1990, vol. 12, February

growth phase. The other term, /zX, implies that the microorganisms grow in proportion with their concentration when they are free of the effect of o v e r c r o w d ing, i.e. X <
Mixed culture growth kinetics: T. Berkman et al. Table 1

N u m e r i c a l v a l u e s o f t h e parameters used in t h e m o d e l

Fig u re

X2,0

Xl,0

number

(cfu ml

1)

5.5 × 10 2 1.5 × 10 4 1.1 × 10 2 1.0 × 10 6 2.3 × 10 s

la lb lC 2a 2b

X l max (cfu 'ml 1)

(cfu 'm1-1)

4.0 × 10 3 2.5 × 10 3 2.1 × 10 2 7.8 X 10 5 1.9 × 10 5

6.9 × 10 8 1.9 × 10 7 5.6 x 10 7 1.8 × 10 8 9.5 × 10 7

1.4 1.1 1.8 2.7 2.2

contains a pH indicator, bromo cresol purple, and an appropriate combination of sucrose and lactose. S. thermophilus can use both of these sugars and produce substantial amounts of acid. A yellow zone is produced around S. thermophilus colonies due to the color change of the pH indicator. Because L. bulgaricus colonies cannot utilize sucrose, they produce smaller amounts of acid and therefore do not affect the color of the pH indicator. This method cannot be used with all of the S. thermophilus and L. bulgaricus strains. Bautista et al. 6used different selective agars to enumerate L. bulgaricus and S. thermophilus separately in the mixed culture. In that study, tripticase soy agar was found suitable for growth of S. thermophilus. This medium did not support growth ofL. bulgaricus. Acidified lactic agar at pH 5.25 was suitable for growth of L. bulgaricus and was totally inhibitory for growth of S. thermophilus. Lactic agar at pH 6.8 was reported to be the best medium for determining the total number of the mixed culture, 4'7 implying that it was suitable for growth of both of the species. Mixed cultures of Streptococcus thermophilus and Lactobacillus bulgaricus are used in yogurt production. In the mixed culture, L. bulgaricus and S. thermophilus have identical effects on the growth environment. They produce the same inhibitory products, i.e. lactic acid, and consume the same nutrients, i.e. lactose; therefore the logistic equation can be modified to simulate their growth: dx

dt =

13"lXl

dX2 dt

-- IJ'2 X2

l - X l , m T x 7 X22,max'

(

xl q-x2 ) l

--

X2max

1)

(cfu ml

Xl.m--~-x JT- X2"2,max

(2)

(3)

where subscripts 1 and 2 refer to L. bulgaricus and S. thermophilus, respectively. In the present study, the validity of equations (2) and (3) was tested with the experimental data.

Materials and methods The strains of S. thermophilus and L. bulgaricus were purified in our earlier studies. The microorganisms

× × × × x

10 8 10 8 10 8 10 8 10 8

l't',Xlo, \

IX2.0

1:7 1:2 1:0.4 1:0.8 1:0.8

Xl,

....

\X2 .... /

(l/h)

(l/h)

1:2 1:6 1:3 1:1.5 1:2

1.6 1.5 2.4 0.7 1.5

1.5 1.6 2.7 0.8 1.7

were cultivated in 500-ml flasks with no aeration at 37°C. Mild agitation was supplied with a common laboratory magnetic stirrer to obtain homogeneous fermentation broth. Growth media consisted of 2% lactose (Oxoid, England), 2% peptone (Oxoid, England), and 1% yeast extract (Difco, USA). The pH was measured with a pH meter (Corning, Model 10, England). Total microbial counts (L. bulgaricus plus S. thermophilus) were obtained using pour plate technique on Elliker's lactic agar at pH 6.8. Elliker's lactic agar was made by adding 1% agar (Oxoid, England) to Elliker broth (Difco, USA). S. thermophilus did not grow on Elliker's lactic agar when pH was adjusted to 5.25 by the addition of 1 M HCI, 8 therefore, only L. bulgaricus of the mixed culture was enumerated on the acidified agar. The difference between the total number of the colonyforming units and the number ofL . bulgaricus colonies was regarded as the number ofS. thermophilus colonyforming units. All counts were an average of duplicate plates.

Results and discussion Our strains were not good acid producers. Lee's Agar was not suitable for differential counting, since yellow zones around S. thermophilus colonies were not observed. The total number of the colonies and the number of the L. bulgaricus colonies were determined as explained in Materials and methods. The accuracy of this method was confirmed by enumerating the colonies in the mixed cultures with known composition. We did not need to employ another selective agar for enumerating S. thermophilus. This method was simpler than those of Bautista et al. 6 because only pH adjustment, instead of preparation of different agars, was needed. Equations (2) and (3) were solved using Euler integration 9 with the appropriate values of/~l, 1,2, X~,o, X2,o, Xl.max, and X2.m,x (Table 1), where Xi.0 and X2,0 were the initial concentrations of L. bulgaricus and S. thermophilus, respectively. These simulations were compared to the experimental data in Figures 1 and 2. The model was shown to be valid regardless of the initial ratio and the initial concentration of the microorganisms. The specific growth rate of S. thermophilus was mostly higher than that of L. bulgaricus, and the ratio of microorganisms changed mostly in favor of S. thermophilus (Table 1). The only exception to this observation is shown in Figure la. It might be caused by the

Enzyme Microb. Technol., 1990, vol. 12, February

139

Papers It/

9I(b)

(o)

?

•

1

i

o ~ m

4

=

I •

•.

The growth of two competing species in a closed environment might be simulated by Volterra's competition model:

f i 2

i 4

dX] dt - [txl

14~

•

dX2

dt i i 6 8

ilo L 14 12 i

I

n

2

4 6 8 I0 12 T~rne (h)

i

I

i

i

i

i

0

2

4

6

8

i

i

I0 [2 4

1 Comparison of the model with the data. Ratios of the initial population size of L, bulgaricus to that of S. thermophilus were: (a) 1 : 7, (b) 1 : 2, (c) 1 : 04 (see Table I). (©) L. bulgaricus; (1) S. thermophilus; (0) p H , - - - simulation) Figure

-

- °gl (/~lXl q- [~2X2)]X1

[,l/.2 - o~2 ( 5 1 X I -}- j~2X2)]X2

(4)

(5)

where ~], o~2, /31, and /~2 a r e positive constants. The t e r m s oL1 ([~lXl -~- /~2X2) and ~2 (/3iX1 +/~2X2) introduce

the inhibitory effects of overcrowding into the equations. In a special case, when these microorganisms exert similar effects: /3 = /31 = /32

(6)

and the incremental decrease in specific growth rate per unit biomass grown in the culture is constant: 9

o

/x]

(7)

t'2

(8)

O~1/~ = Xl,max -f- X2 . . . . e ~ "e

• •o

boo 31-

o ~'o

• •

O~2j~ = Xl,max if- X2,ma x

f

Equations (4) and (5) reduce to the same form as equation (2) and (3). 3F

I 2

i 4

i

6

i 8

i I0

i

I

t2

0 Time

I

i

2 4

i

6

i

8

i10 112

t

(hi

Figure 2 Comparison of the model with the experimental data. Total initial population size was 1.8 × 106 cfu ml 1 in (a) and 4.2 × 105 cfu ml 1 in (b). Ratio of initial population size of L. bulgaricus to S. thermophilus was 1 : 0.8 in both of the figures ( s e e Table 1). ((7))L. bulgaricus; (1) S. thermophilus; (O) p H , - - simulation)

brief lag phase experienced by S. thermophilus. The numerical values of the specific growth rates were significantly high with extremely small initial biomass concentrations (i.e. Figure lc, see Table 1). The numerical values of these specific growth rates were significantly small with extremely large initial biomass concentrations (i.e. Figure 2a, see Table 1). The major advantage of our model is the small number of differential equations that need simultaneous solution, i.e. equations (2) and (3) only. This facilitates the computations in the fermenter design. A mixed culture growth model which had substrate and product concentration dependence would require simultaneous solution of two more differential equations, i.e. substrate balance equation, product balance equation, and two equations for the microorganisms.

140

Enzyme Microb. Technol., 1990, vol. 12, February

Conclusions The growth of S. thermophilus and L. bulgaricus was satisfactorily enumerated with a simple microbiological technique and simulated with a set of modified logistic equations. The model was valid for various initial biomass concentrations and their ratios and it did not need substrate or product data for simulation of biomass growth.

References I 2 3 4 5 6 7 8 9 10

Weiss, R. M. and Ollis, D. F. Biotech. Bioeng. 1980, 22, 859 Klimek, J. and Ollis, D. F. Biotech. Bioeng. 1980, 22, 2321 Ozilgen, M. Enzyme Mierob. Technol. 1988, 10, 110 Hamann, W. T. and Marth, E. H. Milchwissenschaft 1984, 39, 147 Lee, S. Y., Vedamuthu, E. R., Washam, C. J. and Reinbold, G. W. J. Mill~lood Technol. 1974, 37, 272 Bautista, E. S., Dahiya, R. S. and Speck, M. L. J. Dairy Sci. 1966, 33, 299 Moon, N. J., Hamann, A. C. and Reinbold, G. W. Appl. Microbiol. 1974, 28, 1076 Berkman, T. M. S. Thesis, Middle East Technical University, Turkey, 1988 Burden, R. L., Fairs, D. J. and Reynolds, A. C. Numerical Analysis PWS Publishers USA, 1981 Bailey, J. E. and Ollis, D. F. Biochemical Engineering Fundamentals, Second ed. McGraw-Hill Book Co., USA, 1986