BIOTECHNOLOGY AND BIOENGINEERING, VOL. XIX, PAGES 365-375 (1977)
Characteristics of Yeast Invertase Immobilized on Porous Cellulose Beads PAUL A. DICKENSHEETS, LI FU CHEN, and GEORGE T. TSAO, School of Chemical Engineering, Purdue University, West Laf ay ette, Indiana 47907
Summary Invertase from Candida utilis was immobilized on porous cellulose beads by an ionic-quanidino bond. The immobilized invertase showed optimum activity between pH 4.0 and 5.4, while the free enzyme had a sharp optimum a t pH 4.1. Both temperature profiles were fairly similar up to 55°C. However, above this temperature the immobilized enzyme was more stable than the free enzyme. From the temperature data, the activation energies were found to be 7,322 and 4,052 cal/g mol for the free and the immobilized enzyme, respectively. Candida invertase shows characteristics of substrate inhibition. Both the K , and Ki for the free and the immobilized enzymes were determined. The apparent Ki for the immobilized invertase was much higher than the Ki of the free enzyme, suggesting a diffusion effect. Immobilized invertase molecules deep in the pores only see sucrose concentrations much less than the bulk concentrations. Immobilization, thus, offers certain processing advantages in this regard.
INTRODUCTION Sucrose inversion adds total weight and sweetness to the sugar product. Current industrial practice makes use of strong cationic resins for sucrose inversion in a continuous column process. Enzymatic inversion has the advantage over the acid process in that less amounts of undesirable oligosaccharides are formed when a n enzyme is used as the catalyst. On the other hand, most invertase preparations suffer from substrate (sucrose) inhibition. Immobilization of invertase on porous supports may minimize the inhibitory effect of sucrose because the enzyme molecules are protected by a diffusion barrier, i.e., the apparent bulk sucrose concentration is generally higher than the substrate concentration in the microenvironment of the immobilized enzyme molecules. Furthermore, immobilized enzyme will make it easy to conduct a continuous column process 365 @ 1977 by John Wiley & Sons, Inc.
366
DICKENSHEETS, CHEN, AND TSAO
for the reaction, while sucrose inversion is usually done batchwise when soluble invertase is used. This paper reports the immobilization of invertase from Candida utilis on porous cellulose beads. Characteristics of the immobilized invertase are t o be described.
MATERIALS AND METHODS Porous cellulose beads were prepared by our own technique. Physical properties and preparation procedures of the porous cellulose beads were reported recently by Chen and Tsa0.l For all the experiments, beads of 35 mesh were used, except where noted, Invertase, Grade X, of Sigma Chemical derived from C. utilis was used throughout this work. According t o Sigma Chemical, the preparation has 575 invertase units per mg of solid. Each enzyme unit will hydrolyze 1 Fmol of sucrose per min at p H 5.4 and 55°C. Chemicals used in this study are all of reagent grade from either Mallinckrodt or Fisher. “Domino” granulated pure cane sugar from Amstar Corporation was used as the substrate. Buffer solutions made of varying mixtures of citric acid (O.lM), and dibasic sodium phosphate (0.2M) solutions were used for the inversion experiments for their applicability over a broad p H range (PH 2.2-8.0). The immobilization procedure is outlined in Figure 1. Porous cellulose beads were first treated with hexamethyl diisocyanate. The complex was then hydrolyzed, after which a quanidino group was added by reacting with o-methylisourea. After the addition of o-methylisourea, the beads were left at 4°C for four days. They were then rinsed with acetate buffer a t pH 5 and stored wet a t room temperature until use. By adding 4 g of the wet beads with 50 mg of Grade X invertase dissolved in 5 ml of water, enzyme immobilization was accomplished after standing at 4°C overnight. An invert sugar assay was done by the well-known dinitrosalicylic acid (DNS) method first described by Sumner.2 The 3,4-dinitrosalicylic acid was reduced by glucose and fructose formed by sucrose inversion t o 3-amino-5-nitrosalicylic acid. The amount of reduced dinitrosalicylic acid was then read in a spectrophotometer (PerkinElmer Model 124). A Water Associates liquid chromatograph was also employed to examine the amounts of glucose, fructose, and oligosaccharides in reaction mixtures. The reactor for the immobilized invertase was a jacketed ECONO Column (catalog No. 737-1231) of Bio-Rad Laboratories 1 cm i.d.
IMMOBILIZED YEAST INVERTASE cellulose bead
cellulose
- OH
+ 0=C
1 1
-(CH2I6
= N
-N
= C =
367
0 hexamethylene
diisocyanate
0
It
- 0 - C -
N-(CH)
2 6
- N = C = = O
H2°
0
II
cellulose
- 0 - C--N
I
I
)
CHO-C-NH
3
- NH2
+
CO
2
2
o-methylisourea
+ 0
n
cellulose
-(CH
- 0 - C - N -(CH2)6
NH2 I
- NH - C - NH2 +
CH30H
Fig. 1. Reaction procedure for activating cellulose beads for ionicquanidino attachment of enzyme molecules.
Reactions of free invertase were carried out in test tubes submerged in a constant temperature water bath.
EXPERIMENTS AND RESULTS A set of experiments with free invertase were conducted to examine the time course sucrose inversion at pH 4.7 and 55°C employing 75, 125, and 175mM initial sucrose concentrations. The results of the experiment with 125mM initial concentration are given in Figure 2. At the given enzyme loading, for a t least the first five minutes, the reaction rate remained essentially constant. An initial sucrose concentration of 125mM was used to examine the temperature effect on enzyme activity at pH 4.7 and the pH effect at 45 or 55°C. All experiments with the free enzyme involved a reaction time of 5 min. In the case of immobilized invertase on porous cellulose beads, a flow rate of 7.2 ml/min or more of a solution
DICKENSHEETS, CHEN, AND TSAO
368 IOC
0
I
0
80
H
In
>
60
2
8 40 0
20
I 10
I 20
3
REACTION TIME, min
Fig. 2. Time course sucrose inversion by free invertase. Initial sucrose concentration is 125mM. Reaction conditions: pH 4.7, 55°C.
TEMPERATURE
,OC
Fig. 3. Temperature profiles of free and immobilized invertase. Experimental immobilized data: ( A ) Free enzyme with 125mM initial sucrose, pH 4.5; 0, enzyme a t 7.2 ml/min flow rate; 0 , at 22.0 ml/min, pH 4.7.
IMMOBILIZED YEAST INVERTASE
369
containing 125mM sucrose was used to feed the column reactor of 1 cm i.d. The resultant temperature and pH profiles for the free and immobilized Candida invertase are shown in Figures 3 and 4, respectively. Apparently the immobilized enzyme has a much broader pH optimum than the free enzyme. The immobilized invertase remains active a t 70°C or above; while the free enzyme seems to start to deactivate quickly in this temperature range. From the Arrhenius plots in Figure 5, the activation energy was found to be 7,322 and 4,050 cal/g mol for the free and the immobilized invertase, respectively. At pH 4.1 and 55"C, initial reaction rates were determined at different initial sucrose concentrations ranging from 50 to 600mM. A Lineweaver-Burk plot of the free invertase is given in Figure 6. A linear correlation exists a t low substrate concentration. Deviation at high sucrose concentration suggests a substrate inhibition of the invertase activity. Similar experiments with the immobilized enzyme in a column reactor were also run a t pH 4.7, 45"C, and a feed rate of 7.1 ml/min with feed sucrose concentrations varying from 50 to 2,000mM. The resultant Lineweaver-Burk plot is also
I
2
I 4
I 6
I
PH
Fig. 4. pH profiles of free and immobilized invertase. Free enzyme runs: 125mM initial sucrose, 55°C. Immobilized enzyme runs: 125mM initial sucrose, 45°C and 7.2 ml/min flow rate through the reactor bed.
370
DICKENSHEETS, CHEN, AND TSAO
Fig. 5. Arrhenius plots of free and immobilized invertase. Data from Figure 3.
II
s , MILLIMOLAR
SUCROSE-'
Fig. 6. Lineweaver-Burk plot of free invertase and immobilized invertase on porous cellulose beads. Free enzyme runs: pH 4.1, 55°C. Immobilized enzyme runs: pH 4.7, 45"C, 7.2 ml/min flow rate through the reactor bed.
IMMOBILIZED YEAST INVERTASE
371
given in Figure 6, again showing the pattern of substrate inhibition. From Figure 6, the Michaelis constant, K,, of the free invertase and the apparent K, of the immobilized enzyme on cellulose beads were determined t o be 46.9 and 129.5mMl respectively. Dixon and Webb3 give the following rate equation to account for substrate inhibition :
where V is the reaction velocity; VmaXis the maximum reaction velocity; S is the substrate concentration; K , is the Michaelis constant, and Ki is the inhibition constant. Equation (1) can be reduced to eq. (2) at high substrate concentrations:
Rearranging eq. (2) yields the following equation which suggests a linear relationship between 1/V and S:
S 1 V KiVmax
+-1
Vmax
(3)
The experimental results in Figure 6 were replotted in Figures 7 and 8 according to eq. (3). Indeed reasonably good linear correlations between l / V and S do exist at high substrate concentrations. From the slope l/KiVmaxand the y intercept l/Vma,, K; was determined to be 4,884 and 8,304mM for the free and the immobilized invertase, respectively. The effect of the external film diffusion on the reaction rate of the immobilized invertase was examined a t three temperatures by varying the feed flow rate. The results given in Figure 9 were collected from experiments at pH 4.1 and 125mM sucrose concentration with invertase attached to 35 mesh porous cellulose beads packed in the 1 cm column reactor. The results a t three different temperatures all indicate a minimum flow rate of about 18 ml/min to eliminate the effect of external film diffusion on the apparent enzyme reaction rate. The external film diffusion effect was also examined with three different bead sizes: 28, 35, and 48 mesh. A minimum flow rate of 18 ml/min was also indicated by the data plotted in Figure 10. The maximum rates of different bead sizes were replotted in Figure 11 to give a preliminary indication of the effect of internal pore diffusion on the reaction rate. At 28 mesh, the hindrance by pore diffusion seems t o be quite strong.
DICKENSHEETS, CHEN, AND TSAO
372
4c
L 200
OO
S
, MILLIMOLAR
I 400
60
SUCROSE
Fig. 7. Determination of Ki for free invertase. Data from Figure 6.
5 D
4-
0
>
3-
\
0 0
2-
D
B 0
0
-
-
I
I
I-
0
I
S. MILLMOLAR
SUCROSE
Fig. 8. Determination of Ki for immobilized invertase on porous cellulose beads. Data from Figure 6.
373
IMMOBILIZED YEAST INVERTASE
" i kj
20
20
E
0
0
5
10
FLOW RATE
IS
i
, ml /min.
Fig. 9. Effect of external film diffusion a t different temperatures. pH 4.1, 1 2 5 d initial sucrose. (O),35°C; (O), 40°C; (A), 45OC.
Fig. 10. Effect of external film diffusion examined a t different bead sizes. pH 4.7, 125mM initial sucrose. (O), 28 mesh; ( O ) , 35 mesh; (A), 48 mesh.
374
DICKENSNEETS, CHEN, AND TSAO
L,
f
48
f
28 Mesh
I 0.4
I 0.5
I
I
0.6
0.1
0,
AVERAGE BEAD DIAMETER, mm
Fig. 11. Effect of pore diffusion on immobilized invertase activity. Data from Figure 10.
DISCUSSION Diffusional hindrance has been generally considered undesirable in practical enzyme applications because it usually reduces the effectiveness of a n immobilized enzyme. The present work of immobilized invertase, however, is a case where diffusion hindrance actually helps to minimize substrate inhibition. According to Figures 9 and 10, apparently there was considerable resistance to diffusion through the external liquid film surrounding the cellulose beads under the present experimental feed flow rate of 7.2 ml/min. For large bead size (28 mesh), the pore diffusion effect is also quite strong as shown in Figure 11. Consequently, the actual sucrose concentration exposed t o the immobilized enzyme molecules is much less than that of the apparent bulk sucrose concentration. The values of K , and Ki for the invertase were found to be 46.9 and 4,884mM1respectively. The intrinsic K , and K i of the immobilized invertase are assumed to be the same. Consequently, if the actual local sucrose concentration within the microenvironment of the immobilized enzyme molecules is in the range of, say, 450mM, the enzyme reaction rate can still be a t its maximum V,,,. This is because of the fact accord-
IMMOBILIZED YEAST INVERTASE
375
ing to eq. (4), which is equivalent to eq. (l),that both the second and third terms in the denominator can be neglected when S equals 450mM, K , equals 46.9mM, and Ki equals 4,884mM:
Both apparent K, and apparent Ki of the immobilized invertase are much larger than those of the free enzyme. This is another indication of the diffusion effect.
Nomenclature Ki K, S V V-
inhibition constant Michaelis constant substrate concentration reaction velocity maximum reaction velocity
References 1. L. F. Chen and G. T. Tsao, Biotechnol. Bioeng., 18, 1507 (1976). 2. J. B. Sumner, J . Biol. Chem., 47, 5 (1921). 3. M. Dixon and E. C. Webb, Eneymes, Academic Press, New York, 1958, p. 73.
Accepted for Publication October 10, 1976
Characteristics of Yeast Invertase Immobilized on Porous Cellulose Beads PAUL A. DICKENSHEETS, LI FU CHEN, and GEORGE T. TSAO, School of Chemical Engineering, Purdue University, West Laf ay ette, Indiana 47907
Summary Invertase from Candida utilis was immobilized on porous cellulose beads by an ionic-quanidino bond. The immobilized invertase showed optimum activity between pH 4.0 and 5.4, while the free enzyme had a sharp optimum a t pH 4.1. Both temperature profiles were fairly similar up to 55°C. However, above this temperature the immobilized enzyme was more stable than the free enzyme. From the temperature data, the activation energies were found to be 7,322 and 4,052 cal/g mol for the free and the immobilized enzyme, respectively. Candida invertase shows characteristics of substrate inhibition. Both the K , and Ki for the free and the immobilized enzymes were determined. The apparent Ki for the immobilized invertase was much higher than the Ki of the free enzyme, suggesting a diffusion effect. Immobilized invertase molecules deep in the pores only see sucrose concentrations much less than the bulk concentrations. Immobilization, thus, offers certain processing advantages in this regard.
INTRODUCTION Sucrose inversion adds total weight and sweetness to the sugar product. Current industrial practice makes use of strong cationic resins for sucrose inversion in a continuous column process. Enzymatic inversion has the advantage over the acid process in that less amounts of undesirable oligosaccharides are formed when a n enzyme is used as the catalyst. On the other hand, most invertase preparations suffer from substrate (sucrose) inhibition. Immobilization of invertase on porous supports may minimize the inhibitory effect of sucrose because the enzyme molecules are protected by a diffusion barrier, i.e., the apparent bulk sucrose concentration is generally higher than the substrate concentration in the microenvironment of the immobilized enzyme molecules. Furthermore, immobilized enzyme will make it easy to conduct a continuous column process 365 @ 1977 by John Wiley & Sons, Inc.
366
DICKENSHEETS, CHEN, AND TSAO
for the reaction, while sucrose inversion is usually done batchwise when soluble invertase is used. This paper reports the immobilization of invertase from Candida utilis on porous cellulose beads. Characteristics of the immobilized invertase are t o be described.
MATERIALS AND METHODS Porous cellulose beads were prepared by our own technique. Physical properties and preparation procedures of the porous cellulose beads were reported recently by Chen and Tsa0.l For all the experiments, beads of 35 mesh were used, except where noted, Invertase, Grade X, of Sigma Chemical derived from C. utilis was used throughout this work. According t o Sigma Chemical, the preparation has 575 invertase units per mg of solid. Each enzyme unit will hydrolyze 1 Fmol of sucrose per min at p H 5.4 and 55°C. Chemicals used in this study are all of reagent grade from either Mallinckrodt or Fisher. “Domino” granulated pure cane sugar from Amstar Corporation was used as the substrate. Buffer solutions made of varying mixtures of citric acid (O.lM), and dibasic sodium phosphate (0.2M) solutions were used for the inversion experiments for their applicability over a broad p H range (PH 2.2-8.0). The immobilization procedure is outlined in Figure 1. Porous cellulose beads were first treated with hexamethyl diisocyanate. The complex was then hydrolyzed, after which a quanidino group was added by reacting with o-methylisourea. After the addition of o-methylisourea, the beads were left at 4°C for four days. They were then rinsed with acetate buffer a t pH 5 and stored wet a t room temperature until use. By adding 4 g of the wet beads with 50 mg of Grade X invertase dissolved in 5 ml of water, enzyme immobilization was accomplished after standing at 4°C overnight. An invert sugar assay was done by the well-known dinitrosalicylic acid (DNS) method first described by Sumner.2 The 3,4-dinitrosalicylic acid was reduced by glucose and fructose formed by sucrose inversion t o 3-amino-5-nitrosalicylic acid. The amount of reduced dinitrosalicylic acid was then read in a spectrophotometer (PerkinElmer Model 124). A Water Associates liquid chromatograph was also employed to examine the amounts of glucose, fructose, and oligosaccharides in reaction mixtures. The reactor for the immobilized invertase was a jacketed ECONO Column (catalog No. 737-1231) of Bio-Rad Laboratories 1 cm i.d.
IMMOBILIZED YEAST INVERTASE cellulose bead
cellulose
- OH
+ 0=C
1 1
-(CH2I6
= N
-N
= C =
367
0 hexamethylene
diisocyanate
0
It
- 0 - C -
N-(CH)
2 6
- N = C = = O
H2°
0
II
cellulose
- 0 - C--N
I
I
)
CHO-C-NH
3
- NH2
+
CO
2
2
o-methylisourea
+ 0
n
cellulose
-(CH
- 0 - C - N -(CH2)6
NH2 I
- NH - C - NH2 +
CH30H
Fig. 1. Reaction procedure for activating cellulose beads for ionicquanidino attachment of enzyme molecules.
Reactions of free invertase were carried out in test tubes submerged in a constant temperature water bath.
EXPERIMENTS AND RESULTS A set of experiments with free invertase were conducted to examine the time course sucrose inversion at pH 4.7 and 55°C employing 75, 125, and 175mM initial sucrose concentrations. The results of the experiment with 125mM initial concentration are given in Figure 2. At the given enzyme loading, for a t least the first five minutes, the reaction rate remained essentially constant. An initial sucrose concentration of 125mM was used to examine the temperature effect on enzyme activity at pH 4.7 and the pH effect at 45 or 55°C. All experiments with the free enzyme involved a reaction time of 5 min. In the case of immobilized invertase on porous cellulose beads, a flow rate of 7.2 ml/min or more of a solution
DICKENSHEETS, CHEN, AND TSAO
368 IOC
0
I
0
80
H
In
>
60
2
8 40 0
20
I 10
I 20
3
REACTION TIME, min
Fig. 2. Time course sucrose inversion by free invertase. Initial sucrose concentration is 125mM. Reaction conditions: pH 4.7, 55°C.
TEMPERATURE
,OC
Fig. 3. Temperature profiles of free and immobilized invertase. Experimental immobilized data: ( A ) Free enzyme with 125mM initial sucrose, pH 4.5; 0, enzyme a t 7.2 ml/min flow rate; 0 , at 22.0 ml/min, pH 4.7.
IMMOBILIZED YEAST INVERTASE
369
containing 125mM sucrose was used to feed the column reactor of 1 cm i.d. The resultant temperature and pH profiles for the free and immobilized Candida invertase are shown in Figures 3 and 4, respectively. Apparently the immobilized enzyme has a much broader pH optimum than the free enzyme. The immobilized invertase remains active a t 70°C or above; while the free enzyme seems to start to deactivate quickly in this temperature range. From the Arrhenius plots in Figure 5, the activation energy was found to be 7,322 and 4,050 cal/g mol for the free and the immobilized invertase, respectively. At pH 4.1 and 55"C, initial reaction rates were determined at different initial sucrose concentrations ranging from 50 to 600mM. A Lineweaver-Burk plot of the free invertase is given in Figure 6. A linear correlation exists a t low substrate concentration. Deviation at high sucrose concentration suggests a substrate inhibition of the invertase activity. Similar experiments with the immobilized enzyme in a column reactor were also run a t pH 4.7, 45"C, and a feed rate of 7.1 ml/min with feed sucrose concentrations varying from 50 to 2,000mM. The resultant Lineweaver-Burk plot is also
I
2
I 4
I 6
I
PH
Fig. 4. pH profiles of free and immobilized invertase. Free enzyme runs: 125mM initial sucrose, 55°C. Immobilized enzyme runs: 125mM initial sucrose, 45°C and 7.2 ml/min flow rate through the reactor bed.
370
DICKENSHEETS, CHEN, AND TSAO
Fig. 5. Arrhenius plots of free and immobilized invertase. Data from Figure 3.
II
s , MILLIMOLAR
SUCROSE-'
Fig. 6. Lineweaver-Burk plot of free invertase and immobilized invertase on porous cellulose beads. Free enzyme runs: pH 4.1, 55°C. Immobilized enzyme runs: pH 4.7, 45"C, 7.2 ml/min flow rate through the reactor bed.
IMMOBILIZED YEAST INVERTASE
371
given in Figure 6, again showing the pattern of substrate inhibition. From Figure 6, the Michaelis constant, K,, of the free invertase and the apparent K, of the immobilized enzyme on cellulose beads were determined t o be 46.9 and 129.5mMl respectively. Dixon and Webb3 give the following rate equation to account for substrate inhibition :
where V is the reaction velocity; VmaXis the maximum reaction velocity; S is the substrate concentration; K , is the Michaelis constant, and Ki is the inhibition constant. Equation (1) can be reduced to eq. (2) at high substrate concentrations:
Rearranging eq. (2) yields the following equation which suggests a linear relationship between 1/V and S:
S 1 V KiVmax
+-1
Vmax
(3)
The experimental results in Figure 6 were replotted in Figures 7 and 8 according to eq. (3). Indeed reasonably good linear correlations between l / V and S do exist at high substrate concentrations. From the slope l/KiVmaxand the y intercept l/Vma,, K; was determined to be 4,884 and 8,304mM for the free and the immobilized invertase, respectively. The effect of the external film diffusion on the reaction rate of the immobilized invertase was examined a t three temperatures by varying the feed flow rate. The results given in Figure 9 were collected from experiments at pH 4.1 and 125mM sucrose concentration with invertase attached to 35 mesh porous cellulose beads packed in the 1 cm column reactor. The results a t three different temperatures all indicate a minimum flow rate of about 18 ml/min to eliminate the effect of external film diffusion on the apparent enzyme reaction rate. The external film diffusion effect was also examined with three different bead sizes: 28, 35, and 48 mesh. A minimum flow rate of 18 ml/min was also indicated by the data plotted in Figure 10. The maximum rates of different bead sizes were replotted in Figure 11 to give a preliminary indication of the effect of internal pore diffusion on the reaction rate. At 28 mesh, the hindrance by pore diffusion seems t o be quite strong.
DICKENSHEETS, CHEN, AND TSAO
372
4c
L 200
OO
S
, MILLIMOLAR
I 400
60
SUCROSE
Fig. 7. Determination of Ki for free invertase. Data from Figure 6.
5 D
4-
0
>
3-
\
0 0
2-
D
B 0
0
-
-
I
I
I-
0
I
S. MILLMOLAR
SUCROSE
Fig. 8. Determination of Ki for immobilized invertase on porous cellulose beads. Data from Figure 6.
373
IMMOBILIZED YEAST INVERTASE
" i kj
20
20
E
0
0
5
10
FLOW RATE
IS
i
, ml /min.
Fig. 9. Effect of external film diffusion a t different temperatures. pH 4.1, 1 2 5 d initial sucrose. (O),35°C; (O), 40°C; (A), 45OC.
Fig. 10. Effect of external film diffusion examined a t different bead sizes. pH 4.7, 125mM initial sucrose. (O), 28 mesh; ( O ) , 35 mesh; (A), 48 mesh.
374
DICKENSNEETS, CHEN, AND TSAO
L,
f
48
f
28 Mesh
I 0.4
I 0.5
I
I
0.6
0.1
0,
AVERAGE BEAD DIAMETER, mm
Fig. 11. Effect of pore diffusion on immobilized invertase activity. Data from Figure 10.
DISCUSSION Diffusional hindrance has been generally considered undesirable in practical enzyme applications because it usually reduces the effectiveness of a n immobilized enzyme. The present work of immobilized invertase, however, is a case where diffusion hindrance actually helps to minimize substrate inhibition. According to Figures 9 and 10, apparently there was considerable resistance to diffusion through the external liquid film surrounding the cellulose beads under the present experimental feed flow rate of 7.2 ml/min. For large bead size (28 mesh), the pore diffusion effect is also quite strong as shown in Figure 11. Consequently, the actual sucrose concentration exposed t o the immobilized enzyme molecules is much less than that of the apparent bulk sucrose concentration. The values of K , and Ki for the invertase were found to be 46.9 and 4,884mM1respectively. The intrinsic K , and K i of the immobilized invertase are assumed to be the same. Consequently, if the actual local sucrose concentration within the microenvironment of the immobilized enzyme molecules is in the range of, say, 450mM, the enzyme reaction rate can still be a t its maximum V,,,. This is because of the fact accord-
IMMOBILIZED YEAST INVERTASE
375
ing to eq. (4), which is equivalent to eq. (l),that both the second and third terms in the denominator can be neglected when S equals 450mM, K , equals 46.9mM, and Ki equals 4,884mM:
Both apparent K, and apparent Ki of the immobilized invertase are much larger than those of the free enzyme. This is another indication of the diffusion effect.
Nomenclature Ki K, S V V-
inhibition constant Michaelis constant substrate concentration reaction velocity maximum reaction velocity
References 1. L. F. Chen and G. T. Tsao, Biotechnol. Bioeng., 18, 1507 (1976). 2. J. B. Sumner, J . Biol. Chem., 47, 5 (1921). 3. M. Dixon and E. C. Webb, Eneymes, Academic Press, New York, 1958, p. 73.
Accepted for Publication October 10, 1976
