PART 1 Introduction
3.7. SUMMARY
cell wall of gram-positive bacteria, is used as an antibacterial agent; streptokinase is used as an antiinflammatory agent; urokinase is used in dissolving and preventing blood clots.
Asparaginase, which catalyzes the conversion of L-asparagine to L-aspartate, is used as an anticancer agent. Cancer cells require L-asparagine and are inhibited by asparaginase. As- paraginase is produced by E. coli. Glucose oxidase catalyzes the oxidation of glucose to gluconic acid and hydrogen peroxide, which can easily be detected. Glucose oxidase is used for the determination of glucose levels in blood and urine. Penicillinases hydrolyze penicillin and are used to treat allergic reactions against penicillin. Tissue plasminogen activator (TPA) and streptokinase are used in the dissolution of blood clots (particularly following a heart attack or stroke).
The development of biosensors using enzymes as integral components is proceeding rapidly. Two examples of immobilized enzyme electrodes are those used in the determina- tion of glucose and urea by using glucose oxidase and urease immobilized on the elec- trode membrane, respectively. Scarce enzymes (e.g., tissue plasminogen activator) are finding increasing uses, as the techniques of genetic engineering now make it possible to produce usable quantities of such enzymes.
The preceding list of enzymes and uses is not exhaustive, but merely illustrative.
enzyme loading need to be optimized, and a support material with the correct surface characteristics must be selected.
Enzymes are widely used in industry and have significant medical applications.
Among the most widely used enzymes are proteases (papain, trypsin, subtilisin); amylases (starch hydrolysis); rennet (cheese manufacturing); glucose isomerase (glucose-to- fructose conversion); glucose oxidase (glucose-to-gluconic acid conversion); lipases (lipid hydrolysis), and pectinases (pectin hydrolysis). Enzyme production and utilization are a multibillion-dollar business with a great potential for expansion.
S U G G E S T I O N S F O R F U R T H E R R E A D I N G
ADAMS, M. W. W., ANDR. M. KELLY, Enzymes from Microorganisms in Extreme Environments, Chemical & Engineering News(Dec. 18), 32–42 (1995).
BAILEY, J .E., ANDD. F. OLLIS, Biochemical Engineering Fundamentals, 2d ed. McGraw-Hill Book Co., New York, 1986.
BLANCH, H. W., ANDD. S. CLARK,Biochemical Engineering, Marcel Dekker, Inc., New York, 1996.
KATCHALSKI-KATZIR, E., Immobilized Enzymes—Learning from Past Successes and Failures, Trends in Biotechnology 11: 471–478, 1993.
MORAN, L. A., K. G. SCRIMGEOUR, H. R. HORTON, R. S. OCHS, ANDJ. D. RAWN, Biochemistry, Pren- tice-Hall, Inc., Upper Saddle River, NJ, 1994.
SELLEK, G. A., AND J. B. CHAUDHURI, Biocatalysis in Organic Media Using Enzymes from Ex- tremophiles, Enzyme Microbial Technol. 25: 471–482 (1999).
STINSON, S. C., Counting on Chiral Drugs, Chemical & Engineering News(Sept. 21), 83–104, 1998.
P R O B L E M S 3.1. Consider the following reaction sequence:
Develop a suitable rate expression for production formation [v= k5(ES)2] by using (a) the equilibrium approach, and (b) the quasi-steady-state approach.
3.2. Consider the reversible product-formation reaction in an enzyme-catalyzed bioreaction:
Develop a rate expression for product-formation using the quasi-steady-state approximation and show that
v v v
= = -
+ +
d dt
/K /K
K K
s m p p
m p
[P S] [P]
[S] [P]
]
( )
[( )
1
E+Sa ES aE P
k k
k k
- -
( ) +
1 1
2
2
S E+ a
(
ES)
a(
ES)
æ Ææ P+Ek k
k
k k
2 1
4 3
5
1 2
98 Enzymes Chap. 3
where .
3.3. The enzyme, fumarase, has the following kinetic constants:
where -k1=109M-1s-1 k-1=4.4 ¥104s-1
-k2=103s-1
a. What is the value of the Michaelis constant for this enzyme?
b. At an enzyme concentration of 10-6M, what will be the initial rate of product formation at a substrate concentration of 10-3M?
[Courtesy of D. J. Kirwan from “Collected Coursework Problems in Biochemical Engi- neering” compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ. Summer School.]
3.4. The hydration of CO2is catalyzed by carbonic anhydrase as follows:
The following data were obtained for the forward and reverse reaction rates at pH 7.1 and an enzyme concentration of 2.8 ¥10-9M.
H O CO2 + 2 a E HCO 3-+H+ S E+ ESa P E
k
k k
-
æ Ææ +
1
1 2
K k k
k K k k
k V k V k
m= + p s p
= +
= =
-
-
-
1 2
1
1 2
2
2 1
and and - [E ]0 , [E ]0
Hydration Dehydration
1/v, M-1 [CO2] 1/v, M-1 [HCO-3]
(s ¥10-3) (M¥103) (s ¥10-3) (M¥103)
36 1.25 95 2
20 2.5 45 5
12 5 29 10
6 20 25 15
vis the initialreaction rate at the given substrate concentration. Calculate the forward and re- verse catalytic and Michaelis constants.
[Courtesy of D. J. Kirwan from “Collected Coursework Problems in Biochemical Engineer- ing” compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ. Summer School.]
3.5. An inhibitor (I) is added to the enzymatic reaction at a level of 1.0 g/l. The following data were obtained for Km=9.2 g S/l.
v S
0.909 20
0.658 10
0.493 6.67
0.40 5
0.333 4
0.289 3.33
0.227 2.5
a.Is the inhibitor competitive or noncompetitive?
b.Find KI.
3.6. During a test of kinetics of an enzyme-catalyzed reaction, the following data were recorded:
E0 T I S V
(g/l) (˚C) (mmol/ml) (mmol/ml) (mmol/ml-min)
1.6 30 0 0.1 2.63
1.6 30 0 0.033 1.92
1.6 30 0 0.02 1.47
1.6 30 0 0.01 0.96
1.6 30 0 0.005 0.56
1.6 49.6 0 0.1 5.13
1.6 49.6 0 0.033 3.70
1.6 49.6 0 0.01 1.89
1.6 49.6 0 0.0067 1.43
1.6 49.6 0 0.005 1.11
0.92 30 0 0.1 1.64
0.92 30 0 0.02 0.90
0.92 30 0 0.01 0.58
0.92 30 0.6 0.1 1.33
0.92 30 0.6 0.033 0.80
0.92 30 0.6 0.02 0.57
a. Determine the Michaelis–Menten constant for the reaction with no inhibitor present at 30∞C and at 49.6∞C.
b. Determine the maximum velocity of the uninhibited reaction at 30∞C and an enzyme con- centration of 1.6 g/l.
c. Determine the KIfor the inhibitor at 30∞C and decide what type of inhibitor is being used.
3.7. An enzyme ATPase has a molecular weight of 5 ¥104daltons, a KMvalue of 10-4M,and a k2 value of k2=104molecules ATP/min molecule enzyme at 37∞C. The reaction catalyzed is the following:
which can also be represented as
where S is ATP. The enzyme at this temperature is unstable. The enzyme inactivation kinetics are first order:
where E0is the initial enzyme concentration and kd=0.1 min-1. In an experiment with a par- tially pure enzyme preparation, 10 mg of total crude protein (containing enzyme) is added to a 1 ml reaction mixture containing 0.02 MATP and incubated at 37∞C. After 12 hours the reac- tion ends (i.e.,t Æ •) and the inorganic phosphate (Pi) concentration is found to be 0.002 M, which was initially zero. What fraction of the crude protein preparation was the enzyme?
Hint: Since [S] >>Km, the reaction rate can be represented by d
dt( ) k P [ ]
= 2 E E=E0e-k td
E+S k ES E P
k
1
2
æ Ææk2 + ATPæATPaseææÆADP+Pi
a
100 Enzymes Chap. 3 3.8. Assume that for an enzyme immobilized on the surface of a nonporous support material the external mass transfer resistance for substrate is not negligible as compared to the reaction rate. The enzyme is subject to substrate inhibition (eq. 3.34).
a. Are multiple states possible? Why or why not?
b. Could the effectiveness factor be greater than one?
3.9. The following data were obtained for an enzyme-catalyzed reaction. Determine Vmaxand Km by inspection. Plot the data using the Eadie–Hofstee method and determine these constants graphically. Explain the discrepancy in your two determinations. The initial rate data for the enzyme-catalyzed reaction are as follows:
[S] v
mol/l mmol/min
5.0 ¥ 10-4 125
2.0 ¥10-4 125
6.0 ¥ 10-5 121
4.0 ¥10-5 111
3.0 ¥10-5 96.5
2.0 ¥10-5 62.5
1.6 ¥10-5 42.7
1.0 ¥10-5 13.9
8.0 ¥10-6 7.50
Do these data fit into Michaelis–Menten kinetics? If not, what kind of rate expression would you suggest? Use graphical methods.
3.10. a. H. H. Weetall and N. B. Havewala report the following data for the production of dex- trose from corn starch using both soluble and immobilized (azo-glass beads) glucoamy- lase in a fully agitated CSTR system.
1. Soluble data: T=60∞C, [S0] =168 mg starch/ml, [E0] =11,600 units, volume =1000 ml.
2. Immobilized data: T=60∞C, [S0] =336 mg starch/ml, [E0] =46,400 units initially, im- mobilized, volume =1000 ml.
Product concentration (mg dextrose/ml)
Time (min) Soluble Immobilized
0 12.0 18.4
15 40.0 135
30 76.5 200
45 94.3 236
60 120.0 260
75 135.5 258
90 151.2 262
105 150.4 266
120 155.7 278
135 160.1 300
150 164.9 310
165 170.0 306
225 — 316
415 — 320
Determine the maximum reaction velocity, Vm(mg/ml-min · unit of enzyme) and the satura- tion constant, KM(mg/ml).
b. The same authors studied the effect of temperature on the maximum rate of the hydroly- sis of corn starch by glucoamylase. The results are tabulated next. Determine the activa- tion energy (DEcal/g mole) for the soluble and immobilized enzyme reaction.
Vmax(m mol/min 106) T, ∞C Soluble Azo-immobilized
25 0.62 0.80
35 1.42 1.40
45 3.60 3.00
55 8.0 6.2
65 16.0 11.0
c. Using these results, determine if immobilized enzyme is diffusion limited.
[Courtesy of A. E. Humphrey from “Collected Coursework Problems in Biochemical En- gineering” compiled by H. W. Blanch for 1977 Am. Soc. Eng. Educ. Summer School.]
3.11. Michaelis–Menten kinetics are used to describe intracellular reactions. Yet [E0] ª[S0]. In in vitro batch reactors, the quasi-steady-state hypothesis does not hold for [E0] ª[S0]. The rapid equilibrium assumption also will not hold. Explain why Michaelis–Menten kinetics and the quasi-steady-state approximation are still reasonable descriptions of intracellular enzyme reactions.
3.12. You are working for company A and you join a research group working on immobilized en- zymes. Harry, the head of the lab, claims that immobilization improves the stability of the en- zyme. His proof is that the enzyme has a half-life of 10 days in free solution, but under identical conditions of temperature, pH, and medium composition, the measured half-life of a packed column is 30 days. The enzyme is immobilized in a porous sphere 5 mm in diameter.
Is Harry’s reasoning right? Do you agree with him? Why or why not?
3.13. The following data were obtained from enzymatic oxidation of phenol by phenol oxidase at different phenol concentrations.
S (mg/l) 10 20 30 50 60 80 90 110 130 140 150
v(mg/l-h) 5 7.5 10 12.5 13.7 15 15 12.5 9.5 7.5 5.7
a. What type of inhibition is this ? b. Determine the constants Vm, Km, and Ksi. c. Determine the oxidation rate at [S] =70 mg/l.
3.14. Uric acid is degraded by uricase enzyme immobilized in porous Ca-alginate beads. Experi- ments conducted with different bead sizes result in the following rate data:
Bead Diameter, Dp (cm) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Rate, v(mg/l.h) 200 198 180 140 100 70 50 30
a. Determine the effectiveness factor for particle sizes Dp =0.5 cm and Dp =0.7 cm.
b. The following data were obtained for Dp =0.5 cm at different bulk uric acid concentra- tions. Assuming negligible liquid film resistance, calculate Vmand Ksfor the enzyme. As- sume no substrate or product inhibition.
S0(mg UA/l) 10 25 50 100 200 250
v(mg UA/l.h) 10 20 30 40 45 46
102 Enzymes Chap. 3 3.15. The enzyme, urease, is immobilized in Ca-alginate beads 2 mm in diameter. When the urea concentration in the bulk liquid is 0.5 mMthe rate of urea hydrolysis is v=10 mmoles-l-h.
Diffusivity of urea in Ca-alginate beads is De=1.5¥10–5cm2/sec, and the Michaelis constant for the enzyme is Km¢ =0.2 mM.By neglecting the liquid film resistance on the beads (i.e., [So] =[Ss]) determine the following:
a. Maximum rate of hydrolysis Vm, Thiele modulus (f), and effectiveness factor (h).
b. What would be the Vm, f, and hvalues for a particle size of Dp =4 mm?
Hint:Assume h =3/ffor large values of f(f > 2).
3.16. Decarboxylation of glyoxalate (S) by mitochondria is inhibited by malonate (I). Using the following data obtained in batch experiments, determine the following:
Glyox,S(mM) Rate of CO2evolution, v(mmoles/l-h) I = 0 I = 1.26 mM I = 1.95 mM
0.25 1.02 0.73 0.56
0.33 1.39 0.87 0.75
0.40 1.67 1.09 0.85
0.50 1.89 1.30 1.00
0.60 2.08 1.41 1.28
0.75 2.44 1.82 1.39
1.00 2.50 2.17 1.82
a. What type of inhibition is this?
b. Determine the constants Vm, Km¢, and KI.
3.17. Urea dissolved in aqueous solution is degraded to ammonia and CO2by the enzyme urease immobilized on surfaces of nonporous polymeric beads. Conversion rate is controlled by transfer of urea to the surface of the beads through liquid film, and the conversion takes place on the surfaces of the beads. The following parameters are given for the system.
kL=0.2 cm/s; Km=200 mg/l
Vm¢ =0.1 mg urea/cm2support surface -s.
Sb=1000 mg urea/l
a. Determine the surface concentration of urea.
b. Determine the rate of urea degradation under mass transfer controlled conditions.
3.18. Two enzymes are both immobilized on the same flat, nonporous surface. For enzyme A the sub- strate is S1. For enzyme B the substrate is S2. The product of the first reaction is S2. That is:
a. Figure 3.P1 depicts the rate of the first reaction on the surface as a function of local con- centrations of S1. If the bulk concentration of S1is 100 mg/l and the mass transfer coeffi- cient is 4 ¥10-5cm/s, what is the rate of consumption of S1for a 1 cm2surface? What is the surface concentration of S1?
b. The rate of the second reaction is:
- = =
d S /dt d P /dt V S+
K S
2
m m
[ ] [ ] ¢¢ 2
2 surface
surface
S S P
EA EB
1æ Ææ 2æ Ææ
where Km=5 mg/l (or 5 ¥10-3mg/cm3) and Vm≤ =4.0 ¥10-6mg/cm2=s. The bulk concentra- tion of S2[S2bulk] is maintained as 5 mg/l and the mass transfer coefficient is the same for S1 and S2. Calculate [S2surface] and the rate of formation of P(assuming all stoichiometric coeffi- cients are one).
3.19. Consider the case of two enzymes immobilized on the same nonporous, planar surface. S is a substrate used by both enzymes in the following reactions:
Figure 3P1. Reaction rate data for prob- lem 3.18. Reaction rate dependence on sub- strate one for reaction catalyzed by EA.
Figure 3P2. Reaction rate data for prob- lem 3.19. The reaction rate data for two dif- ferent enzymes (E1andE2) are shown.
104 Enzymes Chap. 3 (1) and
(2) The final product P3is formed by the spontaneous reaction of P1and P2:
(3) Reactions 1 and 2 occur only at the surface and reaction 3 is a homogeneous reaction occurring throughout the bulk liquid phase.
Figure 3.P2 gives the predicted reaction-rate dependence of reaction 1 (bottom curve) alone and reaction 2 (top curve) alone based on the measured amount of each enzyme immobilized and assuming the intrinsic reaction kinetics are not altered in the process of immobilization.
a. If kL=6 ¥10-5cm/s and the bulk concentration of substrate is 500 mg/l, what is the totalrate of substrate disappearance?
b. What is the overall effectiveness factor under the conditions of part a?
c. What will be the ratio of P2to P1under the conditions of part a?
d. If you want to produce equimolar amounts of P1and P2and if kL=6 ¥10-5cm/s, what value of bulk substrate concentration must you pick?
P1+P2æ Ææ P3 S E+ 2æ Ææ E2+P2 S E+ 1æ Ææ E1+P1