104 chapter 6 homogeneous reaction catalysis: enzymatic reaction fundamental dicky dermawan ...
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Chapter 6Homogeneous Reaction Catalysis:
ENZYMATIC REACTION FUNDAMENTAL
Dicky Dermawanwww.dickydermawan.net78.net
Development of Kinetic Expression in Enzymatic Reactions
ITK-329 Kinetika & Katalisis
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# accelerate specific reaction# very selective# work on mild condition
k1
k2
E + S (ES)*
(ES)* + W P + E k3
W = Solvent, usually water,Considered constant in concentration
Example: Urease
O
NH2CNH2 + Urease NH2CNH2-Urease
O
NH2CNH2-Urease NH2CNH2 + Urease
O O
O
NH2CNH2-Urease + HOH 2NH3 + CO2 + U
General Properties of Enzymes
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3 ESkSEkr 21s
Et
NH2CNH2
OES
]W[kk]S[k
]E][S[k]ES[
]ES])[W[kk(]ES][S[k]E][S[k
])W[kk](ES[]S])[ES[]E([k
321
t1
321t1
32t1
0WESkESkSEkr :PSSH 321ES
Development of Kinetic Expressionk1
k2
E + S (ES)*
(ES)* + W P + E k3 W = Pelarut (konstan)
]ES[]E[]E[ ]ES[]E[]E[ tt Enzyme balance:
]W[kk]S[k
]W[]E][S[kkr
321
t31s
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[S] <<<< Km
]S[K
Vr
m
maxs
m
maxPs
k]W[kkt3p
sp
K]S[
]S[Vrr
]S[
]S[]W[]E[kr
rr
1
32
Michaelis – Menten Equation:
Michaelis – Menten Equation
Property at low substrate concentration:
First order!!!
Property at high substrate concentration: [S] >>>> Km
m
maxs k
Vr Zero order!!!
]W[]E[kV t3max 1
32m k
]W[kkK
where
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]S[
1.
V
K
V
1
r
1
]S[V
K]S[
r
1
max
m
maxs
max
m
s
Burke Lineweaver Plot
Plot of Michaelis – Menten Equation
Estimating Vmax and KM
Alternatively, Eadie plot can be constructed
2maxV
-rs = rp
Km [S]
maxV
1
][
1
S
sr1
max
m
V
Ktan
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Use:a. Burke – lineweaver plotb. Eadie plot
Compare the results and determine which method fits better
Example : 7-7Determine the Michaelis – Menten Parameters for the reaction:
ureaseCONH2*]ureaseurea[ureaseurea 23OH,k
k
k23
2
1
The rate of reaction is given as a function if urea concentration in the following table
Curea [kmol/m3] 0.2 0.02 0.02 0.005 0.002
-rurea [kmol/m3/s] 1.08 0.55 0.38 0.2 0.09
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(a) Determine the Michaelis-Menten parameters Vmax and Km
(b)If the total enzyme concentration is tripled, what will the substrate concentration be after
20 min ?
P7-11B
Beef liver catalase has been used to accelerate the decomposition of hydrogen peroxide to yield water and oxygen. The concentration of hydrogen peroxide is given as a function of time for a reaction mixture with pH of 6.76 and maintain at 30oC,
t (min) 0 10 20 50 100
C H2O2 (mol/liter) 0.02 0.01775 0.0158 0.0106 0.005
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Integration of Rate Equation
Ex. 7-8
Calculate the time needed to convert 80% of the ure xammonia and carbon dioxide in a 0.5 L batch reactor. The initial concentration of urea is 0.1 mol/L, and the urease concentration is 0.001 g/L. The reaction is to be carried out isothermally. At this temperature, if total enzyme concentration used is 5 g/L:
s.L
mol
]S[0266.0
]S[33.1rs
Ex. 7-8
If the reaction is carried out in 15 minutes using enzyme concentration of 0.0002 g/L, what will be the conversion?
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P7-10C Integration of Rate Equation
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Enzymatic Reaction InhibitionIn addition to pH, another factor that greatly influences the rates of enzyme-catalyzed reactions is the presence of an inhibitor.
The most dramatic consequences of enzyme inhibition are found in living organisms, where the inhibition of any particular enzyme involved in a primary metabolic sequence will render the entire sequence inoperative, resulting in either serious damage or death of the organism. For example, the inhibition of a single enzyme, cytochrome oxidase, by cyanide will cause the aerobic oxidation process to stop; death occurs in a very few minutes.
There are also beneficial inhibitors such as the ones used in the treatment of leukemia and other neoplastic diseases.
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Enzymatic Reaction Inhibition
The three most common types of reversible inhibition occurring in enzymatic reactions are competitive, uncompetitive, and noncompetitive.
The enzyme molecule is analogous to the heterogeneous catalytic surface in that it contains active sites.
When competitive inhibition occurs, the substrate and inhibitor are usually similar molecules that compete for the same site on the enzyme.Uncompetitive inhibition occurs when the inhibitor deactivates the enzyme-substrate complex, usually by attaching itself to both the substrate and enzyme molecules of the complex.Noncompetitive inhibition occurs with enzymes containing at least two different types of sites. The inhibitor attaches only to one type of site and the substrate only to the other.
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Competitive inhibition is of particular importance in pharmacokinetics (drug therapy). If a patient were administered two or more drugs simultaneously which react within the body with a common enzyme, cofactor, or active species, this could lead to competitive inhibition of the formation of the respective metabolites and produce serious consequences.
In this type of inhibition another substance, I, competes with the substrate for the enzyme molecules to form an inhibitor-enzyme complex, (E I).
Enzymatic Reaction Inhibition:Competitive Inhibition
k1
k2
S + E ES
I + E EI k3
k4
k5
ES P + E
Mechanism:
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]E[]S[kk
k]ES[
52
1
]SE[k]SE[k]E[]S[k0dt
]ES[d:PSSH 521
]EI[k]E[]I[k0dt
]EI[d:PSSH 43
I = Inhibitor = Penghambat laju reaksi
Competitive Inhibition
Enzyme balance:
52
1
4
3tt kk
]S[]E[k]E[]I[
k
k]E[]E[]ES[]EI[]E[]E[
k1
k2
S + E ES
I + E EI k3
k4
k5
ES P + E
Mechanism:
]E[]I[k
k]EI[
4
3
]S[kk
k]I[
kk
1
]E[]E[
52
1
4
3
t
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]S[]I[k
k
k
kk
k
kk]E[]S[k
r
k
k:
]S[k]I[k
k)kk()kk(
]E[]S[kk
]S[kk
k]I[
k
k1
]E[]S[
kk
kk
]E[]S[kk
kkr
]ES[kr
4
3
1
52
1
52
t5p
1
1
14
35252
t15
52
1
4
3
t
52
15
52
15p
5p
1
52M k
kkK
k1
k2
S + E SE
I + E EI k3
k4
k5
ES P + E
Mechanism:Competitive Inhibition (cont’)
]S[]I[k
kKK
]S[]E[kr
4
3MM
t5p
; substituting expression for [ES]:
; substituting expression for [E]:
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…… Jika penambahan suatu zat I ke dalam kultur menyebabkan kenaikan harga KM tanpa perubahan harga Vmax, maka I menginhibisi secara kompetitif.
3
4i k
kK
]S[K
]I[KK
]S[]E[kr
IMM
t5p
]S[]I[k
kKK
]S[]E[kr
4
3MM
t5p
k1
k2
S + E SE
I + E EI k3
k4
k5
SE P + E
Mechanism:
Competitive Inhibition (cont’)
]S[K
]I[1K
]S[Vr
IM
maxp
t5max ]E[kV
]S['K
]S[Vr
Mmaxp
IMM K
]I[1K'K
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Enzymatic Reaction Inhibition:Uncompetitive Inhibition
Here, the inhibitor does not compete with the substrate for the enzyme; instead, it ties up the enzyme-substrate complex by forming an inhibitor-enzyme-substrate complex, thereby restricting the breakdown of the (E S) complex to produce the desired product.
k1
k2
S + E ES
I + ES EISk3
k4
k5
ES P + E
Mechanism:
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k1
k2
S + E ES
I + ES EISk3
k4
k5
ES P + E
]ES[]I[k
k]EIS[
]EIS[k]ES[]I[k0dt
]EIS[d:PSSH
k]I[kk
]EIS[k]E[]S[k]ES[
]ES[k]EIS[k]I[]ES[k]ES[k]E[]S[k0dt
]ES[d:PSSH
4
3
43
532
41
54321
532
1
532
3
532
31
k]I[kk
]E[]S[k]ES[
k]I[kk
]I[k]ES[
k]I[kk
]ES[]I[k]E[]S[k]ES[
532
1
532
52
532
1
532
3
k]I[kk
]E[]S[k]ES[
k]I[kk
kk
k]I[kk
]E[]S[k]ES[
k]I[kk
]I[k1
Uncompetitive InhibitionMechanism:
]E[]S[kk
k]ES[
52
1
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]S[kk
k]I[
k
k]S[
kk
k1]E[]E[
]E[]S[kk
k]I[
k
k]E[]S[
kk
k]E[]E[
]ES[]I[k
k]E[]S[
kk
k]E[]E[
]EIS[]ES[]E[]E[
52
1
4
3
52
1t
52
1
4
3
52
1t
4
3
52
1t
t
]S[kk
k]I[
kk
]S[kk
k1
]E[]S[
kk
k]ES[
52
1
4
3
52
1
t
52
1
Enzyme balance:
Uncompetitive Inhibition (cont’)k1
k2
S + E ES
I + ES EISk3
k4
k5
ES P + E
Mechanism:
]E[]S[kk
k]ES[
52
1
]S[kk
k]I[
k
k]S[
kkk
1
]E[]E[
52
1
4
3
52
1
t
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k1
k2
S + E ES
I + ES EISk3
k4
k5
ES P + E
Mechanism:
Uncompetitive Inhibition (cont’)
]S[kk
k]I[
kk
]S[kk
k1
]E[]S[
kk
k]ES[
52
1
4
3
52
1
t
52
1
iM
t
iM
t
4
3
1
52
t
1
1
14
3152
t1
K]I[
1]S[K
]S[]E[]ES[
]S[K
]I[]S[K
]E[]S[]ES[
]S[]I[kk
]S[k
kk
]E[]S[]ES[
k
k:
]S[k]I[kk
]S[kkk
]E[]S[k]ES[
3
4i k
kK
1
52M k
kkK
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iM
t5p
5p
K]I[
1]S[K
]S[]E[kr
]E[kr
3
4i k
kK
k1
k2
S + E ES
I + ES EISk3
k4
k5
ES P + E
Mechanism:
1
52M k
kkK
Uncompetitive Inhibition (cont’)
Finally:
t5max ]E[kV
iM
maxp
K]I[
1]S[K
]S[Vr
]S["K
]S["Vr
]S[
K]I[
1
K]S[
K]I[
1
Vr
M
maxp
i
M
i
maxp
i
mm
i
maxmax
K]I[
1
K"K
K]I[
1
V"V
Inhibisi uncompetitive mengakibatkan penurunan harga Vmax dan KM secara bersama-sama
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Non Competitive Inhibition
EI + S EIS
k1
k2
S + E ES
I + E EIk3
k4
k7
k8
ES + I EIS
k9
ES P + E
k5
k6
Mechanism:
In noncompetitive inhibition, the substrate and inhibitor molecules react with different types of sites on the enzyme molecule, and consequently, the deactivating complex, IES, can be formed by two reversible reaction paths: 1. After a substrate molecule
attaches to the enzyme molecule at the substrate site, the inhibitor molecule attaches to the enzyme at the inhibitor site.
2. After an inhibitor molecule attaches to the enzyme molecule at the inhibitor site, the substrate molecule attaches to the enzyme at the substrate site.
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]ES[kr 9p
im
maxp
K]I[
1)KS(
]S[Vr
]E[]S[K]ES[ ]ES[k]E[]S[k S21
Non Competitive Inhibition (cont’)
EI + S EIS
k1
k2
S + E ES
I + E EIk3
k4
k7
k8
ES + I EIS
k9
ES P + E
k5
k6
Mechanism:
Use “rate limiting” concept assuming reaction (5) as rate limiting step:
Other reactions are in equilibrium with equilibrium constant of KS, KI, KS’ and KI’ for reaction (1) to (4), respectively.
Further, assume KS= KS’ and KI = KI’ to obtain:
Ii
SM K
1K;
K
1K
]E[]I[K]EI[ ]EI[k]E[]I[k I43
]S[]E[]I[K'K]EIS[ ]EIS[k]S[]EI[k IS65
]S[]E[]I[K'K]EIS[ ]EIS[k]I[]ES[k SI87
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]I[]S[KK]I[K]S[K1
]E[]E[
]S[]E[]I[KK]E[]I[K]E[]S[K]E[]E[
]EIS[]EI[]ES[]E[]E[
iSiS
t
iSiSt
t
im
maxp
K]I[
1)KS(
]S[Vr
Ii
SM K
1K;
K
1K
Non Competitive Inhibition (cont’)
EI + S EIS
k1
k2
S + E ES
I + E EIk3
k4
k7
k8
ES + I EIS
k9
ES P + E
k5
k6
Mechanism:
Further, assume KS= KS’ and KI = KI’ to obtain:
Enzyme balance:
to obtain:
use
]ES[kr 9p From
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Enzymatic Reaction Inhibition: Comparison & Summary
k1
k2
S + E ES
I + E EI k3
k4
k5ES P + E
a. Competitive Inhibition
b. Uncompetitive Inhibitionk1
k2
S + E ES
I + ES EISk3
k4
k5
ES P + E
c. Non Competitive Inhibitionk1
k2
S + E ES
I + E EIk3
k4
k7
k8
ES + I EIS
k9
ES P + E
k5
k6
EI + S EIS
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No Inhibitionm
maxp K]S[
]S[Vr
Uncompetitive Inhibition
im
Maxp
K]I[
1K]S[
]S[Vr Competitive Inhibition
iM
maxp
K]I[
1]S[K
]S[Vr
Noncompetitive Inhibition
im
maxp
K]I[
1)KS(
]S[Vr
Enzymatic Reaction Inhibition: Comparison & Summary
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Burke – Lineweaver Eadie
(a) ? (b) ? (c) ?
Enzymatic Reaction Inhibition:Comparison in Plot
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P7-14B
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Special Case:Inhibisi oleh Substrat
k1
k2
S + E SE
S + ES SESk3
k4
k5
SE P + E
]S[kkk
]SES[k]E[]S[k]ES[]SES[k]ES[]S[k]SE[k]E[]S[k
dt
]ES[d
352
414321
]ES[]S[k
k]SES[]SES[k]ES[]S[k
dt
]SES[d
4
343
Mechanism:
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]S[kk
k]S[
k
k]S[
kkk
1
]E[]E[
]E[]S[kk
k]S[
k
k]E[]S[
kk
k]E[
]SES[]ES[]E[]E[
]E[]S[kk
k]ES[
]S[kkk
]E[]S[k
]S[kkk
]ES[]S[k]ES[
]S[kkk
]ES[]S[k
kk]E[]S[k
]ES[
52
1
4
3
52
1
t
52
1
4
3
52
1
t
52
1
352
1
352
3
352
4
341
Enzyme balance:
Inhibisi oleh Substrat (cont’)
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2
4
3
1
52
t5P
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]E[]S[kk
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Inhibisi oleh Substrat (cont’)
![Page 31: 104 Chapter 6 Homogeneous Reaction Catalysis: ENZYMATIC REACTION FUNDAMENTAL Dicky Dermawan dickydermawan@gmail.com Development](https://reader030.vdocuments.us/reader030/viewer/2022032415/56649efb5503460f94c0de41/html5/thumbnails/31.jpg)
31
Curve Fittings: Substrate-inhibited Enzymatic Reaction
Perkirakan harga Vmax, KM, dan Ki berdasarkan plot hasil percobaan dari reaksi enzimatik yang diinhibisi substrat di bawah ini.