1

Chapter 6Homogeneous Reaction Catalysis:

ENZYMATIC REACTION FUNDAMENTAL

Dicky Dermawanwww.dickydermawan.net78.net

dickydermawan@gmail.com

Development of Kinetic Expression in Enzymatic Reactions

ITK-329 Kinetika & Katalisis

2

# 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

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

4

[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

5

]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

6

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

7

(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

8

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?

9

P7-10C Integration of Rate Equation

10

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.

11

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.

12

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:

13

]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

14

]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]:

15

…… 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

16

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:

17

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

18

]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

19

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

20

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

21

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.

22

]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

23

]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

24

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

25

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

26

Burke – Lineweaver Eadie

(a) ? (b) ? (c) ?

Enzymatic Reaction Inhibition:Comparison in Plot

27

P7-14B

28

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:

29

]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’)

30

2

4

3

1

52

t5P

14

3152

t15

52

1

4

3

52

1

t

52

15

5p

]S[k

k]S[

k

kk]S[]E[k

r

]S[k]S[k

k]S[k)kk(

]E[]S[kk

]S[kk

k]S[

k

k]S[

kkk

1

]E[]S[

kk

kk

]ES[kr

im

maxs

K]S[

1]S[K

]S[Vr

Inhibisi oleh Substrat (cont’)

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.