bio engineering, enzyme catalysis.pdf

8/12/2019 Bio Engineering, Enzyme Catalysis.pdf

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Bioprocess Engineering

ENZYME CATALYSIS


2/40

Definition

Essential macromolecules that have a keyrole in the catalyzing the chemicaltransformations that occur in all livingsystems metabolisms

The nature and specifity of their catalyticactivity is primarily due to the threedimensional structure of the folded proteinwhich is determined by the sequence of theamino acids that make up the enzyme and theactivity may be regulated by one ore moresmall non protein molecules (cofactors)which cause small conformation changes in

the enzyme structure.


3/40

Cofactor type consit of metal ions and organic molecules (co-enzyme)

Apoenzyme : catalytically inactive enzyme

Haloenzyme : active enzyme that tightly bounded cofactors

Haloenzyme

cofactor

Inactive site

Active Site

ENZYME MECHANISM

Apoenzyme


4/40

Enzyme Classification Oxidoreductase, catalyze the transfer of hydrogen or

oxygen atoms or electrons from one substrate to another

(alcohol dehydrogenase, fatty acid desaturase, glucoseoxidase, peroxidase)

Transferase, catalyze the group transfer reactions(aspartase, transaminase, dextransucrase,phosphorylase)

Hydrolases, catalyze the hydrolitic reactions(amylase,lipase, protease, cellulase, isoamylase, urease,papain)

Lyases, catalyze the non hydrolytic removal of groupsfrom substrate (lactase, tannase, aspartase,

tryptophanase) Isomerase, catalyze isomerization reactions (glucose

isomerase)

Ligases, catalyze the synthesis of various type of bondswhere the reaction are coupled with breakdown of

energy containig materials (microbial enzyme,carbamate kinase)


5/40

Enzyme Activity Enzyme are specific in function; the reaction of an

enzyme with certain substrate involves theformation of an intermediate which then reactsfurther with another substrates or decompose toform products.

Activity is given by the amount of product formed

or substrate consumed in the reaction mixtureunder specified conditions ( T, pH, buffer type,substrate)

Enzyme concentration was defined as the amountof enzyme which gives a certain amount of catalyticactivity under specified condition

ionconcentratenzymeactivityactivityspecific

ml

enzymemmoleml

productmmole

min


6/40

Kinetics of Single Substrate ReactionsL. Michaelis and M. L. Menten (1913)

ESSEk

k

1

1

EPESk

2

ESEE 0

ESESkk

kES

kk

kES

ESkkESkES

ES

dtd

dtd

0

21

1

21

1

211

0

;00ES

M

dtd

dtd

KS

SP

k

kk

S

SEkESkP

max

1

21

022

Michaelis - Menten Mechanism

Derivatived Equation of Michalis-Menten Mechanism

S

k

kk

SE

Skk

k

SEkk

k

ES

1

21

0

21

1

021

1

1


7/40

Haloenzyme

Inactive site

Active Site

Apoenzyme

substrate

cofactor

product

MECHANISM SCHEME


8/40

W.P. Jenks and J. Carriuolo, 1961Jenks-Carriuolo Mechanisms

Derivatived Equation of Jenks-Carriuolo Mechanism

ESSEk

k

1

1

EPESk

2

''ESESp

p

k

k

;0', 00 ESES '0 ESESEE

''

'

0',

2

11

ESkkESkES

ESkkESkESkES

ESES

ppdtd

ppdtd

dtd

dtd

0

'

1

2

1

2

ESkkESkk

kkESk

ESkk

kES

p

p

p

p

p

p

0' 12

10

ESkkES

kk

kkSkESESE p

p

p

p


9/40

Haloenzyme

Inactive I site

inactive II Site

Apoenzyme

substrate

cofactor

product

MECHANISM SCHEME

Active Sitesubstrate


10/40

2

1

2

1

2

1

01

2

1

2

1

01

2

1

2

101

1

2

1

2

0

1

1

1

0

kk

kk

kk

kkkk

S

S

kk

kk

EkES

kk

kkkkS

kk

kk

ESkES

ESkk

k

kESkkESkk

k

ESSkESk

ESkkESkk

kkSkES

kk

kESE

p

p

p

p

pp

p

p

p

p

pp

p

p

p

p

pp

p

p

p

p

p

p

p

p

ESkk

kkESkP

dt

d

p

p

2

2

2 '


11/40

2

1

2

1

2

0

2

2

1

1

kkkk

kk

kkkk

S

S

kk

k

E

kk

kkP

dt

d

p

p

p

p

pp

p

pp

p

2

1

2

221102

2

2

2

1

2

2102

2

2

2

1

2

2102

2

2

1

1

1

1

1

1

kk

k

k

kk

kkkkkkkkkk

S

SEk

kk

k

kk

k

Pdt

d

kkkk

kk

kkkkkk

S

SEk

kk

k

kk

k

Pdt

d

kk

kk

kk

kkkkkk

S

SEk

kk

k

kk

k

Pdt

d

p

p

p

pppppp

p

p

p

p

p

p

p

pppp

p

p

p

p

p

p

p

pppp

p

p

p

p


12/40

2

1

1

2

2

1

02

2

2

2

1

2

22102

2

2

1

1

1

kk

kkk

kk

kkk

S

SEk

kk

k

kk

k

Pdt

d

kkkk

kk

kkkkk

S

SEk

kk

k

kk

k

Pdt

d

p

p

p

p

p

p

p

p

p

p

p

pp

p

p

p

p

2

1

1

2

2

1

02

2

2

max

max

1

:

kk

kkk

kk

kkk

KdanEk

kk

k

kk

k

Pdt

d

here

KS

SP

dt

dP

dt

d

p

p

p

p

M

p

p

p

p

M


13/40

Briggs-Haldane (1925)

Briggs-Haldane Mechanism

Derivatived Equation of Briggs-Haldane Mechanism

ESSEk

k

1

1

EPESk

2

""' ESESESq

q

p

p

k

k

k

k

;0",', 00 ESESES "'0 ESESESEE

"'"

''

'

0",',

2

11

ESkkESkES

ESkESkES

ESkkESkESkES

ESESES

qqdtd

ppdtd

ppdtd

dtd

dtd

dtd

k


14/40

"'

0

0

'

'"

0

1

1

1

1

11

11

2

ESESESESk

kES

ES

k

kES

ESkESk

ESkkESk

kkESk

ESk

kES

ESkk

kES

p

p

p

p

p

p

q

q

ESkk

k

k

kES

k

kESES

k

kES

ESkk

k

k

k

ESk

k

kk

k

ES

q

q

p

p

p

p

q

q

p

p

p

p

q

q

2

0

1

1

22"


15/40

S

kk

kkk

kk

kk

kk

k

k

k

k

k

ES

Skk

k

k

k

k

k

k

k

ESES

kk

k

k

k

k

kS

k

k

ESk

k

ES

ESk

k

kk

k

k

k

k

kS

k

kES

q

q

p

p

p

pq

q

p

p

p

p

q

q

p

p

p

p

q

q

p

p

p

p

q

q

p

p

p

p

1

1

2

2

0

2

1

1

0

21

1

0

1

1

0

1

1

21

1

1

11

11

11

11

ESkk

kk

k

kES

k

k

kk

kkESkP

dt

d

q

q

p

p

p

p

q

q

2

2

2

22 "

S

k

k

kk

k

k

k

k

k

ES

kk

k

k

k

k

k

kk

kk

k

k

ESkk

kk

k

kP

dt

d

q

q

p

p

p

p

q

q

p

p

p

p

q

q

p

p

q

q

p

p

1

1

2

0

2

2

2

2

2

1

1

1


16/40

S

kk

k

k

k

k

k

k

k

S

kk

k

k

k

k

k

Ekk

kk

k

k

Pdt

d

q

q

p

p

p

p

q

q

p

p

p

p

q

q

p

p

2

1

1

2

0

2

2

1

1

SK

SPdt

d

Pdt

d

M

max

2

1

1

2

0

2

2

max1

,

1

:

kk

k

k

k

k

k

k

k

Kdan

kk

k

k

k

k

k

Ekk

kk

k

k

Pdt

d

here

q

q

p

p

p

p

M

q

q

p

p

p

p

q

q

p

p

b (k )


17/40

0

max

EkPdt

dcat

Turnover Number (kcat) Catalytic center activity rate constant

The maximum number of substrate molecules that can be converted to productper unit time per active site on the enzyme (S >> KM)

Jenks-Carriuolo

Michaelis-Menten

2kkcat

2

2

2

1

k

kk

k

kk

k

k

p

p

p

p

cat

2

2

2

1

k

kk

k

k

k

k

k

kk

k

k

k

k

q

q

p

p

p

p

q

q

p

p

cat

Briggs-Haldane


18/40

In case of k-p was assumed very small, then:

Jenks-Carriuolo

Michaelis-Menten

2

22

2

2

2

1

1

1

k

k

k

k

k

k

kk

k

k

k

k

k

k

k

k

k

k

k

qp

p

q

q

p

p

p

p

q

p

p

cat

Briggs-Haldane

In case of k-q was assumed very small, then:

If k-p and kq was equal, then:

2

21

1

k

kkcat

pqpq

cat

kkk

k

k

k

k

kk

111

1

1

1

2

2

22

pp

p

p

cat

kk

k

k

kk

k

k

k

k

k11

1

1

1

1

2

22

2

2

2


19/40

Multiple intermediete Mechanism

Turnover Number

pqrz

cat

kkkkk

k111

...11

1

2

EPESESESESSE

kzz

krkqkpk

pk

k

k

21

1..."'


20/40

J. F. Andrews (1968)

Inhibitory Substrate Mechanisms

ESSEk

k

1

1

2

2

2

ESSESk

k

EPESk

3

Derivatived Equation of Inhibitory Substrate Mechanism

;0, 020 ESES 20 ESESEE

2031

1

31

1

2

222311

2

22

2222

222311

2

0

0;0

ESESESkk

kESkk

kES

SESk

kkSESkESkESkESk

SESkkES

ESkSESkES

ESkSESkESkESkESkES

ESES

dtd

dtd

dtd

dtd


21/40

Haloenzyme

Inactive site

Active Site

Apoenzyme

substrate

cofactor

product

MECHANISM SCHEME

Inactive Site


22/40

Skk

Skkk

EES

Sk

k

Sk

kk

EES

Skk

k

k

kS

kk

k

ESkk

k

ES

ESkk

kS

kk

kS

kk

k

k

kES

ESkk

kESSES

k

kS

kk

kES

ESSESk

kES

kk

kES

SESk

kES

2

2

1

31

0

2

2

1

31

0

2

31

1

2

2

31

1

0

31

1

0

31

1

31

12

31

1

2

2

0

31

1

2

2

31

1

2

20

31

1

2

22

11

11

1

1


23/40

2

2,

1

31,03

max

,

,

max

1

31

033

;;

:

1

11

kkK

kkkKEkP

dtd

here

K

S

S

K

Pdt

d

Pdt

d

Sk

k

Sk

kk

EkESkP

dt

d

sIsA

sI

sA

i

i

In case of high value of S above equation become then:

sIK

S

Pdt

d

Pdt

d

,

max

1

In case of low value of S above equation become then:

SK

SPdt

d

SK

Pdt

d

Pdt

d

MsA

max

,

max

1


24/40

Multisite Enzyme Kinetics

QuestionSuppose that an enzyme has two active sites so that substrate is

converted to product via the reaction sequence:

Derive a rate expression for P formation by assumming quasy

steady state for (ES) and for (ESS).

PEES

PESESS

ESSSES

ESSE

k

k

k

k

k

k

4

3

2

2

1

1

)(

)()(

)()(

)(

Problems (G.F. Webb 1986)


25/40

Answer:

quasy steady state for (ES) and for (ESS).

0)(

0)(

ESS

ES

dt

d

dt

d

and then,

0322 ESSkESSkESk

0322 ESSkkESk ESSkkESk 322

ESkk

SkESS

32

2

042211 ESkESSkSESkESkESk 0322411 ESSkkSESkESkkESk

SESk


26/40

032

2322411

kk

SESkkkSESkESkkESk

0411 ESkkESk

41

1kk

ESkES

ESkk

SkESEESSESEEo

32

2

41

1

32

2

32

2 11kk

ESk

kk

SkEES

kk

SkEEo

41

1

32

2

11 kk

Sk

kk

Sk

EEo

41

1

32

211

kk

Sk

kk

Sk

EE

o

ESk


27/40

41

1

32

241

1

11kk

Sk

kk

Sk

E

kk

SkES o

ESkk

SkESS

32

2

41

1

32

241

1

32

2

11kk

Sk

kk

Sk

E

kk

Sk

kk

Sk

ESS o

derivative rate expression for P formation:

ESkESSkPdtd 43

32

234

41

1

32

241

1

11

kk

Skkk

kk

Sk

kk

Sk

E

kk

SkP o

dtd

if:


28/40

if:

4

3

2

32,

1

41, ,,

k

k

k

kkK

k

kkK sIsA

then:

sI

sAsI

o

sA

dtd

K

S

K

S

K

S

Ek

K

SP

,

,,

4

,

1

11

, odtd EkP 4max

sI

sI

sA

dtd

sI

sIsAsA

o

sA

dtd

K

S

K

S

S

K

P

K

S

K

S

K

S

K

S

Ek

K

SP

,

,

,

max

,

,,,

4

,

1

1

1

1

derivative rate expression for P formation:

sI

sA

sI

dtd

dtd

K

S

S

K

K

S

PP

,

,

,

max

1

1

S


29/40

:

sI

sA

sI

dtd

dtd

KS

SK

K

S

PP

,

,

,

max

1

1

in case 1 , then

sI

sA

sI

dtd

dtd

KS

SK

KS

PP

,

,

,

max

1

1

(Webb Equat ion)


30/40

Name Kinetics (dP/dt)Yano

Ierusalimsky

Chen

Substrate uptake kinetics including inhibition

2

,2,1

,

max

1sIsI

sAK

S

K

SSK

SP

dt

d

sI

sA

K

SSK

SP

dt

d

,

,max1

1

2,2,1,max1

SKSK

S

K

SP

dt

d

sAsAsI

Competitive Inhibition


31/40

Competitive Inhibition

Inhibitory Mechanisms

ESSEk

k

1

1

EIIEi

i

k

k

EPESk

2


;0, 00 EIES EIESEE 0

EIESESkk

kES

kk

kES

IE

k

kkIEkESkESkESk

IEk

kEI

EIkIEkEI

EIkIEkESkESkESkES

EIES

i

iii

i

i

iidtd

iidtd

dtd

dtd

0

21

1

21

1

211

211

0

0;0

Ik

k

ESEEESI

k

kEIE

k

kESEE

i

ii

i

i

i

1

,1 00


32/40

Haloenzyme

Inactive site

Active Site

Apoenzyme

substrate

inhibitor

cofactor

product

MECHANISM SCHEME

ESE


33/40

Ikk

S

kk

k

Ik

k

ES

kk

k

ES

I

k

k

ES

kk

k

I

k

k

S

kk

kES

Ikk

ES

kk

k

Ikk

ESS

kk

kES

Ik

kESES

kkkES

Ik

k

ESEE

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

1

1

1

11

1

11

1

1

21

1

0

21

1

0

21

1

21

1

0

21

1

21

1

0

21

1

0

SEk 1

01


34/40

Ik

k

Sk

kk

EkESkP

dt

d

Ik

k

Sk

kk

EES

SI

k

kk

k

k

k

kk

EES

Sk

kkI

k

kSEES

Sk

kkI

k

k

Ik

kkk

k

SE

Ik

kkkk

ES

Sk

kkI

k

k

Ik

kkk

k

SE

Ik

kkk

ES

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

11

1

11

1

11

1

1

1

1

1

1

1

1

1

1

1

21

022

1

21

0

1

21

1

21

0

1

21

0

1

21

21

1

0

21

1

1

21

21

1

0

21

i

i

IS k

k

Kk

kk

KEkPdt

d

here

;;

:

1

21

02max

I

M

K

I

S

K

Pdt

d

Pdt

d

11

max

Graphical Representation of Kinetic Data


35/40

p p f

Lineweaver-Burk PlotLinearization experimental data of 1/(dP/dt) as function of S-1

Eadie-Hofstee PlotLinearization experimental data of (dP/dt) as function of (dP/dt) /SUnexcessive emphasize points at low substrate concentration

The inhibition constant of Ki can be determined from above plot result correlation

I

M

K

I

S

K

Pdt

d

Pdt

d

11

max

SP

dt

d

K

Pdt

dSP

dt

d

K

IK

Pdt

dP

dt

dP

dt

dP

dt

d

K

I

S

Kapp

MI

M

I

M

1111

11;

111

maxmaxmaxmaxmax

S

Pdt

d

K

IKP

dt

dP

dt

dP

dt

d

K

I

S

KP

dt

d

I

M

I

M

1;11

maxmax

IK

KK

K

IKK

I

MM

I

M

app

M

1

Uncompetitive Inhibition


36/40

Inhibitory Mechanisms

ESSEk

k

1

1

ESIIESi

i

k

k

EPESk

2


;0, 00 ESIES ESIESEE 0

ESIESESkk

kES

kk

kES

IES

k

kkIESkESkESkESk

IESk

kESI

ESIkIESkESI

ESIkIESkESkESkESkES

ESIES

i

iii

i

i

iidtd

iidtd

dtd

dtd

0

21

1

21

1

211

211

0

0;0

ESIk

kEEESI

k

kEIES

k

kESEE

i

i

i

i

i

i

1,10

Uncompetitive Inhibition


37/40

Haloenzyme

Inactive site

Active Site

Apoenzyme

substrate

inhibitor

cofactor

product

MECHANISM SCHEME

Inactive site


38/40

SI

kk

kkk

ESkk

k

ES

ESkk

kSI

k

k

kk

kES

ESkk

kESI

k

kS

kk

kES

ESIkkES

kkkES

ESIk

kEE

i

i

i

i

i

i

i

i

i

i

11

11

1

1

1

21

1

0

21

1

0

21

1

21

1

0

21

1

21

1

0

21

1

0


39/40

S

I

k

k

k

kk

Ik

k

SEk

ESkPdt

d

S

Ik

k

k

kk

Ik

kSE

ES

SIk

k

k

kk

SEES

SIk

k

k

kk

SE

ES

SIk

k

kk

k

SEkk

k

ES

i

i

i

i

i

i

i

i

i

i

i

i

i

i

1

1

1

1

1

1

11

1

21

02

2

1

21

0

1

21

0

1

21

0

21

1

0

21

1

Ik

kKS

S

Ik

k

Pdt

d

Pdt

d

i

i

M

i

i

1

1

max

:

1

;

1

:

;;

:

max

max

1

21

02max

then

I

k

k

KK

I

k

k

Pdt

d

Pdt

d

if

k

kk

KEkPdt

d

here

i

i

Mapp

M

i

i

app

S

app

M

app

KS

SPdt

d

P

dt

d

max


40/40

Graphical Representation of Kinetic Data

Lineweaver-Burk PlotLinearization experimental data of 1/(dP/dt) as function of S-1

SP

dt

d

K

Pdt

dPdt

dP

dt

dSP

dt

d

KSapp

appM

appapp

M 111;11

maxmaxmax

appM

app

KS

SPdt

d

P

dt

d

max

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