Lecture 15

Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of

chemical reactions and the design of the reactors in which they take place.

Lecture 15

Lecture 15 – Tuesday 3/12/2013Enzymatic Reactions

Michealis-Menten KineticsLineweaver-Burk PlotEnzyme Inhibition

CompetitiveUncompetitiveNon-Competitive

2

3

Active Intermediates and PSSH

Review Last Lecture

4

Active Intermediates and PSSH

Review Last Lecture

1.In the PSSH, we set the rate of formation of the active intermediates equal to zero. If the active intermediate A* is involved in m different reactions, we set it to:

2. The azomethane (AZO) decomposition mechanism is

By applying the PSSH to AZO*, we show the rate law, which exhibits first-order dependence with respect to AZO at high AZO concentrations and second-order dependence with respect to AZO at low AZO concentrations.

01

*.*

m

iiAnetA rr

)('1)( 2

2 AZOkAZOkrN

Enzymes

5

Michaelis-Menten KineticsEnzymes are protein-like substances with catalytic properties.

Enzyme Unease [From Biochemistry, 3/E by Stryer, copywrited 1988 by Lubert Stryer. Used with

permission of W.H. Freeman and Company.]

Enzymes

6

Enzymes provide a pathway for the substrate to proceed at a faster rate. The substrate, S, reacts to form a product P.

A given enzyme can only catalyze only one reaction. Example, Urea is decomposed by the enzyme urease.

E S

SlowS P

Fast

Enzymes - Urease

7

A given enzyme can only catalyze only one reaction. Urea is decomposed by the enzyme urease, as shown below.

UREASECONH2UREASECONHNH 23OH

222

EPES OH2

SESE 1k SESE 2k

EPWSE 3k

The corresponding mechanism is:

Enzymes - Michaelis-Menten Kinetics

8

WSEkrP 3

SEWkSEkSEkr SE 3210

WkkSk

EE t

32

11

WkkSEkSE

32

1

SEEEt

Enzymes - Michaelis-Menten Kinetics

9

SKSEk

SkWkkSEWkWSEkr

M

V

tcat

K

t

k

P

M

cat

max

1

32

33

SKSVWSEkr

mP

max3

Enzymes - Michaelis-Menten Kinetics

10

Turnover Number: kcatNumber of substrate molecules (moles) converted to product in a given time (s) on a single enzyme molecule (molecules/molecule/time)

For the reaction:

40,000,000 molecules of H2O2 converted to product per second on a single enzyme molecule.

H2O2 + E →H2O + O + Ekcat

Vmax=k

catEt

Enzymes - Michaelis-Menten Kinetics

11

(Michaelis-Menten plot)Solving:

KM=S1/2

therefore KM is the concentration at which the rate is half the maximum rate.

Vmax

-rs

S1/2 CS

Michaelis-Menten Equation

SKSVrr

M

maxSP

2/1M

2/1maxmax

SKSV

2V

Enzymes - Michaelis-Menten Kinetics

12

S1

VK

V1

r1

max

M

maxS

Inverting yields:

Lineweaver-Burk Plot

slope = KM/Vmax

1/Vmax

1/S

1/-rS

Types of Enzyme Inhibition

13

)inactive( EIIE

Competitive

)inactive( SEIISE

Uncompetitive

)inactive( SEIISE

)inactive( SEISEI

Non-competitive

Competitive Inhibition

14

Competitive Inhibition

15

2

31

k

kk

PESESE

SE3P CkrIEIE

IEIE EPSESESE SESE

1) Mechanisms:

5

4

k

k

)inactive(IEI E

2) Rate Laws:

SE3SE2ES1SE CkCkCCk0r

4

5I

I

EIEI k

kK KCCC

m

ES

32

ES1SE K

CCkkCCkC

m

ES3P K

CCkr

EI5EI4EI CkCCk0r

16

Competitive Inhibition

17

Competitive Inhibition

I

I

m

S

EtotEEISEEEtot

KC

KC1

CC CCCC

SI

I

max

m

maxS C1

KC1

Vk

V1

r1

I

mISm

SEtot3P

KKCCK

CCkr

I

ImS

SmaxS

KC1KC

CVr

18

Competitive InhibitionFrom before (no competition):

S

M

S CVK

Vr111

maxmax

Intercept does not change, slope increases as inhibitor concentration increases

max

slopeVKM

max

1InterceptV

Sr1

SC1

No Inhibition

Competitive

Increasing CI

Competitive

SI

IM

S CKC

VK

Vr1111

maxmax

Uncompetitive Inhibition

19

Uncompetitive Inhibition

20

PSESE 3

2

1k

k

k

SEkrr catSP

Inhibition only has affinity for enzyme-substrate complex

Developing the rate law:

SEIkSEIkSEkSEkSEkr catSE 54210 (1)

0r SEI SEIkSEIk 54 (2)

)inactive(SEISEI5

4

k

k

Adding (1) and (2)

Mcat

cat

KSE

kkSEkSE

SEkSEkSEk

2

1

21 0

M

catcatp

I

MII

KSEkSEkr

kkK

KKSEI

KSEISEI

kkSEI

4

5

5

4

From (2)

21

Uncompetitive Inhibition

MIMM

tcatp

MIM

t

KKSI

KSK

SEkr

KKSI

KSE

SEISEEE

1

1

Total enzyme

IM

PS

KISK

SVrr1

max

22

Uncompetitive Inhibition

Slope remains the same but intercept changes as inhibitor concentration is increased

Lineweaver-Burk Plot for uncompetitive inhibition23

I

M

S

IM

S

KI

VSVK

r

KISK

SVr

1111

111

maxmax

max

Uncompetitive Inhibition

Non-competitive Inhibition

24

Non-competitive Inhibition

25

Both slope and intercept changes

SC1

Sr1

Increasing I

No Inhibition

E + S E·S P + E

(inactive)I.E + S I.E.S (inactive)

+I +I-I -I

I

I

S

M

I

I

S

I

ISM

SS

kC

CVk

kC

Vr

kCCk

CVr

11111

1

maxmax

max

26

Summary: Types of Enzyme Inhibition

Lineweaver–Burk plots for three types of enzyme inhibition.

27

End of Lecture 15