lecture 15 - university of michigan · 2019-08-07 · lecture 15 – tuesday 3/12/2013 enzymatic...

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 3/12/2013

Enzymatic Reactions

Michealis-Menten Kinetics

Lineweaver-Burk Plot

Enzyme Inhibition

Competitive

Uncompetitive

Non-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

i

iAnetA rr

)('1

)( 2

2 AZOk

AZOkrN

Enzymes

5

Michaelis-Menten Kinetics Enzymes 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

Slow S 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 23

OH

222

EPESOH2

SESE 1k

SESE 2k

EPWSE 3k

The corresponding mechanism is:

Enzymes - Michaelis-Menten Kinetics

8

WSEkrP 3

SEWkSEkSEkr SE 3210

Wkk

Sk

EE t

32

11

Wkk

SEkSE

32

1

SEEEt


9

SK

SEk

Sk

Wkk

SEWkWSEkr

M

V

tcat

K

t

k

P

M

cat

max

1

32

33

SK

SVWSEkr

m

P

max3


10

Turnover Number: kcat

Number 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 + E kcat

Vmax

=kcat

Et


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

SK

SVrr

M

maxSP

2/1M

2/1maxmax

SK

SV

2

V


12

S

1

V

K

V

1

r

1

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


15

2

31

k

kk

PESESE

SE3P Ckr

IEIE

IEIE EPSE

SESE SESE

1) Mechanisms:

5

4

k

k

)inactive(IEI E

2) Rate Laws:

SE3SE2ES1SE CkCkCCk0r

4

5I

I

EIEI

k

kK

K

CCC

m

ES

32

ES1SE

K

CC

kk

CCkC

m

ES3P

K

CCkr

EI5EI4EI CkCCk0r

16


17


I

I

m

S

EtotEEISEEEtot

K

C

K

C1

CC CCCC

SI

I

max

m

maxS C

1

K

C1

V

k

V

1

r

1

I

mISm

SEtot3P

K

KCCK

CCkr

I

ImS

SmaxS

K

C1KC

CVr

18

Competitive Inhibition From before (no competition):

S

M

S CV

K

Vr

111

maxmax

Intercept does not change, slope increases as

inhibitor concentration increases

max

slopeV

KM

max

1Intercept

V

Sr

1

SC

1

No Inhibition

Competitive

Increasing CI

Competitive

SI

IM

S CK

C

V

K

Vr

11

11

maxmax

Uncompetitive Inhibition

19


20

PSESE 3

2

1

k

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(SEISEI

5

4

k

k

Adding (1) and (2)

Mcat

cat

K

SE

kk

SEkSE

SEkSEkSEk

2

1

21 0

M

catcatp

I

MII

K

SEkSEkr

k

kK

KK

SEI

K

SEISEI

k

kSEI

4

5

5

4

From (2)

21


MIM

M

tcatp

MIM

t

KK

SI

K

SK

SEkr

KK

SI

K

SE

SEISEEE

1

1

Total enzyme

I

M

PS

K

ISK

SVrr

1

max

22


Slope remains the

same but intercept

changes as inhibitor

concentration is

increased

Lineweaver-Burk Plot for uncompetitive inhibition 23

I

M

S

I

M

S

K

I

VSV

K

r

K

ISK

SVr

1111

111

maxmax

max


Non-competitive Inhibition

24

Non-competitive Inhibition

25

Both slope and intercept

changes

SC

1

Sr

1

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

k

C

CV

k

k

C

Vr

k

CCk

CVr

11

111

1

maxmax

max

26

Summary: Types of Enzyme Inhibition

Lineweaver–Burk plots for three types of enzyme inhibition.

27

End of Lecture 15

lecture 15 - university of michigan · 2019-08-07 · lecture 15 – tuesday 3/12/2013 enzymatic...

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