Lecture 15 Tuesday 3/4/08Enzymes

Michealis-Menten Kinetics

Lineweaver-Burk Plot

Enzyme Inhibition

Last time 2/21/08

Vmax

=kcat

* Et

• Turnover Number: kcat

Number of substrate molecules (moles) converted to product

in a given time (s) on a single enzyme molecule

(molecules/molecule/time)

H2O2 + E H2O + O + E

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

molecule.

Enzymes, InhibitionS + E → E + P

1) Mechanism and active intermediate (E·S)

2) Rates

3) Net Rates

EPOHSE

SESE

SESE

k

k

k

3

2

1

2 3

2

1

SOHSEP

OHSESE

SESE

ESSE

rCCkr

CCkr

Ckr

CCkr

2

2

3

33

22

11

SESESESE rrrr 321

4) Pseudo Steady-State

SOH

SEtotOH

OH

SOH

EtotSOHP

OH

S

EtotEE

OH

ESESEEtot

OH

ESOHP

OH

ES

OHSESEES

Ck

Ckk

CCCk

CkkCk

Ckk

CCCkkr

CkkCk

CCC

Ckk

CCkCCC

Ckk

CCCkkr

Ckk

CCkSE

CCkCkCCk

1

32

3

32

132

31

32

132

1

32

31

32

1

321

2

2

2

2

2

2

2

2

2

2

2

1

1

0

(Michaelis-Menten plot)

Vmax

-rs

S1/2

2/1

2/1maxmaxmax

1

32

max3

2

constant) (michaelis

2

2

Sk

SVVr

Ck

CVr

k

Ckkk

VCkCkk

mS

Sm

SS

OHm

EtotcatOHcat

km=S1/2 therefore km is the concentration at which the rate is half the maximum rate

Competitive Inhibition

E + S E·S E + P

+ I E · I

1) Mechanisms

2) Rates

k1

k2

k3

k4

k5

SEP Ckr

IEIE

IEIEEPSE

SESESESE

3

m

ESESSE

SESEESSE

k

CC

kk

CCkC

CkCkCCkr

32

1

3210

4

5EI

54EI3

0r

k

kk

k

CCC

CkCCkk

CCkr

II

EI

EIEIm

ESP

SI

Im

S

I

ImS

SS

I

mISm

SEtotP

I

I

m

S

EtotEEISEEEtot

Ck

C

V

k

Vr

k

CkC

CVr

k

kCCk

CCkr

k

C

k

CC

CCCCC

11

11

1

1

maxmax

max3

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 competition

Competition

Uncompetitive Inhibition

E + S E·S P

E · S· I

I

k1

k2

k3

k4 k5

ISEISE

ISEISE

PSE

SESE

SESE

k

k

k

k

k

5

4

3

2

1

I

SEISEI

m

SESE

SEISEISEI

SEISEISESESESESEP

k

CCC

k

CCC

CkCCkr

CkCCkCkCkCCkrCkr

0

0

54

543213

I

ISm

SEtotS

mI

SI

m

S

EtotESEISEEEtot

kC

Ck

CCkr

kkCC

kCC

CCCCC

1

1

3