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

Today’s lectureEnzymes

Michealis-Menten KineticsLineweaver-Burk PlotEnzyme Inhibition

Competitive Uncompetitive

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Last lecture

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Last lecture

EnzymesMichaelis-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.]

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EnzymesIt provides 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

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

UREASECONH2UREASECONHNH 23OH

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EPES OH2

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SESE 1k SESE 2k

EPWSE 3k

The corresponding mechanism is:

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Michaelis-Menten Kinetics WSEkr 3P

SEWkSEkSEk0r 321SE

WkkSk1

EE

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1

t

WkkSEkSE

32

1

SEEE t

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Michaelis-Menten Kinetics

SKSEk

Sk

WkkSEWkWSEkr

m

V

tcat

K

1

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t

k

33P

max

m

cat

SK

SVWSEkrm

max3P

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Vmax=kcat* Et

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 reaction40,000,000 molecules of H2O2 converted to product per second on a single enzyme molecule.13

H2O2 + E →H2O + O + Ekca

t

Summary

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(Michaelis-Menten plot)Vmax

-rs

S1/2

Solving:KM=S1/2 therefore KM is the concentration at which the rate is half the maximum rate

CS

Michaelis-Menten Equation

SKSVrr

M

maxSP

2/1M

2/1maxmax

SKSV

2V

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S1

VK

V1

r1

max

M

maxS

Inverting yields

Lineweaver-Burk Plot

slope = KM/Vmax 1/Vmax

1/S

1/-rS

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Types of Enzyme Inhibition

)inactive( EIIE

Competitive

)inactive( SEIISE Uncompetitive

)inactive( SEIISE

)inactive( SEISEI

Non-competitive

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Competitive Inhibition

2

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k

kk

PESESE

SE3P CkrIEIE

IEIE EPSESESE SESE

1) Mechanisms:


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4

k

k

)inactive(IEI E

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2) Rates:SE3SE2ES1SE CkCkCCk0r

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5I

I

EIEI k

kK KCCC

m

ES

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ES1SE K

CCkkCCkC

m

ES3P K

CCkr

EI5EI4EI CkCCk0r


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I

I

m

S

EtotEEISEEEtot

KC

KC1

CC CCCC

SI

I

max

m

maxS C1

KC1

Vk

V1

r1

I

mISm

SEtot3P

KKCCK

CCkr


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I

ImS

SmaxS

KC1KC

CVr

From before (no competition): Smax

m

maxS C1

VK

V1

r1

Intercept does not change, slope increases as inhibitor concentration increases


max

m

VKslope

max

1InterceptV

Sr1

SC1

No Inhibition

Competitive Increasing CI

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Competitive

SI

I

max

m

maxS C1

KC1

VK

V1

r1

Uncompetitive Inhibition

PSESE 3

2

1k

k

k

SEkrr catSP

Inhibition only has affinity for enzyme-substrate complex

Developing the rate law

SEIkSEIkSEkSEkSEk0r 54cat21SE (1) 0r SEI SEIkSEIk 54 (2)

)inactive(SEISEI5

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k

k

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Adding (1) and (2)

Mcat2

1

cat21

KSE

kkSEkSE

0SEkSEkSEk

M

catcatp

4

5I

MII5

4

KSEkSEkr

kkK

KKSEI

KSEISEI

kkSEI

From (2)

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E t E E S I E S

E 1S

KM

I S KIKM

rp kcatE t S

KM 1S

KM

I S KIKM

Total enzyme

IM

maxPS

KI1SK

SVrr

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

Lineweaver-Burk Plot for uncompetitive inhibition

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€

1−rS

=1

Vmax S( )KM + S( ) 1+

I( )K I

⎛ ⎝ ⎜

⎞ ⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

1−rS

=KMVmax

1S( )

⎛ ⎝ ⎜

⎞ ⎠ ⎟+

1Vmax

1+I( )K I

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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

Noncompetitive Inhibition (Mixed)

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I

I

Smax

m

I

I

maxS

I

ISm

SmaxS

kC1

C1

Vk

kC1

V1

r1

kC1Ck

CVr

End of Lecture 15

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Lecture 15

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Transcript of Lecture 15