Enzyme Kinetics and Catalysis II

3/24/2003

Kinetics of EnzymesEnzymes follow zero order kinetics when substrate

concentrations are high. Zero order means there is no increase in the rate of the reaction when more substrate is added.

Given the following breakdown of sucrose to glucose and fructose

Sucrose + H20 Glucose + Fructose

O

H

HO

H

HO

H

OH

OHHH

OH

OH

HOH

H OH

O

HH

HO

H

H

H

OH

P EES S E 2

1

1-

kk

k

E = Enzyme S = Substrate P = Product

ES = Enzyme-Substrate complex

k1 rate constant for the forward reaction

k-1 = rate constant for the breakdown of the ES to substrate

k2 = rate constant for the formation of the products

When the substrate concentration becomes large enough to force the equilibrium to form completely all ES the second step in the reaction becomes rate limiting because no more ES can be made and the enzyme-substrate complex is at its maximum value.

ESP

2kdt

dv

[ES] is the difference between the rates of ES formation minus the rates of its disappearance.

ESESSEES

211 kkkdt

d

1

Assumption of equilibrium

k-1>>k2 the formation of product is so much slower than the formation of the ES complex. That we can assume:

ES

SE

1

1

k

kK s

Ks is the dissociation constant for the ES complex.

Assumption of steady state

Transient phase where in the course of a reaction the concentration of ES does not change

0

ES

dt

d

2

ES E E T 3

Combining 1 + 2 + 3

ESk k SES-Ek 21-T1

SEk Sk k kES T1121-

S K

SE ES T

M1

21-

k

k k K

M

rearranging

Divide by k1 and solve for [ES] Where

SK

SEES

P T22

0

Mto

kk

dt

dv

vo is the initial velocity when the reaction is just starting out.

And is the maximum velocity T2max Ek V

SK

SVmax

Mov

The Michaelis - Menten equation

The Km is the substrate concentration where vo equals one-half Vmax

The KM widely varies among different enzymes

The KM

can be expressed as:1

2

1

2

1

1 KKk

k

k

k

k

ksM

As Ks decreases, the affinity for the substrate increases. The KM can be a measure for substrate affinity if k2<k-1

There are a wide range of KM, Vmax , and efficiency seen in enzymes

But how do we analyze kinetic data?

The double reciprocal plot

maxmax

M

V

1

S

1

V

K1

ov

Lineweaver-Burk plot: slope = KM/Vmax,

1/vo intercept is equal to 1/Vmax

the extrapolated x intercept is equal to -1/KM

For small errors in at low [S] leads to large errors in 1/vo

Tmax

E

Vcatk

kcat is how many reactions an enzyme can catalyze per second

The turnover number

For Michaelis -Menton kinetics k2= kcat

When [S] << KM very little ES is formed and [E] = [E]T

and SEK

kSE

K

k

M

catT

M

2 ov

Kcat/KM is a measure of catalytic efficiency

What is catalytic perfection?

When k2>>k-1 or the ratio 21

21

kk

kk

is maximum

Then1

MKk

kcat Or when every substrate that hits the enzyme causes a reaction totake place. This is catalytic perfection.

Diffusion-controlled limit- diffusion rate of a substrate is in the range of 108 to 109 M-1s-1. An enzyme lowers the transition state so there is no activation energy and the catalyzed rate is as fast as molecules collide.

Reaction MechanismsA: Sequential Reactions

• All substrates must combine with enzyme before reaction can occur

Bisubstrate reactions

Random Bisubstrate Reactions

Ping-Pong Reactions

• Group transfer reactions

• One or more products released before all substrates added

Kinetic data cannot unambiguously establish a reaction mechanism.

Although a phenomenological description can be obtained the nature of the reaction intermediates remain indeterminate and other independent measurements are needed.

Inhibition kinetics

There are three types of inhibition kinetics competitive, mixed and uncompetitive.•Competitive- Where the inhibitor competes with the substrate.

Competitive Inhibition

SK

SV

M

max

ov

IK

I1

EI

IEK I

HIV protease inhibitors

Competitive Inhibition: Lineweaver-Burke Plot

Uncompetitive Inhibition

Uncompetitive Inhibition: Lineweaver-Burke Plot

Mixed inhibition

Mixed inhibition is when the inhibitor binds to the enzyme at a location distinct from the substrate binding site. The binding of the inhibitor will either alter the KM or Vmax or both.

EI

IEK I

ESI

IESK I

SK

SV

M

max

ov

IK

I1

The effect of pH on kinetic parameters