Chemical Biology ITIGP0101-00

Enzyme Kinetics B807 TEL:27898662 Institute of Chemistry

Academia Sinica Fall, 2003

Mechanisms: A P1. Kinetics: steady state/pre steady state2. Spectroscopic: structure(or active site) NMR/EPR (fluorescence)3. X-ray: structure determination at active site4. Binding studies: thermodynamic understanding inhibitors transition states. sequence analysis, genomics, genetic manipulation DNA protein sequence mutants

Enzymes: A rate P

T.S.

A

P

overcomeenergy barrier: (1). lower barrier stabilize T.S. (2). destabilize ground state or enzymes substrates (A)

1. rate acceleration: how fast?2. specificity: how selective?

destabilize ground state

or enzymes substrates (A)

lower barrier stabilize T.S.

Rate acceleration: non-enzyme very slow How fast of reaction rate enzyme will facilitate?

*turnover number: the number of substrate molecules converted into product per enzyme molecule per unit time when the enzyme is saturated with substrate.

Vmax moles/min Et moles enz. min-1

1 106, s-1

usually average’s rate, 6 s-1

EX1: UreaseEX2: CatalaseEX3: Carbonic anhydrase

Catalytic Power

Specificity: Enzymes’ active envolved to do some specific things.EX1: Hexokinase phosphorylation:

O

OH

OH

OH

HO

OH + ATPO

OH

OH

OH

O

OH

P

O

O

O

+ ADP 106

rel rate

HO H + ATP OP

OH

HO

O+ ADP 1

:

O

OH

OH

OH

OH C-6 is missing 103

:

EX2: Alcohol dehydrogenase:

Enzyme commission Systematic Namenumber

1 Oxidoreductases(oxidation-reduction reactions)2 Transferases(transfer of functional groups)3 Hydrolases(hydrolysis reaction)4 Lyases(addition to double bonds)5 Isomerases(isomerization reactions)6 Ligases(formation of bonds with ATP cleavage)

Example: EC 1.1.1.1 alcohol dehydrogenase EC 2.1.1.1 nicotinamide N-methyltransferase EC 3.3.1.21 -glucosidase EC 4.1.1.1 pyruvate decarboxylase EC 5.3.1.1 triose-phosphate isomerase EC 6.5.1.3 RNA ligase

Steady state: A P

x

x

x

x

x

x x x x xrate

[A]

first order on [A]

mixed order

zero-orderon [A]

E EA P + E

K1A

K2

K3

EP

Steady-state assumption: 1925, G. E. Briggs and James B. S. Haldance assuming the concentration of the enzyme-substrate complex(EA) quickly reaches a constant value in such a dynamic system.

That is, EA is formed as rapidly from E + A as it disappears byits two possible fates: dissociation to regenerate E + A, and reaction to form E + P.

d[EA] dt = 0 d[E]

dt = 0

A + B P + Q

Nomenclature: by Clelandsubstrates A, B, C, D,.....etcproducts P, Q, R, S,......etcinhibitors I, J, K,......etcenzyme complex E, F, G(stable complex) enzyme complex EA(unstable transitory complex)

enzyme complex EAB EPQ(central complex)

E : free enzymeF : covalent attachementenzyme complex

x

x

x

x

x

x x x x xrate

[A]

first order on [A]

E EA P + E

K1A

K2

K3

EP

Steady state: Michaelis Menten equation =

VmaxAKa + A

reciprocal 1 =

VmaxAKa + A

= +Ka

VmaxA Vmax

1

Derivation of Rate Equations (Biochemistry, 1975, 14, 3320)

1Ka

1/

1/A

1/V

slopek/V

E EA P + E

K1A

K2

K3

EP

rate = dP dt = k3 [EA]

rate = dP dt = k3 [EA]

d[EA] dt = [E]K1A K2[EA] K3[EA]

d[E] dt = K3[EA] K2[EA] K1A[E]

ET = E EA Steady state assumption:

d[EA] dt = 0 d[E]

dt = 0Solve for EA

E = ET EA K1A(ET EA) K2(EA) K3(EA) = 0 K1AET K1A(EA) K2(EA) K3(EA) = 0K1AET = EA(K1A K2 K3)

EA = (K1A K2 K3)

K1AET

because

rate = dP dt = k3 [EA] = k3

(K1A K2 K3)

K1AET

E EA P + E

K1A

K2

K3

EP

rate = dP dt = k3 [EA] = k3

(K1A K2 K3)

K1AET

rate

ET

= (K1A K2 K3)

k3K1A divide by K1

= VmaxAKa + A

= k3A

A K1

K2 K3

(1) rate as A , k3 is predominate, k3 = Vmax

(2) rate as A 0, K1A 0 ,

rate

ET

= (K2 K3)

k3K1A

(K2 K3)

k3K1 = V

Kbecause K3 = Vmax

K = K1

(K2 K3)

(initial rate)

A P

E EA P + E

K1A

K2

K3EP

K4

K5

Steady-state Rate Law for a One-substrate,One-product Reaction with Two Reversible Steps

binding chemical dissociation

Replacing every equilibrium rate constant by net rate constant:Net rate constant:

E1 E2 E3 E1

K1 K3

K5

steady state

each [E] depend on next net rate constant K magnitudeif K3

large, [E2]

if K3 small, [E2]

Therefore, E1 K1

1,

E1

Et

=K1

1

K1

1

K3

1

K5

1+ +

•Flux is constant at steady state:

rate =E1(K1) =E2(K3

) =E3(K5) at steady state

velocity = E1(K1) =

ET

{because }E1

Et

=K1

1

K1

1

K3

1

K5

1+ +

K1

1

K3

1

K5

1+ +

Et

= 1

n

i Ki

1

<Homework> Go back to derive an equation for a one-substrate,one-product reaction with one reversible steps

1 =

VmaxAKa + A

= +Ka

VmaxA Vmax

1

Lineweaver-Burk double-reciprocal plot

Kinetic Mechanisms

forward V1 ; reverse V2

Michaelis complexes Ka, Kb

inhibition constants(thermodynamic)Kia, Kib

(A). Sequential mechanism: All substrates bind before chemical events. 1. Order: Enzyme binds in different order with substrates. If the mechanism is ordered, the substrates will add to the enzyme as A first, B second, etc., and the first product to dissociate from the enzyme will be P, followed by Q etc. (a). Order sequential mechanism: NAD+-dependent dehydrogenases

E EA

K1A

K2

K3B

K4

EABK5

K6

EPQK7

K8P

EQ EK10

P

K9

E EA EAB

Order sequential mechanism:

A B P Q

E EA (EAB EAP) EQ E

(b). Theorell-Chance mechanism:steady state concentration of central complexs are low.

A B P Q

E EA EA E

*It may be impossible for B to bind until after A binds and promotes aconformational change in the enzyme that exposes the B binding site.

example: liver alcohol dehydrogenase.

2. Random:A enzyme catalyzing a random mechanism would possess two distinct sites, one for each substrate(orproduct), so that the reaction of one substrate with the enzyme may occur before or after the other.

E

EA

EBEAB

A B P Q

B A Q P

E EEAB

EPQ

(a). Ordinary random mechanism: if slowest step is one other than the interconversion of the central complex, EAB EPQ. (no enzyme is known to have this mech.)(b). Random-rapid equilibrium mechanism: If the slowest is central complex. example:yeast hexokinase, creatine kinase.

(B). Ping Pong mechanism: Chemistry occurs prior to binding of all substrates

The addition of one substrate to the enzyme causes a reactionwhich results in the formation of one product and a new stableform of the enzyme which in turn reacts with the second substrates. examples: thioltransferase, phosphoglucomutasetransaminase.

A P B Q

E (EA FP) F FB EQ E

a new stable form of the enzyme

Kinetics of Enzyme-catalyzed Reactions Involving Two or more Vary Substrates

A + B P + Q

1. Intersecting Pattern:indicates sequential combination of both substrates prior to release of a product.

1/

1/A

[B]

= V1AB

KiaKb + KaB + KbA + AB

1/

1/B

[A]

Kinetics of Enzyme-catalyzed Reactions Involving Two or more Vary Substrates

A + B P + Q

2. Parallel Pattern: An irreversible step intervenes between the timesof combination of the two substrates in the mechanism.

1/

1/A

[B]1/

1/B

[A]

= VAB

KaB + KbA + AB

Kinetics of Enzyme-catalyzed Reactions Involving Two or more Vary Substrates

A + B P + Q

3. Equilibrium Ordered Pattern:

= VAB

KiaKb + KbA + AB

Since it corresponds to ordered addition of A and B, with addition of A at equilibrium, looks different when [A]and [B] are varied.

1/

1/B

[A]1/

1/A

[B]

•This pattern is most commonly seen with metal activators which are not consumed during the reaction, but must be present to permit substrate binding.

Slope and Intercept

intercept---velocity at sat. substrate , observe intercept. A BSlope---rate at low substrate concentration

A B P Q

E EA (EAB EAP) EQ E

*Sequential mech.

intercept change enzyme different

A EA B EABE EA

slope will change if change [B]

A P B Q

E (EA FP) F FB EQ E

Slope and Intercept

*Ping pong mech.

intercept changeslope no slope effect by change [B]

Enzyme Inhibition

product, dead-end substrate inhibited enzyme

1. Competitive inhibition (C): A competitive inhibitor is a substance that combines with free enzyme in a manner that prevents substrate binding. That’s, theinhibitor and the substrate are mutually exclusive, often becauseof true competition for the same site.

1/

1/A

[I]

Slope change onlyVmax is the same

Competitive inhibition (C):

Active siteof enzyme

Substrate

Inhibitor

Products

Inhibitor preventsbinding of substrate

Substrate and inhibitorcan bind to the active site

Enzyme Inhibition

2. Uncompetitive inhibition (UC):A classical UC inhibitor is a compound that binds reversibly to the enzyme-substrate complex yielding an inactive ESI complex. The I does not bind to free enzyme.

1/

1/A

[I]

E + A EA P + E

+

I

EAI NO REACTION

KI

K1

K2

K3

Intercept changeSlope is the same

Enzyme Inhibition3. Noncompetitive inhibition (NC):

A classical NC inhibitor has no effect on substrate bindingand vice versa, A and I bind reversibly, randomly and independently at different sites.

1/

1/A

[I]

Slope changeIntercept change

Noncompetitive inhibition (NC):

Active site

Inhibitor site

Binding ofinhibitordistorts theenzyme

In the absenceof inhibitor,products areformed

Substrate andinhibitor can bindsimultaneously

The presence ofthe inhibitorslows the rate ofproduct formation

Effects of Inhibitors on Michaelis-Menten Reactions

Type ofInhibition

Michaelis-Menten Equation

Lineweaver-Burk Equation

Effect of Inhibitor

NoneVmaxA

Km + A =

1

= + Km

VmaxA Vmax

1

None

CompetitiveVmaxA

Km + A =

1

= +Km

VmaxA Vmax

1

Increase Km

UncompetitiveVmaxA

Km+ ’A =

1= +

Km

VmaxA Vmax

’ Decrease Km and Vmax

NoncompetitiveVmaxA

Km+ ’A =

1= +

Km

VmaxA Vmax

’Decrease Vmax; may increase or decrease Km

= 1 + [I]/KI ’ = 1 + [I]/K'I

1/

1/A

[I]

Intercept Idea:competitive pattern

if A No inhibition by [I]

1/A 0

I and A competiting for the same site(for the same enzyme)No intercept

I and A bind to different enzyme intercept effectwill become NC inhibition

Exceptions:

Slope effect:

EAK1A

K2

raised

E

E EA respect

lower EEA respect

I reversibly connected to either or EA E

show slope effectactual product inhibitors

example: dead-end inhibitor

Catalysis

1. Covalent catalysis:rate acceleration from the formation ofcovalent bonds between enzyme and substrate.

Enz-X: better attacking group and better leaving groupexample: ping-pong mechanism

smaller

2. Acid/base catalysis:(a) specific acid-base catalysis(b) general acid-base catalysis

N N

O

H3CHN NO

H3C

H2O

HO H

N NH

O

+

This reaction accelerated by imidazole.Usually increasing concentration ofproduct(imidazole) will decrease the rate.However, imidazole help to extract H+fromwater molecules in T.S.

general acid-base catalysis

3. Entropy: entropy loss in the formation of EA

The rotational and translational entropies of the substrate have been lost already during formation of EA complex

example: Strain/distortion

Transition state:Enzyme stablize T.S. to accelerate the reaction rate.Enzyme should bind tighter in T.S. than in substrate and product states.

example: Proline racemase and Isocitrate lyase (Prof. Robert Abeles)