Chemical Biology I
TIGP0101-00
Enzyme Kinetics
Mechanisms:
1.
2.
3.
4.
B807 TEL:27898662
Institute of Chemistry
Academia Sinica
Fall, 2003
A
P
Kinetics: steady state/pre steady state
Spectroscopic: structure(or active site) NMR/EPR (fluorescence)
X-ray: structure determination at active site
Binding studies: thermodynamic understanding inhibitors
transition states.
sequence analysis, genomics,
genetic manipulation
DNA
protein sequence
mutants
Enzymes:
A
rate
T.S.
P
overcome
energy barrier: (1). lower barrier
stabilize T.S.
(2). destabilize ground state
or enzymes substrates (A)
A
P
1. rate acceleration: how fast?
2. specificity: how selective?
destabilize ground state
or enzymes substrates (A)
lower barrier
stabilize T.S.
Rate acceleration:
Catalytic Power
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
Et
 moles/min
 moles enz.
min-1
1
106, s-1
usually average’s rate, 6 s-1
EX1: Urease
EX2: Catalase
EX3: Carbonic anhydrase
Specificity:
Enzymes’ active envolved to do some
specific things.
EX1: Hexokinase
phosphorylation:
rel rate
O
HO
O P O
O
OH
O
OH
+ ATP
O
OH
OH
OH + ADP
:
OH
OH
O
HO H
+ ATP
HO P O
OH
OH
OH
OH
+ ADP
OH
O
6
10
C-6 is missing
OH
EX2: Alcohol dehydrogenase:
1
:
103
Enzyme commission
number
1
2
3
4
5
6
Systematic Name
Oxidoreductases(oxidation-reduction
reactions)
Transferases(transfer of functional groups)
Hydrolases(hydrolysis reaction)
Lyases(addition to double bonds)
Isomerases(isomerization reactions)
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
E
K1A
K2
P
zero-order
on [A]
rate 
x
x
K3
EA
P
EP
x
x
+ E
x
x
x
x
x
x
mixed order
first order on [A]
[A]
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 by
its two possible fates: dissociation to regenerate E + A, and
reaction to form E + P.
d[EA] = 0
dt
d[E] = 0
dt
A + B
P +
Q
Nomenclature: by Cleland
substrates A, B, C, D,.....etc
products
P, Q, R, S,......etc
inhibitors
I, J, K,......etc
enzyme complex E, F, G
(stable complex)
E : free enzyme
F : covalent attachement
enzyme complex
enzyme complex EA
(unstable
transitory complex)
enzyme complex
(central complex)
EAB
EPQ
E
K1A
K2
EA
K3
P
EP
+ E
rate 
x
x
x
x
x
Steady state:
Michaelis Menten equation
VmaxA
=
Ka + A
1
Ka + A
reciprocal  =
VmaxA
x
x
x
x
x
first order on [A]
[A]
=
Ka
VmaxA
+
1
Vmax
Derivation of Rate Equations (Biochemistry, 1975, 14, 3320)
1/
slope
k/V
1/V
1/A

1
Ka
E
rate =
dP
dt
K1A
K2
EA
= k3 [EA]
K3
P
EP
+ E
rate =
dP
dt
E
= k3 [EA]
K1A
K2
EA
K3
P
EP
d[EA]
= [E]K1A  K2[EA]  K3[EA]
dt
d[E]
dt
= K3[EA]  K2[EA]  K1A[E]
ET = E  EA
Solve for EA
E = ET  EA
Steady state assumption:
d[EA]
d[E]
=0
dt
dt
K1A(ET  EA)  K2(EA)  K3(EA) = 0
K1AET  K1A(EA)  K2(EA)  K3(EA) = 0
K1AET = EA(K1A  K2  K3)
EA =
because
dP
rate = dt
K1AET
(K1A  K2  K3)
= k3 [EA] = k3
K1AET
(K1A  K2  K3)
=0
+ E
rate =
rate
ET
dP
dt
= k3 [EA] = k3
k3K1A
=
(K1A  K2  K3)
(1) rate as A
K1AET
(K1A  K2  K3)
divide by K1
 = VmaxA
Ka + A
=
, k3 is predominate, k3 = Vmax
(2) rate as A
0, K1A
(initial rate)
k3K1
V
=
(K2  K3)
K
0,
rate
ET
=
k3K1A
(K2  K3)
because K3 = Vmax
K=
(K2  K3)
K1
k3A
A  K2  K3
K1
Steady-state Rate Law for a One-substrate,
One-product Reaction with Two Reversible Steps
E
K1A
EA
K3
EP
K2
K4
binding chemical
K5
A
P + E
dissociation
Replacing every equilibrium rate constant by net rate constant:
Net rate constant:
E1
K1
E2
K 3
K5
E3
E1
steady state
each [E] depend on next net rate constant K magnitude
if K3
large, [E2]
if K3
small, [E2]
Therefore,
E1 
1
K1
,
E1
Et
=
1
K1
1
K1
+
1
K3
+
1
K5
P
•Flux is constant at steady state:
rate =E1(K1) =E2(K3) =E3(K5) at steady state
velocity =
E1(K1)
{because

Et
=
ET
=
E1
Et
n

1
K1
1
K3
+
1
K5
1
K1
=
1
+
1
K1
1
Ki
+
1
K3
+
1
K5
}
i
<Homework> Go back to derive an equation for a onesubstrate,one-product reaction with one reversible steps
Lineweaver-Burk double-reciprocal plot
1

=
Ka + A
VmaxA
=
Ka
VmaxA
+
1
Vmax
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
E EA EAB
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
K9
K1A
K3B
K5
K7
EQ
E
EAB
EPQ
E
EA
K2
K10P
K4
K
K8P
6
Order sequential mechanism:
A
B
P
Q
E
EA
(EAB
EAP)
EQ
E
*It may be impossible for B to bind until after A binds and promotes a
conformational change in the enzyme that exposes the B binding site.
(b). Theorell-Chance mechanism:steady state concentration of
central complexs are low.
A
E
B
EA
P
EA
example: liver alcohol dehydrogenase.
Q
E
E
2. Random: A enzyme catalyzing a random mechanism would
possess two distinct sites, one for each substrate(or
EA
product), so that the reaction of one substrate with
EAB the enzyme may occur before or after the other.
EB
A B
E
P Q
E
EAB
B
EPQ
A
Q
P
(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 reaction
which results in the formation of one product and a new stable
form of the enzyme which in turn reacts with the second
substrates. examples: thioltransferase, phosphoglucomutase
transaminase.
A
E
(EA
P
FP)
B
F
Q
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/
[B]
[A]
1/A
=
V1AB
KiaKb + KaB + KbA + AB
1/B
Kinetics of Enzyme-catalyzed Reactions Involving Two
or more Vary Substrates
A +
B
P + Q
2. Parallel Pattern: An irreversible step intervenes between the times
of combination of the two substrates in the
mechanism.
1/
1/
[A]
[B]
1/A
=
VAB
KaB + KbA + AB
1/B
Kinetics of Enzyme-catalyzed Reactions Involving Two
or more Vary Substrates
A +
B
P + Q
3. Equilibrium Ordered Pattern: Since it corresponds to ordered
addition of A and B, with addition of A
at equilibrium, looks different when [A]
and [B] are varied.
[A]
[B]
1/
1/
1/B
=
1/A
VAB
KiaKb + KbA + AB
•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
B
Slope---rate at low substrate concentration
*Sequential mech.
A
B
E
EA
P
(EAB
intercept change
A
E
EA
EAP)
Q
EQ
E
enzyme different
B
EA
slope will change if change [B]
EAB
Slope and Intercept
*Ping pong mech.
A
E
(EA
intercept
slope
P
FP)
B
F
Q
FB
EQ
change
no slope effect by change [B]
E
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, the
inhibitor and the substrate are mutually exclusive, often because
of true competition for the same site.
1/
[I]
1/A
Slope change only
Vmax is the same
Competitive
inhibition (C):
Active site
of enzyme
Substrate
Inhibitor
Products
Inhibitor prevents
binding of substrate
Substrate and
inhibitor
can 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/
E + A
K1
K2
EA
+
K3
P + E
I
[I]
KI
1/A
Intercept change
Slope is the same
EAI
NO REACTION
Enzyme Inhibition
3. Noncompetitive inhibition (NC):
A classical NC inhibitor has no effect on substrate binding
and vice versa, A and I bind reversibly, randomly and
independently at different sites.
1/
[I]
1/A
Slope change
Intercept change
Noncompetitive
inhibition (NC):
Active site
Binding of
inhibitor
distorts the
enzyme
Inhibitor site
In the absence
of inhibitor,
products are
formed
Substrate and
inhibitor can bind
simultaneously
The presence of
the inhibitor
slows the rate of
product formation
Effects of Inhibitors on Michaelis-Menten Reactions
Type of
Inhibition
None
Competitive
Michaelis-Menten Lineweaver-Burk
Equation
Equation
VmaxA
 =
Km + A
1

VmaxA
 =
Km + A
VmaxA
Uncompetitive  =
Km+ ’A
Noncompetitive  =
 = 1 + [I]/KI
VmaxA
Km+ ’A
1

1

1

=
=
Km
+
VmaxA
 Km
VmaxA
+
Km
=
+
VmaxA
=
Km
VmaxA
’ = 1 + [I]/K'I
+
Effect of
Inhibitor
1
None
Vmax
1
Increase Km
Vmax
’
Vmax
’
Vmax
Decrease Km
and Vmax
Decrease
Vmax; may
increase
or decrease
Km
Intercept Idea:
competitive pattern
1/
if A
1/A
[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 effect
will become NC inhibition
Exceptions:
No inhibition by [I]

Slope effect:
E
K1A
K2
EA
lower EA respect E
raised E respect EA
I reversibly connected to either EA or
show slope effect
actual product inhibitors
example: dead-end inhibitor
E
Catalysis
1. Covalent catalysis: rate acceleration from the formation of
covalent bonds between enzyme and
substrate.
Enz-X: better attacking group and better leaving group
example: ping-pong mechanism
smaller
2. Acid/base catalysis: (a) specific acid-base catalysis
(b) general acid-base catalysis
general acid-base catalysis
H2O
O
H3C
N
N
O
+
H3C
HN
N
O
HO H
N
NH
This reaction accelerated by imidazole.
Usually increasing concentration of
product(imidazole) will decrease the rate.
However, imidazole help to extract H+from
water molecules in T.S.
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)