Enzimas parte 4

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Foued S. Espindola 
PARTE IV
UFO1-Bioquímica
Cinética 
enzimática
Leonor Michaelis (1875-1949) Maud Menten (1879-1960)
Michaelis-Menten equation describes substrate concentration 
and enzymatic reaction rate quantitatively 
E + S ES E + P
k1 k2
k-1 k-2
The following assumptions allow M-M model to explain V vs S kinetics
1. Enzyme and substrate combine to form ES complex
2.Assume reverse rxn, k-2, is negligible
3.Assume [ES] is constant, steady state assumption: d[ES]/dt = 0
4. [E] <<<[S]. Does NOT mean enzyme is saturated with substrate
From these assumptions and simple rate equations derive M-M equation
Berg, pp. 201-203
v = Vmax [S]
Km + [S]
E + S ES E + P
k1 k2
k-1 k-2
Vmax = v at [S] = infinity
Km = [S] at 1/2 Vmax
Enzymes bind substrate transition states
Formation of the enzyme-substrate complex, [ES]
Enzyme kinetics
V
[S]
enzyme catalyzed rxn
non-catalyzed rxn
pp. 197
Saturation
curve,
Saturation
Kinetics
“Active site”
Michaelis – Menten Kinetics
1
E + S [E*S] E + P
k1
k-1
k2
(fast) (slow)
Rate of Reaction: 
By rearrangement we can get
Michaelis – Menton rate equation:
V= kcat [E*S]
V = Vmax [S]
Km + [S]
Here, kcat= k2
-For any reaction that follows M-M kinetics, Km =[S] where Vmax/2
-How do you find Vmax and Km? Use double reciprocal plot
 
E + S ES E + P
k1
k-1
k2
Derivation of the Michaelis-Menten equation
Rate of reaction:
 v  k 2[ES ]
Equation (1)
During the steady-state, [ES] is constant 
i.e. the rate of formation = rate of breakdown
 k 1[E ][S]  k  1[ES ] k 2[ES ]
Therefore:
 
[ES ] 
k 1[E][S]
k  1 k 2
 
[ES ] 
k 1[E][S]
k  1 k 2
 
KM 
k  1k 2
k 1
 
[ES ] 
[E][S]
KM
Equation (2)
If we introduce a constant KM defined as
This equation becomes
The total concentration of enzyme introduced at the start of the reaction is 
still present, it is either bound to substrate or it is not, i.e. 
[E0] = [E] + [ES]
Or rearranged: [E] = [E0] - [ES]
Substituting this into Equation (2) gives us:
 
[ES ] 
([E0] [ES ])[S ]
KM
Opening the bracket on the right-hand side gives:
[ES] = 
[E0][S] - [ES][S] 
KM 
[ES] = 
([E0] - [ES])[S] 
KM 
Therefore:
KM [ES] = [E0][S] - [ES][S] 
KM [ES] + [S][ES] = [E0][S] 
(KM + [S])[ES] = [E0][S] 
Collect [ES]:
Therefore:
[ES] = 
[E0][S] 
[S] + KM 
[ES] = 
[E0][S] 
[S] + KM 
Substituting this back into equation (1):
 v  k 2[ES ]
Gives us:
v = k2 
[E0][S] 
[S] + KM 
The maximum rate for the enzyme (Vmax) will be achieved when all of the 
Enzyme is saturated with substrate, i.e. [ES] = [E0]
Putting this again into equation (1) we get: Vmax = k2 [E0]
Notice that the term k2[E0] features in equation (3), which can now be written 
Equation (3)
v = 
Vmax [S] 
KM + [S] 
Michaelis-Menten
equation
What does the KM actually tell us?
Consider the case when the reaction rate (v) is half of the maximum 
rate (Vmax). Under these conditions the MM equation becomes:
 = 
Vmax [S] 
KM + [S] 
Vmax 
2 
This leaves us with:
2[S] = KM + [S]
Which simplifies to:
[S] = KM
KM is the substrate concentration at which the reaction 
proceeds at half of the maximum rate (Vmax)
v = 
Vmax [S] 
KM + [S] 
= 
KM 1 1 1 
v [S] Vmax 
+ 
Vmax 
. 
Taking the reciprocal of both sides can give
This is in the general form y = m x + c
i.e. a plot of 1/v against 1/[S] will give straight line
This is a Lineweaver-Burk plot
1/V
1/[S]
-1/KM
1/Vmax
KM/Vmax
slope =
Lineweaver-Burk plot
1 Km 1 1
V Vmax [S] Vmax
* +=
Enzimas
Inibidores de Enzima 
Irervesível
Reversível
Inibidores de Enzima Competitivos 
versus Não-Competitivos
Enzimas
Fatores que Afetam a Atividade 
Enzimática: pH, Temperatura, e 
Concentração de Substrato
Factors that influence enzyme activity
1. Substrate concentration
2. Coenzyme concentration
3. Temperature
4. pH
pepsin urease trypsin
%
max 
activity
100
pH
1 2 3 4 5 6 7 8 9 10
Temp
25 30 35 40 45 50 55 60 65
a
c
t
i
v
i
t
y
enzyme rxn
chemical rxn
Interesting biology:
thermophilic organisms
acidophilic organisms
Complexo Multienzimas
Enzimas
Isoladas
Sistema de Ligação de
Membrana
Regulação da atividade enzimática
ALOSTERIA:
HOMOTRÓPICA 
MODULADOR = SUBSTRATO
POSITIVA
NEGATIVA
HETEROTRÓPICA
MODULADOR  SUBSTRATO
POSITIVA
NEGATIVA
ALOSTERIA
Substrato
v
e
lo
c
id
a
d
e
Substrato
Enzima alostéricaEnzima michaeliana
Glucagon
PKA
+
+
P
+
Fosforilase b quinase
(inativa)
Fosforilase b quinase
(ativa)
P
Glicogênio fosforilase 
(inativa)
Glicogênio fosforilase 
(ativa)
Degradação do glicogênio
+
Mecanismo de catálise 
enzimática
Enzima e 
diagnóstico
•ISOENZIMAS
Harper’s Illustrated Biochemistry, Twenty-Sixth Edition
Harper’s Illustrated Biochemistry, 
Twenty-Sixth Edition
Harper’s Illustrated Biochemistry, 
Twenty-Sixth Edition
Harper’s Illustrated Biochemistry, 
Twenty-Sixth Edition
SUMÁRIO
Harper’s Illustrated Biochemistry, Twenty-Sixth Edition
H
a
rp
e
r’s
 Illu
s
tra
te
d
 B
io
c
h
e
m
is
try
, T
w
e
n
ty
-S
ix
th
 E
d
itio
n
Harper’s Illustrated Biochemistry, Twenty-Sixth Edition