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Michaelis-Menten Model
17
* This equation, the reciprocal of the Michaelis-Equation, is also another important equation in enzyme dynamics. It is called the Lineweaver-Burk Equation.
MICHAELIS-MENTEN model
Enzyme Kinetics/Dynamics
By: Nicole Iu, Daniel Taheri, Angela Wang
THE Chemistry Behind the Model
1
2
E + S
ES
E + P
E : Enzyme
S : Substrate (substance upon which the enzyme acts)
P : Product
Background and Information
Fun Mathematical Applications of the M-M Model!!
Michaelis-Menten Kinetics -->
1. Using the M-M equation, find the substrate (Acetylcholine) concentration, [S], when the reaction catalysed by acetylcholinesterase reaches 90% of its V .
2. Find the reciprocal of the Michaelis-Menten equation.
- model was created by two scientists in the 20th century
- Leonor Michaelis & Maud Leonora Menten
max
M
Given: K of carbonic anhydrase = 9.5 x 10
-5
Michaelis-Menten Model
V [S]
max
v =
o
K + [S]
M
Purpose
V [S]
max
v =
>> to help explain enzyme dynamics
K + [S]
M
- the study of chemical reactions catalyzed by enzymes
V
- 'catalyzing' >> to speed up the reaction
max
the theoretical maximum velocity
Velocity vs. [Substrate] Graph
y = mx + b
the Michaelis constant; defined as the substrate concentration [S], when V= 50 % of the Vmax
1
K
1
M
=
1
(
v
)
+
o
V
[S]
max
V
max
V
max
Rate (V)
[S]
[S] = 8.55 x 10
-5
-5
[S] = 0.9(9.5 x 10 ) x 10
The substrate concentration is
8.55 x 10 mol/L
-5
1
K
M
=
[S]
+
v
o
V [S]
max
V [S]
max
V [S]
max
v =
o
K + [S]
M
v
= 0.9 V
o
max
[S]
0.9 =
K + [S]
M
0.9 (K + [S]) = [S]
M
0.9K + 0.9[S] = [S]
M
Rate = k [E][S]
1
V
max
Rate (V)
1/2 V
max
Km
[S]
1
K + [S]
M
=
v
o
V [S]
max
V [S]
max
0.9V =
max
K + [S]
M
K
M
0.9K = 0.1[S]
M
Rate = k [ES]
2