Michaelis Menten equation

1. Enzyme
Catalysis
D. JIM LIVINGSTON
FACULTY OF CHEMISTRY
St. JOHN’S COLLEGE

2. ENZYMEKINETICS
 Enzyme kinetics is the study of the chemical reactions that are
catalysed by enzymes.
 In enzyme kinetics, the reaction rate is measured and the effects of
varying the conditions of the reactions are investigated.
 Enzyme kinetics reveals the catalytic mechanism of that enzyme, its
role in metabolism, how its activity is controlled, and how a drug or an
agonist might inhibit the enzyme.

3. MICHAELIS-MENTEN MODELFOR ENZYME KINETICS
• Michaelis–Menten kinetics is one of the simplest and best-
known models of enzyme kinetics.
• This model explain how an enzyme can cause kinetic rate
enhancement of a reaction and why the rate of a reaction
depends on the concentration of enzyme present.
Leonor Michaelis Maud Menten
1913 -Mech. Of
Enzyme catalysis

5. •
• Overall reaction is composed of two elementary reactions
in which the substrate forms a complex with the enzyme
that subsequently decomposes to products and enzymes.
k1 k2
E + S ES P + E
k-1
Here E, S, ES and P symbolize the enzyme, substrate,
enzyme-substrate complex and products

6. • According to this model
• When the substrate concentration becomes high enough
to entirely convert the enzyme to the ES form, the second
step of the reaction becomes rate limiting step.
• The general expression of the (rate) of this
reaction is
2
[ E S ]
d t
v 
d [ P ]
 k

7. Mechanism
•Now: Based on steady state assumption, d[ES]/dt = 0
• d[ES]/dt = k1[E][S] –k-1[ES] – k2[ES] = 0
•
• d[ES]/dt = k1{[E]0-[ES]}[S] –k-1[ES] – k2[ES] = 0
• k1[E]0[S]-K1[ES][S] –k-1[ES] – k2[ES] = 0
• k1[E]0[S]-K1[ES][S] = k-1[ES] + k2[ES]
• k1[E]0[S] = k-1[ES] + k2[ES]+K1[ES][S]
• k1[E]0[S] = {k-1+ k2+K1[S]}[ES]
• [ES] = [E]0[S] k1/(k-1 + k2+K1[S])
[E]0  [E]+[ES]
[E]  [E]0 [ES]
Enzyme conservation equation

8. Michaelis menten eqn.

K1K2 [E]0[S]
K-1+K2+K1[S]
Dividing by K1,
r = K2 [E]0[S]
(K-1+K2)/K1+[S]
r
K2[E ]0[S]
Km [S ]
r
Rate of the product formation r = K2 [ES]
Km 
k1+K2
k1
Km – Michaelis constant

9. Plot of [S] vs rate
If [E]0 = [ES]
Then,
rmax= K2[E]0 = Vmax
Sub in MM eqn,
r = Vmax[S]
Km+[S]
K2[E ]0[S]
Km [S ]
Rate of the product formation r = K2 [ES]

10. If Km = [S]
Plot of [S] vs rate

11. MICHAELIS - MENTEN CONSTANT
• It is the substrate concentration, [S] at which half maximum
velocity of reaction is observed.
• K m implies that half of the active sites on the enzymes arefilled.
• It is the measure of the binding strength between substrate and the
enzyme. (lower K m value indicates a strong affinity betweenthe
substrate and enzymes.
40 M in 2 day
40 M in 12 days

12. Plot of [S] vs rate
Case – I:
If Km >>>> [S]
Linear plot
Case – II
If [S] >>>> Km
Plateau region
First order
Zero order

13. Vmax
It is the maximum velocity of reaction or rate at which
the enzyme catalyzed a reaction under given conditions.
Vmax is reached when all enzyme sites are saturated with the
substrate.
This will happen when substrate concentration [S] is greater than
K m.