Enzyme kinetics is the study of chemical reactions catalyzed by enzymes. The reaction rate is measured under varying conditions to investigate the catalytic mechanism of the enzyme. The Michaelis-Menten model describes enzyme kinetics as a two-step process where the substrate forms a reversible enzyme-substrate complex that then decomposes into products. This model derives the Michaelis-Menten equation which relates reaction rate to substrate concentration and defines kinetic parameters like the Michaelis constant Km and maximum reaction rate Vmax.

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.