this will give you a brief idea of how the enzyme works, how enzyme kinetics work, Michaelis constant (Km) , Michaelis-Menten’s equation derivation, rate of reaction, Significance of Michaelis-Menten, Constant Km, enzyme efficiently etc

1. enzyme kinetics and
michael menten’s constant
Manisha
Roll no. 201636
Msc biotechnology 2nd year
Department of biotechnology
Central university of Haryana 2021

2. ENZYME
• Enzymes are proteins or rna that act as biological
catalysts.
• Catalysts are substances that increases the rate of a
reaction without itself being consumed.
ENZYME
substrates
ENZYME substrate complex
Free ENZYME
product
increases the rate of
formation of product

3. A + B = P
Rate of reaction
Rate of reaction = rate of disappearance of reactant or rate of formation of products
velocity V
Rate = -ΔAdt or -ΔBdt or ΔPdt
Rate of a reaction ∝ concentration of substrate reactant
Rate of rxn ∝ [A] [B]
Rate of rxn or V = K [A] [B]
K rate constant , can be calculated expermantly for specific
reactions.
T=0
T=t
A large value of the rate constant means that the reaction is relatively
fast, while a small value of the rate constant means that the reaction is
relatively slow.

4. Vmax
When
Enzyme concentration is taken constant.
At low concentrations of substrate ,
V0 increases with an increase in [S]. Linear curve
After a certain concentration of substrate,
Vo stop increasing with substrate
concentration . When all enzymes are
occupies .
Vo = v max .
All enzymes are occupied by substrate .
Under these conditions, the enzyme is
“saturated” with its substrate, so that further
increases in [S] have no effect on rate.
S + E = ES = E +P
Source -Lehninger principal of biochemistry.pdf

5. relatively fast reversible step.
The ES complex then breaks down in a
slower second step to yield the free
enzyme and the reaction product P
Early in the reaction, the concentration of the product, [P], is
negligible, that the reverse reaction, can be ignored.
Assumptions in Michaelis-Menten’s equation derivation
1st Assumption

6. Rate of ES formation = k1 [E] [S]
Rate of ES breakdown = k2 [ES] + k-1 [ES]
[ES] remain constant over time i.e d[ES] = 0 steady-state assumption.
Rate of ES formation = Rate of ES breakdown
k1 [E] [S] = k2 [ES] + k-1 [ES]
k1 [E] [S] = [ES] (k2 + k-1 )
[E] [S]
[ES]
k2 + k-1
k1
=
dt
= km Michaelis constant 1
2nd assumption

7. 3rd assumption
Total enzyme concentration does not
change over time.
[Et] = [E] + [ES].
total enzyme
concentration =
[E] = [Et] - [ES].
Source -Lehninger principal of biochemistry.pdf
free enzyme +substrate bound enzyme
[Et]
[Et] = [E] + [ES].
[Et] = [ES].
2

8. Because the slower second reaction limit the rate of the overall reaction,
the overall rate must be proportional to the concentration of the species that reacts in
the second step, that is, ES.
The ES complex breaks down in a
slower second step to yield the free
enzyme and the reaction product P
V0 ∝ [ES]
V0 = K [ES]
At saturation [Et] = [ES]
vo = vmax
Vmax = k2 [Et]
Vmax
k2
= [Et] 4
3

9. Michaelis-Menten equation derivation
[E] [S]
[ES]
= km
from eq. 1
Substitute value of E from eq. 2 ([Et] - [ES]) [S]
[ES]
= km [E] = [Et] - [ES] ………2
[Et] [S] - [ES] [S]
[ES]
= km
[Et] [S] - [ES] [S]
[ES]
= km
[ES]
[Et] [S] - [S]
[ES]
= km
Rearrangment

10. Michaelis-Menten equation derivation
[Et] [S] - [S]
[ES]
= km
Substitute value of Et from eq 4 Vmax [S] - [S]
[ES]
= km
k2
Vmax
k2
= [Et] ….4
Substitute value of K2[ES] from eq 3
V0 = K [ES] …..3
Vmax [S] - [S]
= km
V0
Rearrangment
Vmax [S]
= V0
km + [S]
Lehninger principal of biochemistry.pdf

11. Vmax [S]
= V0
km + [S]
Michaelis-Menten equation, the rate equation
for a one-substrate enzyme-catalyzed reaction.
The initial reaction velocity Vo of an enzyme
catalyzed reaction is determined by km , vmax
and initial concentration of substrate S.
V0 is the initial velocity of the reaction.
Vmax is the maximal rate of the reaction or rate of rxn when all
enzymes are saturated with substrate .
[S] is the concentration of the substrate.
Km Michaelis constant
Michaelis-Menten equation

12. That concentration of the
substrate when the reaction
velocity is equal to one half of the
maximal velocity for the reaction.
Units - M or mM
Michaelis constant (Km)
k2 + k-1
k1
= km
https://en.wikibooks.org/wiki/Structural_Biochemistry/Enzyme/Michaelis_and_
Menten_Equation

13. Significance of Michaelis-Menten Constant Km
k2 + k-1
k1
= km Rate constant for breakdown of ES
Rate constant for formation of ES
Km =
Low value of Km High affinity of enzyme with substrate
High value of Km Low affinity of enzyme with substrate
Lehninger principal of biochemistry.pdf
Tells affinity of an enzyme for a substrate

14. Significance of Michaelis-Menten Constant
Tells affinity of an enzyme for a substrate
An equation with a low Km value indicates a large binding
affinity, as the reaction will approach Vmax more rapidly .
Vmax will reached at lower substrate concentration .
An equation with a high Km indicates
that the enzyme have low binding
efficiently with the substrate,
Vmax will only be reached at higher
substrate concentration.
Significance of Michaelis-Menten Constant Km
HOW?

15. • Lehninger principal of biochemistry.pdf
• https://en.wikibooks.org/wiki/Structural_Biochemistry/Enzyme/Mich
aelis_and_Menten_Equation
• https://www.researchgate.net/figure/Rectangular-hyperbola-plot-of-
the-Michaelis-Menten-equation-relating-catalytic-rate-
and_fig1_225038972
Refrences