Brief understanding of enzymes and enzyme inhibitors, the main classes of enzyme inhibitors , the types of reversible inhibitors and proofs of their Michaelis-Menten equations.

1. ENZYME INHIBITORS
Presented
By
ARREYETTA BAWAK AUGUSTINE BESONG
M.Sc. Biochemistry and Molecular Biology
UNIVERSITY OF BUEA REPUBLIC OF CAMEROON
PEACE – WORK – FATHERLAND

2. OUTLINE
• Introduction
• Classes of enzyme inhibitors
• Types of reversible inhibitors
 Competitive Inhibitors
 Uncompetitive Inhibitors
 Mixed Inhibitors
Note: To best understand
these proves, use a pen
and paper to write out and
follow the various steps

3. Introduction
• Enzymes basically, are biological molecules which speed up
the rate of biological reactions in the body and are not affected
by those reactions.
• An enzyme’s activity in the body could be hindered or inhibited
by molecules called inhibitors.
• Enzyme inhibitors are molecular agents that interfere with
catalysis by slowing or halting enzymatic reactions.

4. Introduction
• Enzyme inhibitors are among the most important pharmaceutical agents
known. For example, aspirin (acetylsalicylate) inhibits the enzyme that
catalysis the first step in the synthesis of prostaglandins, compounds
involved in many processes, including some that produce pain.

5. Classes of enzyme inhibitors
• Two main classes of enzyme inhibitors do exist
- Reversible enzyme inhibitors
- Irreversible enzyme inhibitors
Just as the name, reversible inhibitors are those that can bind the enzyme
and halt its catalytic activities and after a while, they detach from the
enzyme while irreversible inhibitors bind permanently to the enzymes and
inactivates it.

6. Types of Reversible Inhibitors
• There are three types of reversible inhibitors
- Competitive Inhibitors
- Uncompetitive Inhibitors
- Mixed Inhibitors

7. Competitive Inhibitors 1
• These are inhibitors that compete with the substrates for the active site of
an enzyme.
• While the inhibitor (I) occupies the active site of the enzyme, the substrate
will be prevented from fitting at the active site hence, no reaction occurs.
Note: The inhibitors at
this point, resemble
the substrate and binds
to the enzyme to form
an EI complex but does
not lead to a catalytic
reaction.

8. Competitive Inhibitors 2
• In the presence of an inhibitor, the Michaelis-Menten equation becomes
• In order to prove this equation, several considerations need to be done:
- The reaction equation when an inhibitor is present and when not present
When inhibitor is absent
When inhibitor is present
where
E + I EI

9. Competitive Inhibitors 3
- The dissociation constants of both reactions in the reverse direction
When inhibitor is absent
When inhibitor is present
Km = [E][S] Eq….. 1
[ES]
KI = [E][I] Eq…… 2
[EI]

10. Competitive Inhibitors 4
- The total enzyme concentration in the reaction
When inhibitor is absent
The total enzyme concentration will be equal to the number of free or
unbound enzyme minus the amount of enzyme-substrate or bound enzyme.
When inhibitor is present
When the inhibitor is present, it means that, the solution contains the free
enzyme, enzyme complexed to substrate and enzyme complexed to
inhibitor.
[Et] = [E] + [ES] Eq……3
[Et] = [E] + [ES] + [EI] Eq……4

11. Competitive Inhibitors 5
The rate expression is
With these on mind, making the enzyme complexes [ES] and [EI]
the subject of the equation from their dissociation equation, it will
give
Note: Normally, in the
presence of the inhibitor,
[ES] complex is said not to
be formed but that does
not mean that, in the
presence of the inhibitor, a
small amount of the [ES]
complex is not formed.
This mostly occurs when
the concentration of
inhibitor in the system is
smaller than that of the
substrate. At this point, the
[ES] complex is formed
(since an increase in
substrate concentration
kicks the inhibitor out of
the active site) and a small
amount of [EI] is present in
the body still.
Rate of the reaction (V) = K[ES] Eq……5
[ES]=[E][S]
Km
and [EI]=[E][I]
KI

12. Competitive Inhibitors 6
• Substituting these complexes in equation 4, will give
• Making [E] the subject,
• Substituting [E] in either equation 1 or 2 and making [ES] the subject of the
resultant reaction the substituting in equation 5
[Et] = [E] + [E][S] + [E][I]
Km KI
[E] = [Et]
(1 + [I]/KI + [S]/Km)
V = K[Et][S]
(Km + [Km][I]/KI + [S])

13. Competitive Inhibitors 7
• Making Km the subject in the denominator
• But α = (1 + [I]/KI ) and Vmax = K [Et]
This implies,
V = K[Et][S]
(Km (1 + [I]/KI) + [S])
V= Vmax[S]
αKm + [S]

14. Uncompetitive Inhibitors 1
• These are inhibitors that bind to a site distinct from the active site and
unlike the competitive inhibitors, they bind only to the ES complex.

15. Uncompetitive Inhibitors 2
• In the presence of an uncompetitive inhibitor, the Michaelis-Menten
equation becomes
• Remember that this uncompetitive inhibitor only bind to ES complex.
Therefore, the total enzyme concentration expression will be
Note: Proving this equation
will require that, the previous
ideas be applied.
[Et] = [E] + [ES] + [ESI]

16. Uncompetitive Inhibitors 3
• The rate equations and dissociation constants will be
• Making enzyme complexes the subject of the dissociation expression and
substituting it in the total enzyme concentration expression, will give
ES + I ESI
Km = [E][S]
[ES]
KI = [ES][I]
[ESI]
[Et] = [E] + [E][S] + [ES][I]
Km KI
Note that this is still a
complex. So, needs to be
expressed

17. Uncompetitive Inhibitors 4
• [ES] could be deduced from them Km constant expression and then
substituted in the expression above to give
• Making [E] the subject of the equation
[Et] = [E] + [E][S] + [E][S][I]
Km Km KI
[E] = [Et]
(1 + [S]/Km + [S][I]/Km KI)

18. Uncompetitive Inhibitors 5
• Substituting [E] in the Km or KI constant expression and making [ES] the
subject will be
• When bracket is opened
[ES] = [Et][S]
Km (1 + [S]/Km + [S][I]/Km KI)
[ES] = [Et][S]
Km + [S] + [S][I]/ KI)

19. Uncompetitive Inhibitors 6
• Factorizing [S] in the denominator
• But hence
[ES] = [Et][S]
Km + [S] (1+ [I]/ KI)
[ES] = [Et][S]
Km + α’[S]

20. Uncompetitive Inhibitors 7
• Substituting it in the rate law expression will give
• Which will be
V = K [Et][S]
Km + α’[S]
V = Vmax[S]
Km + α’[S]

21. Mixed Competitive Inhibitors 1
• A mixed inhibitor also binds at a site distinct from the substrate active
site, but it binds to either E or ES.

22. Mixed Competitive Inhibitors 2
• The rate equation describing mixed inhibition is
• The total enzyme concentration expression will be
• Making the enzyme complexes [ES], [ESI] and [EI] the subject of the
dissociation expression and substituting it in the total enzyme
concentration expression, will give
[Et] = [E] + [ES] + [ESI] + [EI]
Note: ES + I ESI or
EI + S ESI have
same dissociation constant
because they form the
same ESI complex.
[Et] = [E] + [E][S] + [ES][I] + [E][I]
Km KI KI

23. Mixed Competitive Inhibitors 3
• [ES] could be deduced from them Km constant expression and then
substituted in the expression above to give
• Making [E] the subject of the equation
[Et] = [E] + [E][S] + [E][S][I] + [E][I]
Km Km KI KI
[E] = [Et]
(1 + [S]/Km + [S][I]/Km K’I + [I]/ KI)
Note: This substitution could
be done using any of the
dissociation constant reactions
but using that of the normal [E]
[S] reaction will make it less
cumbersome to solve

24. Mixed Competitive Inhibitors 4
• Opening brackets and bringing like terms together will give
• Factorizing common constants
[ES] = [Et][S]
Km + [I] Km/KI + [S] + [S][I]/K’I
[ES] = [Et][S]
Km (1 + [I]/Km) + [S] (1+ [I]/K’I)

25. Mixed Competitive Inhibitors 5
• But and
• Implies
• Substitution in V = k [ES]
α = (1 + [I]/KI)
[ES] = [Et][S]
α Km + α’[S]
V = K[Et][S]
α Km + α’[S]

26. Mixed Competitive Inhibitors 6
• Vmax = K[Et]
V = Vmax[S]
α Km + α’[S]

27. Reference
• Lehninger's Principles of Biochemistry 4th Edition - D L Nelson, Cox
Lehninger - W H Freeman 2004.