Enzyme kinetics can provide information about enzyme activity under different conditions. The Michaelis-Menten approach models enzyme-catalyzed reactions and describes reaction rates with the Michaelis-Menten constant (Km) and maximum reaction rate (Vmax). Enzymes can be inhibited reversibly or irreversibly by inhibitors that reduce reaction rates. Different types of reversible inhibition include competitive, uncompetitive, and mixed inhibition. Temperature, pH, and allosteric effectors can regulate enzymatic activity through various mechanisms.

1. Enzyme Kinetics
Presented By:
Prasodhan Niraula

2. Enzyme kinetics (reaction rates)?
• measurement of velocity = reaction rate
• compare enzymes under different conditions, or
from differenttissues or organisms
• compare activity of same enzyme with different
substrates (understand
specificity)
• measure enzyme purity (specific activity = amount
of activity/amount of
protein)
• study/distinguish different types of inhibitors
 development of specific drugs (enzyme inhibitors)

3. At this point, an assumption is required to
achieve an analytical solution.
- The rapid equilibrium assumption
Michaelis - Menten Approach.
- The quasi-steady-state assumption.
Briggs and Haldane Approach.
Enzyme Kinetics

4. Michaelis - Menten Approach
The rapid equilibrium assumption:
- Assumes a rapid equilibrium between the enzyme
and substrate to form an [ES] complex.
EP
k
ES 2E+S
K-1
K1
][1]][[1 ESkSEk

5. Michaelis - Menten Approach
The equilibrium constant can be expressed by the
following equation in a dilute system.
][
]][[
1
1'
ES
SE
k
k
mK
'
mK
EP
k
ES 2E+S
K-1
K1

6. Michaelis - Menten Approach
Then rearrange the above equation,
Substituting [E] in the above equation with enzyme
mass conservation equation
yields,
'
]][[
][
mK
SE
ES
][]0[][ ESEE
'
]])[[]0([
][
mK
SESE
ES

7. Michaelis - Menten Approach
[ES] can be expressed in terms of [S],
]['
]][0[
][
SmK
SE
ES
Then the rate of production formation v can be
expressed in terms of [S],
]['
][
]['
]][0[
][
][ 2
2
SmK
SmV
SmK
SEk
ESk
dt
Pd
v
Where ]0[2
EkmV
represents the maximum forward rate of reaction (e.g.moles/L-min).

8. Michaelis - Menten Approach
]['
][
2
1
SmK
SmV
mVv
- The prime reminds us that it was derived by assuming rapid
equilibrium in the step of enzyme-substrate complex formation.
- Low value indicates affinity of enzyme to the substrate.
- It corresponds to the substrate concentration, giving the
reaction velocity.
Re-arrange the above equation,
1
1'
k
k
mK
][' SmK When mVv
2
1
'
mK is often called the Michaelis-Menten constant, mol/L, mg/L.

9. Simple Enzyme-Catalyzed Reaction
Measurement of velocity:
– V = rate of appearance of product = change in [P] per unit time
Plot of [P] vs. time

10. Enzyme-substrate cycle

11. Rate enhancements
Enzymatic rate enhancements are 103 to 1017 x

12. • Simple uncatalyzed S 􀋠 P reaction shows linear dependence
of Vo on [S]:
• Enzyme-catalyzed reactions
Rate is saturable: there's a maximum rate
• Half-maximal velocity occurs at a specific
• substrate concentration, independent of [E].
Km = substrate concentration
that gives Vo = 1/2 Vmax.

13. Dependence of Vo on [S] in enzyme-catalyzed
reaction
Plot of Vo vs. [S]) for an enzyme that follows Michaelis-Menten kinetic
3 parts of [S] concentration range
1. At very low [S]: Vo is proportional to [S];
2. In mid-range of [S], Vo is increasing
less as [S] increases (where Vo is around
1/2 Vmax).
Km = [S] that gives
Vo = 1/2 Vmax.
3. At very high [S], Vo is independent of [S]:
Vo = Vmax.

14. Michaelis-Menten model to explain hyperbolic
dependence of Vo on [S] in enzyme catalyzed reactions
• Before the chemistry occurs, enzyme binds substrate to
make a noncovalent ES complex.
• Turnover number (def.): number of substrate molecules
converted into product by one molecule of enzyme active
site per unit time, when enzyme is fully saturated with
substrate. = k2 in M-M scheme above = kcat (general term)
• kcat = turnover number (general term used, independent of
specific kinetic mechanism)

15. The Michaelis-Menten Equation describes a
rectangular hyperbola.
• The Michaelis-Menten Equation
• where Vmax = k2[ET] (so Vmax is indeed proportional to [ET])
• Km: an "aggregate" constant (sum of rate constants for breakdown of ES
divided by rate constant for formation of ES):
• Michaelis-Menten equation explains hyperbolic Vo vs. [S] curve:
1. At very low [S] ([S] << Km), Vo approaches (Vmax/Km)[S].
Vmax and Km are constants, so linear relationship between Vo and [S]
at low [S].
2. When [S] = Km, Vo = 1/2 Vmax
3. At very high [S], ([S] >> Km), Vo approaches Vmax (velocity
independent of [S])

16. Meaning of Km
• By definition,
Km = substrate concentration at which velocity (V) is exactly 1/2 of Vmax
(operational definition that holds for ANY kinetic mechanism).
• Km is a SUBSTRATE CONCENTRATION.
Compare:
Km = KES (dissoc. constant for ES complex) only if k2 << k–1.

17. • In vivo, most enzymes operate below saturation (V < Vmax)
(important for regulation)
Activity of some metabolic enzymes is regulated: V can be "tuned"
up or
down depending on cell's metabolic needs.
• Remember:
Vo = kcat[ES] = rate of appearance of P, and
Vmax = kcat[ET] so
(divide 1st equation by the second):
= fractional
saturation!
• Ratio of actual velocity at a given substrate concentration (Vo) to
Vmax
indicates ratio of occupied active sites to total active sites at that
[S].

18. Michaelis-Menten Equation:
Divide both sides by Vmax:
Can calculate fractional saturation
{ratio of (occupied sites / total active sites)} as

19. Reciprocal
The Michaelis-Menten equation can be recast into a linear form
The y-intercept gives the Vmax value and the slope gives Km/Vmax
To obtain parameters of interest
Reciprocal form of equation
1 = Km 1 + 1
V Vmax S Vmax
Y= m x + b

20. Uses of kcat/Km
kcat/Km used as a measure of 2 things:
1. enzyme's substrate preference
2. enzyme's catalytic efficiency
1. enzyme's preference for different substrates
(substrate specificity)
– The higher the kcat/Km, the better the enzyme
works on that substrate.
– e.g., chymotrypsin: protease that clearly "prefers"
to cleave after bulky
hydrophobic and aromatic side chains.

21. Catalytic efficiency of enzymes
• the higher the kcat/Km, the more
"efficient" the enzyme
kcat/KM for an enzyme can have a value
close to the limit of diffusion control
either because its kcat is very high, or
because its Km is very low, or some
combination.

22. Lineweaver-Burk (double reciprocal plot)
If the reciprocal (1/X) of the Michaelis-Menten equation
Comparing, y = mx + b,
where y = 1/vo,
m (slope) = Km/Vmax,
x = 1/[S] and
y-intercept, b = 1/Vmax.
When this relation is plotted,
the result is a straight line graph

23. Uses of double reciprocal plot
• The x intercept value is equal to -1/Km. more
accurate determination of Vmax, and hence Km.
• It is also useful in characterizing the effects of
enzyme inhibitors.
• Distinguishing between different enzyme
mechanisms.

24. Enzyme Inhibition

25. Inhibitors..
• chemicals that reduce the rate of enzymatic
reactions
• usually specific and they work at low
concentrations
• block the enzyme but they do not usually
destroy it
• Many drugs and poisons are inhibitors of
enzymes in the nervous system

26. Enzyme Inhibitors
Reversible versus Irreversible
• Reversible inhibitors interact with an enzyme
via noncovalent associations
• Irreversible inhibitors interact with an enzyme
via covalent associations

27. Important of enzyme inhibitor
• Shape of active site
• Information about chemical mechanism
• Regulation and control of metabolic pathways
• Drug design

28. • Reversible Inhibition
-bind with non-covalent interactions such
as hydrogen bonds, hydrophobic interactions
and ionic bonds.
-do not undergo chemical reactions when
bound to the enzyme and can be easily removed
by dilution or dialysis.

29. • three kinds of reversible enzyme inhibitors.
• classified according to the effect of varying the
concentration of the enzyme's substrate on
the inhibitor.
• Competitive inhibition
• Uncompetitive inhibition
• Mixed inhibition

30. Competitive inhibition
- competes with the
substrate for the active
site of an enzyme.
- inhibitor (I) occupies
the active site it prevents
binding of the substrate to
the enzyme.
- compounds that
resemble the substrate
and combine with the
enzyme to form an EI
complex.

31. • In the presence of
competitive inhibitor
michaelis-menten equation
becomes
Vₒ=Vmax[S]/αKm[S]
• The experimentally
determined variable αKm
(the Km observed in the
presence of the inhibitor) is
often called the “apparent”
Km.

32. • Overcome by sufficiently
high concentrations of
substrate i.e., by out-
competing the inhibitor.
• Vmax remains constant
• However, the apparent Km
will increase as it takes a
higher concentration of the
substrate to reach the Km
point.
• Competitive inhibitors are
often similar in structure to
the real substrate

33. Malonate is
competitive
inhibitor of
succinate for
succinate
dehydrogenase.

34. Uncompetitive Inhibition
• Binds at a site distinct from the
substrate active site
• Unlike competitive inhibitor,
binds only to the ES complex.
• The inhibitor binds to a site other
that the substrate and is thus
independent of the presence or
absence of substrate.
• This action results in a
conformational change in the
protein that affects a catalytic
step and hence decreases or
eliminates enzyme activity
(formation of P)

35. • The effect of
uncompetitive
inhibitor cannot be
overcome by higher
concentration of
substrate.

36. Mixed Inhibition
• Binds at a site distinct
from the substrate
active site
• But it binds to either E
or ES.
• The binding of the
inhibitor affects the
binding of the
substrate, and vice
versa.

37. • In the presence of an
mixed inhibitor, the
Michaelis-Menten
equation is altered to
V􀋠=Vmax[S]/αKm+α’*S]
• Decrease in Vmax and
either decrease or
increase in Km value.
• The effect can only be
partially overcome by
high concentration of
substrate.

38. Irreversible Inhibition
• Bind covalently with or destroy a functional
group on an enzyme that is essential for the
enzyme’s activity, or those that form a
particularly stable non-covalent association.
• Range from fairly simple, to complex inhibitors
that interact specifically and irreversibly with
active site amino acids.
.

39. • A special class of irreversible inhibitors is the suicide
inactivators.
• Unreactive until they bind to the active site of a
specific enzyme.
• Undergoes the first few chemical steps of the normal
enzymatic reaction, but instead of being transformed
into the normal product, the inactivator is converted to
a very reactive compound that combines irreversibly
with the enzyme.
• Also called mechanism-based inactivators
• Play a significant role in rational drug design

40. Inhibitor (I) binds only to E, not to ES
Inhibitor (I) binds only to ES, not to E.
This is a hypothetical case that has
never been documented for a real
enzyme, but which makes a useful
contrast to competitive inhibition
Inhibitor (I) binds to E and to ES.
Enzyme Inhibition
From Lehninger
Principles of Biochemistry

41. Competitive Uncompetitive Noncompetitive
Inhibition Inhibition (Mixed) Inhibition
Kmchanges
while Vmax
does not
Km and Vmax
both change
Km and Vmax
both change
From Lehninger
Principles of Biochemistry

42. Succinate dehydrogenase is a classic example of competitive inhibition
From Lehninger
Principles of Biochemistry
Malonate is a strong
competitive inhibitor of
succinate
dehydrogenase

43. Temperature Dependence

44. Effect of changes in temperature on enzyme
reactions
• Effects of changes in temperature on enzyme reactions is
important in poikilothermic organism, different intracellular
temperature.

45. • Above a certain temperature, enzyme will lose activity
because of denaturation of enzyme structure.
• Some enzymes contain two different Ea at various
temperature, and have a different plot of Arrhenius
expression.
• Enzymes from intertidal species (anemones, winkles) have
values of Q10=1.
• Enzymes from thermal bacteria (Bacillus stearothermophilus)
are stable at higher temperature

46. Effect of pH
V0
pH
pKa of reaction 1
~ 4.0
pKa of reaction 2
~ 9.0
2 124 6 8 10
max
low
Activity decreases due
to lysine deprotonation
Activity decreases due
to glutamate/aspartate
protonation
Maximal activity
range

47. Effect of changes of pH on enzyme-catalysed
reaction
Change of pH will cause :
• Inactivation of the enzyme outside a certain pH.
• Change of ionization state of substrate.
• Change in the equilibrium position of H+ if H+ is
involved in the reaction.
• Most common, change of pH will change the
ionization state of amino acid group(s) which is
the active group(s).

48. (A) For a single side chain in enzyme
• EH＋  E + H＋ EH＋isinactive and E is active
Dissociation constant Ka
• Ka = [E] [H＋] / [ EH＋] , [ EH＋] = [E] [H＋] / Ka
• Fraction F of enzyme in the unprotonated (active) form:
F = [E]/ [H＋]{ [E] [H＋]} Total enzyme conc. = [E] [H＋]
=Ka/{Ka+ [H＋]}
• If (Vmax )m is the maximum rate at all enzyme that is in
unprotonated state [E] : then at any pH, the Vmax should be:
Vmax = ( Vmax )m x F = ( Vmax )m x Ka / ( Ka + [H＋] )
• If pH values are well below the pKa ( [H＋] >> Ka )
Vmax = ( Vmax )m x Ka / [H＋]
Log Vma x =log (Vmax)m - pKa+ pH
Y = mX +C
Linear slope = 1.
• If pH values are well above the pKa ( [H＋]<<Ka )
Vmax = ( Vmax ) x Ka / ( Ka+ [H＋] )
= ( Vmax )m

50. pH must be specified!

51. Regulation of enzymatic activity
Two ways that this may occur:
1) Control of enzyme availability
Depends on rate of enzyme synthesis & degradation
2) Control of enzyme activity
Enzyme-substrate binding affinity may vary with binding
of small molecules called allosteric effectors (ex: BPG for
Hb)
Allosteric mechanisms can cause large changes in
enzymatic activity

52. Regulatory Enzymes
important in controlling flux through metabolic pathways
2. Regulation by covalent modification
Allosteric enzymes
From Lehninger
Principles of Biochemistry

53. Conversion of L-threonine to
L-isoleucine catalyzed by a
sequence five enzymes, E1-E5
L-isoleucine is an inhibitory
allosteric modulator of E1
Regulation by Feedback Inhibition
From Lehninger
Principles of Biochemistry

54. Two substrate reaction
• Two substrate reactions can be divided into two
categories-
1. Reactions involving a ternary complex.
2. Reactions not involving a ternary complex.

55. Reactions involving a ternary complex.
Consider a reaction-
E + A + B → E + P + Q
In this type, the reaction proceeds via ternary complexes
E + A + B → EAB → EPQ → E + P + Q
The ternary complex of this kind can be further subdivided into two kinds-

56.  Reactions in which ternary complex is formed in ordered manner. e.g.,
E + A → EA
EA + B → EAB (but not E + B → EB)
 Reactions in which ternary complex is formed in random manner. e.g.,
E + A → EA E + B → EB
Or
EA + B → EAB EB + A → EAB

57. Reactions not involving a ternary complex
In this type, the reaction proceeds via the formation of new modified enzyme
along with the first product which then binds with the second substrate.
E + A → E’ + P
E’ + B → E + Q
This class of reaction is known as enzyme substitution or ping-pong
mechanism.

58. In a second class of reaction, a ternary complex is presumably formed but breaks down
very fast to yield first product so that the ternary complex is kinetically insignificant. This
category of reaction is known as Theorell-Chance mechanism.
E + A ----> EA → E + P
An alternative way of representing enzyme-catalyzed reaction is proposed by Cleland
which shows the picture view of the substrates added to the enzyme and the product
formed after catalysis.

59. The random ternary mechanism of the above can be represented as-
Similarly, the non-ternary complex mechanism can be represented as-
A BP Q
E E' E
(EA E'P) (E'B EQ)
E
Q P
QPB A
BA
EA
EB
EP
EQ
(EAB EPQ) E

60. Reference
• Principle of biochemistry
• Fundamental of Enzymology
• http://www.slideshare.net/Pammy98/lecture-
3-enzyme-kinetics#btnNext
• www.inf.ed.ac.uk/teaching/courses/.../CSB_le
cture_enzyme_kinetics.pdf