3. Enzyme kinetics
• Kinetics: study of the rates of chemical reactions
• Enzyme kinetics:
– study of the rate of enzyme-catalyzed reactions (velocity, v
rate where a product is formed from substrate)
Substrate (S) Product (P)
• The rate of enzyme catalyzed reactions, velocity (V) are often
influenced by the concentration of substrate (i.e. more
substrate, the faster the rate of forming product)
3
Enzyme (E)
V
VS
Low [substrate] High [substrate]
4. Enzyme kinetics
4
• The rate V is the disappearance of substrate in a specified unit of
time.
• It is also equal to the rate of the appearance of product that
appear in a specified unit time under certain assumptions, such as
the [enzyme] being much less than the [substrate].
V = -ΔS/ΔT = ΔP/ΔT
• The unit for v are usually moles or millimoles or micromoles per
minutes or seconds.
Consider only the change in
the [S], the reaction rate is
directly related to [S] by a
constant, k called the rate
constant.
V = k [S]
5. Enzyme kinetics
5
–Reactions in which the velocity is directly proportional
to the reactant concentration are called first-order
reactions. First-order rate constants have the unit of s−1
(per second).
–Many important biochemical reactions are
biomolecular; that is, they include two reactants. Such
reactions are called second-order reactions, have the
units M−1 s−1 (per mole per second).
6. Enzyme kinetics
6
• Initial rate (velocity) of reaction, V0:
• the rate of reaction when the
enzyme just begins to catalyze the
reaction (time ≈ 0 minutes, in
practical - first few minutes)
• Determined from the slope of the
curve at the beginning of a
reaction.
• The rate of catalysis rises linearly
as substrate concentration
increases and then begins to level
off and approach a maximum at
higher substrate concentrations.
[S]1 < [S]2 < [S]3 < [S]4
8. Initial velocity (v0)
• For many enzymes, V0 varies with the substrate concentration [S].
V0 increases linearly as initial substrate concentration [S t = 0]
increase and then begin to level off (reach plateau) & approach
a maximum V0 (i.e. Vmax) at higher [S t = 0]
8
V0 =K [S t = 0]
The initial velocity (v0) for each
substrate concentration is
determined from the slope of the
curve at the beginning of a
reaction.
9. 1 2 3 4 5 6
1
6
5
4
3
2
[S]1 [S]2 [S]3 [S]4 [S]5 [S]6
Increasing substrate concentration (> chance for enzyme to meet up with substrate)
The values for initial
velocity are then plotted
against substrate
concentration. The
resulting curve is
hyperbolic in shape.
10. Maximum velocity (Vmax)
10
At higher concentration of substrate, the rate increase becomes
less until a point is reached where the rate becomes constant not
matter how much substrate is present.
Vmax = K [S E, t = 0]
[S E, t = 0] = concentration of substrate that is high enough to fill up
all enzyme active sites found in the reaction environment
Increasing
concentration
does not affect
reaction rate.
11. Michaelis-Menten kinetics
• When the rate of the reaction is measured over a range of
substrate concentrations, the reaction rate (v) increases as [S]
increases. However, as [S] gets higher, the enzyme becomes
saturated with substrate and the rate reaches Vmax.
• In 1912, Michaelis & Menten proposed a simple model to
account for the kinetic characteristics of single-substrate
enzymes.
11
Enzyme E combines with
substrate S to form ES complex,
with a rate constant k1
ES complex has 2 possible fates. It can be
dissociate to E and S with a rate constant
k-1 OR it can proceed to form product P
with a rate constant k2
12. Michaelis-Menten kinetics
• For enzyme reaction that obeys Michaelis-Menten kinetics :
• Vmax = maximal initial rate (velocity) of reaction
• V0 = Initial rate (velocity) of reaction
• Km = The Michaelis constant,
the substrate concentration yielding
a rate of Vmax/2
12
V0 =
Vmax [S]
[S] + Km
At high substrate concentration, when [S] is much
greater than KM, V0 = Vmax; the rate is maximal,
independent of substrate concentration.
13. Kinetic data can provide values of
Vmax and KM
13
There are several methods for determining the values of the
parameters of the Michaelis–Menten equation (Vmax and KM).
The plot of v versus [S] is not linear; although initially linear at
low [S], it bends over to saturate at high [S].
In practice, however, it is very
difficult to assess Vmax accurately
from direct plots of νo versus [S],
because the value of Vmax will
almost certainly be underestimated.
14. Linear plots of the Michaelis–Menten
equation
• A better method for determining the values of Vmax and KM, which
was formulated by Hans Lineweaver and Dean Burk, uses the
reciprocal of the Michaelis– Menten equation.
• This is a linear equation in 1/νo and 1/[S]. If these quantities are
plotted to obtain Lineweaver–Burk or double-reciprocal plot, the
slope of the line is KM/Vmax, the 1/νo intercept is 1/Vmax, and the
extrapolated 1/[S] intercept is −1/KM
14
Disadvantage: Most data are
crowded at the left side of the graph.
For small values of [S], small errors in
νo lead to large errors in 1/νo and
hence to large errors in KM and Vmax.
15. Km and Vmax values are important
enzyme characteristics
• Use #1: Km is the initial concentration of substrate [S] required so as to
push the initial rate of reaction (V0) to reach half of the maximum
initial reaction rate (Vmax) achievable in the reaction environment.
• Provides a measure of substrate concentration required for significant
catalysis to take place.
• If the [S] is equal to KM, the enzyme will display significant activity and
yet the activity will be sensitive to changes in [S].
• At [S] < KM, enzymes are very sensitive to changes in [S] but display
little activity.
• At [S] > KM, enzymes have great catalytic activity but are insensitive to
changes in [S].
15
16. Km and Vmax values are important
enzyme characteristics
16
If you want the reaction to happen rapidly, the substrate
concentration must be > Km value of the reaction
You can compare 2 reaction to see which one is more effective
(i.e. require lesser [substrate] to attain 0.5 Vmax
Lower Km = more effective
Which is the
best substrate?
17. Km and Vmax values are important
enzyme characteristics
• Use #2: Km of a reaction may reflect the rate constant of a certain
individual step in the reaction scheme:
In the reaction, if K-1 is much more greater than K2:
– ES complex will tend to dissociate back to E & S rather than
becoming E + P.
Under the conditions where K-1 >> K2:
Km ≈ K-1 / K1
Km = Dissociation constant of the ES complex
= [E][S] / [ES]
= KES
17
High Km: weak binding
Low Km: strong binding
An enzyme with a high Km has a low affinity for its substrate, and
requires a greater concentration of substrate to achieve Vmax.
18. Use of the maximal initial reaction
rate, Vmax
18
• Vmax reveals the turnover number of an
enzyme when all the enzyme
molecules in the reaction environment
are fully saturated with substrates.
Vmax = k2 [E]T
• turnover number of an enzyme :
the number of substrate molecules
converted into product by an enzyme
molecule in 1 unit time (e.g. 1 second)
• turnover number of an enzyme
= rate constant k2
= kcat
Higher Vmax enzyme more effective
19. Kcat/Km is used as a measure of catalytic
efficiency
19
Chymotrypsin has a
preference for
cleaving next to bulky,
hydrophobic side
chains
The rate constant Kcat/Km = measure of catalytic efficiency:
take into account both the rate of catalysis with a particular
substrate (Kcat) & the strength of enzyme-substrate interaction (Km)e.g.
: using Kcat/Km values, one can compare an enzyme’s preference for
different substrates.
20.
21. Multiple substrate reactions
• The simplest way to explain Michaelis–Menten kinetics is to use
a one-substrate reaction as an example. However, most
biochemical reactions have multiple substrates.
• Many such reactions transfer a functional group, such as a
phosphoryl group, from one substrate to the other. Those that
are oxidation-reduction reactions transfer electrons between
substrates.
• Multiple substrates reactions:
– Sequential reactions
– Double-displacement (ping-pong)
reactions
21
A + B P + Q
22. Multiple substrate reactions:
Sequential reactions
• All substrates must bind to the enzyme before any product is
released. Consequently, in a bisubstrate reaction, a ternary
complex consisting of the enzyme and both substrates forms.
Sequential mechanisms are of two types: ordered, in which the
substrates bind the enzyme in a defined sequence, and random.
22
23. Multiple substrate reactions: Double-
displacement reactions
• One or more products are released before all substrates bind the
enzyme. The defining feature is the existence of a substituted
enzyme intermediate, in which the enzyme is temporarily
modified, eg reactions that shuttle amino groups between amino
acids and a-ketoacids. The substrates and products appear to
bounce on and off the enzyme just as a Ping-Pong ball bounces
on and off a table.
23
24. Allosteric enzyme
• Allosteric enzymes do not obey M-M kinetics, they are more
complex)
• Allosteric enzyme:
– enzyme with multiple subunits & multiple active sites.
– The binding of substrate to one active site can alter the
properties of other active sites enzyme shows cooperative
binding properties
– Often display sigmoidal plots of the reaction velocity versus [S]
24
** Cooperative binding :
the binding of substrate to one
active site facilitates the binding of
substrate to the other active sites.
25. Allosteric enzymes are regulated by products
of the pathways under their control
25
• The first reaction, A → B, is the committed step in this
hypothetical metabolic pathway; after this reaction has taken
place, B is committed to conversion into F.
• Allosteric enzymes always catalyze the committed step of
metabolic pathways.
• When sufficient F is present, F can bind reversibly to e1, the
enzyme catalyzing the committed step, and inhibit the reaction, a
common means of biochemical regulation called feedback
inhibition.
26. Allosteric enzymes are regulated by products
of the pathways under their control
26
• Feedback inhibitors usually bear no structural resemblance to the
substrate or the product of the enzyme that they inhibit.
• Moreover, feedback inhibitors do not bind at the active site but
rather at a distinct regulatory site on the allosteric enzyme.
• Allosteric (from the Greek allos, meaning “other,” and stereos,
meaning “structure”) enzymes are so-named because they are
regulated by molecules that bind to sites other than the active
site.
27. Allosterically regulated enzymes do not
conform to Michaelis–Menten kinetics
• Allosteric enzymes are distinguished by their response to
changes in substrate concentration in addition to their
susceptibility to regulation by other molecules.
• Allosteric enzymes display a sigmoidal dependence of
reaction velocity on substrate concentration in contrast to the
hyperbolic curve seen with Michaelis–Menten enzymes.
27
28. Allosteric enzymes display threshold
effects
28
The activity of allosteric enzymes is
more sensitive to changes in substrate
concentration near KM than are
Michaelis–Menten enzymes with the
same Vmax. This sensitivity is called a
threshold effect: below a certain
substrate concentration, there is little
enzyme activity. However, after the
threshold has been reached, enzyme
activity increases rapidly. In other
words, cooperativity ensures that most
of the enzyme is either on or off. The
vast majority of allosteric enzymes
display sigmoidal kinetics.
29. Enzymes commonly employ 1 or more
strategies to catalyze specific reactions
1. Covalent catalysis:
– Active site contains a reactive group, usually a powerful nucleophile,
that become temporarily covalently attached to a part of substrate.
2. General acid-base catalysis:
– Molecule other than water plays the role of a proton donor/acceptor.
3. Catalysis by approximation:
– Reaction rate may be considerable enhanced by bringing the 2
substrates together along a single binding surface on an enzyme.
4. Metal ion catalysis:
– A metal ion may facilitate the formation of nucleophiles such as
hydroxide ion by direct coordination, may serves as a bridge
between E & S.
29
30. Enzyme activity can be modulated by
temperature
30
Temperature enhances the rate of enzyme-catalyzed reactions
As the temperature rises, the rate of most reactions increases. The
rise in temperature increases the Brownian motion of the molecules,
which makes interactions between an enzyme and its substrate more
likely. For most enzymes, there is a temperature at which the
increase in catalytic activity ceases and there is a loss of activity due
to protein denaturation.
Tyrosinase synthesizes the
pigment that results in dark
fur, has a low tolerance for
heat in Siamese cats. It is
inactive at normal body
temperatures but functional at
slightly lower temperatures.
31. 31
Enzyme activity can be modulated by
pH
The activity of most enzymes displays a bell-shaped curve when
examined as a function of pH.
How can we account for the pH effect on enzyme activity?
Imagine an enzyme that requires the ionization of both glutamic
acid and lysine at the active site for the enzyme to be functional.
Thus, the enzyme would depend on the presence of a COO–
group as well as an NH3+ group.
• pH is lowered, COO− ⇒
COOH, loss of enzyme
activity.
• pH is raised, NH3
+ ⇒ NH2,
loss of enzyme activity
32. Enzyme activity can be modulated by
inhibitory molecules
32
• Major control mechanism in biological systems
• Enzyme inhibition can be either irreversible or reversible.
• Irreversible enzyme inhibition:
– irreversible inhibitor molecules bind themselves tightly
(covalently / noncovalently) to the target enzyme,
resulting enzyme conformation change and thus enzyme
inhibition.
– e.g. irreversible enzyme inhibition:
Inhibition of transpeptidase (enzyme involves in the
synthesis of bacterial cell wall) by penicillin.
33. Reversible enzyme inhibition
• Reversible inhibition is characterized by a rapid
association and dissociation of the enzyme-inhibitor
complex.
• The subtypes of reversible enzyme inhibition include :
– Competitive inhibition
– Uncompetitive inhibition
– Noncompetitive inhibition
33
34. Competitive inhibition
• Competitive inhibitor reduces the rate of enzyme catalysis by
competing directly with the substrate for the enzyme’s active site,
reducing substrate binding to the active site
• Competitive inhibitor molecules often have conformations that are
resembled to the enzyme’s substrate.
• Increasing the substrate concentration can relieve competitive
inhibition in a biological system.
34
CI binds to the
active site
prevents the
substrate from
binding.
eg. Inhibition of dihydrofolate
reductase (enzyme involves in
the biosynthesis of purines and
pyrimidines) by methotrexate
in cancer treatment.
35. Michaelis-Menten graph-Competitive
inhibition
35
How can we determine whether a reversible inhibitor acts by
competitive, uncompetitive, or noncompetitive inhibition?
In competitive inhibition, the inhibitor
competes with the substrate for the
active site. It can be overcome by a
sufficiently high concentration of
substrate. As the concentration of a
competitive inhibitor increases, higher
concentrations of substrate are
required to attain a particular reaction
velocity.
36. Double-reciprocal/Lineweaver–Burk plot:
Competitive inhibition
36
In competitive inhibition, the intercept on the y axis, 1/Vmax, is the
same in the presence and in the absence of inhibitor, although the
slope (KM/Vmax) is increased. The inhibitor has no effect on Vmax
but increases KM.
37. Uncompetitive inhibition
• Uncompetitive inhibitor (UI) binds only to the enzyme – substrate
(ES) complex.
• UI’s binding site is created only on the interaction of the E & S.
• Inhibition cannot be overcome by the addition of more S.
• e.g. uncompetitive inhibition:
Inhibition of lipase in fat and fatty acid metabolism by nicotine
37
UI binds only to
the ES complex
38. 38
In uncompetitive inhibition, the inhibitor
binds only to the ES complex. This enzyme–
substrate–inhibitor complex, ESI, does not
proceed to form any product. Because
some unproductive ESI complex will always
be present, Vmax will be lower in the
presence of an inhibitor. The uncompetitive
inhibitor also lowers the apparent value of
KM, because the inhibitor binds to ES to
form ESI, depleting ES.
Michaelis-Menten graph-
Uncompetitive inhibition
40. Noncompetitive inhibition
e.g. noncompetitive
inhibition: Inhibition of
collagenase (proteolytic
enzyme) by deoxycycline in
periodontal disease
treatment (inhibit bacterial
growth inside in the gum).
40
• Non competitive inhibitor & substrate bind simultaneously to an
enzyme molecule at different binding sites.
• Binding of NCI changes the enzyme’s conformation
inhibit the catalysis of the substrate bound to the enzyme
decrease the turnover number.
• Inhibition cannot be overcome by increasing the [S].
NCI does not
prevent the S
from binding
41. 41
In noncompetitive inhibition, a
substrate can bind to the enzyme–
inhibitor complex and to the enzyme
alone. It cannot be overcome by
increasing the substrate
concentration. The reaction rate
increases more slowly at low
substrate concentrations than for
uncompetitive competition.
Michaelis-Menten graph-
Noncompetitive inhibition
44. Irreversible inhibitors can be used
to map the active site
44
In irreversible inhibition, the inhibitor is covalently linked
to the enzyme or bound so tightly that its dissociation
from the enzyme is very slow. Covalent inhibitors
provide a means of mapping an enzyme’s active site.
e.g. Penicillin acts by
covalently modifying the
enzyme transpeptidase,
thereby preventing the
synthesis of bacterial cell
walls and thus killing the
bacteria
45. Irreversible inhibitors can be used
to map the active site
45
• Determination of the chemical mechanism of enzyme:
to identify functional groups required for enzyme
activity.
• Irreversible inhibitors can be assorted into four
categories:
• Group-specific reagents: modify specific R groups of amino
acids)
• Affinity labels (substrate analogs): molecules that are
structurally similar to an enzyme’s substrate.
• Suicide inhibitors: chemically modified substrates
• Transition-state analogs: resemble the transition state
molecule
46. Transition state analogs are potent
inhibitors of enzymes
46
• Transition state analogs:
– Compounds resembling the transition state molecule of a catalyzed
reaction , are effective & more specific inhibitors of enzymes
• e.g. : inhibition of proline racemase.
– Racemization of proline by proline racemase proceeds through a
transition state in which the tetrahedral α-carbon atom has become
trigonal rather than tetrahedral.
Pyrrole 2-carboxilic acid, a proline transitional state
analog that has trigonal geometry, a potent inhibitor
of proline racemase
47. Enzyme regulatory strategies
• The activity of enzymes often must be regulated:
– so that they function at the proper time and place.
– essential for coordination of the vast array of biochemical
processes taking place at any instant in an organism.
• Enzymatic activity is regulated in 5 principle ways:
– Enzyme allosteric control
– Isoenzyme production
– Reversible covalent modification
– Proteolytic activation
– Enzyme quantity regulation
47
48. Enzyme allosteric control
• Allosteric enzymes
– contain distinct regulatory sites & multiple functional sites.
– activities of these protein are controlled via binding small
signaling molecules at the regulatory sites cooperativity.
48
e.g.: catalysis reaction
by aspartate
transcarbamoylase
(ATCase) in the first
step of pyrimidine
biosynthesis is
inhibited by cytidine
triphosphate.
49. Isoenzymes production
• A particular biochemical activity can be regulated through the
use of isozymes.
• Isozymes or Isoenzymes:
– are homologous enzymes within a single organism.
– catalyze same reaction but differ slightly in their structures,
Km and Vmax values & regulatory properties.
– are expressed in a distinct tissue or organelle or at a distinct
stage of development.
Different isoenzymes are synthesized and used to regulate
the biochemical reaction at different timing and occasion.
49
50. Isozyme: Lactate dehydrogenase (LDH)
• LDH - functions in anaerobic glucose metabolism and glucose synthesis.
• Human beings have two isozymic polypeptide chains for this enzyme:
• H isozyme highly expressed in heart; M isozyme found in skeletal muscle.
Many different combinations of the two subunits are possible.
50
51. Reversible covalent modification of
enzyme
• Catalytic properties of many enzymes can altered by the covalent
attachment of a modifying group (phosphoryl group).
• e.g. process: phosphorylation & dephosphorylation
– Phosphorylation is used as a regulatory mechanism in every
metabolic process in eukaryotic cells.
51
53. Proteolytic activation
• Proteolytic activation: Inactive enzymes are activated by the
hydrolysis of a few peptide bond on their structure.
Inactive precursor: zymogen/proenzyme.
Generates digestive enzymes, and enzyme for blood clotting.
53
54. Enzyme quantity regulation
• Enzyme quantity regulation: Enzyme activity can be regulated by
adjusting the amount of enzyme present.
This form of regulation usually takes place at the level of
transcription.
54
55. Summary
1. Enzymes are powerful and highly specific catalysts.
2. Free energy is a useful thermodynamic function for
understanding enzymes.
3. Enzymes accelerate reactions by facilitating the formation of the
transition state.
4. The Michaelis-Menten model accounts for the kinetic
properties of many enzymes.
5. Enzymes can be inhibited by specific molecules.
55
56. Study questions
1. What is enzyme kinetics?
2. What is Michaelis-Menten kinetics?
3. What information can you obtain about enzyme from Km and
Vmax values?
4. How do you identify the types of inhibitions using graphs?
5. What is the application of the transition state analog?
6. What is an allosteric enzyme?
7. Describe the type of reversible enzyme inhibitions.
8. Describe enzyme regulatory strategies.
9. What types of covalent modification regulates the enzymatic
activities?
56
Editor's Notes
The amino acid sequences are 75% identical.
Protein kinase (PKA) – phosphorylation
Protein phosphatase – dephosphorylation-removal of phosphoryl groups by hydrolysis
