CP504 – ppt_Set 03
Enzyme kinetics and associated reactor design:
Determination of
the kinetic parameters of
enzyme-induced reactions
- learn about the meaning of kinetic parameters
- learn to determine the kinetic parameters
- learn the effects of pH, temperature and substrate
concentration on enzyme activity (or reaction rates)
- learn about inhibited enzyme kinetics
- learn about allosteric enzymes and their kinetics
Prof. R. Shanthini
Updated: 23 Nov 2012
Simple Enzyme Kinetics (in summary)
k1
E+S
k3
ES
E+P
k2
which is equivalent to
[E]
S
Prof. R. Shanthini
Updated: 23 Nov 2012
P
S
for substrate (reactant)
E
for enzyme
ES
for enzyme-substrate complex
P
for product
Simple Enzyme Kinetics (in summary)
[E]
S
rP = - r S =
P
rmaxCS
KM + CS
where rmax = k3CE0 = kcatCE0
and KM = f(rate constants)
rmax is proportional to the initial concentration of the enzyme
KM is a constant
Prof. R. Shanthini
Updated: 23 Nov 2012
Simple Enzyme Kinetics (in summary)
-rs
Catalyzed reaction
rmax
- rS =
rmax
2
KM
Prof. R. Shanthini
Updated: 23 Nov 2012
rmaxCS
KM + CS
uncatalyzed reaction
Cs
An exercise
Consider an industrially important enzyme, which catalyzes the
conversion of a protein substrate to form a much more valuable
product. The enzyme follows the Briggs-Haldane mechanism:
An initial rate analysis for the reaction in solution, with E0 = 0.10 μM
and various substrate concentrations S0, yields the following
Michaelis-Menten parameters: Vmax = 0.60 μM/s; KM = 80 μM.
A different type of experiment indicates that the association rate
constant, k1, is k1 = 2.0 x 106 M-1s-1 (2.0 μM-1s-1).
a. Estimate the values of k2 and k-1.
b. On average, what fraction of enzyme-substrate binding events
result in product formation?
Prof. R. Shanthini
Updated: 23 Nov 2012
Source: Jason Haugh, Department of Chemical &
Biomolecular Engineering, North Carolina State University
Simple Enzyme Kinetics (in summary)
Catalytic step
E+S
k1
ES
k3
E+P
k2
Substrate binding step
k3 = kcat
Prof. R. Shanthini
Updated: 23 Nov 2012
- learn about the meaning of kinetic parameters
- learn to determine the kinetic parameters
- learn the effects of pH, temperature and substrate
concentration on enzyme activity (or reaction rates)
- learn about inhibited enzyme kinetics
- learn about allosteric enzymes and their kinetics
Prof. R. Shanthini
Updated: 23 Nov 2012
How to determine the kinetic parameters rmax and KM ?
Carry out an enzyme catalysed experiment, and
measure the substrate concentration (CS) with time.
t
0
Cs
given
- rs
given
10
given
given
15
given
given
Prof. R. Shanthini
Updated: 23 Nov 2012
- rS =
rmaxCS
KM + CS
How to determine the M-M kinetics rmax and KM ?
Carry out an enzyme catalysed experiment, and
measure the substrate concentration (CS) with time.
t
0
Cs
given
- rs
given
10
given
given
15
given
given
Prof. R. Shanthini
Updated: 23 Nov 2012
- rS =
rmaxCS
KM + CS
We could rearrange
- rS =
rmaxCS
KM + CS
to get the following 3 linear forms:
CS
- rS
1
- rS
- rS
Prof. R. Shanthini
Updated: 23 Nov 2012
=
KM
rmax
+
1
=
=
rmax
+
rmax -
1
rmax
CS
KM
1
rmax
CS
KM
- rS
CS
(14)
(15)
(16)
The Langmuir Plot
CS
- rS
=
KM
rmax
+
1
CS
(14)
rmax
CS
- rS
1
rmax
- KM
Prof. R. Shanthini
Updated: 23 Nov 2012
CS
The Langmuir Plot
CS
- rS
=
KM
rmax
+
1
CS
(14)
rmax
CS
- rS
1
rmax
- KM
Prof. R. Shanthini
Updated: 23 Nov 2012
Determine rmax
more accurately
than the other
plots.
CS
The Lineweaver-Burk Plot
1
- rS
1
=
rmax
+
KM
1
rmax
CS
(15)
1
- rS
KM
rmax
1
- KM
Prof. R. Shanthini
Updated: 23 Nov 2012
1
CS
The Lineweaver-Burk Plot
1
- rS
1
=
1
- rS
1
- KM
Prof. R. Shanthini
Updated: 23 Nov 2012
rmax
+
KM
1
rmax
CS
(15)
- Gives good estimates of rmax, but
not necessarily KM
KM
- Data points
at low substrate
rmax
concentrations influence the slope
and intercept more than data points
at high Cs
1
CS
The Eadie-Hofstee Plot
- rS
=
rmax -
KM
- rS
CS
(16)
- rS
KM
rmax
KM
Prof. R. Shanthini
Updated: 23 Nov 2012
-rS
CS
The Eadie-Hofstee Plot
- rS
=
rmax -
KM
- rS
CS
(16)
- rS
- Can be subjected to large errors
since both coordinates contain (-rS)
KM
- Less bias on point at low Csrmax
than
with Lineweaver-Burk plot K
M
Prof. R. Shanthini
Updated: 23 Nov 2012
-rS
CS
Data:
CS
-rS
(mmol/l)
-(mmol/l.min)
1
0.20
2
3
0.22
0.30
5
0.45
7
0.41
10
0.50
Prof. R. Shanthini
Updated: 23 Nov 2012
Determine the M-M kinetic
parameters for all the
three methods discussed
in the previous slides.
The Langmuir Plot
25
CS/(-rS) min
20
15
10
y = 1.5866x + 4.6417
R2 = 0.9497
5
0
0
2
4
6
CS (mmol/l)
8
10
rmax = 1 / slope = 1 / 1.5866 = 0.63 mmol/l.min
K = rmax x intercept = 0.63 x 4.6417 = 2.93 mmol/l
Prof. R. Shanthini
M
Updated: 23 Nov 2012
The Lineweaver-Burk Plot
1/(-rS) l.min/mmol
6
5
4
3
2
y = 3.4575x + 1.945
R2 = 0.8463
1
0
0
0.2
0.4
0.6
1/CS l/mmol
0.8
1
rmax = 1 / intercept = 1 / 1.945 = 0.51 mmol/l.min
K = rmax x slope = 0.51 x 3.4575 = 1.78 mmol/l
Prof. R. Shanthini
M
Updated: 23 Nov 2012
The Eadie-Hofstee Plot
(-rS) mmol/l.min
0.6
y = -1.8923x + 0.5386
2
R = 0.6618
0.5
0.4
0.3
0.2
0.1
0
0
0.05
0.1
0.15
(-rS)/CS per min
0.2
rmax = intercept = 0.54 mmol/l.min
Prof. R. Shanthini
Updated: 23 Nov 2012
KM = - slope = 1.89 mmol/l
0.25
Comparison of the results
The
Langmuir
Plot
rmax
KM
R2
Prof. R. Shanthini
Updated: 23 Nov 2012
The
LineweaverBurk Plot
The EadieHofstee Plot
Comparison of the results
The
LineweaverBurk Plot
0.51
The EadieHofstee Plot
rmax
The
Langmuir
Plot
0.63
KM
2.93
1.78
1.89
R2
94.9%
84.6%
66.2%
Prof. R. Shanthini
Updated: 23 Nov 2012
0.54
Comparison of the results
The
LineweaverBurk Plot
0.51
The EadieHofstee Plot
rmax
The
Langmuir
Plot
0.63
KM
2.93
1.78
1.89
R2
94.9%
84.6%
66.2%
Determine
rmax more
accurately than
the other plots
Gives good
estimates of
rmax, but not
necessarily KM
Can be
subjected to
large errors
Prof. R. Shanthini
Updated: 23 Nov 2012
0.54
- learn about the meaning of kinetic parameters
- learn to determine the kinetic parameters
- learn the effects of pH, temperature and substrate
concentration on enzyme activity (or reaction rates)
- learn about inhibited enzyme kinetics
- learn about allosteric enzymes and their kinetics
http://www.youtube.com/watch?v=D2j2KGwJXJc
Prof. R. Shanthini
Updated: 23 Nov 2012
Effects of temperature on enzyme activity:
Increases in the temperature of a system results from
increases in the kinetic energy of the system.
Kinetic energy increase has the following effects on the
rates of reactions:
1) More energetic collisions
2) Increase in the number of collisions per unit time
3) Denaturation of the enzyme or substrate
Prof. R. Shanthini
Updated: 23 Nov 2012
http://academic.brooklyn.cuny.edu/biology/bio4fv/page/enz_act.htm
Effects of temperature on enzyme activity:
More energetic collisions:
When molecules collide, the kinetic energy of the molecules can
be converted into chemical potential energy of the molecules.
If the chemical potential energy of the molecules become great
enough, the activation energy of a exergonic reaction can be
achieved and a change in chemical state will result.
Thus the greater the kinetic energy of the molecules in a system,
the greater is the resulting chemical potential energy when two
molecules collide.
As the temperature of a system is increased it is possible that
more molecules per unit time will reach the activation energy.
Thus the rate of the reaction may increase.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://academic.brooklyn.cuny.edu/biology/bio4fv/page/enz_act.htm
Effects of temperature on enzyme activity:
Increase in the number of collisions per unit time:
In order to convert substrate into product, enzymes must collide
with and bind to the substrate at the active site.
Increasing the temperature of a system will increase the
number of collisions of enzyme and substrate per unit time.
Thus, within limits, the rate of the reaction will increase.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://academic.brooklyn.cuny.edu/biology/bio4fv/page/enz_act.htm
Effects of temperature on enzyme activity:
Denaturation of the enzyme:
Enzymes are very large proteins whose three dimensional shape is
vital for their activity.
When proteins are heated up too much they vibrate.
If the heat gets too intense then the enzymes literally shake
themselves out of shape, and the structure breaks down.
The enzyme is said to be denatured.
A denatured enzyme does not have the correct 'lock' structure.
Therefore it cannot function efficiently by accepting the 'key'
substrate molecule.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://www.woisd.net/moodle/mod/resource/view.php?id=44
Effects of temperature on enzyme activity:
Denaturation of the enzyme:
Prof. R. Shanthini
Updated: 23 Nov 2012
Effects of temperature on enzyme activity:
Denaturation of the enzyme:
As temperature increases, enzyme activity increases
until its optimum temperature is reached. At higher
Prof. R. Shanthini
temperatures, the enzyme activity rapidly falls to zero.
Updated: 23 Nov 2012
Effects of temperature on enzyme activity:
Denaturation for most human enzymes:
The optimum
temperature for most
human enzymes to
work at is around
37ºC which is why
this temperature is
body temperature.
Optimal for most
human enzymes
Enzymes start to
denature at about
45°C.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://www.woisd.net/moodle/mod/resource/view.php?id=44
Effects of temperature on enzyme activity:
Reaction rate
Optimal for most
human enzymes
Prof. R. Shanthini
Updated: 23 Nov 2012
Optimal for some
thermophillic
bacterial
enzymes
Temperature (deg C)
https://wikispaces.psu.edu/display/230/Enzyme+Kinetics+and+Catalysis
Effects of pH on enzyme activity:
The structure of the protein enzyme can depends on how
acid or alkaline the reaction medium is, that is, it is pH
dependent.
If it is too acid or too alkaline, the structure of the protein is
changed and it is 'denatured' and becomes less effective.
If the enzyme does not have the correct 'lock' structure, it
cannot function efficiently by accepting the 'key' substrate
molecule.
In the optimum pH range, the enzyme catalysis is at its
most efficient.
Prof. R. Shanthini
Updated: 23 Nov 2012
Effects of pH on enzyme activity:
Optimal for trypsin
(an intestinal
enzyme)
Reaction rate
Optimal for pepsin
(a stomach
enzyme)
Prof. R. Shanthini
Updated: 23 Nov 2012
pH
https://wikispaces.psu.edu/display/230/Enzyme+Kinetics+and+Catalysis
Effects of pH on enzyme activity:
Amylase (pancreas) enzyme
Optimum pH: 6.7 - 7.0
Function: A pancreatic enzyme that catalyzes the
breakdown/hydrolysis of starch into soluble sugars that can
readily be digested and metabolised for energy generation.
Amylase (malt) enzyme
Optimum pH: 4.6 - 5.2
Function: Catalyzes the breakdown/hydrolysis of starch into
soluble sugars in malt carbohydrate extracts.
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Catalase enzyme
Optimum pH: ~7.0
Function: Catalyses the breakdown of potentially harmful
hydrogen peroxide to water and oxygen. Important in
respiration/metabolism chemistry.
2H2O2(aq) ==> 2H2O(l) + O2(g)
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Invertase enzyme
Optimum pH: 4.5
Function: Catalyses the breakdown/hydrolysis of sucrose
into fructose + glucose, the resulting mixture is 'inverted
sugar syrup'.
C12H22O11 + H2O ==> C6H12O6 + C6H12O6
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Lipase (pancreas) enzyme
Optimum pH: ~8.0
Function: Lipases catalyse the breakdown dietary fats, oils,
triglycerides etc. into digestible molecules in the human
digestion system.
Lipase (stomach) enzyme
Optimum pH: 4.0 - 5.0
Function: As above, but note the significantly different
optimum pH in the acid stomach juices, to optimum pH in
the alkaline fluids of the pancreas.
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Maltase enzyme
Optimum pH: 6.1 - 6.8
Function: Breaks down malt sugars.
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Pepsin enzyme
Optimum pH: 1.5 - 2.0
Function: Catalyses the breakdown/hydrolysis of proteins
into smaller peptide fragments.
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Trypsin enzyme
Optimum pH: 7.8 - 8.7
Function: Catalyses the breakdown/hydrolysis of proteins
into amino acids. Note again, the significantly different
optimum pH to similarly functioning pepsin.
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of pH on enzyme activity:
Urease enzyme
Optimum pH: ~7.0
Function: Catalyzes the breakdown of urea into ammonia
and carbon dioxide.
(NH2)2(aq) + H2O(l) ==> 2NH3(aq) + CO2(aq)
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effects of substrate concentration on enzyme activity:
Prof. R. Shanthini
Updated: 23 Nov 2012
www.docbrown.info/page01/ExIndChem/ExIndChema.htm
Effect of shear
Prof. R. Shanthini
Updated: 23 Nov 2012
Complex enzyme kinetics
- learn about the meaning of kinetic parameters
- learn to determine the kinetic parameters
- learn the effects of pH, temperature and substrate
concentration on enzyme activity (or reaction rates)
- learn about inhibited enzyme kinetics
- learn about allosteric enzymes and their kinetics
Prof. R. Shanthini
Updated: 23 Nov 2012
Inhibited enzyme reactions
Inhibitors are substances that slow down the rate of enzyme
catalyzed reactions.
There are two distinct types of inhibitors:
- Irreversible inhibitors form a stable complex with enzymes
and reduce enzyme activity (e.g. lead, cadmium,
organophosphorous pesticide)
- Reversible inhibitors interact more loosely with enzymes
and can be displaced.
Prof. R. Shanthini
Updated: 23 Nov 2012
Inhibited enzyme reactions - applications
Many drugs and poisons are inhibitors of enzymes in the
nervous system.
Poisons: snake bite, plant alkaloids and nerve gases
Medicines: antibiotics, sulphonamides, sedatives and stimulants
Prof. R. Shanthini
Updated: 23 Nov 2012
Primary constituents of Snake Venom
Enzymes - Spur physiologically disruptive or destructive processes.
Proteolysins - Dissolve cells and tissue at the bite site, causing local
pain and swelling.
Cardiotoxins - Variable effects, some depolarise cardiac muscles and
alter heart contraction, causing heart failure.
Harmorrhagins - Destroy capillary walls, causing haemorrhages near
and distant from the bite.
Coagulation - Retarding compounds prevent blood clotting.
Thromboses - Coagulate blood and foster clot formation throughout
the circulatory system.
Haemolysis - Destroy red blood cells.
Cytolysins - Destroy white blood cells.
Neurotoxins - Block the transmission of nerve impulses to muscles,
especially those associated with the diaphragm and breathing.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://www.writework.com/essay/biochemistry-snake-venom
Inhibited enzyme reactions
Inhibitors are also classified as competitive and non-competitive
inhibitors.
Prof. R. Shanthini
Updated: 23 Nov 2012
Competitive inhibition
- The structure of inhibitor molecule closely resembles the
chemical structure and molecular geometry of the substrate.
- The inhibitor competes for the same active site as the
substrate molecule.
- It does not alter the structure of the enzyme.
- The inhibitor may interact with the enzyme at the active site,
but no reaction takes place.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://www.elmhurst.edu/~chm/vchembook/573inhibit.html
Competitive inhibition
- The inhibitor is "stuck" on the enzyme and prevents any
substrate molecules from reacting with the enzyme.
- However, a competitive inhibition is usually reversible if
sufficient substrate molecules are available to ultimately
displace the inhibitor.
- Therefore, the amount of enzyme inhibition depends upon
the inhibitor concentration, substrate concentration, and the
relative affinities of the inhibitor and substrate for the active
site.
Prof. R. Shanthini
Updated: 23 Nov 2012
http://www.elmhurst.edu/~chm/vchembook/573inhibit.html
Competitive inhibition
Competitive inhibitors (denoted by I) compete with substrate to
occupy the active site of the enzyme.
E+S
k1
ES
k3
E+P
k2
E+I
k4
EI
k5
where
rP = k3 CES
CE0 = CE + CES + CEI
Prof. R. Shanthini
Updated: 23 Nov 2012
(17)
(18)
Competitive inhibition
Assuming rapid equilibrium, we get
k1 CE CS = k2 CES
KM =
k2
k1
=
CE CS
CES
(19)
k4 CE CI = k5 CEI
KI =
Prof. R. Shanthini
Updated: 23 Nov 2012
k5
k4
=
CE CI
CEI
(20)
Competitive inhibition
Combining (17) to (20), we get
rP =
where
k3CE0CS
=
KM (1 + CI / KI) + CS
rmax = k3CE0
KM,app = KM (1 + CI / KI)
KM = k2 / k1
Prof. R. Shanthini
Updated: 23 Nov 2012
rmaxCS
KM,app + CS
(5)
(22)
(6)
KM,app > KM
(21)
Competitive inhibition
The Lineweaver-Burk Plot
1
CI > 0
- rS
CI = 0 (no inhibitor)
1
1
- KM
- KM, app
1
rmax
1
CS
Prof. R. Shanthini
Updated: 23 Nov 2012
Competitive inhibition
In the presence of a competitive inhibitor,
the maximal rate of the reaction (rmax) is unchanged,
but the Michaelis constant (KM) is increased.
Prof. R. Shanthini
Updated: 23 Nov 2012
Competitive inhibition – an example
Ethanol is metabolized in the body by oxidation to acetaldehyde,
which is a toxic compound and a known carcinogen.
Prof. R. Shanthini
Updated: 23 Nov 2012
The enzyme alcohol dehydrogenase (ADH)
converts ethanol into acetaldehyde plus two
hydrogen atoms.
Competitive inhibition – an example
Acetaldehyde is generally short-lived; it is quickly broken down to
a less toxic compound called acetate in a rapid reaction so that
acetaldehyde does not accumulate in the body.
.
Prof. R. Shanthini
Updated: 23 Nov 2012
The enzyme aldehyde dehydrogenase
(ALDH) converts acetaldehyde to acetyl
(acetate) radical and a hydrogen atom.
Competitive inhibition – an example
A drug, disulfiram (Antabuse) inhibits the aldehyde
dehydrogenase.
Such inhibition results in the accumulation of acetaldehyde in
the body.
High levels of acetaldehyde act directly on the heart and blood
vessels, causing flushing, a racing heartbeat and a drop in
blood pressure that causes dizziness. Other unpleasant
symptoms include headache, shortness of breath, palpitations,
nausea and vomiting.
This drug is sometimes used to help people overcome the
drinking habit.
Prof. R. Shanthini
Updated: 23 Nov 2012
Non-competitive inhibition
- The structure of inhibitor molecule is entirely different from
that of the substrate molecule.
- The inhibitor forms complex at a point other than the active
site (remote from or very close to the active site).
- It does not complete with the substrate.
- It alters the structure of the enzyme in such a way that the
substrate can no longer interact with the enzyme to give a
reaction.
Prof. R. Shanthini
Updated: 23 Nov 2012
https://ibhumanbiochemistry.wikispaces.com/C.7.5
Non-competitive inhibition
- Non competitive inhibitors are usually reversible,
- but are not influenced by concentrations of the substrate as
is the case for a reversible competitive inhibitor.
Prof. R. Shanthini
Updated: 23 Nov 2012
https://ibhumanbiochemistry.wikispaces.com/C.7.5
Non-competitive inhibition
E+S
k1
ES
k2
E+I
k4
EI
k5
EI + S
k6
ESI
k7
ES + I
k8
k9
Prof. R. Shanthini
Updated: 23 Nov 2012
ESI
k3
E+P
Non-competitive inhibition
We could drive the rate equation (given on the next page)
assuming the following:
k2
k1
k5
k4
Prof. R. Shanthini
Updated: 23 Nov 2012
= KM =
= KI =
k7
k6
k9
k8
= KIM
= KMI
Non-competitive inhibition
rP =
rmax,appCS
(23)
KM + CS
where
rmax,app =
rmax
(1 + CI / KI)
(24)
rmax = k3CE0
(5)
KM = k2 / k1
(6)
Prof. R. Shanthini
Updated: 23 Nov 2012
rmax,app < rmax
Non-competitive inhibition
The Lineweaver-Burk Plot
1
CI > 0
- rS
1
rmax,app
1
- KM
CI = 0 (no inhibitor)
1
rmax
1
CS
Prof. R. Shanthini
Updated: 23 Nov 2012
Non-competitive inhibition
In the presence of a non-competitive inhibitor,
the maximal rate of the reaction (rmax) is lower
but the Michaelis constant (KM) is unchanged.
Prof. R. Shanthini
Updated: 23 Nov 2012
Uncompetitive inhibition
E+S
k1
ES
k2
ES + I
k4
ESI
k5
Inhibitor can only bind to the
enzyme-substrate complex,
reversibly forming a
nonproductive complex.
Prof. R. Shanthini
Updated: 23 Nov 2012
k3
E+P
Uncompetitive inhibition
An uncompetitive inhibitor binds only to the enzyme-substrate
complex preventing the formation or release of the enzymatic
products.
Unlike with competitive inhibition an uncompetitive inhibitor
need not resemble the structure of the enzymes natural
substrate.
An uncompetitive inhibitor is most effective at high substrate
concentration as there will be more enzyme-substrate
complex for it to bind.
Unlike with competitive inhibitors the effects of an
uncompetitive inhibitor cannot be overcome by increasing the
concentration of substrate.
Prof. R. Shanthini
Updated: 23 Nov 2012
Non-competitive inhibition
rP =
rmax,appCS
(23)
KM + CS
where
rmax,app =
rmax
(1 + CI / KI)
(24)
rmax = k3CE0
(5)
KM = k2 / k1
(6)
Prof. R. Shanthini
Updated: 23 Nov 2012
rmax,app < rmax
Uncompetitive inhibition
rmax,appCS
rP =
KM,app + CS
(25)
where
rmax,app =
rmax
(1 + CI / KI)
KM,app = KM / (1 + CI / KI)
(24) rmax,app < rmax
(26) KM,app < KM
rmax = k3CE0
(5)
KM = k2 / k1
(6)
Prof. R. Shanthini
Updated: 23 Nov 2012
Uncompetitive inhibition
KM is reduced
rmax is also reduced
This is because the total ‘pool’ of enzymes available to react
has been reduced, effectively our enzyme concentration has
reduced.
Can be explained by rmax = k3CE0 = kcatCE0
Prof. R. Shanthini
Updated: 23 Nov 2012
Uncompetitive inhibition
The Lineweaver-Burk Plot
1
- rS
CI > 0
1
rmax,app
CI = 0 (no inhibitor)
1
- KM, app
1
1
Prof. R. Shanthini - K
Updated: 23 Nov 2012 M
rmax
1
CS
Competitive versus Uncompetitive inhibition
Prof. R. Shanthini
Updated: 23 Nov 2012
Mixed inhibition
Prof. R. Shanthini
Updated: 23 Nov 2012
An exercise
The kinetic properties of the ATPase enzyme, isolated from yeast,
which catalyzes the hydrolysis of ATP to form ADP and Pi, are
assessed by measuring initial rates in solution, with various ATP
concentrations S0 and a total ATPase concentration E0 = 0.60 μM.
From these experiments, it is determined that
Vmax = 1.20 μM/s; KM = 40 μM.
a. Calculate the values of kcat and the catalytic efficiency for ATPase
under these conditions.
b. An inhibitor molecule is added at a concentration of 0.1 mM, and
the experiments are repeated. The apparent Vmax and KM are now
found to be 0.6 μM/s, and 20 μM, respectively. Speculate on how
this inhibitor works (i.e., specify which species are engaged by the
inhibitor).
Prof. R. Shanthini
Updated: 23 Nov 2012
Source: Jason Haugh, Department of Chemical &
Biomolecular Engineering, North Carolina State University
Substrate / Product inhibition
Either the substrate or product of an enzyme reaction inhibit
the enzyme's activity.
This inhibition may follow the competitive, uncompetitive or
mixed patterns.
In substrate inhibition there is a progressive decrease in
activity at high substrate concentrations.
Product inhibition is often a regulatory feature in metabolism
and can be a form of negative feedback.
Prof. R. Shanthini
Updated: 23 Nov 2012
Substrate / Product inhibition
Prof. R. Shanthini
Updated: 23 Nov 2012
Assignment
Get the rate equations for substrate and product inhibition
Prof. R. Shanthini
Updated: 23 Nov 2012
“Food for Thought”
Problem 3.13 from Shuler & Kargi:
The following substrate reaction rate (-rS)
data were obtained from enzymatic
oxidation of phenol by phenol oxidase at
different phenol concentrations (CS).
By plotting (-rS) versus (CS) curve, or
otherwise, determine the type of inhibition
described by the data provided?
Prof. R. Shanthini
Updated: 23 Nov 2012
CS
(mg/l)
10
-rS
(mg/l.h)
5
20
30
7.5
10
50
60
80
12.5
13.7
15
90
110
130
15
21.5
9.5
140
150
7.5
5.7
Sigmoid/Hill kinetics
A particular class of enzymes exhibit kinetic properties that
cannot be studied using the Michaelis-Menten equation.
The rate equation of these unique enzymes is characterized
by Sigmoid/Hill kinetics as follows:
rP =
Hill constant
rmaxCSn
K + CS n
(27) The Hill
equation
Hill coefficient
n = 1 gives Michaelis-Menten kinetics
n > 1 gives positive cooperativity
n < 1 gives negative cooperativity
Prof. R. Shanthini
Updated: 23 Nov 2012 http://chemwiki.ucdavis.edu/Biological_Chemistry/Catalysts/Enzymatic_Kinetics/Sigmoid_Kinetics
Sigmoid/Hill kinetics
Examples of the “S-shaped” sigmoidal/Hill curve, which is
different from the hyberbolic curve of M-M kinetics.
n=6
n=4
n=2
Prof. R. Shanthini
Updated: 23 Nov 2012
Sigmoid kinetics
For an alternative formulation of Hill equation, we could
rewrite (25) in a linear form as follows:
θ =
ln
θ
1-θ
rP
rmax
=
CSn
K + CS n
= n ln(CS) – ln (K)
(28)
Prof. R. Shanthini
Updated: 23 Nov 2012 http://chemwiki.ucdavis.edu/Biological_Chemistry/Catalysts/Enzymatic_Kinetics/Sigmoid_Kinetics
Allosteric enzyme
Find out what it is on your own
Prof. R. Shanthini
Updated: 23 Nov 2012 http://chemwiki.ucdavis.edu/Biological_Chemistry/Catalysts/Enzymatic_Kinetics/Sigmoid_Kinetics