Download Lecture * 4 The Kinetics of Enzyme

Lecture – 4
The Kinetics of Enzyme-Catalyzed
Reactions
Dr. AKM Shafiqul Islam
School of Bioprocess Engineering
University Malaysia Perlis
08.01.10
Michaelis-Menten Kinetics
• Enzyme E and substrate S combine to form a
complex ES, which then dissociates into
product P and free or uncombined enzyme E:
Michaelis-Menten Kinetics
• Equilibrium Constant
• Enzyme balance
• Decomposition of the complex to product and free
enzyme is irreversible.
• Product formation Rate, v
Michaelis-Menten Kinetics
• Solving the equations
e  eo  es 
• Substitute e in following equation
se
k 1

 Km
es  k1
se0
se  
Km  s
Michaelis-Menten Kinetics
• From Product formation equation
e0 s
 k2
Km  s
vmax s
v
Km  s
Where
vmax  k2e0
Quasi-steady-state Approximation
• Briggs and Haldane first proposed Quasisteady-state assumption
• Applying mass balance for substrate and
intermediate
ds
v    k1se  k 1 es 
dt
d es 
 k1se  k 1  k 2 es 
dt
Quasi-steady-state Approximation
• In a batch reactor at closed system [E0] is considered
very small compared S
Therefore, d(es)/dt ≈0
From equation
d es 
 k1se  k 1  k 2 es 
dt
k1se
es  
k 1  k 2 
Quasi-steady-state Approximation
• Substituting e
se0
es   k  k
1
2
s
k1
Production formation kinetics
ds dp
v 
 k 2 es 
dt dt
k 2 e0 s

k 1  k 2  / k1   s
Quasi-steady-state Approximation
Substituting
vmax  k2e0
and
k 1  k 2
Km 
k1
vmax s
v
Km  s
There is difference between Michaelis-Menten
and Quasi-steady-state constant.
Evaluation of Parameters in MichaelisMenten Equation
Lineweaver-Burk plots are convenient
for determination of Km
• Double reciprocal plot
Eadie–Hofstee plot
plot v versus v/[S] gives a
line of slope –Km and y-axis
intercept of Vm
Hanes–Woolf plot
• Plot of [S]/v versus [S] gives
line of slope I/Vm and y-axis
intercept of Km/Vm.
• This plot is used to
determine Vm more
accurately.
Modulation and Regulation of Enzyme
Activity
• Chemical species other than the substrate can
combine with enzymes to alter or modulate
their catalytic activity.
• Such substances are called modulators or
effectors, may be normal constituents of the
cell.
• They enter from the cell's environment or act
on isolated enzymes.
Modulation and Regulation of Enzyme
Activity
• The combination of an enzyme with an
modulator is chemical reaction
• Modulator can be fully reversible, partially
reversible, or essentially irreversible.
• Examples of irreversible inhibitors include poisons
such as cyanide ions, which deactivate xanthine
oxidase,
• Nerve gases, which deactivate cholinesterases
(enzymes which are part of nerve transmission).
Modulation and Regulation of Enzyme
Activity
• Reversible modulation of enzyme activity is one
control mechanism employed by the cell to achieve
efficient use of nutrients.
• The enzyme regulation involve interconnected
networks of reactions with several control loops
Modulation and Regulation of Enzyme
Activity
• Example, five-step sequence for the
biosynthesis of the amino acid L-isoleucine.
Regulation of this sequence is achieved by
feedback inhibition:
Modulation and Regulation of Enzyme
Activity
The final product, L-isoleucine, inhibits the
activity of the first enzyme.
Thus, if the final product begins to build up,
the biosynthesis process will be stopped
Modulation and Regulation of Enzyme
Activity
• enzyme-substrate inhibitors systems classify by their
influence on the Michaelis-Menten equation
parameters vmax and Km
• Reversible inhibitors are termed competitive if their
presence increases the value of Km but does not alter
vmax The effect of such inhibitors can be countered or
reversed by increasing the substrate concentration.
• On the other hand, by rendering the enzyme or the
enzyme-substrate complex inactive, a noncompetitive
inhibitor decreases the vmax of the enzyme but does
not alter the Km value.
Mechanisms of Reversible Enzyme
Modulation
• Many competitive inhibitors bear close
relationships to the normal substrates. This
are called substrate analogs.
It is thought that these inhibitors have the key
to fit into the enzyme active site, or lock,
But the key is not quite right so the lock does
not work; i.e., no chemical reaction results.
Mechanisms of Reversible Enzyme
Modulation
• For example, inhibition of succinic acid
dehydrogenation by malonic acid:
The malonic acid can complex with succinic
dehydrogenase, but it does not react
Mechanisms of Reversible Enzyme
Modulation
• How the sulfa-drug act against bacteria?
The action of one of the sulfa drugs,
sulfanilamide, is due to its effect as a
competitive inhibitor.
Mechanisms of Reversible Enzyme
Modulation
• Sulfanilamide is very
similar in structure to paminobenzoic acid, an
important vitamin for
many bacteria.
By inhibiting the enzyme which causes paminobenzoic acid to react to give folic acid, the
sulfa drug can block the biochemical machinery of
the bacterium and kill it.
• Some noncompetitive inhibition and is
thought to be the dominant mechanism for
noncompetitive inhibition and activation.
These are called allosteric control
• An enzyme which possesses sites for
modulation as well as catalysis has
consequently been named an allosteric
enzyme.