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Lecture 20

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Lecture 20
Mechanisms of enzyme inhibition
• Michaelis-Menten mechanism
E + S → ES
ES
→E + S
ES
→P + E
k1
k2
k3
• Competitive inhibition: the inhibitor (I) binds only to the active site.
EI ↔ E + I
• Non-competitive inhibition: binds to a site away from the active site.
It can take place on E and ES
EI ↔ E + I
ESI ↔ ES + I
• Uncompetitive inhibition: binds to a site of the enzyme that is
removed from the active site, but only if the substrates already
present.
ESI ↔ ES + I
• The efficiency of the inhibitor (as well as
the type of inhibition) can be determined
with controlled experiments
vmax
v
a'  aK M /[ S ]0
or
1
a'  aK M  1


 
v vmax  vmax  [ S ]0
where a  1  [ I ] / K I and
a' 1  [ I ] / K I'
Autocatalysis
• Autocatalysis: the catalysis of a reaction by its products
A + P →
2P
d[ P ]
The rate law is
= k[A][P]
dt
To find the integrated solution for the above differential equation, it is
convenient to use the following notations
[A] = [A]0 - x; [P] = [P]0 + x
One gets
d[ P ]
dt
= k([A]0 - x)( [P]0 + x)
integrating the above ODE by using the following relation
1
1
1
1

(

)
([ A]0  x )([ P ]0  x ) [ A]0  [ P ]0 [ A]0  x [ P ]0  x
gives
or rearrange into
 ([ P ]0  x )[ A]0 
1
  kt
ln 
[ A]0  [ P ]0  [ P ]0 ([ A]0  x ) 
x
e at  1

[ P ]0 1  be at
with a=([A]0 + [P]0)k and b = [P]0/[A]0
• Exercise 23.12a The pKa of NH4+ is 9.25 at 25.0 oC for
the reaction of NH4+ and OH- to form aqueous NH3 is 4.0
x 1010 dm3 mol-1 s-1. Calculate the rate constant for
proton transfer to NH3. What relaxation time would be
observed if a temperature jump was applied to a solution
of 0.15 mol dm-3 NH3(aq) at 25.0 oC?
• Solution:
pKa corresponds: NH4+ + H2O(l) ↔ NH3(aq) + H3O+(aq)
The rate constant to be calculated is from
NH3 + H2O(l) ↔ NH4+(aq) + OH-(aq)
Utilizing the relationship pKa + pKb = pKw
• Time constant and relaxation time
• 22.14a The rate constant for the
decomposition of a certain substance is
2.8 x 10-3 dm3 mol-1 s-1 at 30 oC and 1.38 x
10-2 dm3 mol-1 s-1 at 50 oC. Evaluate the
Arrhenius parameters of the reaction.
• Hint: Arrhenius parameters include A and
Ea
k = A e(-Ea/RT), where R is the universal
constant
• Numerical Problem 25.1 (7th edition)
The data below applies to the formation of urea
from ammonium cyanate NH4CNO →
NH2CONH2. Initially 22.9 g of ammonium
cyanate was dissolved in enough water to
prepare 1.00 L of solution. Determine the order
of the reaction, the rate constant, and the mass
of ammonium cyanate left after 300 min.
t/min
0
20.0 50.0 65.0 150.0
M(urea)/g 0
7.0 12.1 13.8 17.7
• Solution
• Discussion problem: Bearing in mind distinctions
between the mechanisms of stepwise and chain
polymerization, describe ways in which it is
possible to control the molar mass of a polymer
by manipulating the kinetic parameters of
poltmerization.
• Answers:
For stepwise polymerization the degree of
polymerization is given by
<n> = 1 + kt[A]0
For chain polymerization the kinetic chain length
is calculated through
<n> = kp(f ki/kt)-1/2 [M] [I]-1/2
• Distinguish between competitive, noncompetitive, and uncompetitive inhibition
of enzymes. Discuss how these modes of
inhibition may be detected experimentally.
• Hint: Using Lineweaver-burk plot, look for
differences in the intercept with y-axis and
changes in the slope.
• Exercise 26.6b (7th edition) or 23.2b (8th edition)
Consider the following mechanism for the thermal
decomposition of R2
(1) R2 → R + R
(k1)
(2) R + R2 → PB + R’
(k2)
(3) R’ → PA + R
(k3)
(4) R + R → PA + PB (k4)
Where R2, PA and PB are stable hydrocarbons and
R and R’ are radicals. Find the dependence of
the rate of decomposition of R2 on the
concentration of R2.
• Solution
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