Mechanisms of enzyme inhibition
• 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
substrate us already present.
ESI ↔ ES + I
• The efficiency of the inhibitor (as well as the type of
inhibition) can be determined with controlled experiments
• Lineweaver–Burk plots
characteristic of the three
major modes of enzyme
inhibition:
• (a) competitive inhibition,
• (b) uncompetitive
inhibition, and
• (c) non-competitive
inhibition, showing the
special case α = α′ > 1.
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
23.7 Kinetics of photochemical reactions
• Primary photochemical process:
products are formed directly from the
excited state of a reactant.
• Secondary photochemical process:
intermediates are formed directly from the
excited state of a reactant.
• Photophysical processes compete with the
formation of photochemical products via
deactivating the excited state
• Times scales of photophysical processes
Within 10-16 ~ 10-15 s for electronic transitions induced by
radiation and thus the upper limit for the rate constant of a
first order photochemical reaction is about 1016 s-1.
10-12 ~ 10-6s for fluorescence
10-12 ~ 10-4s for intersystem crossing (ISC)
10-6 ~ 10-1s for phosphorescence (large organic molecules)
• A slowly decaying excited species can undergo a very large
number of collisions with other reactants before deactivation.
• The interplay between reaction rates and excited state
lifetimes is a very important factor in the determination of
the kinetic feasibility of a photochemical process.
• The primary quantum yield, φ, the number of
photophysical or photochemical events that lead to
primary products divided by the number of photons
absorbed by the molecules in the same time interval,
or the radiation-induced primary events divided
by the rate of photo absorption.
 
number of events
v (rate of the process)

number of photonsabsorbed I abs (intensity of light absorbed)
• The sum of primary quantum yields for all
photophysical and photochemical events must
be equal to 1
 i  1
i
vi
i i  i I
abs
• From the above relationship, the primary
quantum yield may be determined directly from
the experimental rates of ALL photophysical
and photochemical processes that deactivate
the excited state.
vi
i 
 vi
Decay mechanism of excited singlet state
• Absorption:
S + hvi → S*
vabs = Iabs
S* → S + hvi
vf = kf[S*]
• Fluorescence:
• Internal conversion: S*
→ S
vIC = kIC[S*]
• Intersystem crossing: S*
→ T*
vISC = kISC[S*]
S* is an excited singlet state, and T* is an excited triplet state.
The rate of decay
•
d [ S*]
dt
= - kf[S*] - kIC[S*] - kISC[S*]
When the incident light is turn off, the excited state decays exponentially:
[ S*]t  [ S*]0 e
t / 0
with
0 
1
k f  k IC  k ISC
• If the incident light intensity is high and the absorbance
of the sample is low, we may invoke the steady state
approximation for [S*]:
Iabs - kf[S*] - kIC[S*] - kISC[S*] = 0
Consequently,
Iabs = kf[S*] + kIC[S*] + kISC[S*]
The expression for the quantum yield of fluorescence
becomes:
vf
kf
 f ,0 

I abs k f  k IC  k ISC
• The above equation can be applied to calculate the
fluorescence rate constant.
Quenching
• The presence of a quencher, Q, opens an additional channel for the
deactivation of S*
S* + Q → S + Q
vQ = kQ[Q][S*]
Now the steady state approximation for [S*] gives:
Iabs - kf[S*] - kIC[S*] - kISC[S*] - kQ[Q][S*] = 0
The fluorescence quantum yield in the presence of quencher
becomes
k
f 
f
k f  k IC  k ISC  kQ [Q]
• The ratio of Φf,0/ Φf is then given by
 f ,0
 1   o kQ [Q]
f
• Therefore a plot of the left-hand side of the above equation against
[Q] should produce a straight line with the slope τ0kQ. Such a plot is
called Stern-Volmer plot.
• The fluorescence intensity and lifetime are both
proportional to the fluorescence quantum yield, plot of
If,0/I0 and τ0/ τ against [Q] should also be linear with
the same slope and intercept as
f
 1   o k Q [Q ]

• Self-test 23.4 The quenching of tryptophan
fluorescence by dissolved O2 gas was monitored by
measuring emission lifetimes at 348 nm in aqueous
solutions. Determine the quenching rate constant for
this process
[O2]/(10-2 M) 0
2.3
5.5
8
10.8
Tau/(10-9 s) 2.6
1.5
0.92 0.71 0.57
Three common mechanisms for
bimolecular quenching
1. Collisional deactivation:
S* + Q → S + Q
is particularly efficient when Q is a
heavy species such as iodide ion.
2. Resonance energy transfer:
S* + Q → S + Q*
3. Electron transfer: S* + Q → S+ + Qor
S* + Q → S- + Q+