Biomedical Engineering Reference
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where it would be effective during the excited-state lifetime of the fluorophore. The num-
ber of quenchers in V q can be expressed by a Poisson distribution:
n
n
n
[2.9]
P
exp
n
n
!
where P n is the probability of finding Q in the quenching sphere volume dimensions and
n represents the mean number of quenchers that occupy the volume of the quenching
sphere:
[2.10]
VnVN
q
:
Q
q
a
Similarly, the probability of Q not being in the quenching sphere can also be defined as a
Poisson distribution:
P
exp
n
exp
V N
Q
[2.11]
0
q
a
Therefore, fluorescence intensity would be proportional to P 0 because this population
would represent the distribution of fluorophores not affected by the quencher, as it lies
outside the sphere of effective quenching (17). This leads to the following expression of
Perrin's model for quenching in terms of intensity:
I
I
[2.12]
0
exp
VN
q
Q
a
A plot of ln( I 0 / I ) vs. [Q] will give the value of V q where the typical sphere radius is ~10 Å (17).
In the Perrin model of the presence of a sphere of effective quenching, the quencher and the
fluorophore do not form a complex, but are rather just in very close proximity to one another.
Another form of static quenching exists where the fluorophore and quencher form a 1:1
complex that is nonfluorescent.
2.2.3.11 Formation of a Ground-State Nonfluorescent Complex (Preassociation)
The equilibrium of a complex formed between and F and Q can be expressed as:
[2.13]
FQ FQ
Analogous to the Perrin model for static quenching, the fluorescence decay lifetime after
time-resolved pulse excitation for unassociated (uncomplexed) fluorophore is unaffected
while the overall fluorescence intensity of the solution decreases due to the presence of
quencher in solution (17). The expression for the above equilibrium situation can be
written in terms of an association constant, K s :
FQ
FQ
[2.14]
K s
and according to the law of conservation of mass:
[2.15]
FFFQ
0
In turn, this allows the complex ([FQ]) to be replaced such that:
 
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