Biomedical Engineering Reference
In-Depth Information
quencher, respectively,
K
SV
is the Stern
-
Volmer constant,
k
q
represents the rate of decay of
the fluorophore in the presence of quencher, and
0
is the excited-state lifetime of the flu-
orophore in the absence of quencher. In a plot of
I
0
/
I
vs. [Q] (Stern
-
Volmer plot),
K
SV
can
be extracted as the slope if the plot yields a linear relationship of
I
0
/
I
vs. [Q] (17).
In reality, quenching of fluorescence is a time-dependent process, as a result of being a
diffusion-controlled process (17). During the excited-state lifetime of the fluorophore, the
quencher can approach the fluorophore to meet the proximity condition required to
induce a quenching phenomenon. In this case, the
k
q
rate constant must be replaced by a
rate constant that is a function of time,
k
1
(
t
). In the diffusion-controlled model,
k
q
is equal
to the diffusion rate constant
k
1
, where
k
1
can be represented by the following equation:
N
[2.6]
k
4
a
RD
c
1
1000
where
N
a
represents Avogadro's number,
R
c
is the distance of closest approach of the flu-
orophore and quencher (in cm), and
D
is the diffusional coefficient (in cm
2
s
-1
) which can
be expressed by the Stokes-Einstein equation:
kT
f
11
DD D
[2.7]
F
Q
RR
F
Q
where
D
F
and
D
Q
are the translational diffusion coefficients of fluorophore and quencher,
respectively,
k
is the Boltzmann constant,
T
is temperature,
R
F
and
R
Q
are the radii of the
fluorophore and the quencher, respectively,
represents the viscosity of the medium, and
f
is a coefficient of boundary condition (17). This leads to a variation in the Stern
-
Volmer
relationship:
I
I
14
NR D
Y
Q
[2.8]
0
C
0
where
Y
is the “error function” and serves as a multiplying factor for the transient term
that leads to deviations in the linearity of the Stern
-
Volmer plot (17).
2.2.3.9 Static Quenching
The argument for dynamic quenching suggests that the concentration of the quencher is not
in large excess with respect to the fluorophore and therefore must approach the fluorophore
to a distance where quenching would occur (17). If the quencher is in large enough excess
with respect to the fluorophore, Q can be sufficiently close to F such that the interaction
between F and Q is significant and no approach of F to Q (or vice versa) is necessary because
of the high probability of the excited F and Q being in close proximity to each other (17). This
type of quenching is called static quenching and refers to two different possible models.
2.2.3.10 Perrin/Sphere of Effective Quenching
If Q is located within a defined “sphere of quenching” of volume
V
q
, it has the ability to
quench F. The constraint applied on this model is that the F and Q are in fixed positions
brought upon by being in a viscous medium or a rigid matrix (17). A quencher that lies
outside of the sphere of effective quenching does not have an effect on the fluorescence
emission of the fluorophore in that the fluorescence decay after pulse excitation is not
affected because the quencher is too far away from the fluorophore to reach a proximity