Principles of Fluorescence Spectroscopy

PRINCIPLES OF FLUORESCENCE SPECTROSCOPY 299
to be the volume fraction of membrane phase, one obtains 87
(8.39)
Substitution of this expression for the membrane concentration
of quencher into the Stern-Volmer equation yields
(8.40)
where k m is the bimolecular quenching constant for the
membrane-bound fluorophore. The apparent quenching
constant is given by
1
k app
Q m
(8.41)
When the fluorophore is present in the membrane phase,
the apparent quenching constant is dependent upon P, α m
and k m . A plot of k app –1 vs. α m allows P and k m to be determined.
Thus, the quenching method allows simultaneous
quantitation of both the extent to which a quencher partitions
into a bilayer and its diffusion rate (D q ) in this bilayer.
The successful determination of the quencher diffusion
and partition coefficients requires that the range of lipid
concentrations results in a range of fractional partitioning of
the quencher. The fraction of the quencher partitioned in the
membrane (f m ) is given by
f m
P Q T
Pα m (1 α m)
1 1 kmP QT 1
k
τ τ0 Pαm (1 αm) τ
appQT 0
1
αm (
km 1 1 )
kmP kmP Pα m
Pα m (1 α m)
(8.42)
To calculate the volume fraction of the lipid, the usual
assumption is equal densities for the water and membrane
phases. In this case a 10-mg/ml membrane suspension corresponds
to α m = 0.01. The above method of determining
the lipid–water partition coefficient only applies when the
quencher molecules are present in the bilayer at the moment
of excitation. If the diffusional encounters involve molecules
in the aqueous phase, which diffuse into the lipid
phase during the lifetime of the excited state, then no
dependence of the apparent quenching on lipid concentration
is expected. The situation is more complex when the
quenching results from quenchers in both the lipid phase
and in the water phase.
Figure 8.33. Quenching of 1-oleoyl-2-hexanoyl-NBD-glycerol
(NBD-DG) by 5-doxylstearate (5-NS). α m refers to the volume fraction
of the egg PC phase. Revised from [92]. Copyright © 1994, with
permission from Elsevier Science.
A number of publications have appeared on the effect
of partitioning and quenching. 87–92 One example is quenching
of a NBD-labeled lipid by the nitroxide fatty acid 5doxylstearate
(5-NS). In contrast to the nitroxide-labeled
PCs, the fatty acids have a low but significant solubility in
water. When NBD-labeled vesicles are titrated with 5-NS
the Stern-Volmer plots are dependent on lipid concentration
(Figure 8.33). At lower lipid concentrations addition of the
same total amount of 5-NS results in larger amounts of
quenching than observed at higher lipid concentrations. At
low lipid concentrations, the added quencher results in a
higher quencher concentration in the membrane. This is
because there is less lipid into which the quencher can partition.
It is this dependence of the apparent quenching constant
on lipid concentration that allows the partition coefficient
to be determined. This is done by a plot of k app –1 vs.
α m (Figure 8.34). The data indicate that 5-NS partitions
almost 10,000-fold into the lipid phase, and that the bimolecular
quenching constant is 1.1 x 10 9 M –1 s –1 . Use of the
Smoluchowski equation yields a mutual diffusion coefficient
for the probe and quencher near 3 x 10 –6 cm 2 /s. This
value is larger than expected for a quencher in a membrane,
and 100-fold larger than the diffusion coefficient of lipid in
membranes determined by fluorescence recovery after photobleaching
(FRAP). This difference is probably the result
of different diffusion coefficients for short- and long-range
diffusion in membranes, the so-called anomalous sub-diffusion
(Chapter 24).