Chemistry Reference
In-Depth Information
FREToperates through a dipole
-
dipole interactionmechanism, accounting for the
distance dependence in Equation 9.4. The angular dependence is absorbed in
the Forster radius R
0
using the orientation factor
2
, which depends on the relative
orientation of the donor and acceptor transition dipoles.
The FRETef
ciency E is the quantum ef
ciency of the FRETprocess. We calculate
E similarly to Q
r
,
E
k
¼
k
FRET
=ð
k
FRET
þ
k
r
þ
k
nr
þ
k
ISC
þ
k
bl
Þ
k
FRET
=ð
k
FRET
þ
k
r
þ
k
nr
Þ:
ð
9
:
5
Þ
During the repeated cycling through the Jablonski diagram during single molecule
measurements, E is the probability that a D excitation will be transferred to A. Even
without a change in R, some excitations will cause D emission, and others will be
transferred to A, causing A emission. Using Equations 9.1 and 9.4, Equation 9.5 can
be rewritten as
!
6
R
R
0
E
¼
1
=
1
þ
ð
9
:
6
Þ
The distance dependence of E allows its use as measure of the distance between D
and A near R
0
(typically 5
-
7 nm for dyes used in single-molecule
uorescence
spectroscopy).
9.2.5
Single-molecule Electron Transfer-Ångstrøm-scale Ruler
Electron transfer between a donor and an acceptor molecule occurs at a rate k
ET
that
depends on two main factors: the coupling between the reactant and product
electronic wave functions V
R
, and the Franck
-
Condon weighted density of states
FC [20, 21]. The latter is usually constant for macromolecules and therefore one is left
with the electronic coupling term, which depends exponentially on the distance
between donor and acceptor:
V
R
¼
V
0
exp
ðb
R
Þ
ð
9
:
7
Þ
has been measured for different systems to vary from 1.0 to 1.4 Å
1
in
proteins. The electron transfer rate k
ET
can be accessed by measuring the donor
fluorescence emission, or the donor
fluorescence lifetime, assuming that no other
process in
uences these two observables. Fluorescence quenching by electron
transfer can be used to monitor minute conformational changes in biopolymers as
it requires close contact between thedonor and acceptormolecules. This approachhas
been used at the single-molecule level to study dye-labeled polypeptides containing a
tryptophan residue [22], and a
avin reductase enzyme inwhich the
uorescence of an
isoalloxazine is modulated by photo-induced electron transfer to a tyrosine [23].
This brief overview of some of the photophysical characteristics of
uorophores
used in single-molecule spectroscopy has illustrated theoretically how sensitive the
absorption and emission can be to the local environment of the
where
b
uorophore.
Therefore, any modi
cation or
fluctuation of
fluorescence intensity or lifetime (the
