Biomedical Engineering Reference
In-Depth Information
Förster developed a series of expressions that define this long-range dipole-dipole
transfer of energy from a donor to an acceptor, and as a consequence, FRET is sometimes
referred to as Förster resonance energy transfer.
The dipole-dipole energy transfer rate constant can be defined as:
6
6
R
r
1
R
r
[2.19]
dd
0
0
k
k
T
D
0
D
where
k
D
represents the emission rate constant of the donor in the absence of energy trans-
fer, is the excited-state lifetime of the donor in the absence of energy transfer (absence of
the acceptor),
r
is the separation distance between the donor and the acceptor, and
R
0
is
the Förster distance, where the transfer to acceptor and decay of the excited donor are both
equally probable (17). In other words, the transfer efficiency is 50% at the Förster distance.
The Förster distance can be defined using the following equation:
1
6
[2.20]
2
4
∫
4
R
0.2108
n
I
( )
( )
d
0
D
D
A
0
where
2
is the orientation factor of the transition dipole moments of the donor and the
o
D
is the fluorescence quantum yield of the donor in the absence of acceptor,
n
is the refractive index of the medium in the wavelength region of spectral overlap, and the
integral expression represents the overlap integral between the donor emission and the
acceptor absorption spectrum (17). This equation can be simplified by allowing
J
(
acceptor,
) to
represent the overlap integral expression:
o
1
6
[2.21]
5
4
2
R
8.79
10
n
J
( )
A
0
D
The orientation factor,
, can then be defined using the angles involved in the orientation
of the transition dipoles of the donor and acceptor relative to one another:
[2.22]
2
cos
3 cos
cos
sin
sin
cos
2 cos
cos
T
D
A
D
A
D
A
2
can range from 0 to 4 where zero represents a perpendicular transition
moment orientation between donor and acceptor and four represents parallel transition
moments between the two species (17):
The transfer efficiency of the fluorescence energy transfer can be written in terms of the
Förster distance and the separation distance between the donor and the acceptor:
The values of
6
[2.23]
E
1(1 (
r R
) )
0
From this expression, it is clear that a 1/
r
6
distance dependence exists for FRET.
Fluorescence resonance energy transfer and the information that can be gathered from
spectroscopic measurements using FRET pairs is a very valuable tool for determining dis-
tances within biomolecules and for biomolecular associations and assemblies. One such bio-
molecular association would be the hybridization of nucleic acid strands. When
determination of distances within or between molecules is desired, FRET can be used as a
“spectroscopic” or “molecular” ruler in the distance range of 1-10 nm (17). There are several
