From FRET Imaging to Practical Methodology for Kinase Activity Sensing in Living Cells - Progress in Molecular Biology and Translational Science - page 156

3.2. FRET basis
FRET is one possible pathway for the relaxation of the excited state mole-
cules. This phenomenon occurs only under appropriate conditions of prox-
imity and orientation between two fluorophores (donor and acceptor),
which are as follows:
1. This form of energy transfer occurs in the near field of the donor. In
other words, the distance ( r ) between D and A must be less than
10 nm ( r 0.

2. The energy transfer is achieved between molecules with resonant oscil-
lation dipole moments (overlapping wave functions). This requires an
overlap between the D emission spectrum and the A excitation
spectrum.
3. The orientation of the emission dipole moment of D with respect to the
excitation dipole moment of D must be such as for FRET to occur.
The theoretical concept for FRET was developed following both the clas-
sical model by Perrin in 1925 followed by the quantummechanical model in
1932 and by F ¨ rster in 1946-1949 13-15 (for review see Refs. 5,6 ).
If one considers a single donor and acceptor separated by a distance r , the
rate of energy transfer K T ( r ) can be calculated as a probability of the transfer
of an energy quantum from D to A per time unit, given by the fundamental
equation

< 10 nm) so that K T 6¼

J ðÞ

ð 1

2

F D k 9000 ln 1 ðÞ

128p

K T r ðÞ¼ F D ðÞ dl ½ 5 : 14

t D r 6

5 n 4 N A

0

where F D is the donor quantum yield (as previously described in this chap-
ter) in the absence of acceptor, t D the donor lifetime in the absence of ac-
ceptor, n is the refractive index of the medium, N A is the Avogadro's
number, J ( l ) is the overlap integral, F D is the normalized fluorescence in-
tensity of the donor, and k

2 is a dimensionless orientation factor describing
the relative spatial orientation of the donor and acceptor transition moments.
Note that e A , F D , and n are fixed by the choice of FRET pairs and the me-
dium. Therefore, K T ( r ) variation is mainly dependent on r and k.
Equation (5.14) is not easy to use for the design of biochemical exper-
iments 6 . This is why the F ¨ rster distance R 0 was introduced by F ¨ rster in
1948. When the transfer rate K T ( r ) is equal to the decay rate of the donor
in absence of an acceptor, one-half of the donor molecules decay by the en-
ergy transfer process. Once the value of R 0 is known, the rate of energy
transfer K T can be easily calculated as