From FRET Imaging to Practical Methodology for Kinase Activity Sensing in Living Cells - Progress in Molecular Biology and Translational Science - page 158

where F D (l) is the corrected fluorescence donor (dimensionless) and e A is
the extinction coefficient of the acceptor at l (expressed in M -1 cm -1 ).

2

3.4. Orientation factor k

2

k can vary from 0 to 4 according to the following equation:

2

2

k ¼ ð cosy T 3cosy D cosy A Þ

2

¼ ð siny D siny A cosF 2cosy D cosy A Þ ½ 5 : 20

where y A , y D , y T , and F are as shown in in Fig. 5.8 .
Additionally, the fluctuation of refractive index n can induce errors in the
calculated distance r but this effect is not usually considered.
The orientation factor (k

2

) characterizes the statistical average of the rel-
ative fluorophore orientations, and determines both how well the fluo-
rophore dipoles are coupled and how efficiently energy is transferred
( Fig. 5.8 ). However, if the dipoles are perpendicular, k

2

becomes zero,
which would result in serious errors in the calculated distance. This question
has been discussed in detail. 16-18

2

does not
induce major errors in the calculated distance; however, for
intramolecular FRET in biosensors this question is of importance. In fact,
in a rigid molecule (such as a polypeptide with four to nine amino acid
residues) with isotropic orientational distribution (statistically randomly
distributed) of the donor and the acceptor transition moments but with
no rotation during the lifetime of excited state (frozen), the value of
k

In general, the variation of k

2 2 at room temperature is

¼ 0.476 can be used. The optimal value of k

2/3. 19 For a fluorophore bound to macromolecules (i.e., fluorescent

D em

q D

2 =1

f K

2 =0

K

q T

q A

2 =4

K

A ex

2

Figure 5.8 Parameters involved in the calculation of the orientation factor k .