From FRET Imaging to Practical Methodology for Kinase Activity Sensing in Living Cells - Progress in Molecular Biology and Translational Science - page 176

concentrations. It allows determining quantitatively the proportion of inter-
acting donor and the FRET efficiency in living cells.

5.2.1 Frequency-domain lifetime imaging
5.2.1.1 Recovering phase shift and modulation depth in single frequency
experiments
The first step of FD FLIM data analysis consists in retrieving the phase and
modulation values ( ' and m ) from fluorescent images acquired with either
the heterodyne or the homodyne method (see Section 4 ).
With the heterodyne method, the detector is modulated at a frequency
o þD o (where D o is a low frequency in the kilohertz range), which is
slightly different from the modulation frequency o of the excitation source.
The resulting signal collected by the FLIM system ( S heterodyne ) is thus mod-
ulated in time at the low frequency D o:

m ex m de m
2

S heterodyne / 1 þ cos D o t þD f ' ð Þ ½ 5 : 31

where D f is the phase shift between excitation and detection, m ex and m de
are, respectively, the modulation amplitude of excitation and detection. By
recording this signal S heterodyne at various time delays t and fitting it as a func-
tion of time with a cosine function of the low cross-correlation frequency
D o, we can extract the phase shift ' and modulation depth m for each pixel

of the FLIM image.
In the homodyne implementation (when the frequencies of excitation
and detection are identical), the collected signal, which is no longer mod-
ulated, is a direct current (DC) component defined by

m ex m de m
2

S homodyne / 1 þ cos D f ' ð Þ ½ 5 : 32

with m ex and m de , respectively, the modulation amplitude of excitation
and detection. The phase shift D f between excitation and detection varies
from 0 to 360 (2p) with K equally spaced intervals. For each phase shift
D f, the DC collected signal is recorded for each pixel of the FLIM
image. By fitting this collected signal S homodyne with a cosine function of
D f, the resulting phase ' and modulation m are calculated pixel by pixel

(cf. Fig. 5.17 ).

5.2.1.2 Calculation of the fluorescence lifetime and data representation
Once the phase and modulation m have been determined for each pixel of

the image, these m and

'

values are further manipulated for evaluating the
fluorescence lifetime of the sample. In order to obtain correct lifetime values

'