Biology Reference
In-Depth Information
and TD
89,92
FLIM acquisition systems and it has been recently used with
biosensors.
75,99
In TD FLIM experiments, the
u
and
v
coordinates are, respectively, the
cosine and sine transforms of the fluorescence intensity decay
I(t)
and they
are defined by
ð
It
ðÞ
cos o
t
ðÞ
d
t
ð
It
u
¼
½
5
:
38
ðÞ
d
t
ð
It
ðÞ
sin o
t
ðÞ
d
t
ð
IðÞ
d
t
v
¼
½
5
:
39
where o is the laser repetition angular frequency.
For FD FLIM experiments, o is the angular frequency of light modula-
tion, and the
u
and
v
coordinates, which are directly related to the phase
'
and modulation
m
measured with the FD FLIM system, are given by
u
¼
m
cos
ðÞ
½
5
:
40
In both cases (TD and FD FLIM experiments), determination of the
[
u, v
] coordinates can be performed instantaneously. However, the polar
representation gives just visual information on the biosensor state and does
not allow for obtaining really quantitative information on FRET
parameters.
Recently, Leray and coworkers have demonstrated that it is possible to
retrieve quantitatively the FRET parameters from the polar coordinates.
91
In fact, the fraction of interacting donors a
1
and the fluorescence lifetime of
the donor in the presence of the acceptor t
1
can be analytically expressed as
91
v
¼
m
sin
ðÞ
½
5
:
41
1
u
v
t
2
o
o
v
t
1
¼
½
5
:
42
ð
u
t
2
o
Þ
1
2
2
2
2
t
2
1
þ
t
1
o
u
u
t
2
o
a
1
¼
½
5
:
43
2
2
2
2
ð
t
1
t
2
Þ
ð
1
þ
u
þ
u
t
1
o
2
þ
t
1
t
2
o
2
þ
u
t
2
o
2
þ
u
t
1
t
2
o
4
Þ
If the lifetime of the donor alone, t
2
, is monoexponential and has been
measured in a previous experiment (requiring a modified biosensor without
acceptor), from Eqs.
(5.42) and (5.43)
both the lifetime of the donor in the
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