Biology Reference
In-Depth Information
autocorrelation and cross-correlation functions can be written as follows, in the
absence of cross talk:
h
dF
ðÞdF
t
ð
t
þ t
Þ
i
G
i
ðÞ¼
(2.1)
2
h
Ft
ðÞ
i
h
dF
B
t
ðÞdF
R
t
ð
þ t
Þ
i
G
x
ðÞ¼
(2.2)
h
F
B
t
ðÞ
i
h
F
R
t
ðÞ
i
where
t
is the lag time. In the particular case of a system of freely diffusing species
and assuming a 3D Gaussian excitation profile, closed expressions are derived from
Eqs.
(2.1) and (2.2)
:
1
1
=
2
o
0
t
z
0
t
Di
t
t
Di
G
i
ðÞ¼
G
i
0
ðÞ
1
þ
1
þ
(2.3)
1
1
=
2
o
0
t
z
0
t
Dx
t
t
Dx
G
x
ðÞ¼
G
x
0
ðÞ
1
þ
1
þ
(2.4)
where
i
¼
B or R (blue or red).
o
0
and
z
0
are the waist and length, respectively, of the
3D Gaussian excitation volume at which the intensity drops to 1/e
2
. Here,
t
Di
and
t
Dx
are the translational diffusion time of species
i
and of the complex, respectively, and
G
i
(
0
) and
G
x
(
0
) are the amplitudes of the auto- and cross-correlation functions,
respectively.
If no changes in the brightness of the fluorophores occur upon complexation,
the amplitudes of the auto- and cross-correlation curves can be expressed as follows:
1
V
eff
C
i ;t
G
i
0
ðÞ¼
(2.5)
C
x
V
eff
C
G;t
C
R
;t
G
x
0
ðÞ¼
(2.6)
(
p
/2)
3/2
o
2
z
0
, and
C
i
,
t
and
C
x
are the total concentration of
species
i
and of the complex, respectively.
In general, the amplitudes of the auto- and cross-correlation curves for similarly
diffusing species of different brightness can be expressed as
where
i
¼
BorR,
V
eff
¼
X
i
2
i;
B
C
i
V
eff
X
i
i;
B
C
i
G
B
0
ðÞ¼
(2.7)
2
X
i
i
R
C
i
V
eff
X
i
i;
R
C
i
;
G
R
0
ðÞ¼
(2.8)
2
X
i
i;
B
i;
R
C
i
V
eff
X
i
i;
B
C
i
G
x
ðÞ¼
X
i
i;
R
C
i
(2.9)
