Biomedical Engineering Reference
In-Depth Information
2 - photon volume
(< 10
−
15
≈ 1 µ
m
3
)
12000
cell
A
10000
8000
FCS -
τ
6000
4000
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
Time (s)
100
0.05
B
C
0.05
10
0.04
0.04
1
0.03
0.03
0.02
0.1
0.01
0.00
0.02
0.01
0.0001
0.001
0.01
0.1
1
10
100
0.01
Delay time(s)
0.001
0.00
0.0001
0.0
0.5
1.0
2.0
1.5
0
1
2
3
4
5
6
counts per Bin
Delay time(s)
Fig. 10.6.
Principle of fluorescence fluctuation spectroscopy. The number of mole-
cules can change because of diffusion in and out of the volume, then fluorescence
intensity fluctuates. (
a
) The time of the diffusion process causes characteristic fre-
quencies to appear in the fluorescence intensity trace. (
b
) The time structure is
analyzed by the autocorrelation function (ACF);
Inset
: original data are plotted
in log scale. (
c
) The amplitude of the fluctuation depends on brightness (i.e., the
aggregation state of a protein) and it can be analyzed by PCH
Instead, if the number of molecules in the excitation volume changes, even
if the quantum yield is constant, the fluorescence intensity will change with
time (Fig. 10.6a). The number of molecules can change because they can dif-
fuse out of the volume. The time of the diffusion process causes characteristic
frequencies to appear in the fluorescence intensity trace. Assume that we have
two molecules in the volume and one leaves, the relative change in intensity
will be one-half. However, if there are 10 molecules in the excitation volume
P
(
x, µ
)=
e
−µ
µ
x
X
!
,
(10.1)
where
x
= 0,1,2,3, (number of emitted photons) and
µ
= mean number of successes
in the given time interval or region of space (number of counts). If
µ
is the average
number of successes occurring in a given time interval or region in the Poisson
distribution, then the mean and the variance of the Poisson distribution are both
equal to
µ
:
E
(
x
)=
m
, and
V
(
x
)=
σe
2
=
µ
. In a Poisson distribution, only one
parameter,
µ
, is needed.
