Chapter 4 – Making Light Work Harder in Biology 127
Assuming that there are initially ~120 photoactive GFP-X molecules per cell,
to end up with just 5 per cell requires a continuous photobleach of duration t
such that
5
120
30
120 2
95
≈
×
−
≈
×
(
) ≈
exp
t t
t
ln
b
/
therefore
ms. This equ
,
/
aates to ~(95/3)
32 frames
≈
c
The distribution of integrated spot intensity values cannot be explained here
by aggregation/oligomerization. A possible explanation is that two or more
fluorescent spots are detected when they are closer than the limiting dis
tance of ~2w in this instance. The robust calculation of the probability of
this occurring is in Chapter 7, but for a simple approximation, we could say
that the probability that a second spot is within ~2w of a first is p1 = Vspot/Vcell
where Vspot is the volume of a sphere of radius 2w and Vcell is the total access
ible volume. With (N − 1) such spot, the overall probability p2 for such a double
is ~(N − 1)p1 and similarly for a triple spot is p
N
p
N
N
p
3
1
1
2
2
1
2
~
−
(
)
=
−
(
)
−
(
)
,
and p
N
p
N
N
N
p
4
1
1
3
2
1
2
3
~
−
(
)
=
−
(
)
−
(
)
−
(
)
Setting N ~ 5 and using Vspot = 4π × (2w)3/3 and Vcell, = (2/3) × 4π × (1)3/3 indicates
p
p
p
p
p
p
p
1
2
3
4 1
1
2
3
0 14
0 56
0 24
1
0 06
≈
≈
≈
≈−
+
+
(
) ≈
+
.
,
.
,
.
,
.
These probability predictions are close to the observed intensity distributions.
d
If all protein X molecules in a typical cell oligomerize, then the stoichiometry will
be equivalent to ~120 molecules of GFP. Thus, the lateral resolution might be
~50/V(120) ≈ 4.6 nm. The width of the cell membrane is ~5 nm (see Chapter 2),
which is marginally higher than the localization lateral resolution, so we might
just be able to observe the translocation process.
4.3 FÖRSTER RESONANCE ENERGY TRANSFER
Förster resonance energy transfer (FRET) is a nonlinear optical technique that operates over
length scales, which are approximately two orders of magnitude smaller than the optical
resolution limit. Thus it be considered a super-resolution technique, but is discussed as
a separate section due to its specific utility in probing molecular interactions in biology.
Although there is a significant body of literature now concerning the application of FRET
in light microscopy investigations, the experimental technique was developed originally
from bulk ensemble in vitro assays not using light microscopy. FRET still has enormous
applications in that context. Changes to FRET efficiency values can be measured in a suit
able fluorimeter, which contains two-color detector channels, one for the so-called donor
and the other for acceptor fluorescence emissions. However, the cutting edge of FRET
technology uses optical microscopy to probe putative molecular interactions at a single-
molecule level.
4.3.1 EFFICIENCY OF FRET
This is a nonradiative energy transfer between a donor and acceptor molecule over a length
scale of ~1–10 nm, which occurs due to overlapping of the electronic molecular orbitals
in both spatial localization and in transition energy level gaps. Often, in practice, as an
experimental technique, FRET utilizes fluorescent molecules for donor and acceptor whose