126 4.2 Super-Resolution Microscopy
width in the microscope focal plane during ~1 image frame, with the lateral spatial reso
lution using super-resolution localization microscopy algorithms being ~50 nm.
a
Estimate the 1/e photobleaching time for GFP-X during the narrow-field experiments,
stating any assumptions.
b
Explain what the observation of a dimmer central region might imply with regard
to the bacterial nucleoid. How many image frames would be acquired using narrow
field before you might expect to see distinct fluorescent spots?
c
Explain with quantitative reasoning the observed distribution of fluorescent spots in
narrow-field.
d
The conditions of the experiment were changed such that all of the protein X
molecules in the cell can oligomerize to form a globular chain, which can translocate
across the cell membrane. Discuss if it might be possible to observe the translocation
process directly.
Answers
a
Assuming that photon absorption is linear in the range of excitation intensity, and
since the measure of typical spot emission intensity is the same, the excitation
intensity of narrow-field must be greater than that of standard epifluorescence
by a factor equal to the reciprocal of the ratio of the exposure times used, that is,
~(33 ms)/(3 ms) = 11. The photobleach 1/e time will also be inversely proportional
under these conditions to excitation intensity, so under epifluorescence this time
is ~10 × 33 ms; therefore, in narrow-field the photobleach time tb is tb = (10 × 33)/
11 = 10 × 3 ms = 30 ms (in other words, the total number of consecutive image
frames before a typical GFP molecule bleaches is the same as it was for standard
epifluorescence).
b
The dim central region of the cell is consistent with the nucleoid being an
excluded volume to GFP-X. The typical volume of this for bacteria is ~1/3 of
the total cell volume (see Chapter 2); thus, the volume accessible to GFP-X
may only be ~2/3 of the total cell volume. To just resolve distinct fluorescent
spots, assuming the Rayleigh criterion, requires the nearest-neighbor separ
ation to be such that a first-order minimum of the Airy pattern of a fluorescent
spot coincides with the peak of another. A simple approximation suggests that
this distance equates to the PSF width w plus the typical distance diffused in
one image frame, which in this instance is also w. For a more robust analytical
treatment of this, see Chapter 7. For simplicity, one possible approximation is
then to say that at this limiting density of photoactive GFP-X, the effective radius
of the equivalent sphere is (w + w) = 2w such that a total of N spheres are all
tightly packed to occupy the accessible volume of the cell (assumed to be ~2/3
total cell volume):
N
w
×
×
(
) ≈(
)×
×
4
3
2 3
4
3
3
3
π
π
(2
/
(1) /
) /
Using the Abbe limit and assuming the characteristic emission, wavelength is
given roughly by the emission peak for GFP of ~509 nm (see Chapter 3):
w =
×(
)
=
0 61
0 509 1 2
0 26
.
.
.
.
/
m
µ
Therefore,
N ≈
×(
) ≈
2 3
1 0 52
3
/
/
photoactive molecules of GFP-X per cell
.