156 Questions
4.10 A bespoke STED microscope used a white-light laser emitting at wavelengths from
~450 to 2000 nm of total power 6 W, generated in regular pulse bursts at a frequency
of 60 MHz such that in each cycle, the laser produces a square-wave pulse of 10 ps
duration.
a
What is the mean power density in mW per nm from the laser?
b
How does this compare with the peak power output?
The excitation laser was split by a dichroic mirror and filtered to generate a blue
beam that would transmit 90% of light over a 20 nm range centered on 488 nm
wavelength, and zero elsewhere, before being attenuated by an ND1 filter and
focused by a high NA objective lens onto a sample over an area equivalent to
a diffraction-limited circle of effective diameter equal to the PSF width. A red
beam was directed through a loss-free prism that would select wavelengths
over a range 600–680 nm, before being attenuated by an ND4 filter, phase
modified to generate a donut shape and focused by the same objective lens
in the sample of area ~0.1 μm2. The oil-immersion objective lens had an NA
of 1.49 and a mean visible light transmittance of 80%. A biological sample
in the STED microscope consisted of fibers composed of microtubules (see
Chapter 2) or diameter 24 nm, which were labeled on each tubulin monomer
subunit with a fluorescent STED dye. Assume here that the saturating intensity
of STED is given by the mean in the ring of the donut.
c
Discuss, with reasoning, if this microscope can help to address the question of
whether fibers in the sample consist of more than one individual microtubule.
4.11 A typical FCS experiment is performed for a single type of protein molecule labeled
by GFP, which exhibits Brownian diffusion through a confocal laser excitation volume
generated by focusing a 473 nm laser into the sample solution to generate a diffraction-
limited intensity distribution.
a
Show, stating any assumptions you make, that the number density autocorrel
ation function is given by 〈〉
−
−
(
) (
)
(
)
′
′
′
C
r
r
Dt
Dt
exp
/
/
/
2
3 2
4
1 4π
/ and r is pos
itional vector of a fluorophore relative to the center of the confocal excitation
volume of light, r′ is the equivalent autocorrelation positional vector interval, and
t′ is the autocorrelation time interval value.
b
The effective confocal volume V can be defined as ∫( )
(
)
∫( )
(
)
P r
V
P r
V
d
/
d
2
where
P is the associated PSF. Demonstrate that V can be approximated by Equation
3.53. (You may assume the Gaussian integral formula of ∫
−(
)
= √(
)
exp
d
/
r
r
2
2
π
if
the integral limits in r are from zero to infinity.)
c
In one experiment, the autocorrelation function at small time interval values
converged to ~2.6 and dropped to ~50% of this level at a time interval value of ~8
ms. Estimate with reason the diffusion coefficient of the protein and the number
of protein molecules that would be present in a 1 μL drop of that solution.
4.12 A protein is labeled with a donor–acceptor FRET pair whose Förster radius is 5.1 nm
to investigate a molecular conformational change from state I to II. The fluorescence
lifetimes of the donor and the acceptor fluorophores are known to be 5.3 and 1.1 ns,
respectively.
a
The donor lifetime for state I has a measured value of 54 ps. Calculate the FRET
efficiency in this state and the distance between the FRET dye pair.
b
There is a decrease in this distance of 0.9 nm due to the conformational change
of state I–II. Estimate the fluorescence lifetime of the donor in this state, and
comment on what the error of the FRET efficiency measurement must be below
in order to observe this distance change.
4.13 A gold-coated AFM tip was used as a fluorescence excitation source for TERS by
focusing a laser beam on to the tip and then scanning the tip over a fluorescently
labeled sample. The fluorescence intensity measured from the sample when the tip
was close to the surface was ~106 counts, which decreased to only ~102 counts when