Chapter 3 – Making Light Work in Biology 107
detector with pixel edge length 18.4 μm and a magnification of 300 between the sample
and the camera, was used to monitor the localization of the protein with millisecond
sampling, suggesting the protein was freely diffusing with a mean of two fluorescent
spots detected at the start of each acquisition if the focal plane of the microscope was
set to the midpoint of each cell. Estimate the intracellular concentration in nanomolar
of the protein.
3.7 What do we mean by the Stokes shift, and where does it originate from? Why does the
normalized excitation spectrum of a fluorophore look like a rough mirror image of
the normalized emission spectrum?
3.8 A fluorescence microscopy experiment using an objective lens of numerical aper
ture 0.9 was performed on a zebrafish embryo (a “model organism” used to investi
gate multicellular tissues, see Chapter 7) to investigate a single layer of GFP-labeled
cells of 10 μm diameter, focusing at the midheight level of the cells. These cells were
expected to express a mean number of 900 GFP-tagged protein molecules per cell
with a standard deviation of 500 molecules per cell. Typical cells had a measured
intensity during fluorescence microscopy of ~107 counts per cell integrated over the
whole of the data acquisition prior to cells being completely photobleached. Data
were acquired from a high-efficiency camera detector whose magnification per pixel
was equivalent to 200 nm at the sample, gain was 300. Similar cells from another
zebrafish in which there was no GFP had a total measured intensity during the same
fluorescence microscopy imaging of ~2 × 106 counts.
a
Assuming that captured fluorescence emissions come from a cell slice whose
depth is equivalent to the depth of field of the objective lens, estimate the number
of fluorescence emission photons detected from a single molecule of GFP.
b
The quantum efficiency of the camera was ~90%, the transmission function of
the dichroic mirror transmits a mean of 85% of all GFP fluorescence emissions,
and an emission filter between the dichroic mirror and camera transmits 50%
of all GFP fluorescence emissions. The transmission losses due to other optical
components on the emission pathway of the microscope resulted in ~25% of all
light not being transmitted. Estimate the mean number of photons emitted in
total per GFP molecule, stating any assumptions.
3.9 A similar experiment was performed on the cells from Question 3.5, but on a thicker
tissue section 80 μm thick, consisting of a 70 μm layer of similar cells not labeled with
GFP close to the microscope’s coverslip surface, above which are the single layer of
GFP-labeled cells.
a
Assuming that the rate at which light is absorbed when it propagates through
a homogeneous tissue is proportional to its intensity and to the total number
of molecular absorption event, derive the Beer–Lambert law, stating any
assumptions.
b
If each layer of cells attenuates, the excitation beam by 4% calculates the total
integrated emission signal due to GFP from a single cell using the same micro
scope and camera detector and of focusing at mid-cell height for the GFP-labeled
cells, acquiring data until the cells are completely photobleached as before.
c
Estimate the total noise per cell detected during these data acquisitions.
d
To detect a given cell reliably above the level of noise, the effective SNR needs
to be above ~2. If the tissue area is ~100 × 100 μm, estimate how many cells you
would expect to detect, stating any assumptions you make.
3.10 Describe the technique of TIRF microscopy and give an example of its application in
biophysics. Most TIRF in vivo studies investigate membrane complexes; why is this?
Would TIRF still be effective if there was a high concentration of auto-FPs in the cyto
plasm? Can TIRF be applied to monitoring the nucleus of cells?
3.11 The wave equation for a plane wave of light has solutions of the form
E
E
i kx
ky
t
=
+
−
[
]
{
}
0exp
sin
cos
θ
θ
ω