108 Questions

For real angles θ, this represents a traveling wave in the focal xy plane of the sample.

a

Show that the same solution but with complex θ describes the electric field in

water near a water–​glass interface in the case where plane wave illumination is

totally internally reflected within the glass at the interface.

b

Obtain an expression in terms of the angle of incidence in glass, angular fre­

quency ω, and the refractive indices of glass and water, for the electric field in

water for the aforementioned case. Describe using a sketch the wave that this

represents.

3.12 Does TIRF illumination require a coherent laser source, or would a noncoherent

white-​light source be okay?

3.13 A fluorescence imaging experiment was performed at video rate on a bespoke

inverted microscope using Escherichia coli bacteria that have a shape close to a

cylinder of length 2 μm capped by hemispheres of diameter 1 μm, in which a diffused

cell membrane protein was tagged using GFP, with biochemical assays suggesting

200 proteins per cell, using a simple flow cell that consists of a glass coverslip in

optical contact with a high numerical aperture objective lens via immersion oil, with

a cell stuck to the coverslip surface in a water-​based buffer, with the walls of the flow

cell being 120 μm high stuck on the upper side to a glass microscope slide, above

which was then simply air. The cells were first imaged using epifluorescence in which

the emergent 473 nm laser excitation beam traveled from below and then straight up

through the sample, resulting in a halolike appearance in fluorescence to cells that

were stuck with their long axis parallel to the glass coverslip surface (a bright fluor­

escence at the perimeter of the cell when setting the focal plane to be at the midpoint

of the cylinder).

a

Explain these observations. The angle of incidence of the excitation beam was

then increased from zero (epifluorescence), which resulted in the beam emerging

from the top of the microscope slide at increasingly shallow angles. Eventually,

the emergent beam angle was shallow enough that it just dipped below the

horizon and could not be seen exiting the microscope slide. At that point, the

experimentalists concluded that the system was set for TIRF imaging. However,

they were surprised to still see a halolike appearance to the fluorescence images

of the cells when they had expected to see a brighter region that marked the

cell body.

b

Explain these observations. (Hint: think about the microscope slide as well as the

coverslip.)

3.14 A confocal microscopy experiment is performed where the focused laser volume had

a lateral width measured at 230 nm and an axial width measured at 620 nm. Bacteria

in the sample were rodlike with end-​to-​end micron length and 1 μm width, shaped

like a cylinder capped at either end by a hemisphere, and contained a GFP-​tagged

protein in their cytoplasm.

a

How much of a typical cell is excited by the confocal volume?

b

If the focused laser beam is occupied by a single GFP-​tagged protein in the cyto­

plasm of the cell for 50% of the time, what is the molarity of that protein?

The laser beam is focused on to the cell’s midpoint in the cytoplasm. From measurements

of GFP-​tagged proteins diffusing through the confocal volume of fluorescence

pulses from a few fluorescently tagged molecules, the range of time taken to tra­

verse the confocal spot in the sample plane was estimated at 1.7 ± 0.7 ms.

c

Estimate the effective diameter of the protein, stating any assumptions you make.

(Assume that the viscosity of the cytoplasm in this case is ~0.002 Pa⋅s.)

3.15 An epifluorescence microscope with oil immersion (refractive index =​1.515) objective

lens NA 1.4, focal length 2 mm, was used to monitor a dye called Hoerchst, fluores­

cence emission peak wavelength 454 nm, which labels the DNA in a single rod-​like

E. coli bacterium lying flat with its long axis (length 3 µm, width 1 µm) on a cover­

slip. The downstream imaging path after the objective lens comprised a focal length

200 mm lens that makes a telescope with the objective lens, and another telescope with