Chapter 4 – Making Light Work Harder in Biology  155

diffraction-​limited microscopy are separated by less than the optical resolution limit,

we may interpret them as a single “spot.”)

4.4 A synthetic molecular construct composed of DNA was labeled with a bright

organic “intercalating” PALM dye, which decorated the DNA by binding between

every other nucleotide base pair. Each organic dye molecule, once stochastic­

ally activated during PALM imaging, could fluorescently emit an average of ~10⁷

photons of peak wavelength at ~550 nm, before irreversibly photobleaching, and

could emit these at a maximum flux rate of ~10⁸ photons per second. If the total

detection efficiency for all photons emitted is 10% at the EMCCD camera of the

PALM imaging device, calculate, stating any assumptions you make, what the max­

imum theoretical imaging frame rate on the PALM imaging device would be to

permit two neighboring dye molecules on the DNA to be resolved in the focal

plane of the microscope.

4.5

The PALM imaging device of Question 4.4 was modified to permit 3D localization of

the organic dye using astigmatism imaging. If the DNA construct was aligned with the

optic axis, what then is the maximum frame rate that would permit two neighboring

dye molecules on the DNA to be resolved?

4.6

An in vitro fluorescence imaging experiment involving GFP was performed with and

without the presence of the G/​GOD/​CAT free radical quencher. When performed

in pure water without any quencher the GFP bleached rapidly, whereas upon adding

the quencher the rate of bleaching was lower. If the same experiment was performed

with the quencher but in a solution of PBS (phosphate-​buffered saline, a simple pH

buffer) the rate of bleaching was the same, but the brightness of single GFP molecules

appeared to be greater than before. Explain these observations.

4.7 A protein is labeled with a donor and acceptor fluorophore to study a con­

formational change from state 1 to 2 by using single-​molecule FRET. The FRET

acceptor–​donor pair has a known Förster radius of 4.9 nm, and the measured fluor­

escence lifetimes of the isolated donor and the acceptor fluorophores are 2.8 and

0.9 ns, respectively.

a

Show that the FRET efficiency is given by (1 − τDA/​τD) where τDA and τD are the

fluorescence lifetimes of the donor in the presence and absence of acceptor,

respectively.

b

What is the distance between the donor and acceptor if the measured donor life­

time in conformation 1 is 38 ps? Structural data from x-​ray crystallography (see

Chapter 5) suggest that the fluorophore separation may increase in a distinct step

by 12 Å when the protein makes a transition between states 1 and 2.

c

Calculate the donor fluorescence lifetime of conformation 2. How small does the

measurement error of the FRET efficiency need to be to experimentally observe?

See the changes of state from 1 to 2.

d

What is the maximum change in FRET efficiency that could be measured here?

4.8

A FLIM–​FRET experiment using GFP and mCherry FPs as the donor and acceptor

FRET fluorophores, respectively, indicated that the fluorescence lifetimes of both

proteins were 5 ns or less. Both proteins have a molecular weight of ~28 kDa and an

effective diameter of ~3 nm.

a

What, with reasoning, is the typical rotational time scale of these FPs if their

motions are unconstrained?

  The researchers performing the experiment assumed that any dynamic

changes observed in the estimated FRET efficiency were due to relative separ­

ation changes of the GFP and mCherry.

b

Discuss, with reasoning, if this is valid or not.

c

Why is this experiment technically challenging when attempted at the single-​

molecule level?

4.9

A 4π microscope was composed of two matched oil-​immersion (refractive index ≈

1.52) objective lenses of NA 1.49. In an exam answer, a student suggested that this

should be better described as a 3.2π microscope. Discuss.