390 Questions
In practice, however, neurotransmitters are packaged into phospholipid-bound
synaptic vesicles each containing ~10,000 neurotransmitter molecules.
d
If ~300 of such molecules are required to send a signal from the far end of the
neuron to a muscle, what signal rate could be supported by diffusion alone? What
problem does this present, and how does the cell overcome this? (Hint: consider
the frequency of everyday activities involving moving your feet, such as walking.)
8.12 Phospholipid molecules tagged with the fluorescent dye rhodamine were self-
assembled into a planar phospholipid bilayer in vitro at low surface density at a room
temperature of 20°C and were excited with a 532 nm wavelength laser and imaged using
high intensity narrow-field illumination (see Chapter 4) sampling at 1 ms per image to
capture rhodamine fluorescence emissions peaking at a wavelength of ~560 nm wave
length, which allowed ~10 ms of fluorescence emission before each rhodamine mol
ecule on average was irreversibly photobleached, where some molecules exhibited
Brownian diffusion at a rate of roughly 7 μm2s−1 while others were confined to putative
lipid rafts of diameter ~100 nm.
a
Show that for phospholipid molecules exhibiting Brownian diffusion
P
r r
r
r
=
−
/ exp
0
2
0
2
is a solution of the diffusion equation, where Pdr is the prob
ability that the lipid lies in an annulus between r and r + dr after time t.
Experiments on bulk samples suggested that raising the bilayer tempera
ture by 20°C might disrupt the corralling effect of a lipid raft. From intensity
measurements, it was estimated that in some of the rafts two fluorescently tagged
lipid molecules were confined, but it was not clear whether these lipid molecules
were bound to each other or not as each raft could only be resolved as a single
diffraction-limited fluorescent spot. An experiment was devised such that one
image frame was first recorded, the sample temperature was then increased by
20°C very rapidly taking less than 1 ms, and fluorescence imaging was continued
until the sample was bleached. The experiment was performed 1000 times on
separate rafts possessing two tagged phospholipid molecules. In 198 of these
experiments, two distinct fluorescent spots could just be resolved near the site of
the original raft at the end of the imaging, while in the rest only a single fluores
cent spot could be resolved throughout.
b
Explain with quantitative reasoning whether this supports a complete disruption
or partial disruption model for the effect of raising temperature on the lipid raft.
8.13 A particle exhibiting 1D Brownian diffusion has probability P being at a distance x
after a time t, which satisfies P
t
x
x
D
x
=
−
〈
〉
(
)
(
) (
)
〈
〉
1 2
2
2
1 2
2
2
4
/
/
exp
/
/
where
π
is the
mean square displacement, equal to 2Dt. In a single-particle tracking experiment,
a QD-labeled importin molecule (a protein used in trafficking molecules across the
membrane of the nucleus in eukaryotes) is tracked inside a cell, being imported into
the cell nucleus. The QD-importin complex was estimated as having a Stokes radius
of 30 nm.
a
What is the QD-importin complex’s diffusion coefficient in the cytoplasm of
the cell?
b
After a time t, the mean square displacement through an unrestricted channel in
the nuclear membrane might be expected to be 2Dt—why not 4Dt or 6Dt?
It was found that out of 850 single-particle tracks that showed evidence of transloca
tion into the nucleus, only 180 translocated all the way through the pore complex of
channel length 55 nm into the nucleus, a process which took on average 1 s.
c
Explain with reasoning why translocation does not appear to be consistent with
Brownian diffusion, and what might account for this non-Brownian behavior?
8.14 A particular mRNA molecule has a molecular weight of 100 kDa.
a
How many nucleotide bases does it contain, assuming 6.02 × 1026 typical nucleo
tide molecules have a mass of 325 kg?