100 3.6 Basic Fluorescence Microscopy Illumination Modes
a
What % proportion of the nucleus is excited by the laser?
b
If a single particle consistent with one GFP molecule is observed for roughly 60% of
consecutive image frames in a sequence, prior to any GFP irreversibly photobleaching,
what is the LacI nuclear molarity in units of nM?
c
The range of time taken to traverse the confocal volume in the sample plane was
estimated at ~20 ms. Assuming that the frictional drag coefficient of the LacI tagged
with GFP can be approximated from Stokes law as 6πηr where the mean viscosity
η of the nucleoplasm is roughly that of water at ~0.001 Pa·s, and r is the effective
radius of the GFP-tagged LacI, which can be approximated as roughly twice that of
GFP, estimate the effective Brownian diffusion coefficient in μm2 s−1 and comment on
the observed traversal time.
d
If the binding site is chemically induced to be on, what might you expect to observe?
Answers
a
The excitation confocal volume can be estimated:
w
V
=
×
×
(
)
=
×
=
×
×
=
×
−
−
−
0 61
473 10
1 4
206
10
2 5
1 2
10
9
9
3 2
206
19
3
.
/ .
.
(
.
/
m
m
π
Volume of nucleus,
/
Proportion of
nV =
×
×
=
×
=
−
4
3
4 2
10
3
2
18
π
(
.
%
nucleus excited as %
/
/
=
=
×
×
×
=
−
−
100
100
1 2
10
4 2
10
3
19
18
V Vn
.
.
%
b
If the observed “occupancy” of the confocal volume is 60% by time
for a single diffusing molecule of GFP, then on average, there will be
a single molecule of GFP that occupies a characteristic mean volume
V
V
G
of
m
L
=
=
×
=
×
=
×
−
−
−
/ .
.
/ .
.
.
0 6
1 2
10
0 6
2 0
10
2 0
10
19
19
3
16
1 molecule is equivalent to 1/Av moles where Av is Avogadro’s number = 1/(6.022
× 1023) = 1.7 × 10−24 mol
Therefore, the molarity, m= (1.7 × 10−24)/(2.0 × 10−16) M = 8.5 × 10−9 M = 8.5 nM
c
The Stokes radius rL of the LacI molecule tagged to GFP ≈ 2 × 2 nm = 4 × 10−9
m. Therefore, the theoretical diffusion coefficient Dth assuming a room tempera
ture of ~20°C is
Dth
/
m
=
×
×
+
(
)
(
)
×
× ×
×
×
=
×
−
−
−
−
1 38
10
20
273 15
6
1 10
4
10
5 4
10
23
3
9
11
.
.
(
.
π
−
−
−
=
2
1
2
1
54
s
m s
µ
However, the experimental observations indicate that the traversal time in the
(2D) focal plane is 20 ms, which is the time taken on average to diffuse in 2D across
the confocal volume waist (a distance of 2w); thus from rearranging Equation 2.12
assuming n = 2, the observed diffusion coefficient Dobs is
Dobs =
×
×
(
)
×
×
×
(
) =
×
=
−
−
−
−
−
2
206
10
2
2
20
10
2 1 10
2 1
9 2
3
12
2
1
2
1
/
m s
m s
.
. µ
The observed rate of diffusion is smaller by a factor of ~25 compared to theor
etical Brownian diffusion. Thus, the diffusion is likely to be non-Brownian (one
explanation might be that the LacI diffusion is being impeded by the presence of
the tightly packed DNA in the cell nucleus).
d
If the LacI binding sites are accessible to LacI, then there is an increase like
lihood that LacI might bind to these sites, in which case one would expect to
see diffusing spots suddenly stop moving. However, note that the DNA itself has