Biology Reference
In-Depth Information
(A)
(B)
1.0
10
0
Poission curve (expected)
0.8
10
-1
0.6
Power-law curve
(observed)
10
-2
0.4
10
-3
0.2
0.0
10
-4
1
10
100
200
400
600
800
1000
Vesicle radius (nm)
Number of entrapped solute (N+)
(C)
Empty
vesicle
270
Super-filled
vesicle
(ca. 70 ferritins)
200 nm
FIGURE 14.2
Probability of coentrapping the about 80 different components of the PURE system (as single copy) inside a lipid vesicle of a
certain radius.
27
The probability becomes 1 for large lipid vesicles (radius
.
600 nm), whereas it rapidly decreases to zero
for small vesicles (radius
,
250 nm). In particular, for vesicles with a radius of 100 nm, the calculated probability is around
10
26
. (B) Comparison between Poisson and power-law solute occupancy distribution.
29,30
The Poisson curve refers to
vesicles with radius of 100 nm, in the case of the entrapment of 8 μM solutes (one species). In contrast to the expectations,
the analysis of about 8000 vesicles reveals that the distribution of ferritin- and ribosome-containing POPC vesicles does not
follow the Poisson distribution, being shaped instead as a power-law. Note that the power-law probability of finding a lipid
vesicle containing more than 10 solutes lies in the 0.001 probability range, whereas the Poisson curve rapidly decreases to
very low values. (C) Cryo-TEM reveals the existence of super-filled vesicles (in this case, filled with ferritin
29
) together with
empty vesicles. Empty and filled vesicles, when having approximately the same size as shown here, should entrap
approximately the same number of solutes, and the fluctuations should be explained by the Poisson law. But experiments
controvert the expectations.
2.52 10
2
6
C
μ
M
R
3
nm
, where
R
is the vesicle
radius). For example, if vesicles with radius
R
(a shortcut approximate formula gives
N
0
5
50 nm are formed in a
C
3.2
μ
M ferritin
5
5
solution, it is expected then, on average, each vesicle contains 1 ferritin (
N
0
5
1). The
Poisson probability
p
(
N
) of finding a vesicle with
N
ferritin molecules is calculated
accordingly (
Fig. 14.2B
). For example, given the stochastic nature of the entrapment process,
the probability of finding an empty vesicle is not so low (
p
(0)
37%), whereas the
probability of finding a vesicle with two ferritins is 18%. The Poisson curve decreases
rapidly, so that
p
(10)
5
p
(1)
5
10
2
17
% (these values represent, respectively,
the probabilities of finding a vesicle with 10 or 20 ferritins, when on average 1 ferritin is
expected to be entrapped).
10
2
5
%, and
p
(20)
5
5
