Biomedical Engineering Reference
In-Depth Information
This asymmetric distribution shape is the result of a series of potential wells that the
polymer must overcome during its passage through the pore (i.e. from a random or
periodic set of interaction sites with the pore along the polymer). In large pores,
where the DNA is less confined, the contribution of interactions with the pore is
reduced, and the DNA undergoes fast transport. In smaller pores, the DNA driven
through the pore is configurationally restricted, thereby forcing it to repeatedly make
contact with the inner pore structure during its passage. These interactions dominate
the biopolymer dynamics through small pores. Another effect that effectively
reduces the driving force of the DNA through small pores is the electroosmotic ion
current along the DNA backbone (in the direction opposite to DNA motion), which
slows DNA by generating hydrodynamic drag on the translocating polymer [
27
].
To investigate the effect of polymer-pore interactions on the width of the
distribution tail, Luo et al. used Langevin dynamics to model a 2D polymer
translocating through a nanopore [
30
]. In their work, the DNA chains were repre-
sented as bead-spring chains held together by a Lennard-Jones potential, with
additional constraints accounting for the polymer's elasticity and for excluded
volume interactions. Polymer-pore interactions were modeled by placing a
Lennard-Jones potential between the pore and the beads. In Fig.
10.12
, we show
their numerically-obtained translocation distributions for this polymer as a function
of the pore-monomer interaction parameter
e
pm
. As may be seen in these distribu-
tions, increasing interactions result in increased peak dwell times (
t
p
). Even more
strikingly, increasing interactions also increase the width of the dwell-time distri-
bution. Increasing pore-polymer interactions reduce the effective driving force of
the DNA in the pore, which in turn increases its dwell time. However, the increas-
ing number of possible conformations the polymer can assume as it resides in the
pore for a longer time results in broad distributions. In fact, for
t
p
¼
3.0, while the
most probable dwell time is
500,000, the mean dwell time is much higher than
this value. In the limit of very strong pore-polymer interactions, this timescale can
be estimated by fitting the tail of the dwell-time distribution, i.e.
Pðt; t>t
p
Þ
t
p
¼
to a
mono-exponentially decaying function
PðtÞ
e
A
exp
ðtt= Þ
, where,
t
d
is the mean
translocation timescale.
In Fig.
10.13
we show the experimentally measured dwell-time distributions for a
6,000 bp DNA sample through a 4 nm pore [
49
]. To fully characterize the transloca-
tion process, statistical analysis of thousands of DNA translocation events is neces-
sary. The shape of the distribution resembles the first-passage time distribution
shown in Fig.
10.12
: the probability of translocation is close to zero at the very
shortest times, then sharply increases for slightly longer times, reaching a clear peak
at
t
p
~ 200
s. Unlike the theoretical model, the experimental distribution exhibits a
broad decay at the longer times. A systematic study of different DNA lengths
revealed that the distributions clearly follow bi-exponential distributions, with two
distinct timescales [
49
]. The solid line illustrates the typical features of the translo-
cation distribution, with the sharp increase followed by an exponential decay with a
characteristic timescale, here
t
1
¼
m
1.4 ms. We have not shown the actual fit here for
clarity, despite the fact that the
t
2
population becomes the dominant one for DNA
lengths greater than 3,500 bp (see Wanunu et al. [
49
] for further discussion of
t
2
).
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