Biomedical Engineering Reference
In-Depth Information
to the open pore value, near
t ¼
58.8 s in Fig.
12.7c
. We assume that the transient
at
t ¼
58.8 s is indicative of the molecule exiting the pore after 56 s, corresponding
to a translocation velocity of
1 bp/1.8 ms - about
97,000 slower
than the peak
value obtained at a constant bias of 600 mV shown in Fig.
12.7d
. Thus, when the
bias is reduced below the stretching threshold, the pore acts as a trap resisting
the molecular motion.
MD simulations corroborate our interpretation of the experiments by showing
that the motion of the
dsDNA
can be slowed or effectively stopped when the driving
voltage is turned off. Figure
12.8a
illustrates a simulated system that includes a
dsDNA
fragment, 100 mM KCl, and a 2.0 nm diameter pore in a silicon nitride
membrane. The
dsDNA
molecular conformation within the pore was stretched from
0.34 to a 0.41 nm rise per base-pair even at 0 V. The distortion from the B-form
dsDNA
structure can be clearly seen in Fig.
12.8a
. With a 500 mV bias applied, the
dsDNA
was stretched further to 0.44 nm. As illustrated in Fig.
12.8b
, at 250 and
500 mV, the
dsDNA's
motion is arrested: only by applying 1 V could the
dsDNA
coax out of the trap. By analyzing the
dsDNA
displacements at a 0 V (inset of
Fig.
12.8b
), we determined that the pore acts as a harmonic trap with an effective
spring constant of 7.2
>
0.8 nN/nm. The probability of escape from a trap depends
sharply on the force applied, explaining the threshold. The force required to restart
the motion is essentially determined by the product of the spring constant,
k
, and the
distance over which escape of a base-pair from the trap occurs
x
0
: i.e.
q*
E
~kx
0
where
x
0
¼ L
/ 2 with
L
the length / base-pair. Thus, we find that the force required
to move the
dsDNA
one base-pair in a 2.0 nm diameter pore is
kx
0
¼
1.4 nN.
Our estimates also suggest that this trap mechanism is robust with respect to the
stochastic forces that act on the
dsDNA
coils above and below the trap. To estimate
the magnitude of a stochastic force, we approximate the
dsDNA
coil outside the
pore as a bead with the hydrodynamic radius,
r
h
,of
DNA, which is about
750 nm [
63
,
64
]. The stochastic force from the solvent on a bead of that size,
FðtÞ¼ð
l
=tÞ
R
Fð
1
t
Þ
dt follows from the second moment of the stochastic force:
< F
(
t
1
)
F
(
t
2
)
> ¼
6
k
B
T xd
(
t
2
t
1
), where
x
is the friction coefficient of the bead.
Fig. 12.7 (continued) decreases below 0.3 V. The
dotted line
represents a fit to the data.
(c) Triggered by the onset of a current blockade indicating that
-
dsDNA
is translocating through
the pore of (a), the voltage is switched from 600 mV (above the stretching threshold) to 100 mV
(below threshold). As a result the molecule is trapped in the pore till
t ¼
l
58.8 s.
Inset
is a
magnified view of the current fluctuations observed near
t ¼
58.8 s. (d) Histograms of the dwell
times observed at a constant voltage of 600 mV(
grey
) and the distribution of elapsed time
spanning the instant when a blockade event triggers the voltage switch from 600 mV to 150 mV
or 100 mV to the return of the current to the open pore value seconds later. The peak in the
distribution of current blockade durations increases from about 900
m
s to about 200 ms, increasing
200
.(e, f) Histograms showing the distribution of the current during the blockade in the interval
14-14.5 s, when
l
-DNA is trapped (e), and the open pore for
t >
58.8 s (f). The distribution for the
trapped molecule must be fit to at least two Gaussians: one (
right
) offset from the median (
DI ¼
0)
by
DI ¼
+2.9 pA with a width of
s ¼
7.8 pA; and another (
left
) offset by
6.51 pA with a width
of
s ¼
5.9 pA. The
black line
represents the sum. In contrast, the data in (f) representing the open
pore can be fit by a single Gaussian with a width
s ¼
4.3 pA. Adapted from ref. [
21
]
Search WWH ::
Custom Search