Biomedical Engineering Reference
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strained to 1.51 times its length at mechanical equilibrium. In each system, the
DNA was bonded across the periodic system cell, making it effectively infinite. In
the simulations discussed by Luan and Aksimentiev [
62
], the nanopores were also
of effectively infinite length. However, simulations using nanopores of finite length
should be directly comparable to those using nanochannels of effectively infinite
length under the assumptions used in deriving (
14.1
). Each system was immersed in
a solution of 0.1M KCl, and a weak virtual harmonic spring restrained the center of
mass of each molecule. Figure
14.7d
shows the force exerted by the spring as a
function of time after a 1.0 V transmembrane voltage was turned on. In all cases, the
spring initially stretched rapidly. Eventually, the electro-osmotic force on the DNA
was on average balanced by the force of the spring, allowing determination of the
average force on the stationary DNA.
The average steady state force on the unstrained DNA in the 10 nmmembrane was
<F
z
> ¼
471 pN - the negation of the average force on the spring, which is shown
in Fig.
14.7d
. Calculating the effective charge of the DNA by
Q
eff
¼ <F
z
=DV>
,
we obtain
Q
eff
¼
0.97
e
for this 2.9 nm diameter pore - twice the value seen
in larger pores - using
a¼
d(T
n
) DNA. The force
on the unstrained DNA in the 5 nm thick membrane was nearly identical to that
on unstrained DNA in the 10 nm thick membrane. With
0.33 nm for the unstrained d(A
n
)
<F
z
> ¼
365 pN and
a¼
0.50 nm for the strained DNA, we obtain a significantly different value for the
effective charge,
Q
eff
¼
1.14
e
, owing to different hydrodynamic properties of
the strained molecule.
Analyses thus far have ignored the radial component of the force on DNA, which
could also be probed inMD simulations. Simulations [
20
,
64
,
65
] and experiments [
47
]
have highlighted the importance of the interaction between DNA and the surfaces
of a synthetic nanopore during DNA translocation. Future work will be directed
to determine the force on DNA held fixed in nanopores of various geometries, at
different electrolyte conditions and varying strengths of DNA-surface interaction.
14.5 Conclusion
Through the examples of this chapter, we have shown how all-atom MD simulations
can complement NFS experiments. First, the MD method allows the investigator
to “observe” the microscopic behavior of the system, which provides invaluable
insights into and a means to interpret puzzling results of NFS experiments. In some
systems, the simulations can relate the experimentally measured blockage current
to the microscopic conformation of the analyte in the pore [
18
,
20
]. Furthermore,
the simulations can partially compensate for one of the biggest deficiencies of the
NFS method - the lack of direct measurement of the forces applied [
22
,
23
,
62
].
However, while MD can be a useful tool in many aspects of designing and
interpreting NFS experiments, it has some limitations. The timescale accessible to
the MD method, now ranging from a few microseconds to a millisecond, precludes
exploration of many processes of interest. For example, rupture of an enzyme-DNA
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