Nanopore Force Spectroscopy: Insights from Molecular Dynamics Simulations - Nanopores: Sensing and Fundamental Biological Interactions - page 350

distributions of force along the molecule with respect to experiments in which an
electric field drives the translocation [ 60 ]. Grid-steered MD [ 60 ] provides a means
to apply a more realistic distribution of force to the molecule, which can result
in a more realistic permeation trajectory. For example, Wells et al. [ 60 ] derived a
three-dimensional electric field map of

-hemolysin from MD simulations. In grid-
steered MD simulations, this electric field map was scaled by a factor greater than
unity and applied to only the DNA. Thus, the force on DNA had a similar spatial
distribution as it would under a larger transmembrane voltage without disrupting
other portions of the system. The time required for simulation of translocation was
reduced by many times, while the DNA adopted a much more realistic conforma-
tion during the trajectory than it would have using conventional SMD.
Much work remains to be done in understanding DNA duplex dissociation under
force. While simulations revealed possible nanopore-DNA conformations that
could lead to the extreme current values measured in hairpin DNA experiments
[ 18 , 20 ], more comprehensive studies of which arrangements give rise to which
currents and to what extent the current value can be used to predict the arrangement
are needed.

a

14.4 The Force on DNA in a Nanopore

In all of the NFS experiments discussed above, force was applied to the DNA by an
external electric field. However, the force on the DNA as a function of the applied
transmembrane voltage could not be directly measured. We can attempt to calculate
the force on the DNA from a simple model. Suppose we have a system in which a
long DNA molecule is threaded completely through the nanopore. Assuming that
the electrolyte is a sufficiently good conductor, the electric field outside the pore is
negligible compared to that inside; thus, we can consider the force on the DNA to be
due to the electric field in the nanopore and, if necessary, in a small buffer region
above and below the pore. Let the center of the nanopore be at the origin and the
length of the nanopore and buffer be L . Assuming that the DNA between

L= 2 and

L= 2 is positioned along the pore axis and has the shape of a B-form helix, we can

approximate the linear charge density of the DNA as Q=a , where Q¼ 2 e is the

charge of each basepair and a ¼ 0.34 nm is the average rise of a basepair in random-

sequence dsDNA. If we make the approximation that the system is cylindrically
symmetric, we can attempt to estimate the force on the DNA by integration:

Z L= 2

F z ¼ dz E z ðzÞQ=a ¼ DVQ=a (14.1)

L= 2

Here, F z is the force on the DNA along the pore axis, E z is the electric field in

the z direction (along the pore axis) and DV is the transmembrane voltage. How-

ever, the force on the DNA in a nanopore is known to be substantially smaller than