Biomedical Engineering Reference
In-Depth Information
resonance, are added, along with ions, molecules of water, and the atoms of the
synthetic membrane housing the nanopore. Such systems usually comprise tens of
thousands to millions of atoms. In classical all-atom MD, the acceleration of each
atom of the system - including the water - is calculated using Newton's Second
Law: x
i
ðtÞ¼
F
i
ðtÞ=m
i
, where F
i
is the force on atom
i
and
m
i
is its mass. The force
is calculated using a number of simple mathematical functions that include electro-
static forces, van der Waals forces, and various empirical forces that approximate
the behavior of covalently bonded structures as well as external forces, such as
those due to applied electric fields [
32
]. The particular forms of the mathematical
functions and values of the parameters used for each type of atom constitute a force
field. A number of force fields have been developed over the past few decades for
the purpose of accurate simulations of biomolecular systems, notably the AMBER
[
33
,
34
] and CHARMM force fields [
35
]. Using forces calculated in this way, the
trajectory of the entire system can be generated by numerical integration of
Newton's Second Law in time. Using the best algorithms available today, it is
possible to obtain tens or hundreds of nanoseconds of such a trajectory in a 24 h
period. By parallelizing the computation over hundreds or thousands of individual
processing units, systems containing as many as millions of atoms can be simulated
at this rate. The MD simulations presented in this chapter were designed and
executed following the protocols described by Comer et al. [
36
].
14.1.3 Chapter Overview
Through examples given in this chapter, we illustrate how MD simulations can assist
in the design and interpretation of NFS experiments. First, we describe the applica-
tion of the MD method to NFS of enzyme-DNA complexes. We show how the
method is used to estimate the force required to rupture the enzyme-DNA complex as
a function of the loading rate and to make qualitative predictions of the strength
of enzyme binding to sequences that differ from the enzyme's target sequence. Next,
we describe the use of MD simulations to interpret NFS experiments of DNA duplex
unfolding. Here, the simulations have elucidated how the mode by which the duplex
unfolds might be affected by the size of the nanopore and how various values of
the ion current could correspond to particular conformations of the DNA in the pore.
Finally, we describe how the MD method is used to determine the force experienced
by DNA in a nanopore and has resolved the contributions of counterion screening
and electro-osmotic flow to the effective reduction of the DNA charge.
14.2 Rupture of Protein-DNA Assemblies
Protein-DNA interactions are essential to many biological processes including
transcription, packaging, and repair of genetic material. Protein-DNA interactions
have also been exploited in biotechnology. For example, restriction enzymes,
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