Chemistry Reference
In-Depth Information
Non-Bond Parameters
Two copies of the atoms comprising each pseudo-atom were obtained, displaced by
4
˚
in the
z
-direction and individually immersed in a pre-equilibrated box of TIP3
water. The charges were maintained, and hence the only set of atoms with a net
charge were the five atoms comprising the phosphate (PHO/PHP) bead, with a
net
þ
ions and subjected to the same simulation protocol as before. First 100 ps of NPT
dynamics was performed, with snapshots of the last 20 ps (every 2 ps) saved. The
ten snapshots were then superimposed on each other and the average MD solution
structure obtained as previously discussed.
A constrained MD simulation was then run, where the center of mass of each of
the two sets of atoms are constrained by a harmonic potential. Every time step, the
distance between the two centers of mass is checked, and if they are not equal to a
specified distance, a restoring spring of magnitude
-k
1 charge per set of atoms. If necessary, the system was neutralized with Na
D
x
is applied to all of the
atoms in the second set. Here,
x
is the differential distance from equilibrium and
k
is a force constant of 500 kcal mol
1
˚
1
. The center of mass of the two sets of
atoms are constrained, starting at 2.0
˚
, in 0.1
˚
increments, until 10
˚
. After each
increment, 40 ps of NPT dynamics is performed to equilibrate the structure at the
restraint, followed by a further 20 ps of NPT dynamics, during which time the non-
bond energy of both sets of atoms is calculated and tabulated.
The average energy per center of mass separation was then computed and plotted
vs the center of mass (Fig.
15b
). This function was then shifted so that its plateau
was at 0, and fitted to the Morse potential in (17) using the least squares fitting
procedure previously discussed. This fitting is the effective potential of mean force
between both sets of atoms, in the presence of water. This potential has both
electrostatic and van der Waals contributions, which is critical since none of the
pseudo-atoms are charged.
D
Meso-Scale Simulation of B-DNA Dodecamer
Simulation Protocol
Bond stretches are the highest frequency modes in any MD simulation. The largest
time step of any MD simulation is inversely proportional to the highest frequency
modes, which is related to the force constant by
f
p
(assuming har-
k
¼
12
=
p
monic bonds), where
is the reduced mass of the parameter atoms being consid-
ered. A rule of thumb is that the largest time step possible should be 1/(6*f). The
pseudo-atoms of this meso-scale force field are much heavier than those of regular
atoms and the largest bond force constant is one-fifth that of the typical largest
atomistic force constant, which allowed the use of a 10 fs timestep. Furthermore,
the meso-scale system contains fewer particles than its atomistic counterpart (each
nucleotide is composed of 3 pseudo-atoms, compared to about 40 for an atomistic
nucleotide) and it avoids electrostatic interactions because the pseudo-atoms were
m
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