46
A. Jayaraman et al.
involved in the interaction. We note that by modeling the BB-BB non-bonded interaction via WCA potential (Eq. 4), the implicit solvent is considered to be a good
solvent for the ONA.
2.3 Method: Simulations and Analyses
The initial configuration for all simulations is generated by randomly placing fully
hybridized duplexes of ONA or ONA-polymer conjugates without any overlaps in a
cubic simulation box with periodic boundary conditions in x-, y- and z-directions. The
simulation box contains IN counterion beads only when the BB beads are charged.
Apart from the IN beads that are needed to neutralize the charged backbone beads
in the simulation box, an additional amount of 1 mM monovalent salt is added to the
simulation box for the charged backbone systems. For all the results presented below
20 duplexes are placed in a cubic simulation box of length 300σ, which achieves a
6 μM ONA duplex concentration. In principle, other salt and ONA concentrations
can be modeled by selecting appropriate number of IN beads and ONA duplexes,
respectively.
The CG simulations are performed using Langevin dynamics in the NVT ensemble
in LAMMPS [73] package with the damping coefficient set at 10τ. Particle–particle–
particle-mesh (PPPM) [74] method is used for electrostatic interactions with a force
tolerance of 10
−2 , interpolation order of 2 and real space cut-off distance of 20σ .
The equations of motion are integrated using two-level rRESPA [75] multiple time
step algorithm, with a time step of 0.001τ and 0.0005τ for non-bonded and bonded
interactions, respectively. In each simulation run, the first 1.0 × 10
8 to 1.4 × 10
8
time steps are considered as equilibration steps. After that, we store uncorrelated
configurations every 2,000–10,000 time steps over another 1.0 × 10
7 to 2.0 × 10
7
time steps. For every parameter, three independent simulation trials are run with
different initial velocities and random number seeds.
As our interest is to understand thermal stability of ONA duplexes as a function of
ONA design, we calculate from simulations the ONA melting curves of the various
ONA systems at different temperatures. The temperatures are chosen to be able to
sample states where the fraction of hybridized ONA duplexes in the simulation box
is 1 (at low temperatures), states where the fraction of hybridized ONA duplexes in
the simulation box is less than 1 and greater than 0 (at intermediate temperatures)
and states where all duplexes have melted (fraction of hybridized duplexes = 0, at
high temperatures). Any ONA strand is considered to be hybridized if at least half
of its HB sites are engaged in h-bonds with another ONA strand [76, 77]. An HB
site is considered to be engaged in an h-bond with another HB site if the distance
between them is less than 1.5σ
HB . Melting curves are plotted as the fraction of the
hybridized duplexes in the simulation box as a function of temperature ( f 50% vs. T
* ).
Melting temperature (T m ) is defined as the temperature at which half of the duplexes
are dissociated/melted, i.e., f 50% = 0.5. The melting curves we report are an average
from at least three independent runs. Besides melting curves, one can also calculate
A. Jayaraman et al.
involved in the interaction. We note that by modeling the BB-BB non-bonded interaction via WCA potential (Eq. 4), the implicit solvent is considered to be a good
solvent for the ONA.
2.3 Method: Simulations and Analyses
The initial configuration for all simulations is generated by randomly placing fully
hybridized duplexes of ONA or ONA-polymer conjugates without any overlaps in a
cubic simulation box with periodic boundary conditions in x-, y- and z-directions. The
simulation box contains IN counterion beads only when the BB beads are charged.
Apart from the IN beads that are needed to neutralize the charged backbone beads
in the simulation box, an additional amount of 1 mM monovalent salt is added to the
simulation box for the charged backbone systems. For all the results presented below
20 duplexes are placed in a cubic simulation box of length 300σ, which achieves a
6 μM ONA duplex concentration. In principle, other salt and ONA concentrations
can be modeled by selecting appropriate number of IN beads and ONA duplexes,
respectively.
The CG simulations are performed using Langevin dynamics in the NVT ensemble
in LAMMPS [73] package with the damping coefficient set at 10τ. Particle–particle–
particle-mesh (PPPM) [74] method is used for electrostatic interactions with a force
tolerance of 10
−2 , interpolation order of 2 and real space cut-off distance of 20σ .
The equations of motion are integrated using two-level rRESPA [75] multiple time
step algorithm, with a time step of 0.001τ and 0.0005τ for non-bonded and bonded
interactions, respectively. In each simulation run, the first 1.0 × 10
8 to 1.4 × 10
8
time steps are considered as equilibration steps. After that, we store uncorrelated
configurations every 2,000–10,000 time steps over another 1.0 × 10
7 to 2.0 × 10
7
time steps. For every parameter, three independent simulation trials are run with
different initial velocities and random number seeds.
As our interest is to understand thermal stability of ONA duplexes as a function of
ONA design, we calculate from simulations the ONA melting curves of the various
ONA systems at different temperatures. The temperatures are chosen to be able to
sample states where the fraction of hybridized ONA duplexes in the simulation box
is 1 (at low temperatures), states where the fraction of hybridized ONA duplexes in
the simulation box is less than 1 and greater than 0 (at intermediate temperatures)
and states where all duplexes have melted (fraction of hybridized duplexes = 0, at
high temperatures). Any ONA strand is considered to be hybridized if at least half
of its HB sites are engaged in h-bonds with another ONA strand [76, 77]. An HB
site is considered to be engaged in an h-bond with another HB site if the distance
between them is less than 1.5σ
HB . Melting curves are plotted as the fraction of the
hybridized duplexes in the simulation box as a function of temperature ( f 50% vs. T
* ).
Melting temperature (T m ) is defined as the temperature at which half of the duplexes
are dissociated/melted, i.e., f 50% = 0.5. The melting curves we report are an average
from at least three independent runs. Besides melting curves, one can also calculate