Coarse-Grained Modeling and Simulations of Thermoresponsive …
45
Fig. 3 Schematic of our CG model for a representative polymer-conjugated ONA duplex. The
two complementary bases are shown in red and blue, respectively. All backbone (BB) beads are of
the same type but colored differently for visual depiction of the sequence. H-bond (HB) sites are
different for each natural base but are all colored in yellow. Polymer (PL) beads do not have a HB
site and are colored in gray. Reprinted with permission from Ref. [20]. Copyright 2016 American
Chemical Society
10ε/rad
2 . The k
PL
angle force constant could be changed to higher values to model stiffer
polymers. Near the polymer and ONA junction point, the PL-BB-BB and PL-PL-BB
angles are modeled in the same way as the BB-BB-BB angle potential.
All charged ONA or ONA-polymer systems explicit counterions (IN) are represented as spherical beads of size 0.7σ and mass 1 m with charge valency of + 1 and −
1 for positive and negative charges, respectively. Electrostatic interactions between
charged beads are calculated using Coulomb potential
U
coul
i j (r ) =
q i q j
4πr ε 0 ε r (T )
(5)
where q i is the charged valency of bead i, ε 0 is the permittivity of the vacuum,
ε r is relative permittivity of the implicit solvent and T is the temperature. ε r of
water at dilute salt concentration can be estimated as a function of temperature:
ε r (T [K ]) = 249.4 − 0.788T + 0.00072T
2 [72]. In our CG model, the electrostatic
interactions between bonded neighbors are effective only for the nearest neighbor
(1–2) and the dielectric constant is assumed to be distance independent.
To be able to study the solvent quality effects, in ONA-polymer-conjugate systems,
the solvophobic nature of polymer is captured through effective polymer–polymer
interactions and is modeled using LJ [69] potential.
U
PP
i j =
⎧
⎨
⎩
4ε
PP
σ
PL
r
12 −
σ
PL
r
6
; r ≤ 2.5σ
PL
0;
r > 2.5σ
PL
(6)
where ε
PP is the strength of attraction between two solvophobic PL beads.
The non-bonded interaction between all other pairs of beads (BB-BB; BB-HB;
ion-HB; ion-BB; ion-PL; PL-BB; PL-HB) is modeled using WCA purely repulsive
potential (Eq. 4) with σ
r equal to the arithmetic mean of the sizes of the two beads
45
Fig. 3 Schematic of our CG model for a representative polymer-conjugated ONA duplex. The
two complementary bases are shown in red and blue, respectively. All backbone (BB) beads are of
the same type but colored differently for visual depiction of the sequence. H-bond (HB) sites are
different for each natural base but are all colored in yellow. Polymer (PL) beads do not have a HB
site and are colored in gray. Reprinted with permission from Ref. [20]. Copyright 2016 American
Chemical Society
10ε/rad
2 . The k
PL
angle force constant could be changed to higher values to model stiffer
polymers. Near the polymer and ONA junction point, the PL-BB-BB and PL-PL-BB
angles are modeled in the same way as the BB-BB-BB angle potential.
All charged ONA or ONA-polymer systems explicit counterions (IN) are represented as spherical beads of size 0.7σ and mass 1 m with charge valency of + 1 and −
1 for positive and negative charges, respectively. Electrostatic interactions between
charged beads are calculated using Coulomb potential
U
coul
i j (r ) =
q i q j
4πr ε 0 ε r (T )
(5)
where q i is the charged valency of bead i, ε 0 is the permittivity of the vacuum,
ε r is relative permittivity of the implicit solvent and T is the temperature. ε r of
water at dilute salt concentration can be estimated as a function of temperature:
ε r (T [K ]) = 249.4 − 0.788T + 0.00072T
2 [72]. In our CG model, the electrostatic
interactions between bonded neighbors are effective only for the nearest neighbor
(1–2) and the dielectric constant is assumed to be distance independent.
To be able to study the solvent quality effects, in ONA-polymer-conjugate systems,
the solvophobic nature of polymer is captured through effective polymer–polymer
interactions and is modeled using LJ [69] potential.
U
PP
i j =
⎧
⎨
⎩
4ε
PP
σ
PL
r
12 −
σ
PL
r
6
; r ≤ 2.5σ
PL
0;
r > 2.5σ
PL
(6)
where ε
PP is the strength of attraction between two solvophobic PL beads.
The non-bonded interaction between all other pairs of beads (BB-BB; BB-HB;
ion-HB; ion-BB; ion-PL; PL-BB; PL-HB) is modeled using WCA purely repulsive
potential (Eq. 4) with σ
r equal to the arithmetic mean of the sizes of the two beads