Coarse-Grained Modeling and Simulations of Thermoresponsive …
53
capture the underlying physics of CLP melting can guide the design of CLP-based
biomaterials for applications such as drug delivery and tissue engineering.
3.2 Model
Here, we outline only the key features of the CG CLP model which is described
in detail in the original work of Condon and Jayaraman [106]. Each CLP strand is
a chain of XYG triplets where each XYG triplet is represented by five interaction
sites. For example, every (POG) triplet is modeled using a proline backbone (PB)
bead, a proline h-bond (PH) acceptor bead, a hydroxyproline backbone bead (OB),
a glycine backbone (GB) bead and a glycine h-bond (GH) donor bead. The characteristic length, σ , and characteristic energy, ε, for the CLP model are 0.5 nm and
0.1 kcal/mol, respectively. This choice of energy relates the reduced temperature
T
∗
= 5.92 to T = 298 K. The characteristic mass, m, is chosen arbitrarily as the
goal of the CLP model is to capture the correct thermodynamics and not to capture
the correct dynamics of these CLP systems. Therefore, the bead masses do not need
to reproduce the exact masses of the residues they represent. Furthermore, all backbone (BB) beads have a diameter of 1.0σ and a mass of 3.0m while all h-bond beads
have a diameter of 0.3σ and a mass of 1.0m.
Adjacent BB beads are connected via a harmonic bond potential with a bond
length of 0.5σ and force constant of 1000ε/σ
2 and each h-bond bead is connected to
its “parent” BB bead via a harmonic bond potential with a bond length of 0.37σ and
force constant of 1000ε/σ
2 . To account for the rigidity of the PPII conformation of
CLP and to reproduce experimentally observed dimensions (i.e., diameter and end-toend distance) of the CLP triple helix, we include a harmonic angle potential between
three adjacent BB beads with the angle constant set at 20 ε/rad
2 and equilibrium bond
angle set at 180°. It is important to note that the CG CLP model does not reproduce
the experimentally observed helicity of the CLP triple helix. Like the ONA model
of Ghobadi and Jayaraman [19], the main goal of the CLP model of Condon and
Jayaraman [106] was to capture the correct trends in thermal transitions rather than
structure (e.g., triple helix rise and pitch) with varying CLP design. Next, to ensure
that h-bond formation occurs perpendicular to the backbone, a h-bond bead-BB beadadjacent BB bead angle potential is introduced with a force constant of 300ε/rad
2
and equilibrium angle of 90°.
All non-bonded interactions between h-bond donors (D) and h-bond acceptors (A)
are represented using the Lennard–Jones (LJ) potential with ε = ε
HB
D−A , the interaction
strength between D and A beads set to 50.4ε and σ = σ
HB the diameter of a h-bond
bead. For all LJ interactions, a cut-off of 1.9σ
HB with a switching function taken
from GROMACS [70] implemented in the LAMMPS package [73] smoothly ramps
the potential and force to zero at 2.0σ
HB . All other pairwise interactions besides the
h-bond donor–acceptor interactions are modeled using the purely repulsive WCA
potential with σ i j being the arithmetic mean of the diameters of beads i and j and
ε i j , the interaction strength, is set at 1.0ε. For donor–donor and acceptor–acceptor
53
capture the underlying physics of CLP melting can guide the design of CLP-based
biomaterials for applications such as drug delivery and tissue engineering.
3.2 Model
Here, we outline only the key features of the CG CLP model which is described
in detail in the original work of Condon and Jayaraman [106]. Each CLP strand is
a chain of XYG triplets where each XYG triplet is represented by five interaction
sites. For example, every (POG) triplet is modeled using a proline backbone (PB)
bead, a proline h-bond (PH) acceptor bead, a hydroxyproline backbone bead (OB),
a glycine backbone (GB) bead and a glycine h-bond (GH) donor bead. The characteristic length, σ , and characteristic energy, ε, for the CLP model are 0.5 nm and
0.1 kcal/mol, respectively. This choice of energy relates the reduced temperature
T
∗
= 5.92 to T = 298 K. The characteristic mass, m, is chosen arbitrarily as the
goal of the CLP model is to capture the correct thermodynamics and not to capture
the correct dynamics of these CLP systems. Therefore, the bead masses do not need
to reproduce the exact masses of the residues they represent. Furthermore, all backbone (BB) beads have a diameter of 1.0σ and a mass of 3.0m while all h-bond beads
have a diameter of 0.3σ and a mass of 1.0m.
Adjacent BB beads are connected via a harmonic bond potential with a bond
length of 0.5σ and force constant of 1000ε/σ
2 and each h-bond bead is connected to
its “parent” BB bead via a harmonic bond potential with a bond length of 0.37σ and
force constant of 1000ε/σ
2 . To account for the rigidity of the PPII conformation of
CLP and to reproduce experimentally observed dimensions (i.e., diameter and end-toend distance) of the CLP triple helix, we include a harmonic angle potential between
three adjacent BB beads with the angle constant set at 20 ε/rad
2 and equilibrium bond
angle set at 180°. It is important to note that the CG CLP model does not reproduce
the experimentally observed helicity of the CLP triple helix. Like the ONA model
of Ghobadi and Jayaraman [19], the main goal of the CLP model of Condon and
Jayaraman [106] was to capture the correct trends in thermal transitions rather than
structure (e.g., triple helix rise and pitch) with varying CLP design. Next, to ensure
that h-bond formation occurs perpendicular to the backbone, a h-bond bead-BB beadadjacent BB bead angle potential is introduced with a force constant of 300ε/rad
2
and equilibrium angle of 90°.
All non-bonded interactions between h-bond donors (D) and h-bond acceptors (A)
are represented using the Lennard–Jones (LJ) potential with ε = ε
HB
D−A , the interaction
strength between D and A beads set to 50.4ε and σ = σ
HB the diameter of a h-bond
bead. For all LJ interactions, a cut-off of 1.9σ
HB with a switching function taken
from GROMACS [70] implemented in the LAMMPS package [73] smoothly ramps
the potential and force to zero at 2.0σ
HB . All other pairwise interactions besides the
h-bond donor–acceptor interactions are modeled using the purely repulsive WCA
potential with σ i j being the arithmetic mean of the diameters of beads i and j and
ε i j , the interaction strength, is set at 1.0ε. For donor–donor and acceptor–acceptor