Improved Angle Potentials for Coarse-Grained Molecular Dynamics Simulations

TLDR: Two approaches to improve the stability and accuracy of coarse-grained molecular dynamics simulations are proposed: dummy-assisted dihedral (DAD), the torsion potential is applied differently: instead of acting directly on the beads, it acts on virtual beads, bound to the real ones.

Abstract: Potentials routinely used in atomistic molecular dynamics simulations are not always suitable for modeling systems at coarse-grained resolution. For example, in the calculation of traditional torsion angle potentials, numerical instability is often encountered in the case of very flexible molecules. To improve the stability and accuracy of coarse-grained molecular dynamics simulations, we propose two approaches. The first makes use of improved forms for the angle potentials: the restricted bending (ReB) potential prevents torsion angles from visiting unstable or unphysical configurations and the combined bending-torsion (CBT) potential smoothly flattens the interactions when such configurations are sampled. In the second approach, dummy-assisted dihedral (DAD), the torsion potential is applied differently: instead of acting directly on the beads, it acts on virtual beads, bound to the real ones. For simple geometrical reasons, the unstable region is excluded from the accessible conformational space. The benefits of the new approaches are demonstrated in simulations of polyethylene glycol (PEG), polystyrene (PS), and polypeptide molecules described by the MARTINI coarse-grained force field. The new potentials are implemented in an in-house version of the Gromacs package, publicly available.

Figures

Table 1. Parameters of the Dummy-Assisted Dihedral for the MARTINI Protein Force Fielda

Table 2. Gromacs Definitions of the Intramolecular Interaction Concerning the Modified Potentialsa

Figure 5. Schematic of the dummy assisted dihedral (DAD) potential. Bi are the initial particles and Di the associated dummies. The dummy particles are constraint at a fixed distance from the original particles and the angles Bi−1BiDi and DiBiBi+1 are subjected to a harmonic potential with an equilibrium angle complementing the Bi−1BiBi+1 value to 360°. A torsion potential D−D−D−D replaces the original B−B− B−B potential. Associated parameters are given in Table 1.

Figure 6. Snapshot from the simulation of an ensemble of PEG polymer chains in water. The polymer chains are depicted as red ropes and the water is shown as a blue haze. Some polymers are represented as linear chains of beads to show the coarse-grained model.

Table 5. Angle Potentials Used in the PS Simulations: Type, Reference Angle, and Optimum Interaction Parametersa

Figure 9. Atomistic and CG distributions of backbone bending and torsion angles in PS.