Simulation of macromolecular liquids with the adaptive resolution molecular dynamics technique

We extend the application of the adaptive resolution technique (AdResS) to liquid systems composed of alkane chains of different lengths. The aim of the study is to develop and test the modifications of AdResS required in order to handle the change of representation of large molecules. The robustness of the approach is shown by calculating several relevant structural properties and comparing them with the results of full atomistic simulations. The extended scheme represents a robust prototype for the simulation of macromolecular systems of interest in several fields, from material science to biophysics.

Figure 1

AdResS simulation box of liquid pentadecane. Overlaid on the structure is the AdResS weighting function $w\left(x\right)$ used in Eq. (1). It is symmetric along the $x$ coordinate with respect to the center of the box at $x=10$ nm and defines an atomistic region $w\left(x\right)=1.0$, the two hybrid regions $0.0<w\left(x\right)<1.0$, and the coarse-grained region $w\left(x\right)=0.0$ across the periodic boundary.

Figure 2

Illustration of the use of the soft-core potential in the AdResS system. Near the coarse-grained region, the effect of the soft-core potential is the strongest to prevent numerical instabilities due to clashes between atoms that are entering the hybrid region. Near the atomistic region, the soft-core potential is almost identical to the standard Lennard-Jones potential. Here, any clashes that occur when the molecule enters the hybrid region should have been relaxed.

Figure 3

Hybrid coarse-grained/atomistic representation of hexadecane. Only intramolecular forces (bonds, angles, dihedrals) are calculated between the atoms (gray sticks). Nonbonded interactions are only calculated between the coarse-grained interaction sites (cyan spheres) and the resulting forces are distributed between the atoms according to their mass.

Figure 4

Pentacontane (50 monomers) across the hybrid region. Small spheres represent atomistic interaction centers, big spheres represent coarse-grained interaction centers. Bonded interactions (represented by lines in the highlighted molecule) are calculated between atoms in all regions of the AdResS system.

Figure 5

Density profile along the $x$ axis, averaged over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots). The hybrid regions of the AdResS box is marked in gray, the atomistic region is located in the middle, the coarse-grained region at both ends of the plot.

Figure 6

Radial distribution function for the center of mass of the molecules, calculated over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots). For longer chains, the radial distribution of the molecular centers of mass degenerates, as the center of mass of a long bent polymer chain is not necessarily located near any of the monomers of this chain.

Figure 7

Radial distribution function for atom “C1” (the first atom in the polymer chain), calculated for all molecules in the atomistic region over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots).

Figure 8

Intramolecular atomic radial distribution function, averaged over all molecules in the atomistic region over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots). As the first peaks of the distribution are determined by the bond length, the “long-range” tail region is shown in more detail in the insets of the corresponding plots.

Figure 9

Distribution of the radius of gyration, averaged over all molecules in the atomistic region over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots).

Figure 10

Distribution of the end-to-end distance, averaged over all molecules in the atomistic region over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots).

Figure 11

Local average radius of gyration along the $x$ axis of the simulation box. Due to the hybrid topology used in the coarse-grained region, the radius of gyration is defined in this region as well. Values are averaged over all molecules in the atomistic region over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots).

Figure 12

Fraction of atoms initially present in the atomistic region and still present in the atomistic region over time. The calculation was done over 90 ns simulation after a 10 ns equilibration period. As the simulation box is finite, the value converges to an equal distribution of all initially present atoms in the box, resulting in a value of 0.2 (the volume fraction of the atomistic region in the simulation box). Result from AdResS (blue lines) and full atomistic simulation (yellow dots).

Figure 13

Position probability density (along the $x$ axis) for a molecule 0 ns, 4 ns, and 40 ns after it is present in the atomistic region. For longer chains, the difference between fully atomistic and AdResS profiles in the coarse-grained part of the simulation box is caused by the faster diffusion in the coarse-grained part.

Figure 14

Order parameter ($x$ component) along the $x$ axis of the simulation box, averaged over 9000 frames from a 90 ns simulation after a 10 ns equilibration period. Result from AdResS (blue lines) and full atomistic simulation (yellow dots). The hybrid regions of the AdResS box are marked in gray, the atomistic region is located in the middle, the coarse-grained region at both ends of the plot.

Figure 15

Estimation of the performance of AdResS relative to a full atomistic simulation depending on the total system size (number of molecules in the simulation). For each system size, five short (5000 steps) simulations were conducted of both the full atomistic simulation and AdResS system under production conditions (on $2\times$ Xeon Westmere X5650 hexacore processors). Performance according to GROMACS log file (in ns of simulation time per day of wall time). Variations (estimated from standard deviations between each set of five simulations) can be expected in such short simulations due to GROMACS load balancing, domain decomposition, and other random factors. The size of the atomistic and hybrid regions remained constant (the atomistic region contains on average 400 molecules).

Figure 16

Density profile along the $x$ axis (as in Fig. 5) for pentadecane using different widths of the hybrid region.

Figure 17

Order parameter ($x$ component) along the $x$ axis of the simulation box (as in Fig. 14) for pentadecane using different widths of the hybrid region.

Figure 18

Fraction of atoms initially present in the atomistic region and still present in the atomistic region over time (as in Fig. 12) for pentadecane using different widths of the hybrid region.