On the investigation of coarse-grained models for water: balancing computational efficiency and the retention of structural properties

Abstract

Developing accurate models of water for use in computer simulations is important for the study of many chemical and biological systems, including lipid bilayer self-assembly. The large temporal and spatial scales needed to study such self-assembly have led to the development and application of coarse-grained models for the lipid-lipid, lipid-solvent, and solvent-solvent interactions. Unfortunately, popular center-of-mass-based coarse-graining techniques are limited to modeling water with one water per be ad. In this work, we have utilized the K-means algorithm to determine the optimal clustering of waters to allow the mapping of multiple waters to single coarse-grained beads. Through the study of a simple mixture between water and an amphiphilic solute (1-pentanol), we find a four-water bead model has the optimal balance between computational efficiency and accurate solvation and structural properties when compared to water models ranging from one to nine waters per bead. The four-water model was subsequently utilized in studies of the solvation of hexadecanoic acid and the structure, as measured via radial distribution functions, for the hydrophobic tails and the bulk water phase were found to agree well with experimental data and their atomistic target.

Figure 1

Schematic illustration of the K-means algorithm. Circles represent cluster locations, squares represent water locations, and shaded regions represent the allocation of waters to each cluster in a color-coded fashion.

Figure 2

Schematic illustrating the mapping of the atomistic 1-pentanol (left) and C16:0 (right) to the coarse-grained level.

Figure 3

Radial distribution function between two hydrophobic beads (ALK-ALK) from a coarse-grained simulation (diamonds) and the target atomistic simulation (solid line) of pure 1-pentanol.

Figure 4

Probability distribution of a PALC-ALK bond length from an atomistic trajectory (diamonds) mapped to the coarse-grained level and fitted by a Gaussian curve (solid line).

Figure 5

Radial distribution function between a) one-water beads (H2O1-H2O1), b) four-water beads (H2O4-H2O4), c) six-water beads (H2O6-H2O6), and d) eight-water beads (H2O8-H2O8), from a coarse-grained simulation (diamonds) and from the atomistic target simulation (solid line).

Figure 6

Interaction potential between one-water beads (H2O1-H2O1) (diamonds), four-water beads (H2O4-H2O4) (triangles), six-water beads (H2O6-H2O6) (circles), and eight-water beads (H2O8-H2O8) (crosses) fitted from the pure water system.

Figure 7

Radial distribution function between two hydrophobic beads (ALK-ALK) from simulations of 1-pentanol with a) atomistic (crosses), H2O1 (squares), H2O3 (triangles), H2O4 (diamonds), and H2O5 (circles) water models, compared to the target atomistic simulation (solid line) and b) radial distribution function between two hydrophobic beads (ALK-ALK) from simulations of 1-pentanol with H2O4 (diamonds), H2O5 (circles), H2O6 (squares), H2O8 (crosses), and H2O9 (triangles) water models, compared to the target atomistic simulation (solid line).

Figure 8

Radial distribution function between a) one-water beads (H2O1-H2O1) and b) four-water beads (H2O4-H2O4) from a coarse-grained simulation (diamonds) and an atomistic simulation (solid line) of the water-1-pentanol mixture.

Figure 9

Radial distribution function between a) tail beads (TAIL-TAIL), b) four-water beads (H2O4-H2O4), and c) head beads (HEAD-HEAD), for the hexadecanoic acid-water mixture from a coarse-grained simulation (diamonds) and from the target atomistic simulation (solid line).

Figure 10

Radial distribution function between a) alcohol beads (PALC-PALC) from a coarse-grained simulation of pentanol with atomistic water (crosses), H2O4 using the pure potential transferred to the water-pentanol mixture (triangles), H2O4 using the potential fitted to the pentanol mixture (plusses), and H2O4 using the ALK-H2O4 interaction replaced by the attractive PALC-ALK potential (diamonds), compared to the target atomistic simulation (solid line), and (b) radial distribution function between alcohol beads (PALC-PALC) in a simulation of pure pentanol using the potential fitted from a mixture simulation (diamonds) and the atomistic target (solid line) and (c) fitted radial distribution function between the hydrophobic bead of pentanol and a 4-water bead (ALK-H2O4) from a coarse-grained simulation of the water-pentanol mixture (diamonds) and the target atomistic simulation (solid line).

Figure 11

Interaction potential between alcohol beads (PALC-PALC) fitted from a pure simulation (solid line) and fitted from the mixture simulation (dashed line).

Figure 12

Interaction potentials between hydrophobic (ALK) and water (H2O4) beads (solid line) and the hydrophilic (PALC) and hydrophobic (ALK) beads (dashed line).