Grid inhomogeneous solvation theory: hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Abstract

The displacement of perturbed water upon binding is believed to play a critical role in the thermodynamics of biomolecular recognition, but it is nontrivial to unambiguously define and answer questions about this process. We address this issue by introducing grid inhomogeneous solvation theory (GIST), which discretizes the equations of inhomogeneous solvation theory (IST) onto a three-dimensional grid situated in the region of interest around a solute molecule or complex. Snapshots from explicit solvent simulations are used to estimate localized solvation entropies, energies, and free energies associated with the grid boxes, or voxels, and properly summing these thermodynamic quantities over voxels yields information about hydration thermodynamics. GIST thus provides a smoothly varying representation of water properties as a function of position, rather than focusing on hydration sites where solvent is present at high density. It therefore accounts for full or partial displacement of water from sites that are highly occupied by water, as well as for partly occupied and water-depleted regions around the solute. GIST can also provide a well-defined estimate of the solvation free energy and therefore enables a rigorous end-states analysis of binding. For example, one may not only use a first GIST calculation to project the thermodynamic consequences of displacing water from the surface of a receptor by a ligand, but also account, in a second GIST calculation, for the thermodynamics of subsequent solvent reorganization around the bound complex. In the present study, a first GIST analysis of the molecular host cucurbit[7]uril is found to yield a rich picture of hydration structure and thermodynamics in and around this miniature receptor. One of the most striking results is the observation of a toroidal region of high water density at the center of the host's nonpolar cavity. Despite its high density, the water in this toroidal region is disfavored energetically and entropically, and hence may contribute to the known ability of this small receptor to bind guest molecules with unusually high affinities. Interestingly, the toroidal region of high water density persists even when all partial charges of the receptor are set to zero. Thus, localized regions of high solvent density can be generated in a binding site without strong, attractive solute-solvent interactions.

Figure 1

Cucurbit[7]uril, a symmetric ring of seven glycouril units. Right-hand graphic includes rectangular prisms showing the size and position of the GIST grid (green), and the computational definitions of the torus (red), and cavity (blue) regions used in the quantitative solvation studies (Results). The torus region of high water density is shown with a red contour.

Figure 2

Contour plots of $-T\Delta S_{sw}^{trans}\left({\mathbf{r}}_k\right)$, the first-order translational entropy contribution to solvation free energy, for top (left) and side (right) views of CB7. Red: 0.1 kcal/mol/ų. Tan: 0.0 kcal/mol/ų. Note that this quantity is referenced to bulk water. Molecular graphics generated with Visual Molecular Dynamics (VMD).

Figure 3

Local density of water hydrogen atoms in and around CB7, contoured at bulk density.

Figure 4

Radial distribution functions in the x-y plane of regular CB7 (left) and nonpolar host (right) at multiple values of z (Å). Densities were computed for planar layers of thickness 0.5 Å and averaged circumferentially to yield g(r), the water density as a function of distance from the z axis. The equator of the host is at z = 0 and the carbonyl oxygens are at about z = 3.1.

Figure 5

Contributions of orientational entropy to solvation free energy in and around CB7. Left: orientational entropy (−TS^ω) contours at 1.5 kcal/mol/water (violet) and 0.5 kcal/mol/water (yellow). Right: contours of orientational entropy density ($-T\Delta S_{sw}^{orient}$), at 0.15 kcal/mol/ų (violet) and 0.05 kcal/mol/ų (yellow).

Figure 6

Contours of total solvation energy. Left: per-water values, ΔE_sw(r_k) + ΔE_ww(r_k), where $\Delta E_{ww}\left({\mathbf{r}}_k\right)=E_{ww}\left({\mathbf{r}}_k\right)-2E_{ww}^{bulk}$, at 1.8 (tan) and 0.3 (cyan) and −1.0 (red) kcal/mol/water. Right: density-weighted values (ρ^og(r_k)(ΔE_sw(r_k) + ΔE_ww(r_k))) at 0.0125 (orange), 0.001 (cyan), and −0.006 (red) kcal/mol/ų.

Figure 7

Contours of solute–water interaction energy ($\Delta E_{ww}\left({\mathbf{r}}_k\right)=E_{ww}\left({\mathbf{r}}_k\right)-2E_{ww}^{bulk}$) in and around CB7. Orange: −8.5 kcal/mol/water. Blue: −4.0 kcal/mol/water.

Figure 8

Contours of water–water interaction energy (ΔE_ww(r_k)) in and around CB7. Orange: 8.0 kcal/mol/water. Cyan: 3 kcal/mol/water.

Figure 9

Overlays of 200 water coordinates in a low orientational entropy (per water) voxel near two carbonyl groups at one portal of CB7 (left), and a highly occupied voxel in the toroidal region of high water density (middle and right).

Figure 10

Two representative snapshots of water conformations within the cavity of CB7. Hydrogen bonds, based on geometric criteria (oxygen–oxygen distance <3.0 Å and O−H···O angle >155^°), are shown as black dotted lines.

Figure 11

Contour plots of the translational entropy contribution to free energy, for top (left) and side (right) views of nonpolar CB7. Red: 0.008 kcal/mol/ų. Tan: 0.0 kcal/mol/ų.

Figure 12

Overlays of 200 water coordinates in a highly occupied voxel in the toroidal region of high water density, for the nonpolar host.

Figure 13

Normalized thermodynamic quantities, as labeled, on the interior (top row) and exterior (bottom row) of the regular CB7 receptor, as a function of distance along the z axis.

Figure 14

Normalized thermodynamic quantities, as labeled, on the interior (top row) and exterior (bottom row) of the artificial nonpolar receptor, as a function of distance along the z axis. The regions R analyzed here are successive layers normal to the z axis.