Quantifying Water Density Fluctuations and Compressibility of Hydration Shells of Hydrophobic Solutes and Proteins

Sapna Sarupria and Shekhar Garde

Phys. Rev. Lett. 103, 037803 – Published 17 July 2009

Abstract

We probe the effects of solute length scale, attractions, and hydrostatic pressure on hydrophobic hydration shells using extensive molecular simulations. The hydration shell compressibility and water fluctuations both display a nonmonotonic dependence on solute size, with a minimum near molecular solutes and enhanced fluctuations for larger ones. These results and calculations on proteins suggest that the hydration shells of unfolded proteins are more compressible than of folded ones contributing to pressure denaturation. More importantly, the nonmonotonicity implies a solute curvature-dependent pressure sensitivity for interactions between hydrophobic solutes.

Received 12 February 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.037803

Authors & Affiliations

Sapna Sarupria and Shekhar Garde^*

The Howard P. Isermann Department of Chemical & Biological Engineering, and Center for Biotechnology and Interdisciplinary Studies, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180, USA

^*To whom all correspondence should be addressed. gardes@rpi.edu; http://www.rpi.edu/~gardes

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Vol. 103, Iss. 3 — 17 July 2009

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Figure 1
(a) Solute-water RDFs for a range of solute sizes and pressures at 300 K. The black curve is for a solute with a radius of $\sim 1 nm$ . (b) The height of the first peak near different solutes. $R^{*}$ is the peak location. Data are from simulations of 8 WCA [27] solutes in SPC/E [28] water in the ( $N$ , $P$ , $T$ ) ensemble. The WCA potential for a Lennard-Jones methane ( $σ_{sw} = 0.345 nm$ and $ϵ_{sw} = 0.8957 kJ / mol$ ) was shifted horizontally by $- 0.25$ , $- 0.1$ , 0.0, 0.1, 0.3, 0.6, 1.0, and 1.4 nm to represent 8 WCA solutes. Simulations included one solute and 1100—7250 waters depending on the solute size.Reuse & Permissions
Figure 2
(a) Hydration shell compressibility. Hydration shell is defined using solute-water RDF at 1 bar. The inner radius $r_{0}$ , such that $- \ln [g_{sw} (r_{0})] = 5$ , quantifies the solute cavity radius. The outer radius is the location of the first minimum in $g_{sw} (r)$ . (b) Average hydration shell density normalized by the bulk value. (c) Normalized water number fluctuations in the shell. Open symbols in (c) are data at 250, 500, and 750 bar. (d) The same as in (c) for 1 bar. Open symbols in (d) are fluctuations in hydration-shell-shaped volumes centered at an arbitrary point in bulk water.Reuse & Permissions
Figure 3
(a) Water-water pair correlations $g_{ww}^{sh} (r)$ at 1 bar, in the hydration shell of small ( $r_{0} \sim 0.3 nm$ , red) and large ( $r_{0} \sim 1.7 nm$ , blue) solutes. Bulk water RDF (black) is also shown. Panels (b) and (c) zoom into two regions of interest. (d) Normalized fluctuations measured from MD simulations compared to predictions of compressibility equation using different $g_{ww}^{sh} (r)$ : measured $g_{ww}^{sh}$ (red); $g_{ww}^{sh} \approx g_{ww}^{bulk}$ (blue); and $g_{ww}^{sh}$ from the shell of the largest solute (LS) (magenta).Reuse & Permissions
Figure 4
Effects of solute-water attractions on solute-water RDFs [(a),(b)], on $G (R^{*})$ [(c)], on fluctuations [(d)], and on hydration shell compressibility [(e)]. Panels (a) and (b) are for a methane-sized and for a larger solute with $r_{o} \sim 1.5 nm$ , respectively. To add attractions, the WCA part for a methane-sized solute is shifted down by $α ϵ$ and connected smoothly to the attractive part $α u_{LJ} (r)$ at the minimum. This potential is shifted horizontally (as in Fig. 1) to study 8 different solutes. Four values of $α$ are shown: 0.0 (WCA, black), 0.5 (red), 1.0 (blue), and 2.0 (magenta).Reuse & Permissions
Figure 5
Water number fluctuations in hydration shells of folded (F) and unfolded (U) states of staph nuclease (pdb-id: 1EY0) at different pressures. Unfolded states were generated using a water insertion algorithm [25]. Hydration shell waters are within 0.5 nm of protein. Data are from MD simulations of one protein solvated in 10 684 SPC/E water molecules in the ( $N$ , $P$ , $T$ ) ensemble. Snapshots of folded and unfolded configurations are shown: hydrophobic residues (gray), others (blue), and water (not shown).Reuse & Permissions

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