Scrutinizing the protein hydration shell from molecular dynamics simulations against consensus small-angle scattering data

Abstract

Biological macromolecules in solution are surrounded by a hydration shell, whose structure differs from the structure of bulk solvent. While the importance of the hydration shell for numerous biological functions is widely acknowledged, it remains unknown how the hydration shell is regulated by macromolecular shape and surface composition, mainly because a quantitative probe of the hydration shell structure has been missing. We show that small-angle scattering in solution using X-rays (SAXS) or neutrons (SANS) provide a protein-specific probe of the protein hydration shell that enables quantitative comparison with molecular simulations. Using explicit-solvent SAXS/SANS predictions, we derived the effect of the hydration shell on the radii of gyration R_g of five proteins using 18 combinations of protein force field and water model. By comparing computed R_g values from SAXS relative to SANS in D₂O with consensus SAXS/SANS data from a recent worldwide community effort, we found that several but not all force fields yield a hydration shell contrast in remarkable agreement with experiments. The hydration shell contrast captured by R_g values depends strongly on protein charge and geometric shape, thus providing a protein-specific footprint of protein-water interactions and a novel observable for scrutinizing atomistic hydration shell models against experimental data.

Fig. 1. Explicit-solvent MD reveals the hydration shell structure and modified R_g values from SAXS and SANS.

a Simulation of xylanase obtained with ff99SBws and TIP4P/2005s water. Water molecules within the envelope (blue surface) contribute to SAS calculations. Water outside of the envelope is not shown for clarity. The protein is shown in green cartoon, water as red/white sticks. b Electron density of solvent inside the envelope in shades from light gray (bulk water) to blue to orange to red, revealing the first (orange and red) and the second (mostly blue) hydration layers. c Solvent density versus distance R from the Van-der-Waals surface of the protein, averaged over the protein surface (magenta solid line), revealing two pronounced and a third weak hydration shell. The solvent density around a volume of restrained bulk water (dark green dashed line) reveals by far smaller modulations, demonstrating that water–protein interactions lead to a more structured and more dense hydration shell compared to bulk water. The experimental bulk density of 0.334 e/ų is shown by a gray dashed line. d Calculated intensity curves for SAXS (purple), SANS in H₂O (orange), and SANS in D₂O (blue) obtained from MD simulations. Curves are shown in absolute units of e² for SAXS and squared neutron scattering lengths (nsl²) for SANS. Inset: Guinier plots of SAS curves (colored lines) and linear fits (dotted black lines) used to obtain the SAS-derived radii of gyration R_g. e Difference between SAS-derived R_g values and the R_g values of the pure protein ($R_g^{\mathrm{Prot}}$) for SAXS, SANS/H₂O, and SANS/D₂O (color code as in panel d). R_g differences were computed from simulations with restrained heavy atoms (left), restrained backbone (middle), or from unrestrained MD (right). f Differences between R_g from SAXS and SANS/H₂O (pink), as well as from SAXS and SANS/D₂O (gray). All R_g differences are a footprint of the protein hydration shell. Statistical errors denote 1 SE.

Fig. 2. SAS-derived R_g values of xylanase relative to R_g of the bare protein.

Modulations ΔR_g of the SAS-derived R_g values relative to R_g of the bare protein from unrestrained simulations of xylanase, obtained with 18 different combinations of protein force field (labels along the abscissa) and water model (color code, see legend). a ΔR_g from SAXS, b from SANS in H₂O, and c from SANS in D₂O. Statistical errors (1 SE) were obtained from block averaging. For force field abbreviations, see Table S1.

Fig. 3. Difference in R_g values from SAXS relative to SANS in H₂O or D₂O.

Difference between R_g values from SAXS and SANS/H₂O (left column) or between SAXS and SANS/D₂O (right column) obtained from unrestrained simulations of a, b RNaseA, c, d xylanase, and e, f glucose isomerase. R_g values were obtained with 18 different combinations of protein force fields (labels along the abscissa) and water models (color code, see legend). Experimental consensus values and uncertainties from P(r) analysis are shown as horizontal lines and shaded areas, respectively. Statistical errors denote 1 SE.

Fig. 4. Computational consensus ΔR_g values and ΔRgSAS values for five proteins.

a Computational consensus ΔR_g values and b $\mathrm{\Delta }{R}_{\mathrm{g}}^{\mathrm{SAS}}$ values for five proteins (see labels) obtained as average over six combinations of protein force field and water model that showed close agreement with experimental data according to Fig. 3. Color code is chosen following Fig. 1e, f.