^{1,a)}, F. Affouard

^{1}, P. Bordat

^{2}, A. Hédoux

^{1}, Y. Guinet

^{1}and M. Descamps

^{1}

### Abstract

The low-frequency vibrational properties of lysozyme in aqueous solutions of three well-known protecting sugars, namely, trehalose, maltose, and sucrose, have been investigated by means of complementary Raman scattering experiments and molecular dynamics simulations. The comparison of the Raman susceptibility of lysozyme/water and lysozyme/sugar/water solutions at a concentration of 40 wt % with the of dry lysozyme suggests that the proteindynamics mostly appears in the broad peak around that reflects the vibrations experienced by atoms within the *cage* formed by their neighbors, whereas the broad shoulder around mainly stems from the intermolecular stretching vibrations of water. The addition of sugars essentially induces a significant high frequency shift and intensity reduction of this band that reveal a slowing down of water dynamics and a distortion of the tetrahedral hydrogen bond network of water, respectively. Furthermore, the lysozyme vibrational densities of states (VDOS) have been determined from simulations of lysozyme in 37–60 wt % disaccharide aqueous solutions. They exhibit an additional broad peak around , in line with the VDOS of globular proteins obtained in neutron scattering experiments. The influence of sugars on the computed VDOS mostly appears on the first peak as a slight high-frequency shift and intensity reduction in the low-frequency range , which increase with the sugar concentration and with the exposition of protein residues to the solvent. These results suggest that sugars stiffen the environment experienced by lysozyme atoms, thereby counteracting the softening of protein vibrational modes upon denaturation, observed at high temperature in the Raman susceptibility of the lysozyme/water solution and in the computed VDOS of unfolded lysozyme in water. Finally, the Raman susceptibility of sugar/water solutions and the calculated VDOS of water in the different lysozyme solutions confirm that sugars induce a significant strengthening of the hydrogen bond network of water that may stabilize proteins at high temperatures.

The authors wish to acknowledge the use of the facilities of the IDRIS (Orsay, France), the CINES (Montpellier, France), and the CRI (Villeneuve d’Ascq, France) where calculations were carried out. This work was supported by the INTERREG III (FEDER) program (Nord-Pas de Calais/Kent) and by the ANR (Agence Nationale de la Recherche) through the BIOSTAB project (“Physique-Chimie du Vivant” program). A.L. thanks the Nord-Pas de Calais region for a postdoctoral fellowship.

I. INTRODUCTION

II. EXPERIMENTAL AND SIMULATION DETAILS

A. Raman scattering experiments

B. Molecular dynamics simulations

III. RESULTS AND DISCUSSION

A. Native lysozyme

B. Denatured lysozyme

C. Water

IV. SUMMARY AND CONCLUSIONS

### Key Topics

- Proteins
- 40.0
- Solvents
- 24.0
- Raman spectroscopy
- 22.0
- Raman spectra
- 16.0
- Molecular dynamics
- 12.0

## Figures

(a) Raman susceptibility of lysozyme/water and lysozyme/sugar/water solutions at a concentration of 40 wt %. The susceptibility of dry lysozyme (D) is also shown for comparison. The averaged VDOS of lysozyme obtained from MD simulations are represented below for lysozyme: (b) in the lysozyme/water (W) and the 60 wt % lysozyme/trehalose/water (T) solutions, (c) in the different trehalose solutions, and (d) in the different 60 wt % sugar solutions. The curves in (a)–(d) have been smoothed with the Savitzky–Golay algorithm (Ref. 90) to make easier the comparison of results. Moreover, the scale is logarithmic in (c) and (d) to underline these effects in the frequency range. Their statistical significance was confirmed by a detailed analysis of the standard deviations on the VDOS (data not shown).

(a) Raman susceptibility of lysozyme/water and lysozyme/sugar/water solutions at a concentration of 40 wt %. The susceptibility of dry lysozyme (D) is also shown for comparison. The averaged VDOS of lysozyme obtained from MD simulations are represented below for lysozyme: (b) in the lysozyme/water (W) and the 60 wt % lysozyme/trehalose/water (T) solutions, (c) in the different trehalose solutions, and (d) in the different 60 wt % sugar solutions. The curves in (a)–(d) have been smoothed with the Savitzky–Golay algorithm (Ref. 90) to make easier the comparison of results. Moreover, the scale is logarithmic in (c) and (d) to underline these effects in the frequency range. Their statistical significance was confirmed by a detailed analysis of the standard deviations on the VDOS (data not shown).

VDOS of different parts of lysozyme determined from MD simulations of the lysozyme/water (W) and the 60 wt % lysozyme/trehalose/water (T) solutions (maltose and sucrose solutions behave similarly and are thus not shown for clarity reasons). The averaged VDOS of some fragments of the most and the least solvent exposed lysozyme residues are shown in the left [(a)–(d)] and right [(e)–(h)] panels of the figure, respectively. [(a) and (b)]: side chain atoms and methyl hydrogens of the 30 most exposed residues, respectively, (c): groups of the most exposed arginine residues, (d): carboxylate groups of the most exposed aspartic and glutamic acids residues. [(e) and (f)]: side chains and methyl hydrogens of the 30 most buried residues, respectively, (g): ring atoms of aromatic residues (phe, trp, tyr), and (h): backbone carbonyl groups of the 30 most buried residues. An example of the atoms considered in the calculations (represented as purple spheres) is given for each subset of atoms. Curves have been smoothed with the Savitzky–Golay algorithm (Ref. 90) to simplify the comparison of results. Furthermore, a careful analysis of the standard deviations, not shown for clarity reasons, confirmed that the effects of sugars on lysozyme were statistically meaningful.

VDOS of different parts of lysozyme determined from MD simulations of the lysozyme/water (W) and the 60 wt % lysozyme/trehalose/water (T) solutions (maltose and sucrose solutions behave similarly and are thus not shown for clarity reasons). The averaged VDOS of some fragments of the most and the least solvent exposed lysozyme residues are shown in the left [(a)–(d)] and right [(e)–(h)] panels of the figure, respectively. [(a) and (b)]: side chain atoms and methyl hydrogens of the 30 most exposed residues, respectively, (c): groups of the most exposed arginine residues, (d): carboxylate groups of the most exposed aspartic and glutamic acids residues. [(e) and (f)]: side chains and methyl hydrogens of the 30 most buried residues, respectively, (g): ring atoms of aromatic residues (phe, trp, tyr), and (h): backbone carbonyl groups of the 30 most buried residues. An example of the atoms considered in the calculations (represented as purple spheres) is given for each subset of atoms. Curves have been smoothed with the Savitzky–Golay algorithm (Ref. 90) to simplify the comparison of results. Furthermore, a careful analysis of the standard deviations, not shown for clarity reasons, confirmed that the effects of sugars on lysozyme were statistically meaningful.

(a) Raman susceptibility of the lysozyme/water solution at 295 and 368 K, at which lysozyme was shown to be denatured in Refs. 32–34. (b) VDOS of native and denatured lysozyme obtained from MD simulations in water at 300 and 400 K, respectively. The starting conformations for the five simulations of denatured lysozyme were obtained from simulations of lysozyme in implicit solvent at 1000 K (see Sec. II B). Curves in (a) and (b) have been smoothed with the Savitzky–Golay algorithm (Ref. 90). (c) Examples of the conformations used to compute the VDOS in (b).

(a) Raman susceptibility of the lysozyme/water solution at 295 and 368 K, at which lysozyme was shown to be denatured in Refs. 32–34. (b) VDOS of native and denatured lysozyme obtained from MD simulations in water at 300 and 400 K, respectively. The starting conformations for the five simulations of denatured lysozyme were obtained from simulations of lysozyme in implicit solvent at 1000 K (see Sec. II B). Curves in (a) and (b) have been smoothed with the Savitzky–Golay algorithm (Ref. 90). (c) Examples of the conformations used to compute the VDOS in (b).

(a) Raman susceptibility of water and sugar/water solutions at a concentration of 40 wt %. (b) VDOS of water calculated from MD simulations of the lysozyme/water and the different lysozyme/trehalose/water solutions. Curves in (a) and (b) have been smoothed with the Savitzky–Golay algorithm (Ref. 90) to simplify the comparison of results. The low-frequency VDOS of water have been fitted with a log-normal (LGN) and a Gaussian (G) curves. The dependences on the sugar concentration of the frequency positions and of these two functions are displayed in (c) and (d), respectively.

(a) Raman susceptibility of water and sugar/water solutions at a concentration of 40 wt %. (b) VDOS of water calculated from MD simulations of the lysozyme/water and the different lysozyme/trehalose/water solutions. Curves in (a) and (b) have been smoothed with the Savitzky–Golay algorithm (Ref. 90) to simplify the comparison of results. The low-frequency VDOS of water have been fitted with a log-normal (LGN) and a Gaussian (G) curves. The dependences on the sugar concentration of the frequency positions and of these two functions are displayed in (c) and (d), respectively.

## Tables

System compositions (where , , and denote the number of lysozyme, sugar, and water molecules, respectively), densities, and equilibration/total simulation times for the different sugar concentrations (on a protein-free basis). Data corresponding to result from only one simulation of the lysozyme/pure water solution. T, M, and S denote trehalose, maltose, and sucrose, respectively.

System compositions (where , , and denote the number of lysozyme, sugar, and water molecules, respectively), densities, and equilibration/total simulation times for the different sugar concentrations (on a protein-free basis). Data corresponding to result from only one simulation of the lysozyme/pure water solution. T, M, and S denote trehalose, maltose, and sucrose, respectively.

Structural parameters describing the five unfolded conformations used to compute the average VDOS of lysozyme in its denatured state: (i) RMSD from the crystallographic structure of the carbon atoms, (ii) radius of gyration , (iii) solvent accessible surface area (SASA), and (iv) hydration number , defined here as the number of water molecules whose oxygen atom is within 3.4 or 4.5 Å from polar (O, N, S) or apolar (C) heavy atoms of lysozyme, respectively. For comparison, the values for the native lysozyme are given in the last line of the table. Standard deviations from mean values are given in parentheses.

Structural parameters describing the five unfolded conformations used to compute the average VDOS of lysozyme in its denatured state: (i) RMSD from the crystallographic structure of the carbon atoms, (ii) radius of gyration , (iii) solvent accessible surface area (SASA), and (iv) hydration number , defined here as the number of water molecules whose oxygen atom is within 3.4 or 4.5 Å from polar (O, N, S) or apolar (C) heavy atoms of lysozyme, respectively. For comparison, the values for the native lysozyme are given in the last line of the table. Standard deviations from mean values are given in parentheses.

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