sugar solutions

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Chemical Physics 345 (2008) 267–274 www.elsevier.com/locate/chemphys

Molecular dynamics simulations of lysozyme in water/sugar solutions A. Lerbret a, F. Affouard b

b,*

, P. Bordat c, A. He´doux b, Y. Guinet b, M. Descamps

b

a Department of Food Science, Cornell University, 101 Stocking Hall, Ithaca, NY 14853, United States Laboratoire de Dynamique et Structure des Mate´riaux Mole´culaires, UMR CNRS 8024, Universite´ Lille I, 59655 Villeneuve d’Ascq Cedex, France c Laboratoire de Chimie The´orique et de Physico-Chimie Mole´culaire, UMR 5624, Universite´ de Pau et des Pays de l’Adour, 64000 Pau, France

Received 29 March 2007; accepted 7 September 2007 Available online 14 September 2007

Abstract Structural and dynamical properties of the solvent at the protein/solvent interface have been investigated by molecular dynamics simulations of lysozyme in trehalose, maltose and sucrose solutions. Results are discussed in the framework of the bioprotection phenomena. The analysis of the relative concentration of water oxygen atoms around lysozyme suggests that lysozyme is preferentially hydrated. When comparing the three sugars, trehalose is seen more excluded than maltose and sucrose. The preferential exclusion of sugars from the protein surface induces some differences in the behavior of trehalose and maltose, particularly at 50 and 60 wt% concentrations, that are not observed experimentally in binary sugar/mixtures. The dynamical slowing down of the solvent is suggested to mainly arise from the homogeneity of the water/sugar matrices controlled by the percolation of the sugar hydrogen bonds networks. Furthermore, lysozyme strongly increases relaxation times of solvent molecules at the protein/solvent interface. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Biopreservation; Trehalose; Preferential hydration; Protein; Hydrogen bonds; Molecular dynamics simulation

1. Introduction Trehalose (a-D-glucopyranosyl-a-D-glucopyranoside) is a naturally occurring disaccharide that arouse enormous interest in last years due to its exceptional ability to protect biological materials under extreme conditions: low temperatures and/or drying (see [1] and references within). Biopreservation is also carried out by other disaccharides, such as sucrose (b-D-fructofuranosyl-a-D-glucopyranoside), although trehalose seems to be the most effective under conditions far from optimal that exist in nature. Disaccharides are also often used as additives in pharmaceutical, food and biomedical freeze-drying processes to prepare glassy matrices for long term storage of biological materials [2,3] such as various proteins, viruses and antibodies [4]. Despite its great importance in cryoand lyopreservation, the properties that make trehalose a so effective protective agent are still poorly understood. *

Corresponding author. Tel.: +33 3 20 43 68 15; fax: +33 3 20 43 68 57. E-mail address: frederic.aff[email protected] (F. Affouard).

0301-0104/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.09.011

Several hypotheses have been proposed to explain why trehalose is particularly efficient. However, none of them is fully satisfactory with regard to experimental observations. Green and Angell [5] have suggested that the high glass transition temperature of trehalose Tg ’ 120 °C compared to other protectants could explain its exceptional ability to protect. Indeed, at high concentration, trehalose may form an amorphous solid matrix in which biomolecules would be embedded. Therefore, biomolecules would be caged by the glassy solvent and their flexibility highly reduced. However this hypothesis does not explain why a trehalose/glycerol mixture, with a lower Tg than trehalose, is more effective [6,7]. Crowe et al. have proposed a water replacement model for which sugars would replace water molecules during dehydration in order to maintain the three dimensional structure of biomolecules [1,8]. According to this scheme, trehalose would form a larger number of hydrogen bonds (HBs) with biomolecules owing to its larger hydration number [9]. Although many experiments [10] and simulations [11] have shown that trehalose can be directly hydrogen bonded to proteins, trehalose cannot

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enter into internal or confined regions of proteins [12]. Timasheff et al. [13] presented a preferential hydration hypothesis and have shown that many osmoprotectants are excluded from the first hydration shell of proteins at moderate concentrations. This latter behavior has been extended to higher sugar concentrations by Belton and Gil [14] and recently by Cottone et al. who demonstrated that sugars are preferentially excluded from the protein surface [15]. Magazu` et al. [16,17] suggested a destructuring effect based on the fact that the presence of sugars leads to a perturbation on the tetrahedral HB network of water, because of the formation of water–sugar HBs. Therefore, sugars could inhibit ice formation at low temperatures. Trehalose would be the most efficient in destructuring the tetrahedral HB network of water by promoting a more extended hydration than the other disaccharides. This hypothesis seems relevant to explain the cryoprotection but not the lyoprotection. Numerous simulation investigations have been performed on the structure and dynamics of binary sugar/ water solutions [18–29,9] in order to understand the specific physical properties of protective sugars. Work has also been done on ternary biomolecule/sugar/water systems. Sum et al. [30] and Pereira et al. [31,32] published results on simulations of a lipid membrane in presence of sugars and found evidence for direct HBs with specific parts of the lipid molecules, consistently with previous experiments. Moreover, Lins et al. [11] proposed a model for trehalose– lysozyme interaction on the nanosecond scale and at moderate concentration (18 wt%) in agreement with the suggestion of Belton and Gil [14], which was also inferred by Cottone et al. [33] from simulations of carboxy-myoglobin (MbCO) in trehalose at higher concentrations (50–89 wt%). In order to better understand, in the framework of the biopreservation problem, the influence of proteins on the physical properties of their bioprotective solvent, we have performed a comparative study by Molecular Dynamics (MD) simulations of the model protein lysozyme in presence of aqueous solutions of three homologous disaccharides: trehalose, sucrose and maltose (4-O-(a-D-glucopyranosyl)-b-D-glucopyranoside). The HB capabilities of these three sugars are directly comparable since they possess the same chemical formula C12H22O11 and the same number of hydroxyl groups. We have especially focused our study on the structural organization of the solvent and its dynamical counterpart. 2. Computational details Molecular dynamics simulations of lysozyme in trehalose, sucrose and maltose aqueous solutions (see Fig. 1) have been performed using the CHARMM program [34], version 29b1. The all-atom CHARMM22 force field [35] has been used to model the protein. The CSFF carbohydrate force field [36] has been considered for disaccharides and water molecules were represented by the SPC/E model [37]. The production simulations were performed in the

HO2' C2'

O5 C 1'

C1

HO6 C6

C5 C 2

O'5 C ' 3

O2H O 1

O3'H C'4

C4 C5'

C3 HO4HO3

C6'

O4'H

Trehalose (T)

O6'H HO6'

O5

HO6

C1 C6

C 5 C2

C4 HO4HO3

C3

O2H

C4

O'5

C6 C5 C2

O1 HO3'

C3

O'1H C1 O2'H

Maltose (M) HO1f C1f

O5f

O5g C1g

HO6g C6g

C5gC2g

C2f

O4fH C5f

O2gH O 1g

C3f

C4g C3g HO4g HO3g

C4f

C6f

O6fH

HO3f

Sucrose (S)

Fig. 1. Schematic representation of the studied disaccharides. Only hydrogen atoms belonging to hydroxyl groups have been represented for clarity reasons. Moreover, the glucose and fructose rings of sucrose are identified by the g and f subscripts, respectively.

isochoric–isothermal (N, V, T) ensemble. The length of all covalent bonds involving an hydrogen atom as well as the geometry of water molecules were kept fixed using the SHAKE algorithm [38], with a relative tolerance of 105. A 2-fs timestep has been used to integrate the equations of motion with the verlet leapfrog algorithm [39]. During the different stages of the simulations, the temperatures have been maintained constant with weak coupling to a heat bath (Berendsen thermostat [40]) with a ˚ has been relaxation time of 0.2 ps. A cutoff radius of 10 A used to account for van der Waals interactions, which were switched to zero between 8 and 10. A Lennard-Jones potential has been employed to represent van der Waals interactions and Lorentz–Berthelot mixing-rules have been used for cross-interaction terms. Electrostatic interactions have been handled by the particle mesh Ewald (PME) ˚ 1 and the fast-Fourier grid [41] method with j = 0.32 A ˚ (48 and 64 grid points in the X/Y densities set to 1/A and Z-directions, respectively). The starting structure of lysozyme was obtained from ˚ (193L entry the X-ray crystal structure solved at 1.33 A of the Brookhaven Protein Data Bank) [42]. Most probable charge states at pH 7 were chosen for ionizable residues. The total charge of lysozyme (+8e) was then neutralized by uniformly rescaling the charge of protein atoms, similarly to ref. [43]. The disaccharide initial conformations have been deduced from neutron and X-ray studies of trehalose [44], maltose [45] and sucrose [46]. The sugar concentrations on a protein-free basis are 37, 50 and 60 wt%. These concentrations have been purposefully chosen based

A. Lerbret et al. / Chemical Physics 345 (2008) 267–274

on our previous study of sugar/water solutions [29,9]. Indeed, we showed that the relative effect of sugars on water may be distinguished above a threshold concentration of about 40 wt%. Lysozyme and its 142 crystallographic hydration water molecules were first placed in an ˚ orthorhombic box with cell parameters a = b = 46.7 A ˚ and c = 62.2 A. Then, disaccharide molecules were located and oriented randomly around lysozyme, with minimum sugar–protein and sugar–sugar distance criteria, which ensure an isotropic distribution of sugars around lysozyme. Finally, water molecules non-overlapping with either lysozyme or sugars were randomly added in the simulation box. Initial configurations were minimized in three steps, keeping first lysozyme and sugars fixed, then keeping only lysozyme fixed and finally keeping free all molecules. This minimized configuration was heated to 473 K in the canonic ensemble during 1–3 ns, while maintaining fixed the conformation of lysozyme to prevent conformational changes. This aimed at equilibrating solvent configurations, particularly the position and orientation of sugars. Then, the resulting configurations were thermalized at 300 K and simulated in the isobaric–isothermal (N, P, T) ensemble. The stabilized volume of the simulation box during this simulation was considered to compute the averaged density of the system and used to perform the subsequent simulations in the (N, V, T) ensemble. A steepest-descent minimization procedure of 1000 iterations was then performed, while applying a decreasing harmonic potential on atoms of lysozyme. After the minimization procedure, the temperature was raised from 0 to 300 K, with a 5-K temperature increase every 250 steps. Then, an equilibration at 300 K was performed during about 80 ps. Finally, simulations of 10, 12 and 17 ns were performed for the systems at concentrations of 37, 50 and 60 wt%, respectively, and configurations were saved every 0.25 ps. A control simulation of lysozyme in pure water was done in an analogous way as the one described above. In this simulation, the orthorhombic box was directly filled with water molecules. Moreover, this system was not heated at 473 K, since water molecules are much more mobile than sugars. The first two and four ns were not considered to compute the structural and dynamical properties presented in this paper for the 0–50 and 60 wt% systems, respectively. Table 1 Table 1 System compositions (where NL, NS and NW denote the number of lysozyme, sugar and water molecules, respectively), densities, and equilibration/simulation times for the different sugar concentrations / (on a protein-free basis) / (wt%)

0 37 50 60

NL/NS/NW 1/0/3800 1/85/2800 1/125/2400 1/165/2100

269

summarizes some simulation data for the different systems considered in the present study. It is difficult to compare simulation and experiment results on an absolute scale, since the systems and the physical conditions are not exactly identical, but a qualitative agreement is found with the neutron scattering experimental results reported in [47]. 3. Results and discussion 3.1. Solvent HBs Many studies have shown that trehalose is more hydrated than other disaccharides such as maltose and sucrose over a broad concentration range [48,49]. This enhanced interaction with water molecules has been suggested to confer to trehalose a greater destructuring effect on the HB network of water [16], which may inhibit ice formation at sub-zero temperatures. In our previous study of binary aqueous solutions of the present disaccharides [9], trehalose was shown to bind to a larger number of water molecules than sucrose and maltose over the whole ranges of temperatures (273–373 K) and concentrations ranges (4– 66 wt%). The hydration numbers of these sugars not hydrogen bonded to lysozyme have been analyzed in the studied ternary solutions (see Table 2). Trehalose is found more hydrated than sucrose over the whole studied concentration range, but maltose is more hydrated at 60 wt%. It is possible that the hydration of maltose is overestimated, since only its b anomer has been considered. In reality, maltose interconverts permanently between its anomers b and a – which is assumed to be less hydrated. It is also possible that the hydration behaviors of sugars is modified by the presence of the protein and may therefore differ from that in binary aqueous solutions. Indeed, the preferential exclusion of sugars raises their concentration within their corresponding accessible volumes. Since trehalose is globally found more excluded from the protein surface than maltose and sucrose (see Fig. 2), its hydration number is likely to be more reduced. Indeed, there should exist for sugars at high concentrations a compromise between having a large hydration number and being highly preferentially excluded from the protein surface.

Eq./Sim. time (ns)

Table 2 Hydration number nH of sugars not hydrogen bonded to lysozyme, normalized mean number of sugar–sugar intermolecular hnHBiinter/NS and intramolecular hnHBiintra/NS HBs for the different ternary solutions

T

M

S

T, M, S

/ (wt%)

nH

1.04 1.16 1.20 1.24

1.04 1.16 1.21 1.25

1.04 1.15 1.20 1.24

2/8 2/8 2/10 4/13

T

M

S

T

M

S

T

M

S

37 50 60

11.8 10.0 8.0

11.7 9.8 8.4

11.1 9.2 7.9

2.7 3.5 4.7

2.5 3.7 4.7

2.1 3.1 4.0

0.04 0.04 0.25

0.45 0.49 0.48

0.99 0.99 1.03

Density (g cm3)

Data corresponding to / = 0 wt% result from only one simulation of the lysozyme/pure water solution. T, M and S denote trehalose, maltose and sucrose, respectively.

hnHBiinter/NS

hnHBiintra/NS

The brackets h i denote time-averaging over stored configurations. Two molecules were considered to be H-bonded if the donor–acceptor distance ˚ and if the D–H  A angle is larger than 120° [19]. dDA is less than 3.4 A

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3.2. Sugar/water solvent structure

1.6

gOw

1.4 1.2

T M S

37 wt %

T M S

50 wt %

T M S

60 wt %

1.0 0.8 1.6

gOw

1.4 1.2 1.0 0.8 1.6

gOw

1.4 1.2 1.0 0.8

2

3

4

5

6

7

8

9

10

Distance to the protein (Å) Fig. 2. Normalized fraction of water oxygen atoms gOw = nOW(r)/(nOW(r) + nOS(r))/(NOW/(NOW + NOS)) as a function of the minimal distance to any heavy atom from lysozyme. nOW(r) and nOS(r) denote the numbers of water and sugar hydroxyl oxygen atoms at the distance r from the protein surface (see text), respectively. NOW and NOS correspond to the total numbers of water and sugar hydroxyl oxygen atoms found in the simulation box, respectively.

In addition, the number of sugar–sugar intermolecular HBs increases significantly with sugar concentration. At a concentration close to 50 wt%, the HB network of sugars was shown to percolate in both binary [28,9] and ternary solutions [50]. Above this threshold concentration, the activation energy for collective motion increases significantly and protein denaturation may become more unlikely. Morevover, this percolation may explain the decoupling between water and sugars dynamics observed experimentally [51]. Interestingly, differences are observed between trehalose and maltose on one hand, and sucrose on the other hand. The numbers of sugar–sugar intermolecular HBs are indeed significantly smaller in the sucrose solutions than in trehalose and maltose ones. This appears in agreement with the larger solubility of sucrose in comparison with trehalose and matose [52] and may be interpreted by the larger number of intramolecular HBs in sucrose than in trehalose and maltose (see Table 2). The sucrose hydroxyl groups involved in these intramolecular HBs are then less likely to form HBs with other water or sugar molecules. These numbers of intramolecular HBs seem to be consistent with the numbers of intramolecular HBs found in the most stable crystallographic structures of trehalose [44] (0), maltose [45] (1) and sucrose [46] (2). There is a lot of debate in the literature about the number of intraHBs that sucrose forms in solution [53]. Some studies suggest that sucrose intra-HBs are almost fully replaced by water–sucrose HBs [54], whereas other results suggest that intra-HBs are still present in solutions [25].

Many osmolytes such as sugars and polyols have been found preferentially excluded from the protein/solvent interface. Lins et al. [11] showed that trehalose clusters at the protein surface and does not expel the water molecules closest to the protein surface. Furthermore, Cottone et al. [15] have shown that trehalose preferentially hydrate carboxy-myoglobin (MbCO) to a lower extent than maltose and sucrose at a concentration of 89 wt%. In the framework of the preferential hydration hypothesis, this exclusion would stabilize thermodynamically proteins by making unfavorable the increase of the solvent accessible surface area (SASA) of proteins upon denaturation. This may arise from excluded volume effects and an increase in the surface tension of water induced by osmolytes [55]. In order to know if the solvent composition is enriched in water at the protein/solvent interface in our simulations, we have characterized the relative local distribution of water molecules around lysozyme in a similar way to Cottone et al. [15]. We have indeed computed the time-averaged normalized ratio defined as gOw ðrÞ ¼

nOW ðrÞ=½nOW ðrÞ þ nOS ðrÞ N OW =½N OW þ N OS 

ð1Þ

where nOW(r) and nOS(r) are the local numbers of water oxygen atoms and sugar hydroxyl group oxygen, respectively, located at a minimum distance r from any heavy atom of lysozyme. In close proximity of the protein surface, this ratio is greater than one if the protein is preferentially hydrated and lower than one if sugars preferentially interact with the protein. This ratio is represented in Fig. 2 for the different ternary studied systems. The preferential exclusion of sugars seems more and more important as their concentration increases. Besides, a slight water depletion is observed at distances larger than ˚ arising from the presence of sugars. Trehalose prefer5 A entially hydrates lysozyme slightly more than do maltose and sucrose, except for the sucrose solution at 50 wt%, for which there may be shortcomings [50]. In particular, trehalose was systematically found more excluded from the apolar groups of lysozyme than maltose and sucrose (data not shown). This is clearly seen the small peak ˚ of the gOw distributions. It is likely located around 3.7 A that the large hydration number of trehalose (see Table 2) may prevent it from remaining close to apolar groups of lysozyme. These results are in line with the preferential hydration hypothesis proposed by Timasheff et al. [56,13], which suggests that trehalose is more excluded – in the relatively diluted solutions – than other osmolytes, and thus increase the thermodynamical stabilization of the proteins compact native state relative to their extended denaturated state [57]. The water replacement hypothesis [1,8] is, therefore, not validated by these results. Finally, the present results are consistent with those of Lins et al. [11] and Cottone et al. [15], although sucrose and maltose are found less exluded than trehalose. Trehalose might behave slightly

A. Lerbret et al. / Chemical Physics 345 (2008) 267–274

differently at higher concentrations, since the water replacement hypothesis suggests that it is able to form a large number of HBs with proteins. It should also be noted that the differences observed between the three sugars are rather small. 3.2.1. Sugar/water solvent dynamics Many studies have shown that the dynamics of proteins are slaved to those of the solvent. In other words, their dynamics are controlled by the solvent viscosity. As a consequence, the addition of sugars and other bioprotectants to water slows down the dynamics of proteins as they increase the solvent viscosity. Protein denaturation may then be hindered, since the activation energy of motions that may lead to denaturation increases significantly. Reciprocally, the dynamics of solutes are slowed down by proteins. Dirama et al. recently showed that the mean square displacement of trehalose hydrogen atoms at the lysozyme/solvent interface was different from that in the bulk [58]. It is also well-known that proteins modify the structure and dynamics of their hydration water molecules [59]. There is a lot of debate about the extent of the perturbation of the dynamics of hydration water. Indeed, various experimental measurements – NMR spectroscopy, dielectric relaxation, neutron scattering, magnetic relaxation dispersion or time-resolved fluorescence – give different results, since they probe different physical phenomena [60,61]. For instance, Marchi et al. [62] have shown that the water relaxational times of water close to lysozyme are about 3–7 times longer than bulk water, depending on the definition of hydration water, and that the diffusion of water molecules is subdiffusive. In order to clarify how solvent molecules are influenced by proteins at intermediate concentrations, the dynamics of sugar and water molecules have been characterized by their dynamical scattering functions Sinc(Q, t) defined as * + X S inc ðQ; tÞ ¼ b2a;inc ei:Q:½ra ðtÞra ð0Þ ð2Þ

water molecules, respectively. The mean relaxation times of sugar molecules sS are displayed in Fig. 3 as function of the minimal distance r between their glycosidic oxygens and any heavy atom of lysozyme. Given that sugars are preferentially excluded from the protein surface – as shown from the values of gOw in the previous section, the sS of ˚ have been sugars located at a distance r smaller than 4 A ˚ averaged with those of the 4–6 A bin of the histogram, as a means to improve statistics. First of all, sugars close to the protein surface clearly exhibit larger relaxation times than sugars from the bulk. This is probably the consequence of the presence of the protein which induces a decrease in the dimensionality of the diffusion of solvent molecules at the protein/solvent interface. It is also probable that the roughness of the protein as well as strong interactions with polar and charged groups play an important role. This result is consistent with those reported by Dirama et al. [58] for lysozyme embedded in a pure trehalose matrix at 550 K, i.e. above the numerical glass transition temperature Tg  460 K of the pure trehalose matrix [63]. They indeed showed that the mean-square displacement of trehalose molecules close to the surface of lysozyme was lower than that of bulk ones at this temperature. They suggested that the viscosity seen by the protein is different from that of the bulk. Furthermore, it should be noted that the increased dynamical slowing down of sugar molecules with sugar concentration is a direct consequence of the percolation of the sugar HB networks, which occurs at about 40– 50 wt% in both sugar binary [9] and ternary solutions [50]. Indeed, at these relatively high concentrations, the hydration layers of sugars do not surround completely disaccharides because of sugar–sugar HBs (see Table 2), which strongly influence their dynamics. These dynamical changes have been observed experimentally by Rampp 15 10

Sugar mean relaxation time τS (ps)

a

where ba, inc and r denote the incoherent scattering length and the vector position of a given atom a, respectively, and Q is the wavevector. The brackets mean averaging over every time origin of simulations. These functions correspond to the time Fourier transform of dynamic structure factors Sinc(Q, x) obtained in neutron scattering experiments. We have chosen to probe the dynamics at a wave˚ 1, which corresponds to the position of vector of 2.29 A the first peak in the static structure factor SO-O of pure water and which was used in our study of binary sugar/ water solutions [29]. The mean relaxation times of disaccharide and water molecules, noted sS and sW in the following, have been computed as the decay times from 1 to 1/e of their respective Sinc(Q, t) functions. To improve the definition of the curves, the MD trajectories have been splitted into 1-ns and 250-ps long trajectories for computing the mean position and the Sinc(Q, t) of individual sugar and

271

5

T M S

37 wt %

T M S

50 wt %

T M S

60 wt %

0 40 30 20 10

0 150 100 50 0

2

3

4

5

6

7

8

9

10

Distance to the protein (A) Fig. 3. Mean relaxation time of sugar molecules as a function of their averaged minimal distance to any heavy atom of lysozyme.

A. Lerbret et al. / Chemical Physics 345 (2008) 267–274

et al. [51] for a series of carbohydrates – including sucrose and trehalose – at concentrations above 50 wt%. They also appear in the concentration dependences of the diffusion coefficient of sucrose and trehalose in aqueous solutions obtained by Ekdawi-Sever et al. by NMR measurements [27]. Sucrose molecules clearly relax faster than trehalose and maltose, whatever the concentration considered. This is well in line with experimental studies, which show that the dynamics of sucrose is faster than that of maltose and trehalose [49]. This result is also consistent with data reported in Table 2. The hydration number and the number of sugar–sugar intermolecular HBs are found lower for this sugar with respect to maltose and sucrose. As discussed in [9] for binary disaccharide/water mixtures, this is probably related to the higher number of intra-HBs of sucrose molecules compared to maltose or trehalose (see Table 2). Since hydroxyl groups involved in these intramolecular interactions do not remain available for other intermolecular interactions, the interaction of sucrose molecules with both water or other sucrose molecules are more unlikely. This appears consistent with experimental results, which suggest a looser protein–solvent coupling in sucrose–water matrices than in trehalose–water matrices of various water contents [64]. The relaxation times of trehalose are close to those of maltose for the 37 wt% solution – even slightly longer in the distance range displayed. The relaxation times of maltose are however significantly longer than those of trehalose ˚ for the 50 and 60 wt% solutions. at distances closer to 8 A This is somewhat different from the dynamical behavior expected based on experimental measurements on binary sugar/water solutions, where trehalose solutions have been found to relax more slowly than maltose ones [49,65]. It suggests that lysozyme slows down the dynamics of maltose more strongly than that of trehalose, because maltose is less preferentially excluded from the protein surface than trehalose (see Fig. 2). Therefore, maltose molecules are more likely to interact with polar and charged groups of lysozyme and their diffusion may be more hindered by the surface rugosity of lysozyme. These results seem to point out that the dynamical behavior of sugars at the protein/solvent interface cannot necessarily be inferred from their behavior in binary sugar/water solutions, because of the specific organization of the solvent close to the surface of the protein. These results seem also consistent with the lower heat capacity at constant pressure Cp of lysozyme/maltose/water solutions at 40 wt% compared to that of trehalose and sucrose solutions [66] and with the peculiar behavior of maltose observed experimentally by Giuffrida et al. [67]. Similarly to sS, the mean relaxation times of water molecules sW are shown in Fig. 4. The relaxation times sW at ˚ seem close to distances from the protein greater than 5 A that of the bulk. In contrast, water molecules closer than ˚ (particularly when gOw > 1, see Fig. 2) have significantly 5A longer relaxation times and may be considered as hydration water. This is the dynamical counterpart of the structural results reported in the previous section (see Fig. 2). The

10

0 wt % 1

Water mean relaxation time τW (ps)

272

10

T M S

37 wt %

T M S

50 wt %

T M S

60 wt %

1

10

1 100

10

1 2

3

4

5

6

7

8

9

10

Distance to the protein (A) Fig. 4. Mean relaxation time of water molecules as a function of their averaged minimal distance to any heavy atom of lysozyme.

dynamical slowing down of hydration water molecules probably depends on the nature of lysozyme residues and on the local rugosity of lysozyme. Indeed, it is well-known that the nature – hydrophobic, hydrophilic, etc. – of the amino acids exposed to the solvent strongly influences water residence and rotational times [68,59,69]. It must also be pointed out that some molecules considered as hydration occupy cavities within lysozyme. These internal water molecules may rigorously be best regarded as structural water molecules. Besides, the addition of sugars significantly slows down the dynamics of water molecules, which seem to follow that of sugar molecules. The relaxation times sW of the three ternary solutions are very close to each other at 37 wt%, because the concentration of sugars is not large enough for differences between them to emerge. In contrast, larger differences are observed at 50 and 60 wt%, i.e. above the threshold concentration for the percolation of the HB networks of sugars [9,50]. At these concentrations, the dynamics is the slowest in the maltose solutions and the fastest in the sucrose ones, in agreement with the Fig. 3. Similarly to the dynamics of sugars, the dynamics of water molecules cannot be directly extrapolated from those in binary water/sugar mixtures, since the influence of the protein must to be taken into account. 4. Conclusion Structural and dynamical solvent properties in ternary lysozyme/sugar/water solutions in the 37–60 wt% concen-

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tration range have been analyzed. The hydration numbers of sugars not hydrogen bonded to lysozyme have been computed. Trehalose was found more hydrated than maltose and sucrose at 37 and 50 wt%. But, maltose was the most hydrated sugar at 60 wt%. This can partly be attributed to the fact that the protein modifies the solvent structure at the protein/solvent interface. Indeed, trehalose was found more preferentially excluded from the protein surface than sucrose and maltose. As a consequence, its concentration in the bulk may be slightly larger than that of sucrose and maltose. Furthermore, the number of intermolecular sugar–sugar HBs was found smaller in sucrose solutions in comparison with trehalose and maltose ones. This difference has been attributed to the larger number of intramolecular HBs in sucrose. Finally, sugar and water relaxation times were significantly larger at the protein–solvent interface than in the bulk. This may arise from a decrease of the dimensionnality of the solvent diffusion and from solvent–protein interactions. A global important increase of the relaxation times of sugar and water molecules was attributed to the increase of the number of sugar–sugar intermolecular HBs which leads to the percolation of the HB network of sugars [9,50]. Maltose solutions at 50 and 60 wt% were found to relax more slowly than trehalose ones, in contrast to experimental results on binary sugar/ water solutions, which suggest that trehalose solutions are more viscous than maltose ones [49,65]. This seems to points out the influence of the protein on the dynamics of the solvent at the protein/solvent interface. Acknowledgements 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). References [1] J.H. Crowe, L.M. Crowe, A.E. Oliver, N. Tsvetkova, W. Wolkers, F. Tablin, Cryobiology 43 (2001) 89. [2] A.S. Sussmann, H.O. Halvorson (Eds.), Spores: Their dormancy and Germination, Harper and Row, New York, 1966. [3] F. Franks (Ed.), Biophysics and Biochemistry at low Temperatures, Cambridge University Press, Cambridge, 1985. [4] J.H. Crowe, L.M. Crowe, S.A. Jackson, Arch. Biochem. Biophys. 220 (1983) 477. [5] J.L. Green, C.A. Angell, J. Phys. Chem. 93 (1989) 2880. [6] M.T. Cicerone, C.L. Soles, Biophys. J. 86 (2004) 3836. [7] G. Caliskan, D. Mechtani, J.H. Roh, A. Kisliuk, A.P. Sokolov, S. Azzam, M.T. Cicerone, S. Lin-Gibson, I. Peral, J. Chem. Phys. 121 (2004) 1978. [8] L.M. Crowe, R. Mouradian, J.H. Crowe, S.A. Jackson, C. Womersley, Biochim. Biophys. Acta 769 (1984) 141. [9] A. Lerbret, P. Bordat, F. Affouard, M. Descamps, F. Migliardo, J. Phys. Chem. B 109 (2005) 11046. [10] S.D. Allison, B. Chang, T.W. Randolph, J.F. Carpenter, Arch. Biochem. Biophys. 365 (1999) 289.

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