Diffusive Dynamics of Water in the Presence of Homologous

High-pressure dynamics of hydrated protein in bioprotective trehalose environment. S. O. Diallo , Q. Zhang , H. O'Neill , E. Mamontov. Physical Review...
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J. Phys. Chem. B 2001, 105, 1851-1855

1851

Diffusive Dynamics of Water in the Presence of Homologous Disaccharides: A Comparative Study by Quasi Elastic Neutron Scattering. IV. S. Magazu` ,† V. Villari,† P. Migliardo,*,† G. Maisano,† and M. T. F. Telling‡ Dipartimento di Fisica and INFM, UniVersita` di Messina, C. da Papardo S. ta Sperone 31, 98166 Messina, Italy, and ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 OQX, U.K. ReceiVed: June 15, 2000; In Final Form: October 16, 2000

The present paper reports on the study of the disaccharides’ dynamics in aqueous solutions and discusses the role of their interaction with water, which seems to be responsible for the protective action on biological membranes and tissues. In particular, using QENS (IRIS at ISIS, RAL, U.K.) we compared the quasielastic spectra from three homologous disaccharides (trehalose, maltose, and sucrose) with a hydration of 20 water molecules per each disaccharide molecule. The isotopic substitution method allowed us to study also the dynamics of water in the presence of the disaccharides. Our results show that trehalose is the most effective in slowing down the water dynamics, inducing a more extensive hydration layer.

1. Introduction Since the protective action of trehalose (a natural stable disaccharide of glucose) on proteins and membranes was discovered, there has been a remarkable interest in biochemical, microbiological and physiological studies involving this sugar. It was found1-4 that in many elemental organisms the synthesis of a large amount of trehalose causes the “transition”, at ambient temperature, to an amorphous state in which mobility of proteins is strongly reduced. During dehydration, which in the absence of trehalose would lead to the cell microarchitecture damage because of the osmotic stress, such an “anydrobiosis” phenomenon preserves the functionality of cells. A wide variety of seeds, yeast cells, and soil-dwelling organisms that synthesize trehalose can survive decades or centuries in drought conditions and resume all the functional activity when rehydrated.5-8 Survival of some organisms, in fact, is connected with the water which, resting entrapped within the hydration shell or inside the protein, preserves the internal mobility of the protein.9-11 Thanks to its peculiarities trehalose has being extensively used for protecting enzymes during thermal treatment and it is beginning to be used in medicine for prolonging the life of organs for transplantation. These cryoprotective and osmoregulative properties have been documented and discussed extensively, mostly by microbiologists and physiologists, but the underlying molecular mechanisms are not fully understood. This is partly due to the fact that commonly used techniques are difficult to apply to carbohydrate-water interactions and relatively few MD simulations of oligosaccharide-water systems have been performed in the past. There exist at least two main theories that explain the peculiarity of trehalose on a molecular level (but no one can be considered satisfactory): the first hypothesis suggests that the effectiveness of this sugar is to be connected with the high value of the glass transition temperature. However, vitrification alone has been demonstrated not sufficient for preservation; in fact, another carbohydrate, dextran, has a significantly higher glass transition temperature, but it is a much less effective bioprotectant than trehalose. † ‡

Universita` di Messina. Rutherford Appleton Laboratory.

The second hypothesis leads back to the consideration that the tridimensional structure of most biomolecules depends on the stabilization effect of a certain number of water molecules (via hydrogen bonds) with surface residuals. The water involved in such an interaction varies from 25 to 75 wt % with respect to the weight of the protein. A simulation performed by Grigera et al.12 on trehalose aqueous solutions indicates that both the hydrogen bond network of water and its dynamics are not significantly modified by the presence of trehalose. In particular, the hydroxyl groups of trehalose would match with the position of the oxygen atoms in the water structure tetrahedrally coordinated. Hence, the authors conclude that the bioprotective effectiveness of trehalose is to be attributed to the substitution of a certain number of water molecules bonded to the biological structure. This socalled “water replacement” hypothesis6,2 suggests that, during dehydration, membrane lipids pass in a state of liquid crystal. One of the main aims of the present work is to show that, contrary to the results obtained in the simulation by Grigera, the disaccharide-water interaction plays a key role in understanding the bioprotective action of such substances and all the disaccharides, and trehalose in particular, strongly affects the dynamics of water. However, the direct interaction with proteins remains a debated subject and a lot of work has been devoted to study the effect of trehalose on protein function and dynamics. In a recent paper by Gottfried et al.13 it has been stressed that trehalose directly couples the heme to the complex networklinked solvent molecules that form the glass. Moreover, according to these authors, the absence of substantial conformational effects in a trehalose-embedded protein (hemoglobin) suggested that changes in protein dynamics occur. Cordone et al.14 found that the trehalose coating prevents thermal denaturation by damping large scale fluctuations of protein specific motions that could cause protein unfolding. In relation to the proven effectiveness of trehalose over similar disaccharides, most disaccharides display similar H-bonding properties, and all are fairly flexible conformationally (both the motions of hydroxymethyl groups and the inter-ring degrees of freedom). They possess a relatively large number of OH groups,

10.1021/jp002155z CCC: $20.00 © 2001 American Chemical Society Published on Web 02/07/2001

1852 J. Phys. Chem. B, Vol. 105, No. 9, 2001 and these mesh easily with the rapidly changing, but instantaneously gellike hydrogen bond network of the surrounding waters. It is surprising, in view of the basic facts, that trehalose is so effective in a range of conditions often referred to as “water stress”. It is important therefore to probe and quantify the molecular mechanisms underlying the unusual bioprotective properties of trehalose relative to other common disaccharides. Previous works performed by using a range of techniques were focused on establishing the basic hydration behavior and solution structure of this disaccharide as a function of concentration and temperature15,16 and allowed us to go deeper in the understanding of the interaction of water with hydrophilic polymers.17 One of the most striking features found by ultrasonic measurements15 is that trehalose is able to bind almost 15 water molecules at T ) 25 °C. Results of quasielastic light scattering16 and viscosity18 measurements showed a highly “fragile” character of trehalose aqueous solutions at low concentration (up to 50 wt %). Moreover, the tendency of trehalose to strongly bind water molecules is evidenced by Raman scattering measurements,19 which show that the induced destructuring effect on the hydrogen-bond network of water is stronger for trehalose than for the other disaccharides. This occurrence suggests that the effectiveness in preserving biological membranes can be connected with the greater ability in inducing an extensive destructuring effect and in obstructing crystallization phenomenon. Last but not least photon correlation spectroscopy measurements17 on the ternary solution poly(ethylene oxide)/trehalose/ water gave experimental evidence of direct interactions of trehalose with polymer coils, affecting the diffusive polymer dynamics and the coil conformational properties with temperature. In this frame quasielastic neutron scattering measurements performed at ISIS by the IRIS spectrometer (RAL, U.K.) reveal new perspectives for understanding the peculiarities of interactions with water. The aim of the paper is to show if and at what extent the interaction of disaccharides with water is related to the higher effectiveness of trehalose. In particular the comparison provides evidence that although the dynamics of the three homologous disaccharides is not very different, except perhaps for the inter-ring mobility, and although the population of water molecules in the primary hydration shell is quite similar, in the case of trehalose/H2O solutions the dynamics of water is sensitively slowed with respect not only to the bulk water but also to water in the other disaccharides. These results suggest that, instead of remaining umperturbed by the presence of the sugar, the network of water, and consequently the dynamics, appreciably changes, as shown by Fornili et al. in a recent MD simulation. 2. Samples and Experimental Section Trehalose, maltose, and sucrose, purchased by Sigma-Aldrich Co., were used for the experiment at an hydration of 20 water molecules per each disaccharide molecule and at T ) 50 °C. The samples were prepared using ultrapure disaccharides, double distillized deionized water, and heavy water (isotopic purity of 99.9%) furnished by Sigma-Aldrich. Partially deuterated R,Rtrehalose, maltose, and sucrose samples were employed for the measurements in D2O solutions. These homologous disaccharides have the same chemical formula (C12H22O11) and slightly different structures. R,RTrehalose (R,β- and β,β-trehalose are its synthetic isomers) is constituted by two pyranose (six-membered) rings in the same

Magazu` et al. R configuration, linked by a glycosidic bond between the chiral carbon atoms C1 of the two rings. Maltose is also constituted by two pyranose rings of glucose in the R configuration, but the oxygen bridge links the two carbon atoms C1 and C4 of the two rings. Finally, sucrose is constituted by a glucose ring (pyranose) in the R configuration and a fructose ring (furanose) in the β configuration. QENS spectra were collected using the IRIS backscattering spectrometer at the ISIS facility at the Rutherford Appleton Laboratory (U.K.), covering a Q,ω-domain extending from Q ) 0.5-1.7 Å-1 (momentum transfer) and pω ) -0.4 to +0.9 meV (energy transfer). The mean energy resolution was Γ ) 8 µeV of half-width at half-maximum, as determined by reference to a standard vanadium plate. The samples were contained in aluminum cells that allow us to obtain liquid samples in the form of slabs with a thickness of 1 mm for the deuterated solutions and 0.5 mm for the hydrogenated ones in order to minimize multiple scattering. A sample temperature of 50 ( 0.1 °C was maintained during the experiment. The raw spectra were corrected and normalized using the IRIS data analysis package, GUIDE.20 The correlation function formalism21,22 provides a powerful and unifying framework for describing the scattering of neutrons from nuclei. In particular, the intermediate scattering function,

I(q b,t) )

1 N

bibj〈exp iQ B ‚(b r i(t) - b r j(0))〉 ∑ i,j

(1)

which is the sum of both the coherent and the incoherent terms

b,t) ) Icoh(q

b,t) ) Iincoh(q

1

coh bcoh B ‚(b r i(t) - b r j(0))〉 ∑ i bj 〈exp iQ i,j

N

1

)2〈exp iQ B ‚(b r i(t) - b r i(0))〉 ∑i (bincoh i

N

(2)

(3)

reflects collective and individual atomic motions. The Fourier transform of the relation (1), S(Q B ,ω), is the dynamic structure factor related to the double scattering cross section, (d2σ)/(dΩ dω). The latter is obtained experimentally in a neutron scattering experiment and represents the normalized scattered intensity per unit energy and per unit solid angle:

k1 I d2σ dΩ dω1 ) N S(Q ) B ,ω) dΩ dω1 I0 dΩ dω k0

(4)

where the factor k1/k0 results from converting neutron density to flux. The differential scattering cross section in principle contains the superposition and interaction of a large number of vibrational, rotational and diffusive modes; for complex systems such a circumstance implies that the explicit evaluation of S(Q B ,ω) is very difficult or impossible. For the study of the disaccharides and water dynamics we adopted the widely used simplification consisting in the decoupling of the different kind of motions. The dynamic structure factor takes the form23

S(Q,ω) ) Strans(Q,ω) X Srot(Q,ω) X Svib(Q,ω)

(5)

If the vibrational frequencies are sufficiently high, the expansion of the scattering law for vibrations in powers of hω in the quasi elastic region gives a Debye-Waller factor contribution, exp(-Q2〈u2〉), 〈u2〉 being the mean-square vibration amplitude.

Diffusion of Water in the Presence of Disaccharides

J. Phys. Chem. B, Vol. 105, No. 9, 2001 1853

Figure 1. (a) Experimental spectra of disaccharides + 20D2O. The continuous line is the fit result obtained using the relation (6), the dashed Lorentzian refers to the traslational contribution, the dotted Lorentzian refers to the rotational contribution of the disaccharide molecules, and the bars are the residuals. (b) Experimental spectra of disaccharides + 20H2O. The continuous line is the fit result obtained using the relation (9), the dashed line refers to the sum of the two Lorentzians (traslational and rotational contributions) of the disaccharide, the dotted Lorentzian refers to the water molecules translation, and the bars are the residuals.

The fit procedure was performed according to I(Q,ω) ) S(Q,ω) X Res(Q,ω) + const, where Res(Q,ω) is the resolution function as determined by reference to the standard vanadium plate. All the three disaccharides possess hydrogen atoms, belonging to the OH groups, which exchange easily with the deuterium atoms of heavy water. To focus our attention on the disaccharides’ dynamics in D2O, the exchangeable atoms were substituted with deuterium before preparing the solutions. We estimated that in the deuterated solutions (at the investigated concentration) the coherent contribution to the total scattering cross section is around 5% and it has been neglected. Moreover, since the ratio of protons to other nuclei is nearly 1 in all disaccharides, mainly the nonexchangeable hydrogen of the disaccharide molecules contribute to the incoherent spectrum. The basic assumption underlying this study is that the isotopic substitution, essential to discriminate between disaccharides and water dynamics, does not affect the structural and conformational properties of the disaccharides themselves. 3. Results and Discussion The characterization of the translational, rotational, and internal dynamics of the hydrated dysaccharides at the same temperature (T ) 50 °C) and hydration (20 water molecules per each disaccharide molecule) allowed us to determine the effects of their presence on the dynamics of the neighboring water molecules. Parts a and b of Figure 1 report the spectra of the three disaccharide aqueous solutions in light and heavy water, respectively, at Q ) 1.2 Å-1 as an example. The dynamic

structure factor we adopted to describe the disaccharides dynamics in D2O is the following:23,24

Sdisacch(Q,ω) )

[

]

Γ1(Q) Γ2(Q) 1 1 + (1 - F(Q)) (6) A(Q) F(Q) 2 2 2 π Γ (Q) + ω π Γ (Q) + ω2 1 2 In particular, F(Q) is the EISF factor representing the diffraction pattern on all possible final positions of the rotating proton and the two Lorentzians, whose HWHM are Γ1 and Γ2, respectively, take into account translational and rotational motions. In Figure 1a we also reported the fit result together with all the components as obtained adopting the relation (6). As far as the rotational contribution is concerned, it can be shown that, quite generally, the (incoherent) scattering law of any rotational model can be written as25

l(l + 1)Dr 1∞ Fl(Q) (7) Srot(Q,ω) ) F(Q) δ(ω) + π l)1 [l(l + 1)Dr]2 + ω2

∑

with Dr the rotational diffusion coefficient and l the order of the Bessel functions. The relation (6) is the result of the convolution between a Lorentzian representing the translational contribution and Srot(Q,ω) for which we considered only the delta function and the first term of the series in (7). Figure 2 reports Γ1 as a function of Q2 for the three disaccharides: their dependence is almost linear, except for the slight bending at higher wave vector, indicating a translational

1854 J. Phys. Chem. B, Vol. 105, No. 9, 2001

Magazu` et al. rigid and stabilized against conformational transitions by high energy barriers, inter-ring motions can occur. As far as the Γ2’s evolution is concerned, it keeps almost constant at all Q values malt around Γtreh ≈ 110 µeV, and Γsucr ≈ 97 µeV. 2 ≈ 63 µeV, Γ2 2 Such dynamics would occur on a time scale of 10.5 ps for trehalose, 6.0 ps for maltose, and 6.8 ps for sucrose. Once the disaccharides dynamics have been characterized, from the spectra obtained for disaccharides/H2O solutions we subtracted, with suitable weight factors, the spectra relative to the disaccharides/D2O systems. Therefore, the fit law we adopted has the form

S(Q,ω) )

2

Figure 2. Half-width at half-maximum evolution as a function of Q for the three disaccharides. The lines are the fit results according to the RJD model, and the error bar indicates the largest error on the data.

Figure 3. EISF factor as a function of Q. In the box the average values of the characteristic energy of the rotational motions are reported for the three disaccharides.

diffusive dynamics of the molecules. The translational contributions analysis indicates that, although the Γ1 behaviors are very similar, trehalose diffusion is systematically slower than that of sucrose and maltose; in particular, the diffusion coefficents obtained by the random jump diffusion model22 (RJD)

Γ1(Q) ) DsQ2/(1 + DsQ2τ0)

(8)

) 1.63 × 10-6 cm2/s, Dmalt ) 2.12 × 10-6 cm2/s, and are Dtreh s s sucr -6 2 Ds ) 2.24 × 10 cm /s, in good agreement with previous NMR measurements.26 This occurrence could be due to a different disaccharide hydration. The residence times are τtreh ) 13.3 ps, τmalt ) 12.5 ps, and τsucr ) 12.1 ps, which 0 0 0 allow us to evaluate the jump length 〈l2〉1/2 ) 1.3 Å for all the disaccharides. These apparently too small values of the jump lengths are in good agreement with the size of the rotation region of the disaccharide molecules obtained by the Q dependence of the elastic incoherent structure factor (EISF). Figure 3 shows that the EISF factors do not approach zero in the investigated Q range. The results suggest that at this concentration value the disaccharide molecules are not able to fully rotate (which would imply a rotation radius of about 7 Å) but rather undergo highly damped motions, like, for example, hindered rotations. Some molecular dynamics simulations27,28 support this hypothesis establishing that, although the rings themselves are fairly

{

}

Γw(Q) 2 1 exp(-Q2〈u2〉) fdisacchSdisacch(Q,ω) + fwater 2 p π Γ (Q) + ω2 w (9) where fdisacch and fwater, for which fdisacch + fwater ) 1, are the percentage of the scattering from the disaccharide molecule together with its hydration shell and the not directly bound water molecules, respectively. As can be seen from relation (9) we preferred to consider only one Lorentzian for describing water dynamics. Moreover, the weight factors fdisacch and fwater we introduced in the analysis of the spectra of the solutions in light water underly the assumption that24,29 (i) the water molecules tightly bound to the disaccharide (first hydration shell) move together with the disaccharide molecule itself, and therefore, the protons belonging to this population will give rise to the same scattering law, and (ii) the dynamics of the water molecules close to the disaccharide is affected with respect to that of the bulk water. Because the hydration number evaluated from ultrasonic measurements has been estimated to be at T ) 25 °C nH ) 15.2 for trehalose, nH ) 14.7 for maltose, and nH ) 14.1 for sucrose,30 we also assume that no bulk water is present. In Figure 1b the spectra for disaccharides/H2O solutions are reported together with the fit result; the narrower component is the sum of the two Lorentzians relative to the disaccharide dynamics and the broader one represents the water dynamics. First of all, the fwater parameters, obtained by the fit procedure, keep constant with Q at the values of 0.35, 0.38, and 0.40 for trehalose, maltose, and sucrose, respectively; these values correspond to 9, 8.4, and 7.5 water molecules bound to the disaccharides. To check how the water dynamics is affected by the presence of the different disaccharides, we plotted in Figure 4 the Q dependence of Γw. The clear bending at high Q values suggests interpretation of the data according to the random jump diffusion model; the dashed line in Figure 4 represents the fit result. The extrapolation to Q f 0 furnishes the self-diffusion coefficient of the water molecules and the inverse of the asymptotic value at Q f ∞ the residence time of the water molecules between two jumps. We obtained Dtreh w ) 1.55 × malt 10-5 cm2/s and a residence time τtreh 0 ) 3.5 ps, Dw ) 1.73 × malt 10-5 cm2/s and a residence time τ0 ) 3.43 ps, and Dsucr w ) 2〉1/2 ) ) 2.9 ps. From the relation 〈l 1.75 × 10-5cm2/s and τsucr 0 6Dτ the mean jump length is obtained: 〈l2〉1/2 ) 1.8 Å for water in trehalose. Although the diffusion of water molecules is almost the same in the different disaccharides, the residence times are quite different. In fact, the whole water dynamics in trehalose resembles that of water at ∼-5 °C, whereas that of water in maltose (for which we obtain 〈l2〉1/2 ) 1.9 Å) is comparable with that of water at ∼0 °C and water in sucrose (for which 〈l2〉1/2 ) 1.8 Å) behaves like water at ∼5 °C.31

Diffusion of Water in the Presence of Disaccharides

Figure 4. Half-width at half-maximum evolution as a function of Q2 for water in the three disaccharides. The dashed lines are the fit results according to the RJD model, and the error bar indicates the largest error on the data. Finally, the dotted straight line refers to the bulk water translation at 20 °C.31

Figure 5. Debye-Waller factor as a function of Q2. The linear fit in the semilog scale for Q2 g 1 gives the proton mean square displacements of hydrogen atoms.

From the evaluation of the integrated area of the quasielastic spectra relative to the solutions in H2O, we obtained the DebyeWaller factor exp(-Q2〈u2〉) as shown in Figure 5 in a logarithmic scale. The increase at low Q values is likely due to some multiple scattering that affects also the Lorentzian witdth evolution at Q f 0. However, above Q g 1 Å-1 the data present a unique slope that furnishes a value of the mean square displacement: 〈u2〉1/2 ) 0.52 Å for trehalose, 〈u2〉1/2 ) 0.60 Å for maltose, and 〈u2〉1/2 ) 0.69 Å for sucrose, indicating a lower proton mobility in the case of trehalose. 4. Concluding Remarks By using the isotopic substitution method, we studied the wave-vector dependence of the quasielastic peak width relative to the aqueous solutions of three homologous disaccharides. Focusing the attention on the whole sugars’ dynamics, our results, showing that both trehalose translation and rotation are slower than those of the other disaccharides, suggest that a slightly higher hydration is responsible for its more hindered

J. Phys. Chem. B, Vol. 105, No. 9, 2001 1855 dynamics. These differences in the hydration numbers have been evaluated for the solutions in light water from the fit parameters fdisacch and fwater; the obtained values indicated that hydration reasonably corresponds to 9, 8.4, and 7.5 water molecules per each disaccharide molecule for trehalose, maltose, and sucrose, respectively. Finally, from the Q2 evolution of the Lorentzian peak related to the water dynamics, it results that trehalose, promoting a more extensive hydration with respect to the other disaccharides, causes a higher slowed dynamics of water, even if the number of water molecules belonging to the first hydration shell is almost the same for all the disaccharides. These results complete the structural information obtained by Raman spectroscopy,19 suggesting that trehalose binds more strongly water molecules, so destroying their tetrahedral configuration arrangements and reducing more effectively the amount of those H-bond configurations, which, decreasing temperature, promote the formation of ice. References and Notes (1) Bourne, Y.; Cambillau, C. Top. Mol. Biol. 1993, 17, 321. (2) Crowe, J. H.; Crowe, L. M. Biological Membranes; Chapman, D., Ed.; Academic Press: New York, 1984; p 57. (3) Elbein, A. D. Chem. Biochem. 1974, 30, 227. (4) Clegg, J. S. Comp. Biochem. Physiol. 1967, 20, 8. (5) Sussman, A. S.; Halvorson, H. O. Spores: Their Dormancy and Germination; Harper & Row: New York, 1966. (6) Crowe, J. H.; Crowe, L. M. Science 1984, 223, 701. (7) Vegis, A. Annu. ReV. Plant Physiol. 1964, 15, 185. (8) Colaco, C.; Sen, S.; Thangavelu, M.; Pinder, S.; Roser, B. Biotechnology 1992, 10, 1007. (9) Storey, K.; Storey, J. The Biochemist 1997, June. (10) Leslie, S. B.; Israeli, E.; Lighthart, B.; Crowe, J. H.; Crowe, L. M. Appl. EnViron. Microbiol. 1995, 61 (10), 3592. (11) Crowe, J. H.; Carpenter, J. F.; Crowe, L. M. Annu. ReV. Physiol. 1998, 60, 3592. (12) Donnamaria, M. C.; Howard, E. I.; Grigera, J. R. J. Chem. Soc., Faraday Trans. 1994, 90, 2731. (13) Gottfried, S. D.; Peterson, E. S.; Sheikh, A. G.; Wang, J.; Yang, M.; Friedman, J. M. J. Phys. Chem. 1996, 100, 12034. (14) Cordone, L.; Galajda, P.; Vitrano, E.; Gassmann, A.; Ostermann, A.; Parak, F. Eur. Biophys. J. Biophys. Lett. 1998, 27, 173. (15) Magazu`, S.; Migliardo, P.; Musolino, A. M.; Sciortino, M. T. J. Phys. Chem. B 1997, 101, 2348. (16) Magazu`, S.; Maisano, G.; Middendorf, H. D.; Migliardo, P.; Musolino, A. M.; Villari, V. J. Phys. Chem. B 1998, 102, 2060. (17) Magazu`, S.; Maisano, G.; Migliardo, P.; Villari, V. J. Chem. Phys. 1999, 111, 9086. (18) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, P.; Sokolov, A. P.; Villari, V. J. Phys.: Condens. Matter 1999, 11, 3823. (19) Branca, C.; Magazu`, S.; Maisano, G.; Migliardo, P. J. Chem. Phys. 1999, 111, 281. (20) Telling, M. F. T.; Howells, W. S. Guide-IRIS Data Analysis; Tecnical Report RAL-TR-2000-004; CLRC, 2000. (21) Volino, F. NATO ASI Ser. B 1978, 33. (22) Bee, M. Quasielastic Neutron Scattering; A. Hilger: Bristol and Philadelphia, 1988. (23) Volino, F.; Dianoux, A. J. Organic Liquids; Structures Dynamics and Chemical Properties; John Wiley and Sons, Ltd.: New York, 1978; p 17. (24) Deriu, A.; Cavatorta, F.; Di Cola, D.; Middendorf, H. D. J. Phys. IV 1993, 3, 237. (25) Springer, T. Quasielastic Neutron Scattering for the InVestigation of DiffusiVe Motions in Solids and Liquids; Springer-Verlag: Berlin, 1972. (26) Tettamanti, E. Unpublished data. (27) Dowd, M. K.; Relly, P. J.; French, A. D. J. Comput. Chem. 1992, 13, 102. (28) Liu, Q.; Schmidt, R. K.; Teo, B.; Karplus, P. A.; Brady, J. W. J. Am. Chem. Soc. 1997, 119, 785. (29) Middendorf, H. D. Physica B 1996, 226, 113. (30) Branca, C.; Faraone, A.; Magazu`, S.; Maisano, G.; Migliardo, F.; Migliardo, P.; Villari, V. Recent Res. DeV. Phys. Chem. 1999, 3, 361. (31) Teixeira, J.; Bellissent-Funel, M. C.; Chen, S. H.; Dianoux, A. J. Phys. ReV. A 1985, 31, 1913.