Water Structures of Differing Order and Mobility in Aqueous Solutions

Biomacromolecules 2004, 5, 2137-2146

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Water Structures of Differing Order and Mobility in Aqueous Solutions of Schizophyllan, a Triple-Helical Polysaccharide as Revealed by Dielectric Dispersion Measurements Kazuto Yoshiba,*,†,‡ Akio Teramoto,*,† and Naotake Nakamura† Research Organization of Science and Engineering and Department of Applied Chemistry, Faculty of Science and Engineering, Ritsumeikan University, Nojihigashi 1-1-1, Kusatsu, Siga 525-8577, Japan

Toshiyuki Shikata Department of Macromolecular Science, Graduate School of Science, Osaka University, Machikaneyama-machi 1-1, Toyonaka, 560-0043, Japan

Yuji Miyazaki and Michio Sorai Research Center for Molecular Thermodynamics, Faculty of Science, Osaka University, Machikaneyama-machi 1-1, Toyonaka, 560-0043, Japan

Yoshihito Hayashi and Nobuhiro Miura§ Department of Physics, Tokai University, Hiratsuka-shi, Kanagawa, 259-1207, Japan Received March 18, 2004

Dielectric dispersion measurements were made on aqueous solutions of a triple-helical polysaccharide schizophyllan over a wide concentration range 10-50 wt % at -45 to +30 °C. In the solution state, three different water structures with the different relaxation times τ were found, namely, bound water (τl), structured water (τs), and loosely structured water (τls) in addition to free water (τP). Structured water is less mobile and loosely structured water is nearly as mobile as free water, but bound water with τl is much less mobile, thus τl . τs . τls JτP. The order-disorder transition accompanies the conversion between structured water and loosely structured water. However, the species with τs remains even in the disordered state and constitutes part of bound water in the entire temperature range. In the frozen state, in addition to bulk water formed by partial melting, two mobile species existed, which were assigned to liquidlike bound water and found to be a continuation of bound water in the solution state. These relaxation time data are discussed in connection with the entropy levels of the four structures deduced from heat capacity data (cf. Yoshiba, K.; et al. Biomacromolecules 2003, 4, 1348-1356). Introduction Water is abundant in biological systems and helps them perform important biological functions, particularly for proteins, polypeptides, and polynucleic acids. It forms some ordered structure around biological molecules such as bound water on proteins and DNAs.1 This orderliness originates from their hydrogen bond forming nature, which enables water to form immense hydrogen-bonded networks among itself2-5 and with other molecules, particularly with biopolymers.1,6-10 Thus, hydration or bound water has long been studied by a variety of experimental techniques such as heat capacity and dielectric dispersion measurements and simulation, and so forth.6-27 Among them, Grant et al.11-13 were * To whom the correspondence should be addressed. E-mail: kyoshiba@ chem.sci.osaka-u.ac.jp (K.Y.); [email protected] (A.T.). † Crest of Japan Science and Technology Corporation, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan. ‡ Present address: Department of Biological and Chemical Engineering, Faculty of Engineering, Gumma University, 1-5-1, Tenjin-cho, Kiryu, Gumma 355-8515, Japan. § Department of Applied Chemistry, Faculty of Science and Engineering, Ritsumeikan University, Nojihigashi 1-1-1, Kusatsu, Siga 525-8577, Japan.

the first to have performed extensive dielectric dispersion measurements on protein solutions, with the emphasis on temperature and concentration dependence and analyzed them carefully to find a layer of water of hydration one or two water molecules in width. Suzuki et al.21 also proposed a method similar to analyze protein solution data. The first observation of a helical biopolymer was a polysaccharide, but polysaccharides are generally poorly soluble and their conformations are usually less ordered28 with some exceptions.29-36 For these reasons, there is little interest in polysaccharides compared with their counterparts of the above biopolymers,1,10 although recently oligosaccharides in water have been studied by various methods to elucidate the behavior of themselves and interactions with water.22,37-39 In this connection, we note a unique water-soluble polysaccharide schizophyllan, which is an extra-cellular β-1,3-D-glucan produced by a fungus Schizophylumm commune with one β-1,6-D-glucose side chain per each three main-chain glucose residues. Norisuye et al.40-44 discovered that schizophyllan dissolves in water in the form of a triple

10.1021/bm040036+ CCC: $27.50 © 2004 American Chemical Society Published on Web 09/10/2004

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Table 1. Thermodynamic Parameters for D2O Solutions of Schizophyllana wb 0.0405c 0.0754d 0.4218 0.5782 0.6902 0.7179

Ψfus(w)/J g-1

nB

∆Hr/kJ mol-1

Tr/K

ref

298.2

10.90

135.7 67.33

11.34 11.67

4.32c 4.34 4.44 4.52 1.86 0.74

291.5c 290.5 290.7 298.3 308.4 312.5

53 49 54

9.572

11.36

a ∆H : enthalpy of fusion per mol of the schizophyllan repeat unit M . fus O nB: moles of unfreezable water per mole of the schizophyllan repeat unit b c MO. w ) weight fraction of schizophyllan in the solution. Mv ) 340 × 103, Mv ) viscosity-average molecular weight. d Mv ) 183 × 103.

helix, where three glucan chains are held together by interchain hydrogen bonds buried inside the helix core and the side chains are directed outward the helix core with some degree of rotational freedom. It is for these side chains that schizophyllan mixes with water at all compositions unlike most polysaccharides, which find no appropriate solvent. The triple helix of schizophyllan is shown to be intact in water up to 100 °C and shows no sign of conformational transition of the main chains above 10 °C.43 Since the triple helix is rodlike, schizophyllan forms a cholesteric liquid crystal above a certain critical concentration.45,46 Although there is no conformational transition in the main chains, aqueous schizophyllan shows a thermal/solventmediated order-disorder transition with the transition temperature Tr, for example, at 7 °C in H2O and 18 °C in D2O as revealed by such properties as optical rotation, cholesteric pitch, and heat capacity.47-55 This transition is remarkably molecular weight dependent,48,49,54 a characteristic feature of linear cooperative transition, and has been analyzed well by statistical mechanical theories of linear Ising system.56-58 It is also dependent on solvent,48-53 as noted above for the difference in Tr between H2O and D2O; the transition enthalpy ∆Hr is also different. In fact, the ordered state at lower temperatures is formed of the side chains and water molecules in the vicinity as an immense hydrogen bonded network developing over the entire helix length, which is destroyed at higher temperatures in the disordered state. In the previous study,55 detailed heat capacity measurements were made on H2O solutions of schizophyllan in a wide concentration range 30.45-90.93% in the solution as well as in the frozen state. These data were combined with previous data at lower concentrations48,49,55 to obtain the concentration dependence of Tr and ∆Hr, heat of fusion per gram of the solution Ψfus, and the number nB of unfreezable water molecules per schizophyllan repeat unit, revealing four concentration regions associated with the four water structures of differing orderliness. In the present study, heat capacity measurements were made on three D2O solutions of different weight fractions w of schizophyllan in the solution. Table 1 presents the thermodynamic data including the heat of fusion and moles of unfreezable water for schizophyllan-D2O, which supplement those for schizophyllan-H2O reported previously.55 All such data are summarized in Figure 1, where nB, Tr, and ∆Hr are plotted against the volume fraction φ of schizophyllan; Tr and ∆Hr are reduced to their values at lower concentrations: ∆H∞r , the infinite molecular weight ∆Hr,

Figure 1. Number of unfreezable water molecules per schizophyllan repeat unit nB, transition temperature Tr and heat of transition ∆Hr for aqueous schizophyllan plotted against the volume fraction φ of schizophyllan. Here Tr and ∆Hr are reduced to their values at lower concentrations: ∆H∞r , the infinite molecular weight ∆Hr, (∆H∞r ) 3.5 kJ mol-1 for H2O solutions, ∆H∞r ) 4.6 kJ mol-1 for D2O solutions), and Tr(0) ()278.2 K for H2O solutions and 290.5 K for D2O solutions). Unfilled and filled symbols represent the data for H2O and D2O solutions, respectively, which are taken from the previous papers48,49,54,55 except for the three data sets for D2O solutions (cf Table 1).

(∆H∞r ) 3.5 kJ mol-1 for H2O solutions, ∆H∞r ) 4.6 kJ mol-1 for D2O solutions), and Tr(0) ()278.2 K for H2O solutions and 290.5 K for D2O solutions). Unfilled and filled symbols represent the data for H2O and D2O solutions, respectively, which are taken from the previous papers48,49,54,55 except for the three data sets for D2O solutions. The data points for both solvents constitute composite plots and are fitted by the straight lines intersecting each other at critical volume fractions, φ1, φ2, and φ3, which define the four concentration regions, I, φ < φ1; II, φ1 < φ < φ2; III, φ2 < φ < φ3; IV, φ > φ3. It is noted that both transition data and fusion data give the same the critical concentration φ3, indicating that they are concerned with the same event. In the previous publication55 the H2O data are presented by plotting against the weight fraction w of schizophyllan, yielding the corresponding critical weight fractions wi (i ) 1-3), which are transcribed precisely to φi (i ) 1-4); φ1 ) 0.362, φ2 ) 0.529, and φ3 ) 0.674 using the water densities and partial specific volumes of schizophyllan. Thus, we see that the present plots dictate the general feature of the structure of aqueous schizophyllan precisely irrespective of H2O or D2O. The weight fraction w has been transcribed to volume fraction φ as stated in the Experimental Section. Indeed as shown in the previous publication,55 in region I, aqueous schizophyllan consists of triple helices sheathed with layered bound water, structured water, and loosely

Water Structures in Schizophyllan

structured water embedded in free water on going from the helix core outward. In region II, there is no free water but loosely structured water is shared by the triple helices sheathed with bound water and structured water. In region III, the triple helices with sheathed bound water share structured water. Finally, in Region IV, the system consists only of schizophyllan and bound water and nB tends to vanish at φ ) 1 as it should be. The order-disorder transition of aqueous schizophyllan is associated mainly with the conversion between structured water and loosely structured water as shown later explicitly. Bound water, structured water, loosely structured water, and free water are in the decreasing order of orderliness as judged from their enthalpy levels.55 It has been shown from dielectric dispersion measurements53,59,60 that these layers of water differ not only in orderliness but also in mobility. However, these measurements on D2O solutions of schizophyllan by time-domain reflectometry (TDR) were not so extensive in concentration and accurate to be compared with the heat capacity measurements and did not give quantitative information about these dynamic aspects, which could be discussed in conjunction with the heat capacity data. Therefore, in this study, we made dielectric dispersion measurements on D2O solutions of schizophyllan of the weight fractions 0.1-0.5 in the solution state and additional measurements by TDR for frozen solutions. The present data are combined with the previous fragmental ones whenever possible53,59,60 and analyzed to elucidate the dielectric strengths and relaxation times associated with the layer structures of water, and the results are discussed in connection with the static structures derived from heat capacity data. Finally two remarks are in order. Schizophyllan in the triple helical conformation has an antitumor activity43,62 and is actually used to treat cervical cancer.43,63 As noted above, the schizophyllan triple helix molds water molecules in the vicinity into structures of differing orderliness. Bound water is found in aqueous solutions of DNA and proteins, but aqueous schizophyllan is unique that it has structured water and loosely structured water in addition to bound water, which comes from its feature of forming various ordered structures. It is interesting to ask whether this is unique only for schizophyllan or more general for other biopolymers in aqueous environments and can be studied by other methods such as simulations. Experimental Section Dielectric dispersion measurements were performed on the following apparatuses: a system of a Hewllet Packard LCR meter 4284A (100 kHz-lMHz), an Agilent LCR meter 4287A (1 MHz-2GHz), a material probe system HP54120B (Hewllet Packard) containing a network-analyzer 8720ES (50 MHz20GHz),64-66 and a TDR system (Hewllet Packard)53,59,60 The network analyzer was first calibrated with H2O and then recalibrated with D2O.67 This procedure gave accurate results over 1 GHz. The measurements on frozen samples were done only on the TDR system. One of difficulties in handling polymer solutions is their high viscosity, which prohibits using a syringe for injecting the solution in a dielectric cell. This difficulty has been surpassed with aqueous schizophyl-

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Figure 2. Dielectric dispersion curves of D2O solutions of schizophyllan in region I. (a) Temperature dependence for the 40 wt % solution. Arrows indicate the locations of individual dispersions. (b) Concentration dependence at 5 °C. The 50 wt % solution, in region II.

lan, because it is liquid crystalline and very less viscous even at high concentrations compared with anisotropic solutions. It was also crucial to get rid of any bubble from the solution for precise measurements. This was achieved first by centrifuging the solution warmed at 40 °C and transferring it into a dielectric cell by a pipet. Each solution was prepared by mixing known amounts of a schizophyllan sample (KR2A, Mw ) 178 × 103, Mz/Mw ) 1.2), and D2O and the volume fraction φ of schizophyllan was calculated from w by using the partial specific volume of schizophyllan 0.628 cm3 g-1 in D2O and 0.619 cm3 g-1 in H2O and D2O density. Part of the TDR data (OK-2A, Mw ) 184 × 103, Mz/Mw ) 1.3; JA5-A, Mw ) 97.8 × 103, Mz/Mw ) 1.3) is taken from the previous study.53,59,60 All three samples used were completely miscible with water (H2O, D2O) at all compositions. Results Figure 2 shows typical dielectric dispersion curves of schizophyllan solutions in the solution state,where that of D2O is presented for comparison. They differ largely from that of D2O, exhibiting a large S/N ratio due to this high

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concentration. In panel a, the dispersion curves for the 40 wt % solution at three temperatures encompassing Tr are shown. At either temperature, the loss curve exhibits a clear maximum at high frequencies, and the height of this peak does not change with raising temperature. This is concerned with bulk water, because pure D2O has the maximum in this frequency range. Thus, the merit of using D2O as the solvent is that we see a clear water peak within the accessible frequency range, which is difficult with H2O. Another maximum is seen at low frequencies, which is associated with the motion of bound water coupled with side chain motion as discussed below. Each curve except one at 30 °C clearly shows a third dispersion in the middle frequency range seen as a bump, which rapidly fades away with raising temperature. This is ascribed to structured water as noted earlier and indeed the temperature dependence of this maximum reflects the order-disorder transition in aqueous schizophyllan, which has been already shown. Panel b of Figure 2 illustrates how the dispersion changes with schizophyllan concentration at 5 °C. At either temperature, the dispersion at higher frequencies becomes smaller as the schizophyllan concentration increases but still significant for the 50 wt % solution; it appears clearly at lower frequencies compared with that of D2O at all concentrations. On the other hand, the dispersion at lower frequencies is weakened rapidly with decreasing w and disappears at lower w. The middle dispersion clearly seen at 50% is almost invisible at 10%. These are the signals from schizophyllan and useful to extract the information about the dynamic behavior of the water structures concerned because of large polarizability of water; schizophyllan itself has only a negligible contribution to the total dispersion. Data taken for D2O solutions of schizophyllan weight percents between 10 and 50 wt % at temperatures between 5 and 30 °C showed similar behavior. In every case, a high-frequency dispersion shows a clear peak as that for D2O, which facilitates the de-convolution analysis described below. This was not the case with H2O solutions. As shown earlier,60 dispersion curves of 31 and 43% solutions in the frozen state were very broad, indicating that there are more than one mobile species also in the frozen state (cf. Figure 5). The loss curve at lower frequencies was seen to shift to lower frequencies as the temperature was lowered, with its height decreasing only gradually. On the other hand, there was another dispersion at higher frequencies, which disappeared below 230 K. The former dispersion is ascribed to liquidlike bound water, whereas the latter to free water produced by partial melting of the solution. The height of either loss peak is roughly proportional to w, indicating that it is due to the water molecules in the immediate vicinity of the triple helix. Discussion 1. Deconvolution of Dielectric Dispersion Curves. As noted above in the Introduction, aqueous schizophyllan in region I consists of the triple helices of schizophyllan sheathed with multiple layers of water embedded in free water, or free water is shared by the sheathed triple helices. This situation is schematically illustrated in Figure 3I (left).

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Figure 3. Hydrated schizophyllan triple helices in water in the two concentration regions I and II. Orange, helix core; pink, bound water; blue, structured water, green, loosely structured water; yellow, free water, each being separated by a ring; the white ring in the pink separating bound water (s(1)) from bound water (l). Arrows indicate the order-disorder transition due to the interconversion between structured water and loosely structured water.

In region II, there exists no free water but now loosely structured water is shared by the triple helices sheathed with bound water and structured water as in Figure 3II (right). On going from the ordered state to the disordered state, structured water is transformed to loosely structured water, vice versa, as shown by arrows in the figures. As noted in the previous TDR studies,53,59-60 such structures of water should have different mobilities as being revealed by their characteristic dielectric dispersions. It is noted that each dielectric dispersion measurement in the solution state has been done in concentration regions I or II at temperatures between 5 and 30 °C. Thus, such dielectric dispersion data can be discussed in connection with the static structure information as shown in Figure 1 and the transition process illustrated in Figure 3. A similar discussion can be made with the data in the frozen state using the static structure information reported in the previous paper.54,55 Since all of the loss curves have multiple dispersions, we try to de-convolute them into component dispersions. In the previous studies, the Harvrilak-Negami equation68 was used for this purpose. However, this is an empirical one for reproducing the data but has no molecular theoretical basis and is not appropriate for the present purpose. Indeed the analysis using this equation resulted in a physically unrea-



sonable consequence that it had a long high-frequency tail beyond the pure water dispersion. A solution in region I should have free water, whose dispersion appears at highest frequencies. If undisturbed, it would be represented by a dispersion of the Debye type. Therefore, we assume that the total dispersion is represented by a superposition of the Cole-Cole dispersions for bound water and structured water characterized by the dielectric strengths ∆l and ∆s, relaxation times τl and τs, and the Cole-Cole parameters Rl and Rs, respectively, and a Debye dispersion for loosely structured water characterized by the strength ∆ls and relaxation time τls in addition to the Debye dispersion of free water, for which the relaxation time is clamped at the τP for D2O but its strength ∆P is left adjustable. Thus the complex dielectric constant * as a function of angular frequency ω of an aqueous solution of schizophyllan is expressed by * ) ∞(1 - φ) +

∆l 1 + (iωτl)

1-Rl

+

∆s

+ 1 + (iωτs)1-Rs ∆ls ∆P + (1) 1 + iωτls 1 + iωτP

where i ) x-1 and the dielectric constant of the solution extrapolated to infinite frequency is taken to be ∞(1 - φ), with ∞ being that of D2O. Thus, experimental dispersion data were de-convoluted into the two dispersions l and s of the Cole-Cole type and two ones ls, and P of the Debye type using eq 1 with ∆j and τj as adjustable parameters (j ) l, s, ls, P) but τP clamped and the optimal values of the these parameters were obtained by minimizing the parameter σ defined by σ2 )

(n -1 m) ∑ [(′ j

exp

- ′cal)2 + (′′exp - ′′cal)2]

(2)

where the subscripts “exp” and “cal” refer to the observed and calculated dielectric constant and loss, respectively and “j” runs over all the dispersions concerned, and n and m are the numbers of data sets and parameters, respectively, with both ′ and ” being equally weighed. No good fit was obtained with large R1 or Rs, but not bad as far as they were small. Therefore an additional restriction that Rl ≈ 0.3 and Rs ≈ 0.1 was put to ease the analysis, and hence, m ) 7. Figure 4 presents typical results from de-convolution for solutions of different concentrations at different temperatures. In panel b, well-defined peaks are seen at low and high frequencies at either temperature; either peak at 25 °C is located slightly higher frequencies than that at 10 °C. A clear bump in the middle frequencies indicates the existence of a third dispersion. The de-convolution has been done with the τP clamped, with the component dispersions shown by curves, and the involved parameters of τ and ∆ have been determined unambiguously; both ” and ′ curves are fitted well as seen in panels a and b. The dispersion l at the lowest frequency is associated with bound water coupled with side chain motion and the middle dispersion due to structured water. On the other hand the highest-frequency dispersion is located at frequencies lower than that of pure D2O, thus it is separated into the ls dispersion due to loosely structured

water and dispersion P due to pure D2O. Panels c and d present the results for three solutions of different concentrations. Here again the de-convolution is done with reasonable accuracy, although the relaxation strengths get less accurate as polymer concentration is lowered. It is noted that the relaxation times are virtually independent of polymer concentration but change with temperature almost following Arrhenius type equations. This is reasonable because the relaxation time is an intensive property characteristic of the system or phase concerned. Figure 5 shows similar analyses based on the Cole-Cole plot with data in the frozen state, which were reported previously.54,60 Three dispersions lF, sF, and hF are discernible at 0 °C, whereas there is no hF dispersion at -45 °C. The dispersions lF and sF are due to liquidlike bound water, whereas the dispersion hF is due to bulk water produced by partial melting of the solution. It will be shown these assignments conform to the conclusion from heat capacity data presented in the previous publication.55 (The detailed dielectric dispersion data are available in the Supporting Information Table S1-2). 2. Concentration and Temperature Dependence of ∆E and τ. Figure 6 shows the relaxation strengths ∆ in the disordered (a) and ordered (b) states as functions of the volume fraction φ of schizophyllan. All ∆ l, ∆ s, and ∆ ls are seen to increase almost linearly with φ, but ∆ P decreases linearly with φ. It is noted that ∆ s and ∆ ls are larger and smaller, respectively, in the ordered state than in the disordered state. This comes from the mechanism of the order-disorder transition of the conversion between structured water and loosely structured water as noted above. All the solutions examined except for the 50 wt % solution are in Region I and undergo the transition via route I in Figure 3. They have all of the four water species, but the 50 wt % solution, which is in region II, may lack free water. The linear dependence of ∆i (i ) l, s, ls) on φ is reconciled if each water layer is formed around the helix core with a given thickness. Thus, these results are consistent with the structural feature of aqueous schizophyllan illustrated in Figure 3 that the schizophyllan triple helices sheathed with the layers of bound water, structured water and loosely structured water are embedded in pure D2O, so the amount of each layer water would be proportional to polymer concentration. However the linearity does not hold accurately at concentrations higher than 40 wt % in the ordered state particularly for ∆ l and to a less extent for ∆ s. As evident in Figure 3, the peripheries of the triple helices would come in close contact with each other at these high concentrations, thus reducing the motions of the side chains and water molecules in the vicinity and stabilizing the ordered structure. This accounts for the increased ∆ l and ∆ s and also increased τ l shown later in Figure 8, and raising Tr at high concentrations as seen in Figure 1. Figure 7 illustrates how dielectric strengths of individual dispersions for the 40 wt % solution change with temperature in the solution state. It is seen that ∆l stays almost constant throughout the solution region, which is ascribed to bound water. On the other hand ∆ s assigned to structured water (open circles) shows two flat portions encompassing the

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Figure 4. De-convolution of dielectric dispersion curves in the solution state. (a) Dielectric constant curves for the 50 wt % solution at 10 (unfilled circles) and 25 °C (filled circles). (b) Dielectric loss curves for the 50 wt % solution at 10 and 25 °C. (c) Dielectric constant curves at 10 °C for solutions of different concentrations: 40, 30, 20, and 0 wt % from bottom to top; solid curves, total dispersions. (d) Dielectric loss curves for solutions of different concentrations at 10 °C. Curves in the loss curves from left to right: component loss curves for the l, s, ls, and P dispersions; solid curves, total loss curves.

transition temperature Tr of 17.6 °C (panel b; fN, the fraction of residues in the ordered state) and decreases abruptly around Tr, but ∆ ls(triangles) behaves in the opposite way; there is no such singularity in relaxation times (cf Figure 8a). It is noted that the sum ∆ s and ∆ ls is virtually unchanged. The same trend is observed for solutions of different concentrations. This is a clear indication that the order-disorder transition is concerned with the conversion between structured water and loosely structured water. Although ∆ s is assigned to structured water, it persists even above Tr in the disordered state. These findings have led us to conclude that ∆ s consists of two parts, namely, one changing with temperature ∆ s(2), which is concerned with the ordered structure with side chains, and the other ∆ s(1) is insensitive to temperature and constitutes part of bound water such that ∆ s ) ∆ s(1) + ∆s(2). The sum of ∆s(2)

and ∆ls shows only a mild change (dash-dot line). The dashed line in the figure measures the contribution ∆s(1). On the other hand, ∆s(2) parallels with fN as it should be. In Figure 3, a dashed white circle in the pink area separates bound water l and bound water s(l), and the latter has the relaxation time τs throughout the course of the transition. 3. Dynamic Behavior of Water in Aqueous Schizophyllan. Excepting the τ l for the 50 wt % solution, all of the relaxation times in the solution state τi are virtually independent of schizophyllan concentration. Therefore their values are evaluated by averaging those at different concentrations as functions of temperature. On the other hand, the relaxation strengths are almost proportional to φ. Therefore the values for the 40 wt % in the solution state and those for the 43 wt % solution in the frozen state are taken to represent their temperature dependence, with the latter being


Figure 5. De-convolution of dielectric dispersion curves of the 30.8 wt % solution at 0 and -45 °C in the frozen state. Solid curves, total dispersions.

Figure 6. Concentration dependence of dielectric strengths ∆i (i ) l, s, ls, P). (a) Plots of ∆i against the volume fraction φ of schizophyllan at 25 °C in the disordered state. (b) Plots of ∆i against the volume fraction φ of schizophyllan at 10 °C in the ordered state. Symbols: 0, ∆l; O, ∆s; 4, ∆ls; ], ∆P. region I, φ < 0.362; region II, 0.362 < φ < 0.562.

corrected for the concentration difference by multiplying 40/ 43. Figure 8 summarizes these results to clarify the dynamic behavior of water in aqueous schizophyllan. Figure 8a shows Arrhenius plots of the averaged relaxation times over the entire temperature range examined; unfilled and filled


Figure 7. Order-disorder transition for the 40 wt % solution. (a) Dielectric strengths: 0, ∆l; O, ∆s; 4, ∆ls; ], ∆P; dotted line, ∆s(1); dash-dot line, ∆s(2) + ∆ls. (b) fN vs T derived on the basis of heat capacity data.54,55

Figure 8. Dielectric behavior of water in aqueous schizophyllan over the entire temperature range. (a) Relaxation times (b) Dielectric strengths Tr ) 290.5 K, Tf ) 277.0 K. Dotted line, extrapolation of log(τlF/s) to higher temperature.

symbols refer respectively to the solution and frozen states, and Tf is the melting point of the solution. All of the relaxation times observed are much smaller than that of ice. There is no abrupt change in relaxation time in the order-

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disorder transition region; thus, the relaxation times undergo no transition. It is seen that τs and τsF are almost equal at Tf and a composite curve can fit them without discontinuity. Thus, they are assigned to liquidlike bound water. On the other hand, the dispersions l and lF are connected via a significant transition region. This transition is more conspicuous for the 50 wt % solution. This behavior may be reconciled consistently by assigning the l dispersion to the motion of water molecules coupled with that of the side chains. In the solution state the coupled motion is predominant, yielding a longer relaxation time. As seen from Figure 1, at concentrations φ > 0.35, the triple helices sheathed with water layers are in close contact with each other, and their motions are deterred. In the frozen state however the side chain motion is frozen and only water motion is seen. This explains why τlF is smaller than τl, although they are both due to liquidlike bound water; note that water is the main visible component due to its large dielectric constant compared with schizophyllan. If the log(τlF/s) is extrapolated to higher temperature following the dotted line, it is -7.9 at Tf. This would be the value of log(τl/s) for uncoupled bound water at Tf. In the frozen state, there is no relaxation corresponding to free water. However the relaxation hF seen above 240 K continues smoothly to relaxation ls in the solution state. Thus, this is bulk water present in the partially melted solution. These assignments are consistent with the conclusion from the heat capacity data.55 Next we discuss the dielectric strengths over the entire temperature region, which are displayed in Figure 8b. In the solution state, bound water consists of two components, ∆l and ∆s(1), which are essentially temperature-independent. This means that the amount of bound water virtually constant in this temperature range. In the frozen state, there are two dispersions lF and sF, which are assigned to liquidlike bound water. Here, ∆sF decreases with lowering temperature, whereas ∆lF increases; their sum ∆sF + ∆lF gradually decreases with lowering T and tends to vanish below 180 K.61 This decease is due to vitrification of bound water. Indeed this change parallels with the change in excess enthalpy in the frozen state discussed previously.55 At Tf, the sums ∆s(1) + ∆l and ∆sF + ∆lF are nearly the same, indicating that they are both liquidlike bound water, and this is unfreezable water gradually vitrifying below Tf. Large part of free water crystallizes at Tf, and its dispersion is hardly detectable below Tf. However, there exists a highfrequency dispersion hF below Tf, which rapidly decreases to vanish around 240 K. As noted with relaxation time, this is due to rapidly mobile water hF, which is produced by the partial melting detected by heat capacity. Therefore the relaxations ls constitutes main part of hF relaxation surviving in the frozen state. However, at Tf, the sum of ∆s(2) and ∆ls in the solution state is somewhat smaller than ∆hF in the frozen state. Thus it is probable that the relaxation hF may contain a small fraction of free water dispersion. According to the phase diagram shown in Figure 1, 40 wt % (φ ) 0.316) is located nearly the upper bound of Region I, while 50 wt %(φ ) 0.410) is in region II, where no free water would exist. However the dielectric dispersions find small free water dispersion at both concentrations. This may

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be reconciled as follows. Actually there may be a continuous change from free water to loosely structured water, and the separation into the two components is a rough approximation based on the thermodynamic data. The dielectric dispersion data are concerned with microscopic information, which may reflect more subtle differences in dynamic properties compared with the thermodynamic data. However an accurate evaluation of each contribution is beyond the accuracy of the present analysis. 4. Static and Dynamic Orders. In the previous study,55 the enthalpy level of structured water was calculated from ∆H∞r with reference to free water assuming that the amount of the associated water would be the same as bound (or unfreezable) water, which measures the static structural order. Here we discuss their dielectric relaxation times, which reflect their dynamic structural orders, and correlated more reasonably with configurational entropy Sc. In fact, Adam and Gibbs69 formulated the relaxation time correlating with the configurational entropy Sc, which may be compared with the excess entropy ∆SEX, and Takahara et al.70 provided a beautiful example on 3-bromopentane. We try a similar analysis using ∆SEX for Sc. In terms of dielectric strength at Tf, it is ∆lF + ∆sF for unfreezable water, ∆s for structured water, ∆ls for loosely structured water, and ∆P for free water, and ∆lF + ∆sF ≈ ∆s. However, it has been shown that it is not ∆s but ∆s(2) that is responsible for the transition. The amount of such water is given to a first approximation by nB[∆s(2/(∆lF + ∆sF)], which is calculated to be 0.49 nB using the ∆ values in Figure 7. With nB of 11.3, this leads to the difference in enthalpy between structured water and loosely structured water of 830 J mol-1 and the entropy difference of 2.84 J K-1 mol-1. The relaxation τls for loosely structured water is about four times longer than that of free water, and there must be some entropy difference between them, although it could not be determined only from the heat capacity data. For simplicity, we assume that the entropy above ice and logarithm of relaxation time are linearly correlated. This leads to the enthalpy and entropy of loosely structured water lower than those of free water by 9.6%. Thus the entropy levels with reference to ice and free water at Tf are 90.4% for loosely structured water, 78.1% for structured water s(2), and 62.9% for bound (or unfreezable) water. (See the detailed data in Table S3 of Supporting Information). Figure 9 shows the correlation of this entropy level with log(τ/s), where straight line represents the above assumption with the value of log(τlF/s) being -7.9 at Tf according to the discussion in Section 3. The proposed correlation is nearly satisfactory over the entire range of log(τ/s). Indeed the data point for s(2) (open circle) is fitted precisely to the straight line, but those for bound water s(1) and l appear somewhat removed from the line. This suggests that the entropy contributions to these dispersions are yet to be refined. It is noted however that the theory tells nothing about such a dual state as that encountered with structured water. 5. Comparison with Other Aqueous Solutions. Dielectric dispersion measurements have been performed on various aqueous solutions to have information about water structure there, particularly bound water or hydration. Among those



another relaxation is observed around 1 GHz. This is similar to the case of aqueous schizophyllan. However, our knowledge is not detailed enough to make a general statement about the structure and dynamics of water in biopolymer solutions. At present, each system must be treated on its own right. Acknowledgment. A.T. thanks Yamashita Sekkei Co. Ltd. for the Chair-Professorship at Ritsumeikan University. Thanks are due to Shuzo Seki, Professor Emeritus, Osaka University, for his continued interest in our work.

Figure 9. Correlation of log(τ/s) with the excess entropy ∆SEX at Tf of 277.0 K. Ice, [; bound water l, 0: structured water s(1), b; structured water s(2), O; loosely structured water ls, 4; free water P, ]. The straight line: a linear correlation between free water and ice data.

Grant et al.12,13 correctly pointed out the importance of concentration dependence and careful analysis to elucidate the detailed molecular mechanism; indeed they suggested presence of some ordered water close to free water(around 4GHz), which may be compared with loosely structured water in aqueous schizophyllan in addition to another bound water relaxing more slowly with the protein itself, which may be compared with structured water exhibiting a relaxation around 500 MHz. Suzuki et al.21 have also discussed high-frequency dispersions. Miura et al.16 made TDR measurements on aqueous solutions of a number of proteins to find three dispersions, l, m, and h at 25 °C, with τl > τm > τh. They assigned the m relaxation to bound water, with log(τ/s) ≈ -8.6; however ∆m was small, being in the range between 1.5 and 3.9. In another paper17 they reported TDR data for an aqueous solution of serum albumin of 20% over a wide temperature range above and below the freezing point to have observed three dispersions similar to those in aqueous schizophyllan. In the frozen state the middle dispersion m around 100 MHz was assigned to bound water, and the one faster by 60 times to unfreezable water, and the slowest one to those which are not observed in aqueous schizophyllan. Unfreezable water was also found by Singh et al.19 However the results on these biopolymer solutions are less confirmative compared with those for aqueous schizophyllan because of poorer S/N ratio due to relatively low concentrations and high conductance of buffer solutions. It is also noted that extensive data on aqueous oligo-saccharide solutions are discussed in relation to water structures in the solutions.37-39 As emphasized here, it has been highly advantageous to use heat capacity and dielectric dispersion to study water structure. However it is difficult to find such a pair of studies as the schizophyllanwater, where heat capacity and dielectric relaxation are compared consistently. In this connection, lysozyme is a rare case, where both methods were used to obtain g of bound water per g of lysozyme of 0.34 by heat capacity71 and 0.3 by dielectric relaxation;72 they are in agreement with 0.34 obtained by NMR.73 The dielectric relaxation time of the main part of bound water is 8 × 10-10 s (200 MHz) and

Supporting Information Available. Tables containing dielectric relaxation times and strength of schizophyllan in D2O. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Eagland, D. Nucleic Acids, Peptides, and Proteins. InWater: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1982; Vol. 4, Chapter 5, pp 305-518. (2) Eisenberg, D.; Kauzmann, W. The structure and properties of water; Clarendon Press: London, 1969. See here the references for dielectric properties of D2O. (3) Franks, F. The physics and physical chemistry of water. InWater: A ComprehensiVe Treatise. Franks, F., Ed.; Plenum Press: New York, 1982; Vol. 1. (4) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371-374 (5) Haida, O.; Suga, H.; Seki, S. J. Glaciol. 1979, 34, 371-374 (6) Kuntz, I. D., Jr.; Wuthrich; Kauzmann, W. AdV. Protein Chem. 1974, 28, 239. (7) Edsall, J. T.; McKenzie, H. A. AdV. Biophys. 1983, AdV. 16, 53. (8) Rupley, J. A.; Careri, G. AdV. Protein Chem. 1991, 41, 37-172. (9) Wuthrich, K.; Gotting, G.; Liepinish, E, Frarady Discuss. 1992, 93, 35. (10) Pethig, R. Annu. ReV. Phys. Chem. 1992, 43, 177-205. Pethig, R. Dielectric and Electronic Properties of Biological Materials; John Wiley & Sons Ltd.: New York, 1992. (11) Grant, E. H Nature 1962, 196, 1194-1195; Ann. N. Y. Acad. Sci. 1965, 125, 418-427; J. Mol. Biol. 1966, 19, 133-139. (12) Grant, E. H.; Keefe, S. E.; Takashima, S.J. Phys. Chem. 1968, 72, 4373-4380. (13) Grant, E. H.; McClean, V. E. R.; Nightingale, N. R. V.; Sheppard, R. J.; Chapman, M. J. Bioelectromagnetics 1986, 7, 151-162. (14) Hasted, J. B. Aqueous Dielectrics; Chapman and Hall: London, 1973. (15) Takashima, S. Electrical Properties of Biopolymers and Membranes; IOP Publishing Ltd.: Philadelphia, 1989. (16) Miura, N.; Asaka, N.; Shinyashiki, N.; Mashimo, S. Biopolymers 1994, 34, 357-364. (17) Miura, N.; Hayashi, Y.; Shinyashiki, N.; Mashimo, S. Biopolymers 1995, 39, 9-16. (18) Miura, N.; Hayashi, Y.; Mashimo, S. Biopolymers 1995, 39, 183187. (19) Singh, G. P.; Parak, F.; Hunklinger, S.; Dransfeld, K. Phys. Chem. Lett. 1981, 47, 685. (20) Wei, Y.-Z.; Kumbharkhan, A. C.; Sadeghi, M.; Sage, J. T.; Tian, W. D.; Champion, P. M.; Sridhar, S. J. Phys. Chem. 1994, 98, 66446651. (21) Suzuki, M.; Shigematsu, J.; Kodama, T. J. Phys. Chem. 1996, 100, 7279-7282. (22) Bizzarri, A. R.; Cannistraro, S. J. Phys. Chem. B 2002, 106, 66176633. (23) Boresch, S.; Ho¨chtl, P.; Steinhauser, O. J. Phys. Chem. B 2000, 104, 8743-8752. (24) Brunger, A. T.; Brooks, C. L., III.; Karplus, M. Proc. Natl. Acad. Sci. U.S.A. 1985, 82, 8458 (25) Levitt, M.; Sharon, R, Edsall, J. T.; McKenzie, H. A. Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 7557. (26) Karplus, M.; McCammon, Sci. Am. 1986, 254, 30.; Karplus, M.; Petsko, G. A. Nature 1990, 347, 631. (27) Weinga¨rtner, H.; Knocks, A.; Boresch, S.; Ho¨chtl, P.; Steinhauser, O. J. Chem. Phys. 2001, 115, 1463-1472.

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Yoshiba et al. (55) Yoshiba, K.; Teramoto, A.; Nakamura, N.; Kikuchi, K.; Miyazaki, Y.; Sorai, M. Biomacromolecules 2003, 4, 1348-1356. Correction: The ordinate for the lower panel of Figure 8 should be read “10CpE/ kJ K-1 mol-1“. (56) Zimm, B. H.; Bragg, J. K.; J. Chem. Phys. 1959, 31, 526. (57) Nagai, K J. Chem. Phys. 1959, 34, 887. (58) Teramoto, A. Prog. Polym. Sci. 2001, 26, 667-720. (59) Miura, N.; Yagihara, S.; Mashimo, S.; Gu, H.; Teramoto, A. Proc. Jpn. Acad. Ser. B 1998, 74, 1-5. (60) Hayashi, Y.; Shinyashiki, N.; Yagihara, S.; Yoshiba, K.; Teramoto, A.; Nakamura, N.; Miyazaki, Y.; Sorai, M. Biopolymers 2002, 63, 21-31. (61) It is shown from the data for the sum of ∆sF + ∆lF that it is extrapolated to zero around 180 K. (62) Yanaki, T.; Ito, W.; Tabata, K.; Kojima, T.; Norisuye, T.; Takano, N.; Fujita, H. Biophys. Chem. 1983, 17, 337-342. (63) Okamura, K.; Suzuki, M.; Chihara, T.; Fujiwara, A.; Fukuda, T.; Goto, S.; Ichinohe, K.; Jimi, S.; Kasamatsu, T.; Kawai, T.; Mizuguchi, K.; Mori, S.; Nakano, H.; Noda, K.; Sekiba, K.; Suzuki, K.; Suzuki, T.; Takahashi, K.; Takeuchi, K.; Takeuchi, S.; Yajima, A.; Ogawa, N. Cancer 1986, 58, 865-872. (64) Itatani, S.; Shikata, T. Langmuir 2001, 17, 6841-6850. (65) Imai, S.; Shiokawa, M.; Shikata, T. J. Chem. Phys. B 2001, 105, 4495-45. (66) Shikata, T. J. Phys. Chem. B 2002, 106, 7664-7670. (67) The network analyzer was first calibrated against H2O to obtain the dielectric relaxation curve of D2O.; the parameters for H2O are τP ) 8.27 ps, 0 ) 78.39, and ∞ ) 5.085. Since the derived curve agreed well with the literature data, the network analyzer was re-calibrated on the D2O standard. The relaxation curves for schizophyllan solutions obtained on this basis were more accurate than those based on the H2O standard. This is probably because they appeared in similar frequency regions as those for D2O. (68) Harvrilak, S.; Negami, S. Polymer 1967, 8, 161-210. (69) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139-146. (70) Takahara, S.; Yamamuro, O.; Matsuo, T. J. Phys. Chem. 1995, 99, 9589-9592. (71) Miyazaki, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. B 2000, 104, 8044-8052. (72) Harvey, S. C.; Hoekstra, P. J. Phys. Chem. 1972, 76, 2987-2994. (73) Kuntz, I. D. J. Am. Chem. Soc. 1971, 93, 51.

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Water Structures of Differing Order and Mobility in Aqueous Solutions

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