Static Water Structure Detected by Heat Capacity Measurements on

At w2, loosely structured water vanishes and structured water layers start contacting each other and decrease with w until they disappear at w3. Thus,...
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Biomacromolecules 2003, 4, 1348-1356

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Static Water Structure Detected by Heat Capacity Measurements on Aqueous Solutions of a Triple-Helical Polysaccharide Schizophyllan Kazuto Yoshiba,† Akio Teramoto,*,† and Naotake Nakamura† Department of Applied Chemistry, Faculty of Science and Engineering, Ritsumeikan University, Nojihigashi 1-1-1, Kusatsu, Siga 525-8577, Japan

Kyo Kikuchi, Yuji Miyazaki, and Michio Sorai Research Center for Molecular Thermodynamics, Faculty of Science, Osaka University, Machikaneyama-cho 1-1, Toyonaka, 560-0043 Japan Received March 31, 2003; Revised Manuscript Received May 26, 2003

Heat capacity measurements were made on aqueous solutions of a triple-helical polysaccharide schizophyllan by precision adiabatic calorimetry over a wide range of concentrations 30.45-90.93 wt % at temperatures between 5 and 315 K. The heat capacity curves obtained were divided into four groups depending on the weight fraction of schizophyllan w regions I-IV. In region I, triple-helices with the sheath of bound water, structured water, and loosely structured water forming layers around the helix core are embedded in free water. In region II, there is no free water, and loosely structured water decreases until it vanishes, but structured water stays constant with increasing w. In region III, bound water remains unaffected, but structured water decreases with increasing w by overlapping each other. Finally, in region IV, only schizophyllan and bound water exist, the latter decreasing upon increasing w. The maximum thickness of each layer is 0.183 nm for bound water, 0.134 nm for structured water, and 0.236 nm for loosely structured water, and these layers of water are at the enthalpy levels of 53%, 93.7%, and nearly 100%, respectively, between ice (0%) and free water (100%). Introduction Water is a specific solvent, which forms various structures in the liquid state and exhibits many different phases in the solid state. This is due to its intermolecular hydrogen bonding ability, and its properties themselves are of continued interest.1-4 Biological systems usually contain abundant amounts of water, and interactions between water and biological polymers may be important factors for stabilizing such systems and realizing the biological functions concerned. In most cases of biological polymers, which take helical conformations as a whole or part, however, attention has been paid on their main-chain conformations, and water is regarded as a bye-player as in other polymers. On the other hand, it has been pointed out that biopolymer-water interactions play important roles for biological activities. For instance, it is known that part of the water molecules is organized as bound water in aqueous protein and DNA solutions.5-11 However, such an ordered structure develops only on their surfaces and does not spread over a large distance from the surface. In a series of investigations,12,13 we have focused our attention on aqueous solutions of schizophyllan, a β-1, 3-Dglucan. In water, it exists as a triple helix with three glucan chains held together by intermolecular hydrogen bonds buried * To whom the correspondence should be addressed. E-mail: [email protected]. † CREST of Japan Science and Technology Corporation.

in the helix core, with one side chain glucose residue being directing outward the helix core, which has considerable rotational freedom.14-18 Schizophyllan is unique in the following ways. This polysaccharide, whose molecular shape is rigid rod like, is soluble in water even at high concentrations in spite of the fact that it has no ionizable group; note that most natural polysaccharides are not well soluble in water, and their ordered conformations have not been elucidated precisely19 except for some cases.20-27 The triple helix of schizophyllan stays intact even at 100 °C.17 In addition, it undergoes a thermal and/or solvent-mediated order-disorder transition, which is not concerned with the main chain triple helix but with the conformations of the side chains and water in the vicinity.12,13,28-33 At low temperature, the side chain glucose residues and nearby water form an ordered structure, and this water is called structured water.12,13 Thus, this order-disorder transition is very interesting for investigating aqueous biopolymer solutions because water plays a main role in this transition. Indeed, the schizophyllan triple helix organizes surrounding water molecules into structures of differing orderliness in a wide space. This is contrasted with other biopolymers, which form no such structures except for bound water. Finally, it must be added that schizophyllan triple helix has an antitumor activity17,34,35 and is used to treat cervical cancer.17,35 So far the order-disorder transition for schizophyllan has been experimentally studied by optical rotation, heat capacity,

10.1021/bm0300251 CCC: $25.00 © 2003 American Chemical Society Published on Web 07/03/2003

Ordered Water Structures in Polysaccharide Solution

dielectric dispersion, and cholesteric pitch.12,13,28-33,36-39 It is also noted that the transition is highly cooperative from remarkable dependence on the polymer molecular weight.13,29,30 It has been shown13,29,30,40 that the molecular mechanism for this transition obeys the linear cooperative system of Zimm and Bragg41 and Nagai.42,43 From dielectric studies,12,36,37 water in aqueous schizophyllan solutions exists in different structures, which are classified into four different types, i.e., bound water, structured water, loosely structured water, and free water from the surface of the helix core to outward, which are in the increasing order of mobility. However, heat capacity and dielectric dispersion data so far obtained were not detailed enough to analyze such structures in quantitative terms. Therefore, we thought it worthwhile to make use of the concentration dependence of the transition behavior, for example, transition temperature and transition enthalpy, because each structure constitutes a narrow layer of a specific thickness around the surface of helix core, which may be determined separately from the concentration dependence. In this study, heat capacity measurements were done over a wide temperature range (5-315 K) and concentration range (10 concentrations 30.45-90.93 wt %) so that the transition behavior of aqueous schizophyllan would be completely covered. The resulting data are analyzed to elucidate the various water structures quantitatively with respect to the amount and orderliness. Dielectric dispersion data supplementing the heat capacity data will be discussed in a forthcoming publication.44 These techniques are highly sensitive to the state of water because of the large heat capacity and polarizability of water and expected to be particularly suitable for the present purpose.

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started after cooling the solution kept at 315 K for 2 days. Deionized H2O was used throughout all the measurements. Heat Capacity Measurements. Heat capacity measurements in the solution state were made between 265 and 315 K on 10 H2O solutions with different concentrations prepared as above by an adiabatic calorimeter following the procedure established before.45,46 Each time the energy input ∆E and the temperature difference ∆T obtained from temperature drifts before and after energy inputs were measured. The heat capacity Cp was calculated using the following equation: Cp ) [∆E/∆T - (CCell + CHe)](M0/w)/Ws

(1)

where CCell is the heat capacity of the cell and CHe is the contribution of helium gas in the cell. Cp is expressed in units of kJ K-1 mol-1, referring to one mole of repeat unit of schizophyllan (M0 ) 648.6 g mol-1). Measurements of Cp below the melting point of water were made in two different modes: quenched and annealed. In the quenched mode, the solution was rapidly cooled to about 4 or 80 K and heated at 0.5-3 K intervals up to 316 K by measuring the temperature drift on an adiabatic condition. In the annealed mode, the solution was first cooled to 235 K and kept around 235 K until the exothermic temperature drift due to the crystallization of the supercooled water disappeared and then cooled to about 4 or 80 K to start measurements. In each mode, the measurements were repeated more than twice with different temperature increases. In both cases, the cooling rate was faster than -50 mK s-1. Results

Experimental Section Schizophyllan Sample. Sonicated schizophyllan samples supplied by Taito Co. and a stock schizophyllan sample were purified and separated into three fractions by fractional precipitation from aqueous solutions with ethanol or acetone as the precipitant, and the middle fractions were further divided into three fractions. One of these middle fractions was subjected to liquid-crystal fractionation, yielding a middle fraction designated as OK-2A. Its weight average molecular weight MW and z-average molecular weight MZ in aqueous solution were determined at 25 °C on a Beckman Optima XL-I analytical ultracentrifuge equipped with a Rayleigh interference optical system (λ0 ) 675 nm) and charcoal-filled Epon 12-mm-double sector cells: OK-2A (MW ) 18.4 × 104, MZ/MW ) 1.3). Schizophyllan Solutions. The weight fraction w of schizophyllan in the starting aqueous solution of OK-2A was determined gravimetrically (w ) 0.3791). A weighed amount of this schizophyllan solution was put into a gold-plated copper cell (ca. 1.0 cm3) with helium gas at atmospheric pressure and covered with a lid using an indium seal. The amount Ws of the solution in the cell was determined gravimetrically (Ws ) 0.7223 g). The cell was assembled to the calorimeter after it had been kept at room temperature for one month. After each series of measurements, the solution was diluted or concentrated and equilibrated for one or two months. The measurements on each solution were

General Features of Heat Capacity Curves and Heat of Fusion. Figure 1 shows heat capacities Cp between 5 and 315 K for five H2O solutions of schizophyllan by weight between 37.91 and 90.93 wt %; unfilled and filled marks of Cp for all solutions refer to annealed and quenched solutions, respectively. The heat capacity data taken in the quenched mode are seen slightly above the annealed data between 150 and 250 K. In addition, exothermic relaxations on temperature drifts were observed in this temperature range, which suggests that part of the water crystallized during this process. The Cp curves for both 37.81 and 64.33 wt % solutions show large sharp peaks between 250 and 273 K. These peaks are due to the fusion of water in the solution. They are enlarged in the insert, where the dashed line for each solution represents the baseline, with the lower and higher parts being the heat capacities before and after the fusion peak, and the total baseline is approximated by the step function indicated. The enthalpy of fusion Ψfus(w) per gram of the solution was calculated from the energy input ∆E between 250 and 273 K minus the baseline contribution obtained by integrating the baseline curve. Let MP be the molecular weight of water, MPΨfus(0) corresponds to the molar enthalpy of fusion for water (6.007 kJ mol-1 for H2O47). Figure 2 shows MPΨfus(w) plotted against w, where the MPΨfus value at 14.54 wt % is the data of Itou et al.29 It is seen that MPΨfus(w) and w are linearly correlated as fitted by the straight line indicated, which crosses the abscissa at

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Figure 1. Heat capacities of H2O solutions of OK-2A. The concentrations of schizophyllan, wt %: O, b, 37.91; 4, 2, 64.33; 0, 9, 76.90; 3, 1, 83.13; ], 90.93. Dashed lines: baselines for the melting; dashdot lines, the sum of the contributions from solid schizophyllan and ice. Data points and curves are shifted upward by the figures in the parentheses for viewing clarity.

Figure 2. Heat of fusion MPΨfus(w) and number of unfrozen water molecules per schizophyllan repeat unit nB(w). MPΨfus(0) ) 6.007 kJ mol-1.47

w ) 0.7693. This point corresponds to the critical mixture consisting only of schizophyllan and unfrozen water. In fact, the Cp curve of the 76.90 wt % solution has a very small peak at the melting point, but those for 83.13 and 90.93 wt % show no such peak. Therefore, we can estimate the number of unfrozen water molecules per schizophyllan repeat unit (M0 ) 648.6 g mol-1) nB from this critical weight fraction to be 10.8. The water present in the solution consists of free water and unfrozen water, and MPΨfus(w) is due to free water. Assuming that nB(w) molecules of water per schizophyllan repeat unit form unfrozen water, MPΨfus(w) can be expresses as MPΨfus(w) ) MPΨfus(0)[1 - w(1 + nB(w)MP)/M0] (2)

Yoshiba et al.

Figure 3. Heat capacities in the order-disorder transition region of H2O solutions of schizophyllan with the indicated concentrations, wt %.

On this assumption, MPΨfus(w) is a linear function of w, which conforms to the data in Figure 2. This equation allows us to estimate nB(w) at each w from the experimental MPΨfus(w) and w. The insert in Figure 2 shows that the nB(w) values estimated in this way scatter closely about the above estimate 10.8. Thus, we conclude that unfrozen water exists as a layer of 0.183 nm in thickness (one - two water molecules) in the immediate vicinity of the triple helix, and these water molecules are bound around the helical groove of schizophyllan.48 Order-Disorder Transition Curves. In Figure 1, a small but clear peak is observed above the melting point for either the 37.91 or 64.33 wt % solutions. This peak corresponds to the order-disorder transition. Figure 3 shows heat capacity data of six aqueous solutions of schizophyllan with different concentrations between 265 and 315 K. All of the solutions could be supercooled down to 265 K without freezing considerably below the melting point of H2O. Either transition curve of the 30.45 or 43.49 wt % solution has a welldefined endothermic peak around 279 K and a slightly raising plateau at higher temperature. The transition curve at 37.91 wt % is the same except for the peak temperature Tr between them. These transition curves are quite similar to previous ones.29 It is concluded from this insensibility of Tr on w that the order-disorder transition is neither due to gelation nor to aggregation of schizophyllan but due to the organized water molecules with the side chain glucose residues, which form an ordered structure surrounding the helix core; this water is called structured water.12,13 However, it is seen that with increasing w the transition curve is shifted to higher temperature and changes its shape above 50 wt %. In fact, the Cp vs T curve of the 54.54 wt % solution is located at a significantly higher temperature compared with those ones below 43.49 wt %. On the other hand, the Cp vs T curve of 64.33 wt % has a sharp endothermic peak sandwiched by two clear flat portions, which correspond to the ordered state

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at lower temperature and the disordered state at higher temperature, respectively. The transition curve of 70.40 wt % has a lower peak height than those of the other schizophyllan solutions. Finally, Cp data of the 76.90 wt % solution show no transition peak in the temperature range examined. In addition to these changes of heat capacity data, temperature drifts (∆T/∆t) around Tr had a spontaneous endothermic relaxation at high concentrations in the transition region. It was found that the equilibrium temperature was not achieved instantaneously but by an interception with a long endothermic relaxation at 54.54 and 64.33 wt % in the transition region. The drift process over 50 min from the energy input was required to reach the equilibrium temperature. On the other hand, such abnormal temperature drifts were not found in heat capacity measurements below 37.91% solution between 270 and 315 K. Therefore, all heat capacity data in Figures 1 and 3 were obtained from temperature increase ∆T after the solution was kept standing at an adiabatic condition until these temperature drifts rates became -5 ∼ -15 mK h-1 which is a normal leak for our calorimeter in this temperature range. Discussions 1. Analysis of Transition Curves. Baselines for the Transition CurVes. To extract the information about the transition, it is convenient to treat the excess heat capacity CEp , the difference between Cp and contributions from water and schizophyllan (solid), which change monotonically with T in the temperature range concerned. Thus, CEp is defined by

[

CEp ) Cp - Cp,SPG + (1 - w)

( ) ] M0 C /w MP p,P

(3)

where Cp,P and Cp,SPG refer to the molar heat capacities of water47,49 and solid schizophyllan,13 respectively. The transition enthalpy ∆Hr of the order-disorder transition is determined from the integration of the difference between CEp and baselines. However, ∆Hr at the concentration below 43.49% has not been correctly determined from these data alone because a linear portion is not observed in lower temperatures as seen in Figure 3. Similar difficulties were seen in the previous data for lower concentrations.13,29,30 Let us consider that the triple helix of molecular weight M consists of three glucan chains of N polymer repeating units (N ) M/3M0), which exist either in the ordered state or in the disordered state. The excess molar enthalpy of the solution is expressed by the sum of the contribution from the two states using the fraction fN of the units in the ordered state and differentiated with respect to T to give the corresponding heat capacity CEp (T):13 CEp (T) ) -∆H∞r

( )

∂fN(T) + Cp,Base ∂T

(4)

with Cp,Base ) fN(T)Cp,Ord(T) + [1 - fN(T)]Cp,Dis(T)

(5)

Figure 4. Plots of CEP vs T for aqueous solutions of schizophyllan. O, 37.91 wt %; ], 64.33 wt %. Dotted lines: the baselines for the disordered state. Dashed lines: the baseline for the ordered state.

where ∆H∞r () HDis - HOrd) is the enthalpy of orderdisorder transition for infinite N. In eq 4, the first term in the right side is the transition heat capacity ∆Cs and the rest constitutes the baseline. Figure 4 shows typical CEp vs T curves of aqueous solutions of schizophyllan at two concentrations: 37.91 and 64.33 wt %. The transition curve of the 37.91 wt % solution has a well-developed flat portion at higher temperature, which is expected for Cp,Dis illustrated by a dotted line in Figure 4 and a sharp endothermic peak centered around 279 K, which is regarded as the transition temperature Tr. However, the complete ordered state for this solution is not still formed at lower temperature, because the low-temperature tails of the two curves do not agree with one another. The shape of this transition curve resembles the previous ones reported by Itou et al.29 for relatively dilute solutions of R-40 (MV ) 183 000; w < 0.2116) in water. On the other hand, the CEp curve for the 64.33 wt % solution has a sharp peak well above the melting point of H2O sandwiched by flat portions on both sides of the peak. These flat portions shown by dashed and dotted lines are regarded as the baselines for the ordered state Cp,Ord and disordered state Cp,Dis, respectively. No difference is seen in Cp,Dis at higher temperatures between the two solutions, which is regarded as the common baseline (dotted line) for the two solutions. Thus, it is reasonable that the 37.91 wt % solution has the same baseline at lower temperature as that of the 64.33 wt % solutions (dashed line) as shown. The entire baseline Cp,Base is constructed by combining Cp,Ord and Cp,Dis with fN according to eq 5. (See Figure 5.) Transition Temperature and Enthalpy. Figure 5 shows the transition curves for six solutions between 265 and 315 K, with the baseline estimated as above. The peak temperature has been taken as Tr, and the transition enthalpy ∆Hr has been calculated from the area between the CEp curve and the baseline (dash-dot line). These six transition curves are classified into three groups according to the polymer concentration: regions I-IV. Region I contains the curves for the 30.45 and 43.49 wt % solutions. They are very similar, although Tr is different only by 0.5 K between the

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Yoshiba et al. Table 1. Thermodynamic Parameters for H2O Solutions of Schizophyllan w 0.07825 0.1454 0.2116 0.3045 0.3791 0.4349 0.5454 0.5639 0.6433 0.7040 0.7690 0.8313 0.9093 1.000 a

Ψfus(w)a/J g-1

nB

271.0

10.43

169.6

10.66

52.07 2.009 0 0 0

11.22 10.53

0

∆Hr/J mol-1

Tr/K

ref

2810 3100 3150 3100 3100 2910 3040 3240 3150 2150 0 0 0 0

278.7 279.2 279.6 279.4 279.8 280.0 283.3 284.4 288.8 295.1

29 29 29

13

Heat of the fusion per gram of the solution. See the text.

Figure 5. Transition heat capacities in the three concentration regions. Region I: O, 30.45%; b, 43.49%. Region II: 4, 54.54%; 2, 64.33%. Region III: 0, 70.40%; 9, 76.90%. Dash-dot lines: baselines.

two solutions. The 37.91 wt % solution also belongs to this group with Tr between them. Thus, we see that there is virtually no concentration dependence in the transition at least up to 43.49 wt % in this region. The transition curves for the 54.54 and 64.33% solutions are in region II. They change their shapes and shift to higher temperature as w increases. Both of these transition curves cannot be described by the theory,40-43 which is successful for those in Region I.13 In addition to these changes, an endothermic relaxation on temperature drifts was observed between 284 and 295K for the 54.54 wt % solution and between 287 and 294K for the 64.33 wt % solution. Despite the changes mentioned, ∆Hr is constant in this region. The CEp data for the 70.40 and 76.90 wt % solutions in region III are illustrated at the bottom in Figure 5. In this region, the transition curve at 70.40 wt % has a small transition peak but that at 76.90 wt % shows only a trace of the transition. On the other hand, there is no transition peak above 76.90% in region IV. The results are summarized in Table 1. The values of Tr and ∆Hr so estimated are plotted against w in Figure 6. As shown in panel A, ∆Hr stays constant below w2 ) 0.644 in regions I and II and then decreases to vanish above w3 ) 0.769 in region III. This weight fraction is equal to the critical w estimated in Figure 2, where freezable water vanishes. In region I, the triple helices with the sheath of bound water, structured water, and loosely structured water are embedded in free water. Because the transition is concerned with the conversion between structured and loosely structured water, both Tr and ∆Hr should be constant up to w1() 0.478). To be consistent with these findings, the transition curves in region I are precisely described by the theory40 with ∆H∞r ) 3500 J mol-1, σ1/2 ) 0.01, N ) 94.6(Nz/Nw ) 1.2), and T∞r ) 282.0-282.5 K(cf. ref 13);50 σ1/2 is the transition probability between the ordered and disordered states and Nz and Nw are the z-average and weight-average values of N, respectively.

Figure 6. Transition enthalpy ∆Hr and transition temperature Tr as functions of w. Critical concentrations: w1 ) 0.478, w2 ) 0.644, and w3 ) 0.769. Straight lines: eye-guides.

Above w1, all of the solutions are crystalline,38,39 and helical polymers are aligned nearly parallel in the hexagonal packing. Therefore, at w1, the layers of loosely structured water start contacting each other, which are shared by adjacent helices sheathed with structured water, and shrink with increasing w in region II, but the thickness of structured water layer remains unchanged. This brings about the rise of Tr but keeps ∆Hr constant. This suggests that the ordered state is stabilized by some additional factor, yielding a higher Tr and the model does not work in this region. At w2, loosely structured water vanishes and structured water layers start contacting each other and decrease with w until they disappear at w3. Thus, ∆Hr decreases with w in region III. Thus, the number nB of water molecules per repeat unit of schizophyllan can be calculated from these critical concentrations: 10.8 for bound water from w3, 9.2 for structured water from w3 and w2, and 19 for loosely structured water from w2 and w1. Assuming that water molecules of these numbers form the corresponding cylindrical shells around the schizophyllan triple helix, whose diameter is 1.68

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Figure 7. Cross-sectional view of the schizophyllan triple helix in water. The repeat unit of the β-1,3-D-glucan of schizophyllan consists of three glucose residues and one side chain glucose residue, and only the red unit is shown in full. The circles represent the boundaries of the four water structures, with approximate diameters and critical weight fractions in the parentheses: helix core-bound water (1.68 nm, 1.0), bound water-structured water (2.05 nm, 0.769), structured water-loosely structured water (2.31 nm, 0.644), and loosely structured water-free water (2.79 nm, 0.478). Each cylindrical shell is marked in specific color.

nm,17 their thicknesses are calculated to be 0.183, 0.134, and 0.236 nm, respectively.48 This situation is illustrated schematically in Figure 7, where different structures are marked in different colors, with their boundaries by circles roughly to scale. These thickness values imply that the diameter of loosely structured water is 2.79 nm,48 which is consistent with the hydrodynamic diameter of 2.6 ( 0.4 nm derived from viscosity data.15 2. Structure Boundaries and Enthalpy Levels. It is wellknown that water has different kinds of phases under various conditions because of its hydrogen bonding ability. We have seen above that the aqueous schizophyllan solution has the ordered water structures around the triple helix: bound water and structured water and loosely structured water. These water structures of different orderliness are formed in layers around triple helix. We show that these structures may be regarded as different phases characterized by specific thermodynamic properties, namely, enthalpy and entropy, although not separately by clear interfaces. BehaVior in the Frozen State. As noted for D2O solutions of schizophyllan in the previous paper,13 the heat capacity of a solution in the frozen state is close to the sum of the contributions from solid schizophyllan and ice contained below 150 K. Figure 1 illustrates this test with the Cp data for the 37.91 and 64.33 wt % solutions. Here for each solution, the experimental data are represented by symbols, a dash-dot line represents the sum of the two contributions, and a dashed line is an extension of the data points at lower temperatures. The data points are seen to follow the dash-

dot line closely below about 150 K but deviate upward at higher temperature. This temperature may be compared with the glass transition temperature and is referred to as the glasslike transition temperature Tgl and can be detected from dCp/dT vs T plots.13,46,51 It was found that Tgl was around 150 K for all of the solutions examined and also for D2O solutions of w ) 0.4218 and 0.3064.13 It is considered that below Tgl in the glasslike state all of the species including bound water are frozen; frozen bound water may be almost indistinguishable from ice thermodynamically. At temperature above Tgl, part of frozen bound water is released to the liquidlike state, contributing to the upward deviation of CEp . This contribution is estimated from the area between the dash-dot line and dashed line, whereas that between the dashed line and the CEp curve is due to partial melting as noted earlier. With these findings, we assume that an H2O solution of schizophyllan in this temperature range consists of the following species with their weight fractions: schizophyllan (solid), w; ice (including frozen bound water), 1 - w - ξB(T)w; unfrozen (liquidlike) bound water, ξB(T) w. Then, the excess enthalpy HEX of the solution defined similarly to eq 4 is shown to be13 HEX(T) ) ξB(T)(M0/MP)∆HUP(T)

(6)

∆HUP(T) ) HUD(T) - HPI(T)

(7)

with

Here the subscripts “UD” and “PI” stand for unfrozen bound water (H2O or D2O) and ice (or glasslike bound water; H2O or D2O), respectively. Here HEX, H, and HSPG are given in units of kJ mol-1 of schizophyllan repeat unit and ∆HUP, HUD, and HPI in units of kJ mol-1 of water. On the other hand the excess heat capacity CEX is p obtained by differentiating eq 6 with respect to T with eq 7 as13 ∂ CpEX(T) ) (M0/MP) [ξB(T)∆HUP(T)] ∂T

(8)

Equations 6 and 8 indicate that it is impossible to estimate ξB(T) and ∆HUP(T) separately if they are both temperaturedependent. The Cp(T) data in Figure 1 have been used to estimate EX EX EX CEX p (T) and ∆H (T) [)H (T) - H (Tgl)]. The result is EX illustrated in Figure 8A, where CP (T) is given by symbols, which are extended to higher temperature by dashed lines; 52 These note that CEX p (Tgl) is small but not negligible. EX Cp (T) values are integrated from Tgl to T to obtain ∆HEX(T) ≡ HEX(T) - HEX(Tgl), as shown in Figure 8B. It is seen EX that both CEX P (T) and ∆H (T) are substantially independent of concentration below 76.90 wt %, and ∆HEX(T) approaches 34.8 ( 1.0 kJ mol-1 at Tm of 273.2 K. This is converted to ∆HUP(Tm) of 3.15 kJ mol-1 using the ξB(Tm) value of 0.301 obtained from nB of 10.8. This is 53% of the heat of fusion of H2O,47 which agrees with a similar estimate of 55% for the D2O solutions.52 Thus, we confirm the previous conclusion that bound water, which is frozen below Tgl, is completely released to the liquidlike state at Tm13 but is much more ordered compared with free water. In other words,

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Yoshiba et al.

CEp

Figure 8. (A) Excess heat capacities and (B) excess enthalpies ∆HEX for five solutions with different concentrations. Concentrations of schizophyllan, wt %: O, 37.91; 4 64.33; 0, 76.90; 3,83.13; ], 90.93.

bound water has a hard organized structure. This conclusion is consistent with dielectric dispersion data in the previous publication.12 At concentrations higher than 76.90 wt %, CEX p (T) at fixed T tends to decrease linearly with w. This is because bound water decreases in the same way. BehaVior in the Solution State. In the solution state, the structured water and the loosely structured water exist around the bound water layer along the helix core. If the contribution to H from the side chain glucose is negligible, eq 6 is modified to take into account explicitly the contributions from structured water and loosely structured water by using their enthalpies Hs and Hls and weight fractions wξs and wξls as

( )

M0 /w + MP M0 (ξBHB + ξsHs + ξlsHls) (9) MP

H ) HSPG + (1 - w - ξBw - ξsw - ξlsw)HP

( )

where HB is the enthalpy of bound water. Because the transition is concerned mainly with the conversion between structured water and loosely structured water, it is pertinent to correlate ξls and ξs by ξs ) fNξ0s ξls ) (1 - fN)ξ0s + ξ0ls

(10)

where wξ0s and wξ0ls express the weight fractions of structured and loosely structured water, respectively, at fN ) 1. Thus, the transition coverts wξ0s grams of structured water (ns ) (M0/MP)ξ0s moles per schizophyllan repeat unit) into loosely structured water. From eq 9, we obtain the enthalpy of transition ∆H∞r using eq 10 with fN ) 1 and 0 expressed as ∆H∞r ≡ HDis - HOrd ) ns(Hls - Hs)

(11)

This allows us to estimate Hs - Hls to be 380 J mol-1 using ns ) 9.2 and ∆H∞r ) 3500 J mol-1. Thus, if Hls or Hs is

Figure 9. Excess heat capacities CEP at 300 K in the disordered state plotted vs w.

given as a function of temperature, we can estimate the energy levels of these water structures. Differentiating eq 9 with respect to T and noting that fN ) 0 at TDis, we obtain the corresponding heat capacity CEp (TDis) in the disordered region as CEp (TDis) ) ∆CSPG p (solution - solid) + M0 ∂ ∂ ξ (T ) (H - HP) + (ξ0s + ξ0ls) (Hls - HP) (12) MP B Dis ∂T B ∂T

( )[

]

Figure 9 shows concentration dependence of CEp interpolated at 300 K in the disordered state; the data for 70.40 and 76.90 wt % solutions have not been used because their transition enthalpies decrease with w. It is seen that CEX p is independent of w even in region II, where the amount of loosely structured water decreases with w, and hence ξ0ls deceases with w. According to eq 12, this means that loosely structured water is indistinguishable from free water in heat capacity and hence in enthalpy. Therefore, we can estimate energy level of the structured water is lower by 380 J mol-1 from that of free water. This amounts to 6.33% of the heat of fusion of water. In addition, it is noted that structured water freezes at the melting point as shown in Figure 2. This means that structured water forms a soft ordered structure around the triple helix in the ordered state with a weak restriction compared with bound water and perceives sensitively thermal perturbations unlike bound water, which is rather hard and thermally stable. This is the reason Tr depends on w but ∆Hr does not in region II. (cf Figure 6) Enthalpy LeVels. As shown above, the enthalpy level of bound water at Tm measured from the glasslike state is lower than that of free water by 2.86 kJ mol-1. This is consistent with the finding that the dielectric relaxation time of the unfrozen bound water is considerably longer than that of liquid water but much shorter than that in the glasslike state or ice.12 Bound water in the glasslike state is indistinguishable from ice in heat capacity, indicating that the above enthalpy difference is very close to that between liquidlike bound water and ice. Figure 6 indicates the existence of loosely structured water in addition to free water, where ∆Hr and Tr change differently

Ordered Water Structures in Polysaccharide Solution

Figure 10. Enthalpy levels for various structures of water with reference to ice and free water at Tm ) 273.15 K. Ice, 0%; Frozen bound water, ≈0%; liquidlike bound water, 53%; structured water, 93.7%; loosely structured water, ≈100%; free water, 100%.

with w. Loosely structured water and free water are almost indistinguishable thermodynamically but have dielectric relaxation times differing nearly by a factor of 2.12 On the other hand, structured water and loosely structured water are separated by an enthalpy gap coming from ∆H∞r of 3500 J mol-1 which amounts to 380 J mol-1 of water. These considerations are summarized in Figure 10. It can be shown that each layer is arranged similarly in the order of increasing entropy. Although each layer is very thin, it seems to be characterized by a specific dielectric relaxation time as if it is a phase. This point will be pursued using dielectric dispersion data over a wide concentration range in the following publication.44 It is also tempted to consider the possibility of computer simulations, which are now in growing interest in biopolymer systems,4 because the triplehelical structure f schizophyllan is fairly well established.17,53 Acknowledgment. A. T. thanks Yamashita Sekkei Co. Ltd. for the Chair-Professorship at Ritsumeikan University. References and Notes (1) Eisenberg, D.; Kauzmann, W. The structure and properties of water; Clarendon Press: London, 1969. (2) Hasted, J. B. Prog. Bioelect. 1961, 3, 103-149. (3) Franks, F. The physics and physical chemistry of water. In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1982; Vol. 1. (4) Bergman, R.; Swenson, J. Nature 2000, 403, 283-285. (5) Eagland, D. Nucleic Acids, Peptides, and Proteins. In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1982; Vol. 4, Chapter 5, pp 305-518. (6) Grant, E. H.; McClean, V. E. R.; Nightingale, N. R. V.; Shepard, R. J.; Chapman, M. J. Bioelectromagnetics 1986, 7, 151-162. (7) Pethig, R. Annu. ReV. Phys. Chem. 1992, 43, 177-205. (8) Miura, N.; Asaka, N.; Shinyashiki, N.; Mashimo, S. Biopolymers 1994, 34, 177-205. (9) Wei, Y.-Z.; Kumbharkhane, A. C.; Sadeghi, M.; Sage, J. T.; Tian, W. D.; Champion, P. M.; Sridhar, S. J. Phys. Chem. 1994, 98, 66446651. (10) Scatena, L. F.; Brown, M. G.; Richmond, G. L. Science 2001, 292, 908-912.

Biomacromolecules, Vol. 4, No. 5, 2003 1355 (11) Bizzarri, A. R.; Cannistraro, S. J. Phys. Chem. B 2002, 106, 66176633. (12) Hayashi, Y.; Shinyashiki, N.; Yagihara, S.; Yoshiba, K.; Teramoto, A.; Nakamura, N.; Miyazaki, Y.; Sorai, M. Biopolymers 2002, 63, 21-31. (13) Yoshiba, K.; Teramoto, A.; Nakamura, N.; Miyazaki, Y.; Sorai, M.; Hayashi, Y.; Shinyashiki, N.; Yagihara, S. Biopolymers 2002, 63, 370-381. (14) Norisuye, T.; Yanaki, T.; Fujita, H. J. Polym. Sci. Polym. Phys. Ed. 1980, 18, 547-558. (15) Yanaki, T.; Norisuye, T.; Fujita, H. Macromolecules 1980, 13, 1462. (16) Kashiwagi, Y.; Norisuye, T.; Fujita, H. Macromolecules 1981, 14, 1220. (17) Yanaki, T. Thesis, Triple helices of β-1,3-D-glucans schizophyllan and scleroglucan in aqueous solution, Osaka University, Japan, 1984. (18) Norisuye, T. Makromol. Chem. Suppl. 1985, 4, 105-118. (19) Suggett, A. Polysaccharides. In Water: A ComprehensiVe Treatise; Franks, F., Ed.; Plenum Press: New York, 1982; Vol. 4, Chapter 6, pp 519-567. (20) Paradossi, G.; Brant, D. A. Macromolecules 1982, 15, 874. (21) Sato, T.; Norisuye, T.; Fujita, H. Polym. J. 1984, 16, 341. (22) Sato, T.; Norisuye, T.; Fujita, H. Polym. J. 1984, 16, 423. (23) Sato, T.; Norisuye, T.; Fujita, H. Macromolecules 1984, 17, 2696. (24) Coviello, T.; Kajiwara, K.; Burchard, W.; Dentini, M.; Crescenzi, V. Macromolecules 1986, 19, 2826-2831. (25) Norisuye, T. Macromol. Symp. 1995, 99, 31-42. (26) Nakanishi, T.; Norisuye, T. Polym. Bull. 2001, 47, 47-53. (27) Kido, S.; Nakanishi, T.; Norisuye, T.; Kaneda, I.; Yanaki, T. Biomacromolecules 2001, 2, 952-957. (28) Asakawa, T.; Van, K.; Teramoto, A. Mol. Cryst. Liq. Cryst. 1984, 166, 129-139. (29) Itou, T.; Teramoto, A.; Matsuo, T.; Suga, H. Macromolecules. 1986, 19, 1234-1240. (30) Itou, T.; Teramoto, A.; Matsuo, T.; Suga, H. Carbohydr. Res. 1987, 160, 243-257. (31) Kitamura, S.; Kuge, T. Biopolymers 1989, 28, 639-654. (32) Kitamura, S.; Ozawa, M.; Tokita, H.; Hara, C.; Ukai, S.; Kuge, T. Thermochim. Acta 1990, 163, 89-96. (33) Hirao, T.; Sato, T.; Teramoto, A.; Matsuo, T.; Suga, H. Biopolymers 1990, 29, 1867-1876. (34) Yanaki, T.; Ito, W.; Tabata, K.; Kojima, T.; Norisuye, T.; Takano, N.; Fujita, H. Biophys. Chem. 1983, 17, 337-342. (35) Okamura, K.; Suzuki, M.; Chihara, T.; Fujiwara, A.; Fukuda, T.; Goto, S.; Ichinohe, K.; Jimi, S.; Kasamatsu, T.; Kawai, N.; 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. (36) Teramoto, A.; Gu, H.; Miyazaki, Y.; Sorai, M.; Mashimo, S. Biopolymers 1995, 36, 803-810. (37) Miura, N.; Yagihara, S.; Mashimo, S.; Gu, H.; Teramoto, A. Proc. Jpn. Acad. Ser. B 1998, 74, 1-5. (38) Teramoto, A.; Yoshiba, K.; Nakamura, N.; Nakamura, J.; Sato, T. Mol. Cryst. Liq. Cryst. 2001, 365, 373-380. Itou, T.; Van, K.; Teramoto, A. J. Appl. Polym. Sci., Appl. Polym. Symp. 1985, 41, 35-48. (39) Yoshiba, K.; Teramoto, A.; Nakamura, N.; Sato, T. Macromolecules 2003, 36, 2108-2113. (40) Teramoto, A. Prog. Polym. Sci. 2001, 26, 667-720. (41) Zimm, B. H.; Bragg, J. K. Chem. Phys. 1959, 31, 526-535. (42) Nagai, K. J. Phys. Soc. Jpn. 1960, 15, 407-416. (43) Nagai, K. J. Chem. Phys. 1961, 34, 887-904. (44) Yoshiba et al. in preparation for Biomacromolecules. (45) Kume, Y.; Miyazaki, Y.; Matsuo, T.; Suga, H. J. Phys. Solid 1992, 53, 1297-1304. (46) Miyazaki, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. B 2000, 104, 8044-8052. This method is entirely different from DSC. (47) Haida, O.; Matsuo, T.; Suga, H.; Seki, S. J. Chem. Thermodyn. 1974, 6, 815-825. (48) The diameter d0 of schizophyllan triple helix is calculated to be 1.682 nm from the partial specific volume V0 in H2O of 0.619 cm3 g-1.15 Assuming that hydrated triple helices are in the closest packing, the diameter d of hydrated triple helix is related to d0 with nB by (d/d0)2 ) (V0M0 + nB MPVP)/V0M0, where VP is the partial specific volume of water. With nB ) 10.8, d is shown to be 2.05 nm, giving a value of 0.183 nm for the thickness of the cylindrical shell of bound water. In region II, loosely structured water is shared by neighboring triple helices with structured water on their outer sheathes, vice versa.

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(49) Nagano, Y.; Miyazaki, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. 1993, 97, 6897-6901. (50) (a) These are the theoretical values used to reproduce the experimental Cp data. Here ∆H∞r refers to an infinite chain and larger than ∆Hr, which is observed for a finite chain, whose terminals are disordered.13 (b) Yoshiba, K. Ph.D. Thesis, Ordering in Aqueous Schizophyllan Solutions, Ritsumeikan University, Japan, 2003. (51) Miyazaki, Y.; Matsuo, T.; Suga, H. Chem. Phys. Lett. 1993, 213, 303.

Yoshiba et al. (52) As seen in Panel A of Figure 8, every CEp curve has a small residue value at Tgl of 150 K. In the previous study,13 this small residual value was neglected in performing the integral, yielding a smaller ∆HEX of 33.1 kJ mol-1 than the present estimates. (53) Takahashi, Y.; Kobatake, T.; Suzuki, H. Rep. Prog. Polym. Phys. Jpn. 1984, 27, 767-768.

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