Low-Temperature Heat Capacity and Glassy Behavior of Lysozyme

Water Structures of Differing Order and Mobility in Aqueous Solutions of Schizophyllan, a Triple-Helical Polysaccharide as Revealed by Dielectric Disp...
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J. Phys. Chem. B 2000, 104, 8044-8052

Low-Temperature Heat Capacity and Glassy Behavior of Lysozyme Crystal† Yuji Miyazaki,* Takasuke Matsuo, and Hiroshi Suga‡ Research Center for Molecular Thermodynamics and Department of Chemistry, Graduate School of Science, Osaka UniVersity, Toyonaka, Osaka 560-0043, Japan ReceiVed: February 29, 2000; In Final Form: May 22, 2000

Heat capacities of tetragonal hen egg-white lysozyme crystals containing different amounts of water have been measured in the temperature region between 8 and 300 K. A broad glass transition was observed at about 150 K for the crystals with more than 24.0 wt % water content. These crystals also exhibited a spontaneous exothermic effect due to crystallization of the supercooled water contained in the crystals and melting process of the water above the glass transition temperature. The crystals containing 13.6 and 7.4 wt % of water gave rise to only a glass transition at 165 and 218 K, respectively. The fully dried crystal showed no thermal anomaly in the temperature up to 300 K. The amounts of the freezable and unfreezable water were estimated from the enthalpies of fusion of the crystal water. The water content dependence of the glass transition temperature and the magnitude of the excess heat capacity suggest that the observed glass transition arises from the cooperative motion between the segments of the lysozyme molecules and the bound water molecules.

1. Introduction It has been pointed out from recent researches1-5 that the biological activities of proteins are related closely with their three-dimensional structures and their slow fluctuating motion. Protein molecules have a large number of slightly different structures called conformational substates.6-9 They fluctuate over many conformational substates at physiological temperatures. This conformational fluctuation becomes slower and slower with decreasing temperature and finally frozen into a particular conformation. Freezing of the conformational motion of protein molecules is expected to be observed as a glass transition. Since the conformational degrees of freedom carry a significant part of the thermal energy of the protein molecule, their freezing into an immobilized state will result in substantial decrease of the heat capacity signifying a glass transition. The thermal dynamics of proteins in crystalline or noncrystalline state have been studied by Mo¨ssbauer spectroscopy,10-13 neutron scattering,14-17 optical spectroscopy,18-23 X-ray crystallography,24-28 dielectric measurement,29-32 molecular dynamics simulation,33-38 nuclear magnetic resonance (NMR),39-41 and calorimetry.42-49 It was found by differential scanning calorimetry (DSC)18,45-49 that hydrated myoglobin, hemoglobin, lysozyme, and cytochrome c undergo a glass transition around 170 K in common. Glass-like dynamical transitions are observed around 200 K for hydrated myoglobin,10-12,14,18,20,22,29 hemoglobin,13,22 ribonuclease A,27 and bacteriorhodopsin17 by various dynamical methods. Rasmussen et al.28 observed directly by X-ray crystallography that ribonuclease A in crystalline state loses the reactivity with an inhibitor below the dynamical transition at 220 K, around which the average Debye-Waller factors for all of the non* Corresponding author. Tel: +81-6-6850-5524. Fax: +81-6-6850-5526. E-mail: [email protected]. † Contribution No. 23 from the Research Center for Molecular Thermodynamics. ‡ Present address: Research Institute for Science and Technology, Kinki University, Kowakae, Higashi-Osaka 577-8502, Japan.

hydrogen atoms in ribonuclease A change their slope as a function of temperature.27 Ferrand et al.17 pointed out that there is a strong correlation between the change in the mean square displacement of the hydrogen atoms in the bacterorhodopsin as a funcition of temperature at 230 K and relaxation of the intermediate M state back to the ground state in the photocycle of the bacterorhodopsin.50 Such direct comparison of the different experiments concerning protein dynamics in the same situation is very useful for understanding the mechanism of protein functions. We can expect to obtain interesting information about protein dynamics by measuring the heat capacities of proteins in crystalline state by means of adiabatic calorimetry and by comparing with other experimental results such as the temperature change of the mean square displacement of the constituent atoms in crystalline proteins obtained by X-ray or neutron experiments.14,17,27 Water is undoubtedly an important ingredient in many protein crystals. Binding of water by proteins should alter the kinetic properties and structure of the water molecules. The binding alters, in turn, the hydrodynamic properties and structure of the protein molecules, including fluctuation among the conformational substates. Lowering the water content in all active living systems results in either dormancy or death. Water in the biological substances is often divided into “bound” and “free” water. A useful and unambiguous definition of bound water is not easy to settle. Most definitions used in the literature are the following: bound water is that water in the very vicinity of a macromolecule whose properties differ detectably from those of the “bulk” or free water in the same system. In view of the involved weak interactive forces between water and biological substances, however, it is unlikely to expect the existence of a sharp boundary which separates the bound water from the bulk water. One conventional and operational way from the thermodynamic point of view is to regard simply the bulk water as the the water that is freezable on cooling. In the present article, we report calorimetric observation of a glass transition for hydrated tetragonal hen egg-white lysozyme

10.1021/jp0007686 CCC: $19.00 © 2000 American Chemical Society Published on Web 07/28/2000

Heat Capacity of Lysozyme Crystal

J. Phys. Chem. B, Vol. 104, No. 33, 2000 8045

TABLE 1: Compositions, Molar Masses, and Masses of the Lysozyme Crystals Employed for the Calorimetry water content wt %

composition

M g mol-1

m(lysozyme) g

m(NaCl) g

m(H2O) g

m(total) g

45.7 41.0 36.4 31.6 24.0 13.6 7.4 0

lysozyme‚9NaCl‚693H2O lysozyme‚9NaCl‚571H2O lysozyme‚9NaCl‚471H2O lysozyme‚9NaCl‚381H2O lysozyme‚9NaCl‚260H2O lysozyme‚9NaCl‚129H2O lysozyme‚9NaCl‚66H2O lysozyme‚9NaCl

27323 25130 23316 21707 19516 17170 16020 14838

0.51397 0.51397 0.51397 0.51397 0.51397 0.56759 0.56759 0.56759

0.01883 0.01883 0.01883 0.01883 0.01883 0.02079 0.02079 0.02079

0.44827 0.36954 0.30440 0.24663 0.16796 0.09247 0.04686 0

0.98107 0.90234 0.83720 0.77943 0.70076 0.68085 0.63524 0.58838

crystals. We describe in detail the low-temperature heat capacity data of lysozyme crystals with different water contents and the amount of freezable water as determined by the enthalpy of fusion, and we discuss the nature of the glass transition based on a possible correlation with the amount of nonfreezable water existing in each protein crystal. An unexpected observation of an annealing-induced crystallization of a part of water in the crystal over a fairly long period is reported. The ability to detect any slow irreversible process is surely one of the characteristic features of adiabatic calorimetry. 2. Experimental Section Tetragonal lysozyme crystal was prepared following the method described by Jones.51 Hen egg-white lysozyme was purchased from Sigma Chemical Co. Lysozyme 3.6 g (2.5 × 10-4 mol) was dissolved in 100 cm3 of 0.5 mol dm-3 NaCl solution, and its pH was adjusted to 4.2 with HCl. The solution was put in dialyzing tubing and immersed in 2 dm3 of 1 mol dm-3 NaCl solution which was also adjusted to pH ) 4.2 with HCl. Crystallization took place in 4 days. The temperature was kept below 20 °C to avoid crystallization to the monoclinic phase.52 Colorless crystals precipitated at the bottom of the tube. They were filtered and the solution adhering to them was removed with filter paper. The amount of NaCl included in the dried sample was determined to be 3.53 wt % by atomic absorption spectrometry on Na+. This amount of NaCl is larger than the value 1.27 wt % reported for the air-dried crystal.53 We measured the heat capacities of eight samples with different water content: 45.7, 41.0, 36.4, 31.6, 24.0, 13.6, 7.4, and 0 (dried) wt %. The sample with 45.7 wt % water content is the virginal crystal obtained from the solution. The samples containing 41.0, 36.4, 31.6, and 24.0 wt % of water were the same crystals subjected to the heat capacity measurement after successive drying in air. The samples with 13.6 and 7.4 wt % of water were prepared from a portion taken from the same batch. The last sample was made by drying the sample with 7.4 wt % of water in vacuo until its weight became constant. The water content of the fully dried sample was regarded as 0 wt %. The water content of the other hydrated samples was determined from the mass difference relative to the fully dried sample. The composition, molar mass, and mass of the samples are tabulated in Table 1. Heat capacities of all the samples were measured in the temperature range from 8 to 300 K with an adiabatic microcalorimeter.54 The temperature was measured with a Rh-Fe alloy resistance thermometer (nominal 27 Ω, Oxford Instruments Co.) calibrated on the temperature scale EPT-76 (T < 30 K) and IPTS-68 (T > 30 K). The inaccuracy of the heat capacity determination based upon measurement of benzoic acid was within 1% at T < 30 K, 0.5% at 30 < T < 60 K, and 0.3% at T > 60 K. The samples were sealed in a 1.2 cm3 gold-plated copper cell together with helium gas at atmospheric pressure as a heat

Figure 1. Heat capacities per mole of lysozyme of the lysozyme crystals containing 45.7 (circles), 41.0 (triangles), 36.4 (squares), and 31.6 wt % (inverted triangles) of water. Heat capacities of crystals containing 45.7, 41.0, and 36.4 wt % of water are shifted upward by 30, 20, and 10 kJ K-1 mol-1, respectively. Open and closed marks indicate the heat capacities of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively. The inset shows the heat capacities in the vicinity of the peaks due to eutectic melting of NaCl‚2H2O and ice and fusion of ice. Heat capacities of crystals containing 45.7, 41.0, and 36.4 wt % of water are shifted upward by 300, 200, and 100 kJ K-1 mol-1, respectively.

exchange medium using an indium gasket. The heat capacity was measured on the samples which had been kept in the cell at room temperature for several days to allow them to attain hydration equilibrium. 3. Results and Discussion A. Heat Capacity. The heat capacities per mole of lysozyme of the lysozyme crystals are plotted in Figures 1 and 2. All of the samples were first cooled from room temperature at a rate of ca. 1 K min-1. We designate these samples as “quenched” for convenience. The heat capacities obtained on the quenched samples are plotted with open marks in Figures 1 and 2. The hydrated samples with the water content between 24.0 and 45.7 wt % had normal (i.e., vibrational) heat capacities below about 150 K, but above the temperature the heat capacities increased above the normal values. In the temperature region from 150

8046 J. Phys. Chem. B, Vol. 104, No. 33, 2000

Miyazaki et al. TABLE 2: Enthalpies of Fusion per Mole of Lysozyme of the Crystal Water and Amounts of Frozen and Unfrozen Crystal Water for the Lysozyme Crystals

Figure 2. Heat capacities per mole of lysozyme of the lysozyme crystals containing 24.0 (circles), 13.6 (triangles), 7.4 (squares), and 0 wt % (inverted triangles) of water. Heat capacities of crystals containing 24.0, 13.6, and 7.4 wt % of water are shifted upward by 15, 10, and 5 kJ K-1 mol-1, respectively. Open and closed marks indicate the heat capacities of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively.

to 190 K, endothermic temperature drifts were observed, which is a characteristic of a glass transition.55 Exothermic temperature drifts that usually precede a glass transition were not found. Between 190 and 235 K, the samples kept under the adiabatic condition heated spontaneously. This exothermic effect was caused by crystallization of a part of the water contained in the crystals. Eutectic melting of NaCl‚2H2O and ice56 and fusion of ice were observed at 255.0 and 269.4 K for the sample with 45.7 wt % of water, at 255.4 and 268.6 K for the sample with 41.0 wt % of water, at 254.4 and 267.1 K for the sample with 36.4 wt % of water, and at 253.3 and 256.0 K for the sample with 31.6 wt % of water. In the sample containing 24.0 wt % of water, only eutectic melting of NaCl‚2H2O and ice56 was observed at 249.5 K. These observed eutectic points of NaCl‚ 2H2O and ice coincided roughly with the literature eutectic point 252.0 K.56 The samples with water content of 31.6-45.7 and 24.0 wt % were annealed around 215 and 200 K (at which the exothermic effect was the largest), respectively, for a few days until the spontaneous heating ceased. The results on the annealed samples are plotted in Figures 1 and 2 with filled marks. A similar but less pronounced glassy anomaly was found around the same temperatures as observed in the quenched samples. The annealed samples also showed only endothermic temperature drifts between 150 and 190 K. The quenched samples containing 13.6 and 7.4 wt % of water also gave rise to a broad glass transition above about 165 and 220 K, but they did not indicate the exothermic effect which we assigned for more H2Orich samples to crystallization of water, the eutectic melting of NaCl‚2H2O and ice,56 and fusion of ice. The dried sample did

water content wt %

∆Hfus kJ mol-1

45.7 41.0 36.4 31.6 24.0 13.6 7.4

2.55 × 103 1.81 × 103 1.20 × 103 7.20 × 102 75.9 0 0

nH2O(frozen) nH2O(unfrozen) nH2O(total) mol mol mol 424 301 200 120 13 0 0

269 270 271 261 247 129 66

693 571 471 381 260 129 66

not show any of these thermal anomalies in the present temperature range. The heat capacities of the samples containing water between 31.6 and 45.7 wt % have double peaks associated with eutectic melting between NaCl‚2H2O and ice56 and melting of ice, while those of the sample containing 24.0 wt % of water have a single peak due to the eutectic melting. The melting point of the ice decreased as the water content of the lysozyme crystal decreased. This is caused by depression of the freezing point due to NaCl being included in the crystal water. The eutectic point of NaCl‚ 2H2O and ice, which should be independent of the concentration of the two-component system NaCl-H2O, also lowered as the water content decreased in smaller water content region less than 31.6 wt %. This depression occurs probably because of modified behavior of the eutectic melting in the presence of protein. B. Enthalpy of Fusion of Crystal Water. The enthalpies of fusion of the ice in the hydrated and annealed lysozyme crystals were evaluated per mole of lysozyme molecules as follows. For the sample with 45.7 wt % water content, two straight lines were fitted to the heat capacity data between 221 and 234 K and between 277 and 289 K, respectively. The normal heat capacities were determined by extrapolating the lower fitted line up to the eutectic point of NaCl‚2H2O and ice (255.0 K) and the upper fitted line down to the melting point of ice (269.4 K) and interpolating the normal heat capacities at 255.0 and 269.4 K linearly. The enthalpy of fusion was calculated by subtracting the contribution of the normal heat capacity from the whole enthalpy change, where correction for the enthalpy of dissolution of NaCl to the crystal water was made.57 The enthalpies of fusion of the samples with 31.6-41.0 wt % water content were evaluated in a similar way. As to the sample with 24.0 wt % water content, the normal heat capacities were determined by upward extrapolation from the heat capacity data between 200 and 215 K and downward extrapolation from those between 276 and 288 K to the eutectic point 249.5 K. From these evaluated enthalpies of fusion, the amount of frozen water was estimated with the literature enthalpy of fusion of water.58 The amount of unfrozen water was obtained by subtracting the amount of frozen water from the total water content. The enthalpies of fusion for the samples with 24.045.7 wt % water content are listed in Table 2 together with the amount of frozen and unfrozen water for all of the hydrated samples. This result reveals that there are at least two types of water in the hydrated lysozyme crystal: freezable water (free water) and unfreezable water (bound water). However, strictly speaking, the crystals with more than 24.0 wt % water content have two kinds of free water: rapidly freezable water and slowly freezable water, as seen from the existence of the exothermic effect due to freezing of a part of hydrating water above the glass transition temperature. We may call this effect the annealing-induced crystallization. The effect will result in smaller enthalpy of fusion for an experiment with a rapid heating

Heat Capacity of Lysozyme Crystal

Figure 3. Differential coefficients of the heat capacities of the lysozyme crystals containing 45.7 (circles), 41.0 (triangles), 36.4 (squares), and 31.6 wt % (inverted triangles) of water with respect to temperature. Differential coefficients of crystals containing 45.7, 41.0, and 36.4 wt % of water are shifted upward by 600, 400, and 200 J K-2 mol-1, respectively. Open and closed marks indicate the differential coefficients of the heat capacities of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively.

rate. The crystal retains bound water up to about 270 mol per mole of lysozyme or about 0.34 g per gram of lysozyme. This value is in good agreement with the other experimental results 0.40 g per gram of lysozyme by Mrevlishvili,59 0.3 g per gram of lysozyme by Harvey and Hoekstra,60 and 0.34 g per gram of lysozyme by Kuntz.61 The surfaces of the lysozyme molecules in the crystalline state are perhaps covered with a monolayer of the bound water with 320 molecules per molecule of lysozyme estimated by Yang and Rupley.62 C. Glass Transition. All of the wet lysozyme crystals exhibited a broad glassy thermal anomaly. To examine these glassy anomalies more closely, the heat capacities were differentiated with respect to temperature by repeatedly averaging a few heat capacity data and taking the difference of the neighboring averaged values. The random error was reduced by averaging two to three data points before calculating the difference. The temperature derivatives of the heat capacities for all of the samples are shown in Figures 3 and 4. Glass transition temperatures are usually determined as the temperature where an exothermic temperature drift turns to an endothermic one, because a heat capacity jump is observed around that temperature.55 However, only endothermic temperature drifts were observed at the glass transition. This is probably because the exothermic effect was thinly stretched over a wide temperature interval as a result of distributed relaxation time, as discussed below. Also, the long time (about 1 h) needed for one heat capacity determination was not favorable for detection of the exothermic effect. The absence of the exothermic effect is not intrinsic to the glass transition of a protein system.

J. Phys. Chem. B, Vol. 104, No. 33, 2000 8047

Figure 4. Differential coefficients of the heat capacities of the lysozyme crystals containing 24.0 (circles), 13.6 (triangles), 7.4 (squares), and 0 wt % (inverted triangles) of water with respect to temperature. Differential coefficients of crystals containing 24.0, 13.6, and 7.4 wt % of water are shifted upward by 300, 200, and 100 J K-2 mol-1, respectively. Open and closed marks indicate the differential coefficients of the heat capacities of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively.

TABLE 3: Glass Transition Temperatures of the Lysozyme Crystals water content wt %

Tg (quenched) K

Tg (annealed) K

45.7 41.0 36.4 31.6 24.0 13.6 7.4

148 151 152 150 149 165 218

152 148 155 153 152

Actually, an exothermic effect has been observed in another protein by fast cooling and rapid establishment of the adiabatic condition under which the drift rate is measured.63 Therefore, as indicated in Figures 3 and 4, the glass transition temperatures were taken as the intersection of the two fitted lines representing the regions above and below the glass transition temperature. The numerical values of the glass transition temperatures are given in Table 3. The glass transition temperature of ∼150 K for the samples with 24.0-45.7 wt % water content, in which the free water exists, is lower than that obtained by the DSC18,45-49 and the noncalorimetric experiments.10-14,17,18,20,22,27,29 The difference of this glass transition temperature is probably caused by the difference of the cooling rate and/or the observed time scale. As seen Figures 3 and 4, the magnitudes of the differential coefficients for the quenched crystals containing water greater than 24.0 wt % are larger than those for the annealed ones above the glass transition temperature. This, of course, corresponds to the larger increment of the heat capacities for the quenched

8048 J. Phys. Chem. B, Vol. 104, No. 33, 2000

Miyazaki et al.

Figure 5. Typical temperature drifts below and above the glass transition temperature. (a) and (b) indicate the temperature drifts for the lysozyme crystal containing 36.4 wt % of water around 144 and 165 K, respectively. Solid line in (b) shows the fitted curve by eq 1 in the text.

crystals than those for the annealed crystals above the glass transition temperatures. This implies that the glass transitions are closely related to the water included in the crystals, because the quenched samples gave rise to crystallization of a part of the supercooled water contained in them above the glass transition temperature and the glassy thermal anomalies became smaller when a small fraction of the crystal water was frozen on annealing. D. Relaxation Time. The rates of spontaneous heating and cooling of glassy substances found during each equilibration period around the glass transitions include useful information about the configurational relaxation time. The KohlrauschWilliams-Watts function64,65 is often used to analyze spontaneous temperature drifts associated with glass transition which have a distribution of the relaxation times. In the lysozyme crystals, only spontaneous endothermic temperature drifts were observed above the glass transition temperatures as seen in Figure 5. These endothermic temperature drifts seem to obey a Debye-type relaxation process, because the relaxation times are short, typically less than 1000 s. Therefore, to estimate the enthalpy relaxation times of the endothermic temperature drift, we used the following equation for a Debye-type relaxation:

T(t) ) A + Bt - C exp(-t/τ)

(1)

where T(t) is the calorimetric temperature at time t, A - C the initial temperature, B the temperature drift rate due to residual heat leakage, |C| the amplitude of the relaxation, and τ the relaxation time. The positive and negative values of C correspond to the exothermic and endothermic temperature drifts, respectively. We analyzed the temperature drift data only for the crystals with more than 24.0 wt % of water by using eq 1. For the less

Figure 6. Enthalpy relaxation times of the lysozyme crystals containing 45.7 (circles), 41.0 (triangles), 36.4 (squares), 31.6 (inverted triangles), and 24.0 wt % (diamond) of water. Open and closed marks indicate the relaxation times of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively.

hydrated crystals, the temperature drift rate was too small to give a significant value of the relaxation time. A typical result of the analysis is shown in Figure 5(b). The relaxation time was determined essentially from the curved part of the plot. The linear part at later times (t > 1000 s) in Figure 5(b) and the entire plot in Figure 5(a) are spurious effects due to heat leakage. The relaxation times thus derived are plotted in Figure 6. The activation enthalpy obtained from the plots is 8 kJ mol-1 at most. This is in gross disagreement with 50-70 kJ mol-1 based upon protein dynamics studies.7,44 Even though the possibility that the small activation enthalpy obtained here represents a genuine unbiased average dynamic property of lysozyme cannot be dismissed offhand, we consider another interpretation based upon distributed relaxation times. If the relaxation time is distributed over a certain interval of magnitude, an appropriate part of the relaxation spectrum will respond to the temperature change and contribute to the endothermic effect at each of the successive steps of the heat capacity determination. The relaxation times evaluated from the endothermic drift curves are essentially independent of the temperature since the different parts of the distributed relaxation times cause similar endothermic effects at different temperatures. We are inclined to this interpretation of the small value of the activation enthalpy. Together with the discussion about the absence of the exothermic effect presented above, this argues positively for the distribution of the relaxation times. E. Origin of the Glass Transition. We have seen above that the glass transitions of the hydrated lysozyme crystals have close relation to the presence of the water in the crystals. However, a question arises as to whether the glass transitions should be attributed to the motion of the water molecules alone or to the

Heat Capacity of Lysozyme Crystal

J. Phys. Chem. B, Vol. 104, No. 33, 2000 8049

Figure 7. Water content dependence of the glass transition temperature of the lysozyme crystals. Open and closed circles indicate the glass transition temperatures of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively.

combined effect of the lysozyme and the water molecules. Figure 7 shows the plot of the glass transition temperature against the water content represented as the amount per mole of lysozyme molecules. The glass transition temperature is constant at about 150 K for the water content above 260 mol and increases as the water content decreases below 260 mol. Since the crystals with water content greater than 24.0 wt % (i.e., 260 mol H2O/mol lysozyme) have a constant amount of the bound water (ca. 250 mol H2O/mol lysozyme), it follows that the glass transition temperature increases as the amount of the bound water decreases and does not depend on the amount of the free water. This effect can be explained as a plasticizing effect66,67 in that the hydrated water behaves as a plasticizer to enhance the protein flexibility. Consequently, the glass transitions in the lysozyme crystals are a result of immobilization of the cooperative dynamics of the conformations of the lysozyme molecules and the bound water molecules. We indicate another evidence that the motion of the lysozyme molecules as well as that of the bound water is associated with the glass transitions. The apparent heat capacity Cpl of the lysozyme component is defined as

Cpl ) Cp - nwC°pw - nsC°ps

(2)

where Cp is the heat capacity of whole system, C°pw and C°ps are the heat capacities of the pure water and sodium chloride, respectively, and nw and ns, the amounts of H2O and NaCl per mole of lysozyme, respectively. The whole heat capacity C°p of the ideal ternary lysozyme-H2O-NaCl system is

C°p ) C°pl + nwC°pw + nsC°ps

(3)

where C°pl is the heat capacity of the pure lysozyme. For the nonideal system, the excess heat capacity Cex p of the system is expressed by

Cex p ) Cp - C° p

(4)

Hence, the following equation is derived from eqs 2 to 4

Cex p ) Cpl - C° pl

(5)

Similarly, the apparent heat capacity Cpw of the H2O component can be expressed by

Figure 8. Apparent heat capacities per mole of lysozyme of crystalline water in lysozyme crystals containing 45.7 (circles) and 41.0 wt % (triangles) of water. Heat capacities of crystals containing 45.7 wt % of water are shifted upward by 30 kJ K-1 mol-1. Open and closed marks indicate the heat capacities of the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively. Solid and dotted lines show the heat capacity curves of the water in crystalline58 and glassy-liquid states,68-70 respectively. Dashed line shows the heat capacity curve of the free water in crystalline state58 plus the bound water in liquid state.68-70

Cpw ) (Cp - C°pl - nsC°ps)/nw

(6)

Thus, from eqs 3, 4, and 6, the excess heat capacity of the system is also given by

Cex p ) nw(Cpw - C° pw)

(7)

As seen from eq 6, the contribution from the H2O component to the heat capacities of the hydrated lysozyme crystals can be estimated by subtracting the heat capacity of the fully dried crystal from the entire heat capacity. Additivity of the heat capacity of the NaCl component was assumed to be ideal, that is, to give rise to no excess heat capacity. This is a good approximation, because the quantities of NaCl included in the crystals are small. The evaluated heat capacities of the H2O component are shown in Figures 8-10 and compared with the heat capacity of H2O in crystalline58 (solid line), liquid68,69 (dotted line for T > 228 K), and glassy states70 (dotted line for T < 228 K). The discontinuities in the heat capacity of liquid water at 133 and 228 K indicate the glass transition of liquid water70 and the stability limit of supercooled water,71 respectively. The apparent heat capacity of the H2O component is reproduced well by the heat capacity of ice below 100 K. This means that the lysozyme and H2O components in the wet crystals have the same heat capacities as those of the dried lysozyme crystal and ice, respectively, to a very good approximation in the temperature region below 100 K. However, at higher temperatures above the melting point of ice, the heat capacity of the H2O component

8050 J. Phys. Chem. B, Vol. 104, No. 33, 2000

Figure 9. Apparent heat capacities per mole of lysozyme of crystalline water in lysozyme crystals containing 36.4 (squares) and 31.6 wt % (inverted triangles) of water. Heat capacities of the crystals containing 36.4 wt % of water are shifted upward by 20 kJ K-1 mol-1. Open and closed marks indicate the heat capacities in the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively. Solid and dotted lines show the heat capacity curves of the water in crystalline58 and glassy-liquid states,68-70 respectively. Dashed line shows the heat capacity curve of the free water in crystalline state58 plus the bound water in liquid state.68-70

is larger than the heat capacity of liquid water. Also, in the temperature range between the glass transition and the eutectic melting, the heat capacity of the H2O component is greater than the calculated heat capacity (dashed lines in Figures 8-10) of the free crystal water in crystalline state58 plus the bound crystal water in glassy-liquid state.68-70 This shows the existence of the excess heat capacity in these temperature regions. The heat capacity of the H2O component would be between the heat capacities of ice and liquid water, and thus the maximum value would be equal to the heat capacity of liquid water. Hence, from eq 5, these excess heat capacities would indicate the minimum values of the differences between the heat capacities of the lysozyme in the hydrated and the dried crystals. In the dried crystals, the conformational motion of the lysozyme molecules is not excited at room temperatures because of the absence of the glass transition. Therefore it is excited above the glass transition temperatures for the hydrated crystals. Figure 11 shows the excess heat capacities of the hydrated samples calculated according to eq 7. The samples with water content more than 24.0 wt % have roughly the same excess heat capacities. But the excess heat capacities of the samples containing water less than 13.6 wt % become smaller as the water content decreases. As mentioned above, these excess heat capacities correspond to the contribution from the conformational motion of the lysozyme molecules. The same excess heat capacity for the samples with water content more than 24.0 wt % means that the same number of the hydrophilic groups probably associated with the conformational motion of the

Miyazaki et al.

Figure 10. Apparent heat capacities per mole of lysozyme of crystalline water in lysozyme crystals containing 24.0 (circles), 13.6 (triangles), and 7.4 wt % (squares) of water. Heat capacities of crystals containing 24.0 and 13.6 wt % of water are shifted upward by 20 and 10 kJ K-1 mol-1, respectively. Open and closed marks indicate the heat capacities in the crystals quenched from room temperature and those annealed above the glass transition temperature, respectively. Solid and dotted lines show the heat capacity curves of the water in crystalline58 and glassy-liquid states,68-70 respectively. Dashed line shows the heat capacity curve of the free water in crystalline state58 plus the bound water in liquid state.68-70

hydrated lysozyme molecules is excited thermally to the same extent. Two possibilities can be considered for the decrease in the excess heat capacity for the samples with water less than 13.6 wt % in response to the decrease of the water content: (i) the number of the thermally excited hydrophilic groups in the hydrated lysozyme molecules decreases since the water molecules are combined with the hydrophilic groups like islands, i.e., unevenly, and (ii) the same number of the hydrophilic groups as the case of the samples with greater than 24.0 wt % water content is less excited because of the higher activation energy or vibrational frequency. If the former possibility is the case, the heat capacity jump due to the glass transition should be smaller, but the glass transition temperature should remain the same. Since the glass transition temperature rises as the bound water content of the lysozyme crystal decreases, the latter explanation is plausible. Sartor et al.48 concluded that the glass transitions observed in hydrated myoglobin, hemoglobin, and lysozyme are mainly associated with the vitreous and freezable water and not with protein segments, although the water is structurally and dynamically modified by hydrophilic and hydrogen-bonded interaction with protein functional groups via the unfreezable water. However, our present results are understood well if both the dynamics of the lysozyme segments and those of the crystal water participate in the glass transition mechanism. The dynamics of the bound water are of course associated with the glass transition, but those of both the fast and slowly freezable water do not affect the nature of the glass transition, in other words,

Heat Capacity of Lysozyme Crystal

Figure 11. Excess heat capacities per mole of lysozyme of lysozyme crystals containing 45.7 (circles), 41.0 (triangles), 36.4 (squares), 31.6 (inverted triangles), 24.0 (diamond), 13.6 (plus), and 7.4 wt % (cross) of water.

the motion of the slowly freezable water influences the magnitude of the glass transition but not the glass transition temperature. We have found a glass transition at ∼180 K in hydrated monoclinic horse myoglobin crystals before.44 DSC measurements18,45-49 showed that the glass transition temperature of the globular proteins (myoglobin, hemoglobin, and lysozyme) is independent of the kind of protein. However, the glass transition temperature of the lysozyme crystals is different from that of the myoglobin crystals as revealed by adiabatic calorimetry.44 The glass transition of solvated proteins is often referred to as “slaved” glass transition,8 which means that the motion of proteins is “slaved” to that of the solvents surrounding the protein molecules so that glass transition temperature of the protein depends crucially on the solvent. In the case of the myoglobin crystals,44 the myoglobin molecules are surrounded by concentrated phosphate buffer solution. Thus, the glass transition temperature of the myoglobin crystals is higher than that of the lysozyme crystals because of the higher glass transition temperature of the phosphate buffer solution than that of the NaCl solution, in good agreement with the slaved glass transition picture. Acknowledgment. We thank Mr. Shigeru Tamiya of Central Workshop of Osaka University for analyzing Na+ included in the sample by atomic absorption spectrometry. Supporting Information Available: The heat capacities per mole of lysozyme of the lysozyme crystals containing 45.7, 41.0, 36.4, 31.6, 24.0, 13.6, 7.4, and 0 wt % of water are provided as Tables S1-S8. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Petsko, G. A.; Ringe, D. Annu. ReV. Biophys. Bioeng. 1984, 13, 331.

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