pubs.acs.org/Langmuir © 2009 American Chemical Society
Hydration of Lysozyme: The Protein-Protein Interface and the Enthalpy-Entropy Compensation Vitaly Kocherbitov* and Thomas Arnebrant Biomedical Laboratory Science and Technology, Faculty of Health and Society, Malm€ o University, SE-205 06 Malm€ o, Sweden Received August 27, 2009. Revised Manuscript Received October 28, 2009 Water sorption isotherms of proteins are usually interpreted with such models as BET or GAB that imply the formation of multilayers at solid-gas interface. However, this approach is not applicable to globular proteins such as humid lysozyme where a solid-gas interface does not exist. Another popular approach is the D’Arcy-Watt model, where besides the formation of multilayers the heterogeneity of energies of sorption sites of proteins is taken into account. Here we present sorption calorimetric data on the hydration of lysozyme that confirms the existence of the heterogeneity. The magnitude of the heterogeneity is, however, lower than one can expect on the basis of the existence of a solid-gas interface. Moreover, the calorimetric data show a strong enthalpy-entropy compensation that leads to almost constant effective free energy of hydration in the activity range normally used for fitting the data to sorption models. This allows the use of the Langmuir equation for the fitting of the initial part of the sorption isotherm of lysozyme. Assuming the formation of a monolayer of water at the protein-protein interface, one can estimate the size of the lysozyme molecules from the sorption isotherm. The result of this estimation is in good agreement with the structural data on lysozyme, which supports the presented approach.
Introduction It is now commonly agreed that the hydration of proteins strongly affects their function. Investigating the hydration of proteins is therefore an important part of protein science. The hydration of proteins can be studied by two different approaches. In one approach, protein-water interactions are studied in dilute solutions of proteins in water. In the other approach, changes in structural, dynamic, and thermodynamic properties of proteins are monitored as functions of water content at relatively low hydration levels. The latter approach is especially useful in thermodynamic studies of hydration. Changes in thermodynamic variables observed during the slow addition of water to protein are called partial molar quantities of the mixing of water with protein m dA ¼ ð1Þ Am w dnw T , P, np where Am is the change in thermodynamic potential A upon mixing with water and nw is the number of moles of water. The most studied partial molar value of mixing with water is the partial molar Gibbs energy of mixing m dG m ¼ μm Gw ¼ ð2Þ w ¼ RT ln aw dnw T , P, np because it is related to the activity of water, aw, that is relatively easily measured experimentally. Measurements of other partial molar quantities require more complex experimental approaches. For example, an assessment of the partial molar enthalpy of mixing of water Hm w (sometimes called the enthalpy of hydration) requires the differentiation of the water activity with respect *Corresponding author. Tel: þ4640 6657946. Fax: þ4640 6658100. E-mail:
[email protected]. (1) Kocherbitov, V.; Arnebrant, T.; Soderman, O. J. Phys. Chem. B 2004, 108, 19036.
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to temperature or the application of special calorimetric techniques.1,2 Sorption isotherms (water activity as a function of water content) of many proteins have been measured experimentally. Hen egg white lysozyme is probably the most popular protein for hydration studies, and its sorption isotherm is well established.1-5 Typically for proteins the sorption isotherm of lysozyme has a “sigmoidal” shape (i.e., the same shape as for the BET6 sorption isotherm). Several approaches have been used to model the sorption isotherm of lysozyme and other proteins. The BET6 model has two fitting parameters and assumes the adsorption of water at specific sorption sites and the formation of additional layers on top of the first adsorbed layer. The GAB7 model is based on similar assumptions but contains three parameters. The Hailwood and Horrobin model8 assumes the formation of a solid solution of the polymer, the polymer hydrate, and water. A model proposed by D’Arcy and Watt9 is the most often used model for the description of water sorption isotherms of proteins. Its main advantage is the ability to take into account the heterogeneity of sorption sites of the protein surface. Indeed, the protein surface contains different ionizable, polar, and nonpolar groups that may have different energies of interactions with water. The D’Arcy-Watt sorption isotherm consists of at least three terms h ¼ k1
k2 aw k4 k5 aw þ k 3 aw þ 1 þ k2 aw 1 -k5 aw
ð3Þ
where ki are the fitting parameters. The first and the second terms are two Langmuir terms that describe adsorption on sites with two (2) Smith, A. L.; Shirazi, H. M.; Mulligan, S. R. Biochim. Biophys. Acta 2002, 1594, 150. (3) Hnojewyj, W. S.; Reyerson, L. H. J. Phys. Chem. 1959, 63, 1653. (4) Hnojewyj, W. S.; Reyerson, L. H. J. Phys. Chem. 1961, 65, 1694. (5) Leeder, J. D.; Watt, I. C. J. Colloid Interface Sci. 1974, 48, 339. (6) Brunauer, S.; Emmet, P. H.; Teller, E. J. Am. Chem. Soc. 1938, 60, 309. (7) de Boer, J. H. The Dynamic Character of Adsorption, 2nd ed.; Clarendon Press: Oxford, U.K., 1968. (8) Hailwood, A. J.; Horrobin, S. Trans. Faraday Soc. 1946, 42, 84. (9) DArcy, R. L.; Watt, I. C. Trans. Faraday Soc. 1970, 66, 1236.
Published on Web 11/11/2009
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different energies, and the last term describes the multilayer adsorption. Because this equation features five fitting parameters, it provides a good fitting of experimental sorption isotherms of proteins. Even if the equation discussed above and other equations may provide good fitting of experimental data, all sorption models proposed so far have the same limitation. They do not take into consideration either a glass transition or structural changes in proteins that occur during hydration. It is now generally recognized that proteins undergo a glass transition upon increasing temperature or water content.10 Thus, water acts as a plasticizer. However, the exact mechanism of the glass transition is not fully understood. Although in native lysozyme the glass transition occurs over broad ranges of temperature and water content1 and therefore is difficult to register experimentally, in denatured lysozyme it occurs in a more stepwise fasion,11 similar to the glass transition in synthetic polymers. The heterogeneity of sorption sites (that exists in both the native and the denatured lysozyme) is therefore not the main factor that determines the properties of the glass transition. Structural changes that occur in proteins during hydration/ dehydration can also affect the water sorption behavior of proteins. There are reports that show that the R-helix and β-sheet contents of lyophilized proteins and those in aqueous solutions are different.12,13 The transition between the different conformations of proteins may cause a change in the number of available sorption sites as well as in the energy of interaction. None of these aspects are currently considered in the existing sorption models. In this work, we present experimental data on the sorption isotherm and the partial molar enthalpy and entropy of mixing of water with lysozyme. On the basis of the experimental data, we show that the mechanism of enthalpy-entropy compensation makes the heterogeneity of the sorption sites of lysozyme a less important factor for the interpretation of water sorption. On the contrary, the difference in the structure of dry lysozyme compared to that in dilute solution strongly affects its sorption behavior. Furthermore, the applicability of multilayer models is critically discussed. The aim of this work is not to propose an empirical equation that could be used for fitting the sorption isotherm over the entire range of water content but rather to understand the physical meaning of the sorption isotherm at low water content.
Materials and Methods Lysozyme. Hen egg white lysozyme was purchased from Sigma. The lysozyme sample was dried in vacuum at room temperature in contact with molecular sieves for at least 20 h before use. The transfer of the sample from the vacuum gun to the sorption calorimetric cell was performed in a dry nitrogen atmosphere. Sorption Calorimetry. Sorption calorimetric experiments were conducted at 25 °C in a 20 mm two-chamber sorption calorimetric cell inserted in a double-twin microcalorimeter.14 The samples under study were placed in the upper chamber, and pure water was injected into the lower chamber. In a sorption experiment, water evaporates from the lower chamber, diffuses through the tube that connects the two chambers, and is adsorbed by the sample in the upper chamber. The rate of water sorption in (10) Gregory, R. B. Protein-Solvent Interactions; Marcel Dekker: New York, 1995. (11) Kocherbitov, V.; Arnebrant, T. J. Phys.Chem. B. 2006, 110, 10144. (12) Griebenow, K.; Klibanov, A. M. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 10969. (13) Costantino, H. R.; Griebenow, K.; Mishra, P.; Langer, R.; Klibanov, A. Biochim. Biophys. Acta 1995, 1253, 69. (14) Wads€o, I.; Wads€o, L. Thermochim. Acta 1996, 271, 179.
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Figure 1. Sorption isotherm of lysozyme (-) and the Langmuir sorption isotherm (---). The parameters of the Langmuir sorption isotherm were obtained by fitting the experimental isotherm in the range of water activity of 0.1-0.4.
a sorption experiment can be controlled by selecting the diameter of the tube and by choosing the initial mass of the dry sample. For the present study, we selected a narrow tube and a relatively high sample mass. This combination provides a slow diffusion of vapor resulting in a hydration process close to equilibrium conditions. Moreover, to decrease the possible effect of the slow diffusion of water in a lysozyme sample (especially in the glassy state), the size of lysozyme particles was decreased by gentle grinding. The thermal powers released in the two chambers are monitored simultaneously. The activity of water aw in the sorption experiments was calculated from the thermal power of vaporization of water in the lower chamber as described in ref 15. The partial molar enthalpy of the mixing of water was calculated using the following equation Hwmix ¼ Hwvap þ Hwvap
Psorp Pvap
ð4Þ
where Pvap and Psorp are the thermal powers registered in the vaporization and sorption chambers, respectively, and Hvap w is the molar enthalpy of evaporation of pure water. The partial molar entropy of the mixing of water was calculated using the following equation: Swmix ¼
Hwmix - R ln aw T
ð5Þ
Results and Discussion Multilayers versus Monolayers. The water sorption isotherm of lysozyme measured in a sorption calorimetric experiment at 25 °C is shown in Figure 1. It has a sigmoidal shape typical for sorption isotherms of proteins and other hydrophilic biomolecules. Because special measures were taken to ensure a slow, closeto-equilibrium process of water sorption, the data presented in Figure 1 is closer to the equilibrium sorption isotherm than the data reported previously.1 The BET6 sorption isotherm has a similar shape and it is therefore widely used for the interpretation and fitting of experimental data on the sorption of water by biopolymers and porous materials.16 The BET model assumes that multilayers of adsorbed gas molecules form at the solid-gas interface before the (15) Kocherbitov, V. Thermochim. Acta 2004, 414, 43. (16) Kocherbitov, V.; Alfredsson, V. J. Phys. Chem. C 2007, 111, 12906.
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completion of underlying layers. Other models, such as GAB and D’Arcy-Watt, also assume the formation of multilayers on top of the first adsorbed layer. The multilayer assumption is reasonable for porous solid materials such as mesoporous silica,16 where a solid-gas interface exists. In these materials, the solid skeleton exists independently of the level of hydration. At low water activity, water adsorbs on the walls of silica (at the solid-gas interface), and at higher water activity, capillary condensation of water occurs in the pores. However, this scheme is not applicable to soft materials such as proteins and carbohydrates. The existence of a large solid-gas interface in such systems is not realistic because it would result in a very high surface energy. One can roughly estimate the Gibbs energy change corresponding to the formation of a proteinvacuum interface by multiplying the solvent-accessible surface area of the native form of lysozyme17 (6710 A˚2) by the surface tension of water (72 mJ/m2). The result is 2900 kJ/mol of lysozyme, which is much higher than the typical Gibbs energy values associated with structural changes in lysozyme. For example, the Gibbs energy change for the denaturation of lysozyme at 298 K is 60 kJ/mol.18 Therefore, to eliminate the interface with the gas, the biomolecules rearrange their positions and shapes. A comparison of the surface areas calculated using nitrogen and water sorption on biomolecules shows that the “nitrogen” areas are typically 2 orders of magnitude smaller than the “water” areas.19,20 Unlike water that can penetrate between biomolecules, nitrogen is adsorbed only on the existing solid-gas interface. This implies that multilayer models that assume the existence of a solid-gas interface should not be used to interpret the water sorption data of proteins. At high water contents, multilayers of water molecules between protein molecules can be formed. However, the mathematical description of these multilayers should be different from BET and similar models. At low water content, the formation of incomplete monolayers of water between protein molecules is expected. In what follows, we will use the monolayer assumption and show that the use of the Langmuir model provides a reasonable interpretation of the sorption isotherm of lysozyme at low water content. Protein-Protein Bond Disruption Compensation. Proteins have very heterogeneous surfaces, and on the surface of a globular protein one may find ionizable, strongly polar, weakly polar, and nonpolar groups. This implies that the energies of interaction of water with different groups on the surface of protein are different. Indeed, the enthalpy of hydration Hm w normally used as a measure of the strength of the waterbiomolecule interaction undergoes strong changes with changing water content (Figure 2). At very low water content, the Hm w value is low (exothermic heat effect), whereas at high water content it tends toward slightly endothermic values. This might be interpreted as a consecutive change in the hydration energies of ionizable, polar, and nonpolar groups of protein. The mathematical application of this idea is the D’Arcy-Watt model.9 However, the situation is more complicated. As we discussed above, the solid-gas interface does not exist in the case of proteins. In the dry state, protein molecules are in contact with each other and (17) Lee, B.; Richards, F. M. J. Mol. Biol. 1971, 55, 379. (18) Norde, W. Colloids and Interfaces in Life Sciences; Marcel Dekker: New York, 2003. (19) Hageman, M. J.; Possert, P. L.; Bauer, J. M. J. Agric. Food Chem. 1992, 40, 342. (20) Kocherbitov, V.; Ulvenlund, S.; Kober, M.; Jarring, K.; Arnebrant, T. J. Phys. Chem. B 2008, 112, 3728.
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m Figure 2. Partial molar Gibbs energy μm w , enthalpy Hw , and eff entropy Sm of the mixing of water with lysozyme. Δμ is defined w w in eq 15.
Figure 3. Hydration of the protein-protein interface. Plus and minus signs indicate positively and negatively charged groups, respectively. The groups marked with zeros are uncharged. The dipolar spheres represent water molecules.
different groups on the protein surface are in contact with other groups (Figure 3). For example, negatively charged groups of one molecule can be in contact with positively charged groups of another molecule. Therefore, hydration implies not only the formation of water-protein bonds but also the disruption of protein-protein bonds. As a result, the strongest heat effect observed in the hydration of lysozyme (about -20 kJ/mol) is much weaker than the energy of interaction of water with ionizable groups in vacuum. (For example, the energy of interaction of a sodium ion with one water molecule in vacuum is about -100 kJ/ mol,21 or -56 kJ/mol relative to the liquid water). Enthalpy-Entropy Compensation. The chemical potential of water in the bulk can be expressed via its activity: μw ðbÞ ¼ μow ðbÞ þ RT ln aw
ð6Þ
The chemical potential of water at the surface or at the interface can be expressed through the fraction of occupied sorption sites xw (see, for example, ref 22): μw ðsÞ ¼ μØ w ðsÞ þ RT ln
xw 1 - xw
ð7Þ
At equilibrium, the chemical potentials at the surface and in the bulk are equal; therefore, μow ðbÞ þ RT ln aw ¼ μØ w ðsÞ þ RT ln
xw 1 - xw
ð8Þ
(21) Dzidic, I.; Kebarle, P. J. Phys. Chem. 2002, 74, 1466. (22) Evans, D. F.; Wennerstrom, H. The Colloidal Domain: Where Physics, Chemistry, Biology, and Technology Meet; Wiley-VCH: New York, 1999.
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valid not only when μex w = 0 but also when it is constant. In the latter case, the parameter k in eq 9 has the following form: ex μo ðbÞ - μØ w ðsÞ - μw ðsÞ k ¼ exp w RT
!
-Δμeff w ¼ exp RT
! ð13Þ
Despite the fact that μex w (s) can be a constant, it should not be included in μL w(s) because its enthalpic and entropic contributions are in general not constant. The excess chemical potential at the surface μex w (s) can be obtained from eqs 6 and 12: o Ø μex w ðsÞ ¼ μw ðbÞ - μw ðsÞ þ RT ln aw - RT ln
xw 1 -xw
ð14Þ
The condition for the validity of the Langmuir equation expressed through experimentally observable parameters is then m m Δμeff w ¼ Hw - TSw - RT ln
Figure 4. Schematic structures of lysozyme in solution (top) and at a low hydration level (bottom). The structure of lysozyme in solution is from the protein database (193 L); water molecules are not shown. The low-hydration-level structure is for illustration purposes only and does not correspond to any experimentally obtained structure.
By rearranging eq 8, one obtains the Langmuir equation xw ¼
kaw 1 þ kaw
ð9Þ
where k is a constant dependent on the difference in the chemical potential of water in the bulk and at the interface: ! μow ðbÞ - μØ w ðsÞ k ¼ exp RT
ð10Þ
The constant k is usually considered to be an indicator of the strength of interaction between the adsorbent and adsorbate. Equation 10 shows that this constant is dependent not on the enthalpy of hydration Hm w but on the free energy of hydration μm w = RT ln aw. According to eqs 6 and 7, the difference between the standard chemical potentials in the bulk and at the interface corresponds to the transfer of a water molecule from a 50% complete monolayer to the pure bulk liquid water (or to vapor in equilibrium with the latter). Because m m μm w ¼ RT ln aw ¼ Hw -TSw
ð11Þ
the entropy plays an equally important role in the strength of adsorbent-adsorbate interactions, as does the enthalpy. Strictly speaking, eq 7 should include a term that describes the deviation from ideal behavior: xw ex μw ðsÞ ¼ μØ w ðsÞ þ μw ðsÞ þ RT ln 1 -xw μex w (s)
ð12Þ
is equal to zero when the mixing of occupied and The term unoccupied sites is ideal (i.e., the enthalpy of mixing is zero and the entropy of mixing is described by the last term of eq 12). These conditions are usually required for the application of the Langmuir equation (eq 9). However, the Langmuir equation is Langmuir 2010, 26(6), 3918–3922
xw ¼ const 1 - xw
ð15Þ
Figure 2 shows that the enthalpy and the entropy curves have pronounced slopes that compensate for each other and in combination with the monolayer ideal mixing term result in an almost constant value. A molecular interpretation of the enthalpy-entropy compensation effect in this case is the following. When adsorbed at a protein-protein interface, water may form four intermolecular bonds with polar or ionizable groups. For simplicity, we will call all such bonds hydrogen bonds although strictly speaking some of them are ion-dipole bonds. The interaction energies of water with different groups are different (i.e., the strengths of the hydrogen bonds are different). When water is adsorbed at a sorption site where all four hydrogen bonds are very strong, the hydration energy is very exothermic (negative). However, the probability that all four hydrogen bonds in a sorption site are very strong is low. This means that the entropy effect of adsorption at this type of site is strongly negative. When a water molecule is adsorbed at a site where not all four hydrogen bonds are very strong, the energy of hydration is higher (the strength of the interactions is weaker). The entropy of hydration that corresponds to adsorption at this type of site is higher because the number of such sorption sites is larger. An enthalpy-entropy compensation in the lysozymewater system was previously reported by L€uscher-Mattly and R€uegg.23 However, they did not interpret this phenomenon from the point of view of hydration of the proteinprotein interface. Langmuir Monolayer and the Size of the Lysozyme Molecule. The water-to-lysozyme mass ratio hw corresponding to the monolayer coverage obtained from fitting the sorption isotherm with the Langmuir equation in the water activity range of 0.1-0.4 is 0.184. By assuming the area of one water molecule to be 0.105 nm-2, one can calculate the Langmuir area using the equation AðLangmuirÞ ¼
hw Na 0:105 nm2 Mw
ð16Þ
where Na and Mw are Avogadro’s number and the molar mass of water, respectively. The result of this calculation is 645 m2/g. As we showed above, the adsorption of water to lysozyme should be considered to be adsorption at a solid-solid rather than (23) Luscher-Mattli, M.; Ruegg, M. Biopolymers 1982, 21, 419.
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a solid-gas interface. Therefore, the surface area of lysozyme is twice as high as the Langmuir surface area: AðsurfaceÞ ¼ 2AðinterfaceÞ ¼ 2AðLangmuirÞ
ð17Þ
The exact structure of lysozyme in the almost-dry state is unknown. However, it is known that it differs from the structure in solution because in the dry state the R-helix content is lower whereas the β-sheet content is higher than in solution.12,13 This further implies that the shape of a lysozyme molecule may be substantially distorted upon drying. Indeed, the native ellipsoidshaped lysozyme molecules would not be able to pack in a way that essentially eliminates the protein-gas interface. (The absence of such an interface follows from the comparison of water and nitrogen sorption results). Because the exact shape of lysozyme molecules in the dry state is unknown, we suggest (as a first approximation) that they obtain close to a cubic shape. Being simple, this approximation still satisfies the condition of the absence of a solid-gas interface: the cube is the only Platonic solid possessing the property of tessellation; in other words, it is able to fill the space. This approximation is also in reasonable agreement with the structural data on lysozyme. (In dilute aqueous solution, the lysozyme molecules are relatively spherical, which makes the cubic shape an expected outcome of a distortion of the molecules). The surface area of a cube related to its mass can be expressed as follows A ¼ 2AðLangmuirÞ ¼
2
6w 6 ¼ VdðlszÞ wdðlszÞ
ð18Þ
where V is the volume of a cube, w is its width, and d(lsz) is the density of a lysozyme molecule. The size of a cubic molecule can then be calculated from the area obtained from the Langmuir surface area: w ¼
3 AðLangmuirÞ dðlszÞ
ð19Þ
Assuming the lysozyme density to be 1.2 g/cm3, the size of the lysozyme molecule is 3.9 nm. A comparison of this number with the approximate dimensions of the lysozyme molecule24 from the protein data bank (3 nm 3 nm 5 nm) shows good agreement, which indicates that the assumptions used in the calculations here are correct. The monolayer coverage value of 0.184 g/g corresponds to 146 water molecules per lysozyme molecule, which is at least twice lower than the monolayer coverage values estimated using other methods.10 In connection to this, one has to note two important points. First, our number is related to the protein-protein interface, not the surface; therefore, when comparing with other data, it should be multiplied by 2. Second, our data reflects the (24) Vaney, M. C.; Maignan, S.; RiesKautt, M.; Ducruix, A. Acta Crystallogr., Sect. D 1996, 52, 505.
3922 DOI: 10.1021/la903210e
conformation of lysozyme at low water content, which differs from that in dilute solution. For example, the number of bound water molecules that we obtained using the method of desorption calorimetry25 is 420.1 Because this result was obtained during the desorption of water from solution, the protein molecules were in the same configuration as in the solution, not as in the dry powder. Thus, a monolayer of water at a protein-protein interface should not be assumed in the dehydration process. The 420 bound water molecules should in this case be interpreted as a monolayer coverage of every lysozyme molecule (perhaps plus some water to fill the voids in the bulk packing of the hydrated protein molecules). The approach presented here is the first attempt to develop a model of water sorption by a protein that is based on the nature of protein-water interactions, as opposed to the application of standard sorption theories (that are usually derived for adsorption at a solid-gas interface). This approach cannot be used to describe the sorption isotherm over the whole concentration range because the Langmuir equation is valid only in a limited concentration range. Further development of the approach presented here should include the change in the dynamics of the protein-water system occurring at higher water contents as well as the transition from the dry to the wet conformation of the protein.
Conclusions We have presented sorption calorimetric data on the hydration of hen egg white lysozyme and have discussed the applicability of different approaches to the description of the water sorption isotherms of proteins. Our conclusions are the following: • Sorption of water occurs at a protein-protein, not at a protein-gas, interface • Sorption models that assume the formation of multilayers at a protein-gas interface should not be used to describe the hydration of globular proteins • The enthalpy of hydration of lysozyme is strongly dependent on the water content, reflecting the heterogeneity of energies of the sorption sites of the protein • The heterogeneity of the energies at a protein-protein interface is, however, not as strong as it could be at a protein-gas interface • Enthalpy-entropy compensation leads to an almost constant effective free energy of hydration in a certain concentration range, which allows the use the Langmuir model in this concentration range • The result of the fitting of the sorption isotherm to the Langmuir model is in agreement with the structural data on lysozyme. Acknowledgment. Financial support from the Gustav Th Ohlsson Foundation is gratefully acknowledged. (25) Kocherbitov, V.; Wads€o, L. Thermochim. Acta 2004, 411, 31.
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