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Interpretation of water desorption isotherms of lysozyme
Interpretation of water desorption isotherms of lysozyme V. N. Morozov, T. Ya. Morozova, G. S. Kachalova and E. T. Myachin Institute of Biolooical Physics of the USSR Academy of Science, Pushchino, 142292, USSR
(Received 4 August 1987; revised 15 March 1988) The interrelationship between water desorption isotherms and the humidity dependences of the Young's modulus and volume strains of different lysozyme crystals and films has been analysed. The strain of protein samples is shown to be dependent on their elastic properties and to be induced by Laplace' s pressure which can be calculated from the Thomson (Kelvin) relation. The energy of the mechanical deformation of protein samples expended for repacking and deformation of protein molecules considerably contributes to the integral change of free energy upon dehydration. Solid protein samples should be considered as deformable porous materials whose water sorption isotherms are determined not only by the number and properties of individual hydration centres but also by the macroscopic properties of protein solids. Keywords: Hydration; lysozyme;water content
Introduction The role of water in maintaining the native structure of proteins and their ability to function has been studied most intensively on solid protein samples with controlled water content, such as crystals 1-3, amorphous films 4-6, lyophilized powders 7-9, pressed lyophilized powders 1°. The energy of interaction of water with different groups on the protein surface is usually calculated from water sorption isotherms 4'6 thus assuming that no other processes contribute to changes in the free energy of the system. However, as early as 1974, Kuntz and Kausman claimed that 'the measured quantities are properties of the water-protein system as a whole and cannot be solely ascribed to the water' since they reflect protein conformational changes and swelling effects 11. Although some authors deny the possibility of significant structural changes on dehydration 7'12'x3, the occurrence of small changes in conformation may be considered well documented at present. Thus, Chirgadze and Ovsepyan observed by the c.d. method a deformation of ~-helices in molecules of some proteins on their dehydration 14. Using laser Raman spectroscopy Yu and Jo registered changes in the conformation of both the main chain and side residues of lysozyme molecules in dry powder compared with solution 15. Using various techniques, Poole and FinneyS.S,16,17 obtained evidence indicating the distortions of the lysozyme secondary structure in the hydration range 0.08-0.2 g water/g protein, namely, some distortions in 0t-helical conformation and shifts of the side chain tryptophan residues. At water content lower than h = 0.08 g water/g protein they observed a distortion of disulphide bridges, i.e. a deformation of valent bonds. Preliminary X-ray analysis of partially dehydrated lysozyme crystals indicated that dehydration induces small changes in the packing of molecules inside the crystals as well as rotation and approach of domains is and a decrease in the mean atom-atom distances in the molecule (unpublished data). Surely, all these processes 0141-8130/88/060329--08503.00 © 1988Butterworth & Co. (Publishers)Ltd
require expenditure of energy and must contribute to the total energetics of dehydration. In order to elucidate how great are these expenditures, we performed parallel studies of the Young's modulus, deformation and hydration as a function of humidity for different crystals and amorphous films of lysozyme. Analysis of the results indicates that the dehydration-induced deformation of crystals occurs under the action of capillary forces and depends on the elastic properties of samples. The energy of mechanical deformation of the crystal and its constituent protein molecules makes a significant contribution to the total free energy changes upon dehydration.
Materials and methods Materials
Hen egg-white lysozyme from the Olainen factory or from Sigma was used without additional purification; 25 % aqueous glutaraldehyde solution was obtained from Reanal, other reagents were from Reachim, all analytical grade. Triclinic (PI), monoclinic (P21) and tetragonal (P43212) crystals were grown according to the procedure of SteinrauP 9. All the measurements were done using lysozyme crystals and films cross-linked with glutaraldehyde. Glutaraldehyde cross-linking of the crystals and amorphous films and preparation of samples for measuring the Young's modulus were the same as in Ref. 20. Prior to measurements, the crystals and microtome sections of the crystals were stored in solutions identical with those in which they were grown: triclinic and monoclinic crystals and amorphous films in 0.05 MNa acetate buffer, pH 4.5, 2 % NaNO 3; tetragonal crystals in 0.05 M Na acetate buffer, pH 4.7, 5 % NaCI. Hydration
This was determined from the changes in resonance frequency of a tungsten or quartz microneedle with a
Int. J. Biol. Macromol., 1988, Vol. 10, December
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Interpretation of sorption isotherms: V. N. Morozov et al. crystal or a piece of amorphous film on the top. The method enables the changes in the mass of a crystal (greater than 0.01 rag) to be recorded with an accuracy of o/ 0.1/o, and is described in detail elsewhere 21. The required relative humidity in the chamber was adjusted by CaC12 (A = 98-40 %) and LiC1 (A = 15 ~o) solutions or by passing through the chamber air-dried over melted CaC1z (A 1.5~) or silica gel (A~0.01%). To remove strongly bound water, the samples were dried at 130°C for 15 h.
application of the force to the parallel quartz rod (Z~ = Z ' I - Z ; ) were measured (see Figure 1). A simple calculation of the bending of the built-up cantilever beam with circular section of the quartz rod and rectangular section of the specimen yields the value of the relaxation modulus: Er =
37r" Zv" 13. D'*" /~q{16Z l • L3bh 3 [1 + 3(l/L)+ 3(ILL)2 - (alL} 3 - 3al(a + I)/L3] ~ -' ~1)
The method jbr measuring the dynamic Young's modulus, E d
This consists in analysing the transverse resonance vibrations (in a frequency range 1-100KHz) of a cantilever made of crystalline or amorphous samples clamped with micropincers, and placed into a humid thermostatically regulated chamber. The method and the construction of the improved chamber used in the study were described in detail earlier 2°'22. The accuracy of the measurements is approximately 5 °/0. Deformation of the crystalline and amorphous samples on dehydration This was measured directly by observing the changes in macroscopic dimensions of the samples under a microscope equipped with an eyepiece micrometer or by taking the X-ray patterns of (hk0), (hol) and (Okl) reciprocal-lattice sections with/~ = 15°. The accuracy of the first method was about 0.3 ~ for specimens 500/~m long. The lattice cell dimensions were measured with an accuracy of about 0.3-0.5 %. Microscopic measurements were performed in the humid chamber used for the Young's modulus and hydration measurements. For X-ray measurements a special cuvette, with two side inlets for changing CaC12 solution and vacuum drying crystals, was used that enabled one to vary the humidity inside the chamber by CaC12 solution without disturbing the adjustment of the crystal. The crystal was placed into a quartz capillary 10-15 mm from the CaC12 drop and sealed. X-ray patterns were taken daily at room temperature so long as there were changes in the lattice cell parameters at a given humidity. The method for measuring the relaxation Young's modulus at a constant load, Er This consists in analysing the transverse bending of a built-up cantilever beam designed as shown in Figure 1. It is made of the sample and a quartz rod 10-30#m in diameter, D. The sample, in the form of a rectangular plate 0.5-0.9mm long, b=20-40#m wide and h = 8 12 #m thick was dipped with one end into a drop of supercooled sulphur, 0.15-0.3 mm in diameter, and made it crystallize by touching with fine sulphur crystal seed. The solid sulphur drop with the sample was glued with cyanoacrylate adhesive to the quartz rod so that the specimen was parallel to the quartz rod, the free ends of the sample and the rod being at the same level. The construction was placed into the hermetically-sealed humid chamber described in Ref. 22. Using a second quartz rod mounted on a micromanipulator perpendicular to the cantilever beam, the latter was bent by loading the specimen. The deviation of the quartz rod along the line of action of the bending force (ZF) and the changes in the distance from the specimen at the point of
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Here Eo--63 G N m -2 is the Young's modulus of the quartz rod 22, L is the length of the quartz rod from the point of its attachment in the holder to the point of attachment of the specimen (usually 2-3 mm), l is the length of the specimen from the point of its attachment to the point of application of the force, a = 100-300 pm is the length of the rod that cannot bend due to the glue and sulphur drop. All distances and dimensions, except the thickness of the specimen, were measured with an eyepiece micrometer. The thickness was measured with a Linnik microinterferometer as described earlier 2°. The specimen was kept at room temperature under constant load for 15-24 h. The strain of the specimen reached the plateau within the first 6-8 h. The method is fairly simple but it does not provide a high accuracy, since the total contribution of the errors in determination of geometrical dimensions of the quartz rod, specimen, and their displacements under the action of load may cause a 203 0 ~ deviation of the result from the real value. All the measurements of hydration, Young's modulus and length were made at 25°C.
2
l,," 4
0
/,
II
3" i
/
4
Figure 1 Schematicrepresentation of the measurement of the relaxation Young's modulus Er by bending the built-up cantilever beam. 1, The sample; 2, quartz rod; 3, sulphur drops; 4, holders
Interpretation of sorption isotherms: V. N. Morozov et al. , I
", I
i
I
I
I 0.4
0.3
0.2
t
0.1
0
20
40
60
80
A (%)
Fisme 2 Water desorption isotherms of triclinic (--A--), monoclinic (--o--), tetragonal (--[3--) crystals and amorphous films (---O--) of hen egg-white lysozyme2t. Hydration is given as g water/g of dry protein sample. A is the relative humidity in ~o. The measurements were performed at 25°C. The samples are cross-linked with glutaraldehyde and soaked in the buffers the crystals were grown from. The films were soaked in 50 mM Na acetate, pH 4.5 with 2 ~ NaNOa. R.m.s. deviations of the mean values calculated from 5--15 experimental points on crystalline samples and from four points on amorphous ones are presented. The points without error bars are the mean values of two to three measurements
films (if we compared the data presented in Refs 4 and 21). Cross-linking of amorphous films may produce a considerable effect on swelling, elasticity and hydration only at a very high humidity where the cross-links will restrict an infinite swelling and transformation of the solid sample into solution. At A < 9 0 ~ all the properties of cross-linked crystals and amorphous films are mainly dependent upon the properties of protein molecules and direct van der Waals contacts between them 2°'21. The use of crystals as an object of hydration studies has the advantage over other solid protein samples in that it reveals the effect of packing of protein molecules on the form of water adsorption isotherms. Such a dependence is clearly seen when comparing the isotherms of monoclinic and triclinic crystals having the same amounts of intracrystalline water and grown from the same mother liquid. The different shape of the isotherm curves can be explained by no other reason than the different packing of molecules in these crystals. In reality (1) the different parts of the surface of the lysozyme molecule, i.e. different sites of water binding, are exposed to water in these two sorts of the crystals, and (2) the difference in the intermolecular contacts can determine different ability of protein molecules to change their arrangement within crystal, what, in turn, results in a different shrinkage of crystals on dehydration.
Deformation of crystals and films upon dehydration Figure 3 illustrates the results of equilibrium measurements, i.e. those made 1-3 days after keeping the
1.2
Results and discussion
Water desorption isotherms We will analyse only the results obtained upon dehydration of various solid specimens of lysozyme because they are more reproducible than those obtained on hydration of the same samples. The humidity dependence of the deformation, Young's modulus and hydration of crystal is well reproduced if the specimen is allowed to stand for a day in a corresponding buffer solution after drying. That the isotherm curves obtained on dehydration are closer to equilibrium that those obtained on hydration was demonstrated by LiischerMattli and Riiegg23. When studying the isotherms of ~chymotrypsin they showed that the hysteresis observed in the humidity range 0-100~o disappeared when the experiments were performed in the humidity range 1592 ~o, the isotherms in the latter case being coincident with the dehydration isotherms in the range 0--100~. The earlier obtained 2~ water desorption isotherms of different glutaraldehyde treated crystals and films of lysozyme soaked in salt solutions are given in Figure 2. It is clearly seen that the curves h(A) are similar to each other and to isotherms of powders and films of salt-free glutaraldehyde-untreated lysozyme obtained by other authors +'2+'25. An excess in the water content of our samples at A < 20 ~o is readily explainable by the presence of salt. The cross-linking itself was shown to change notably neither the total amount of water in lysozyme crystals 2~ nor the form of the isotherm curve of lysozyme
1.1
E o
1.0
0,9
0.8 o
20
40
60
80
100
A (%)
Figure 3 Humidity dependence of unit cell volume of triclinic (-A-), monoclinic ( - O - ) and tetragonal (-t3-) lysozyme crystals in cm3/g of protein. The volume was calculated from the X-ray data taking into account the number of molecules in the unit cell and the molecular weight of lysozyme of 14 300. The dehydration curves for triclinic and monoclinic crystals were obtained using one crystal in each case. The curve for the tetragonal crystal was obtained using five crystals with two to four measurement at different humidities for each crystal. In the top left comer, changes in the volume of amorphous films (in per cent of the volume of humid samples) calculated from the corresponding changes in linear dimensions measured under a microscope are given. R.m.s. deviations of the mean values calculated from four to eight points are presented. For other experimental conditions see the legend to Figure2
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Interpretation of sorption isotherms: V. N. Morozov et al. I Comparison between the experimental and calculated values of volume strain in the lysozyme tetragonal crystal at different humidities
Table
A (~)
PL (MPa)
97
0
90
9
80
22
70
36
60
54
0.01
-
E~ (GPa) 0.21 + 0.01 (8) 0.22+0.02 (9) 0.29 + 0.02 (6) 0.50+0.04 (5) 0.72+0.04 (5) 2.0 (2)
~v (%) Calcul. 0
~ (%) X-ray 0
-4.2
-2
- 9.4
- 7.9
- 13
- 15.2
- 16
- 19
-
- 32
~ (%) Optics 0 -3+2 (4) - 10 + 1.6 (7) - 15.3___+1.6 (6) - 17.4__+1 (7) - 28 + 1.2
(4)
Er relaxation Young's modulus averaged over the three main crystallographicdirections evis a volumestrain of the crystal in a slow (1-2 days at everyhumidity)dehydration process. The values werecalculatedaccording to (3) and (6) as a result of the effectof Laplace's pressure PL and were measured experimentallyby X-ray or optical methods. R.m.s. deviations of the mean values are presented together with the number of experimental points (in parenthesis)
samples at a given humidity, when the reflections in the Xray patterns ceased to shift. Earlier we have shown for tetragonal lysozyme crystals that the deformation of the crystal depends largely on the drying procedure 26. As the humidity was rapidly decreased to A=70-60~o the crystal could be converted to the metastable state from which it jumped spontaneously to the state which was equilibrium for the given humidity. On fast dehydration (15-20 min at each humidity value) the relative change in the volume of lysozyme tetragonal crystals at A = 7 0 ~ was ev = A V/V o = - 4.2 ~ whereas on slow dehydration (a day and more at each humidity value) ~ increased to -15.3 ~ at the same humidity. The shrinkage of the crystals is seen from Table 1 to be the same independent of whether the changes in the parameters of unit cell or in the dimensions of the sample were used to determine the shrinkage. It means that crystal defects of any kind do not contribute notably to the process. As seen in Fi#ure 3 and Table 1 the deformation of the crystals and films is great and occurs within the entire range of changes in the hydration level. This conflicts with the results of Golton (PhD thesis, London University, 1980), quoted in Ref 8, who noted that amorphous lysozyme films begin to swell markedly only at h > 0.3 g water/g protein. Despite the high value of deformation of the crystal unit cell which ranges from - 5 to - 15 ~o for different crystallographic directions, this shrinkage is reversible (on rehydration the cell dimensions are restored with an accuracy of 1 9/o) and retains unchanged the symmetry of space groups of the studied crystals. Comparison of the results presented in Figures 2 and 3 points to a correlation between the withdrawal of water from the crystal and its deformation, namely, the higher the ability of the crystal for deformation the more water it loses in the same humidity range. Comparison of the data for triclinic and monoclinic crystals shows that the deformation of crystals upon dehydration as well as hydration by itself depends on the packing of molecules in the crystal. However, it should be noted that the dehydrationinduced changes in the volume of the crystal do not
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coincide with the volume of the water withdrawn from lysozyme films and crystals (assuming that the partial specific volume of water in the crystal is equal to that in the bulk phase), as it is clear from comparison of the results presented in Figures 2 and 3. In the case of tetragonal crystals, these differences are particularly great. Thus, as the humidity is decreased to A = 85 ~o these crystals lose 0.15 g H 2 0 / g protein, i.e. about onethird of the total water present in the crystal whereas the specific volume of the crystal decreases by no more than 0.057cm3/g protein, which is 2.6-fold less than the volume of the withdrawn water in the bulk phase. With further decrease of humidity to 40 ~o the specific volume of the crystal changes by 0.28 cm3/g protein approaching the volume of the water lost is equal to 0.30 cma/g protein at this humidity. Such a behaviour indicates that the discrepancy between the volumes at A = 85 9/o is not an artefact which may result, for example, from evaporation of water from the surface or cracks of crystals, without changes in the volume of the unit cell. In other lysozyme crystals and films this discrepancy in the volumes also occurs, though it is not as great. The non-conformity of the volumes indicates convincingly that dehydration of lysozyme crystals and films, particularly at its early stages, induces a lowering of the packing density in the protein-water system. Simple estimates using the compressibility values know from the literature 27 have shown that the energy needed to homogeneously expand protein molecules and intracrystalline water would significantly exceed the total free energy of dehydration. Hence, the homogeneous expansion cannot account for this non-conformity of the volumes. It is assumed, therefore, that the lowering in the packing density is local and occurs, most likely, in water in the vicinity of waterexposed hydrophobic regions of the protein surface which may serve, in some way, as a nucleus for the vapour phase bubble. Surely, such a picture is not more than a macroscopic illustration of the phenomenon. The assumption of the lowering density of water near the hydrophobic regions at early stages of the dehydration is consistent with the modern conceptions of protein hydration according to which at h > 0.25-0.30 g water/g
Interpretation of sorption isotherms: K N. Morozov et al. I
I
I
I
6
hydrogen exchange of amide groups 9 and perturbations in the protein structure s'a'16,la are also observed. Since all these data point to the changes in the properties of the molecules one can relate the increase in the slope of E(h) at h < 0.22 g water/g protein to the increase in the rigidity of lysozyme molecules.
Thermodynamic of dehydration
Z ~4
Protein solid samples as deformable microporous materials
I.u
0
0.1
0.2
0.3
0.4
h (g/g)
Figure 4 Dehydration-induced changes in the elastic properties of differentsolid samples of lysozyme.(c3),dynamic Young's modulus, Ed, of tetragonal crystal along the direction [001] after long-term storage (1-2 days) at every humidity. (A), Ed of triclinic crystal along the [100] direction. (©), Ed of monoclinic crystal along the direction [010]. (e), Ed of amorphous films. (11) relaxation Young's modulus under constant load, Er, for the [001] direction of tetragonal crystal. R.m.s. deviations of the mean values calculated from 4-23 experimentsare presented. The points without error bars are the mean values of two to three measurements. For other experimental conditions see the legend to Figure 2 protein the hydration of polar groups comes to an end and the hydrophobic regions are getting covered with water due to the formation of water bridges between the water molecules which were earlier bound to polar groupsa' 1a.
Changes in the elastic properties of specimens on dehydration These are shown in Figure 4. It is seen that the value of the dynamic Young's modulus for tetragonal crystals is two to four times higher than the value of the relaxation modulus. Both relaxation and dynamic Young's moduli for all solid samples increase several times upon dehydration. The dehydration-induced increase in the Young's modulus of protein solids may be the result of both the shrinkage-induced increase in the surface and rigidity of intermolecular contacts and the increase in the rigidity of the protein globules themselves. As seen from Figure 4, E(h) consists of two linear parts with the break at h>0.17-0.22g water/g protein. At h>0.22g water/g protein different crystals and films show a similar Ed(h) dependence. In this range, solid protein samples behave like a composite material with the elastic properties depending on the protein-water ratio. Such a behaviour points to the independence of the elastic properties of lysozyme molecules on hydration in this range the changes in the intermolecular contacts being the main reason for Ed(h) dependence. The change in the character of the dependence occurs at h<0.22g water/g protein, i.e. a value at which, according to the literature data, a loss of the enzymic activity7'12'13, a significant decrease in the rate of
Water adsorption isotherms of protein samples are often used for estimating the energy of interaction of water with various groups on the protein surface4'6'11,23 It is assumed in these cases, directly or indirectly, that no other processes contribute to the energetics of water adsorption. However, this approach is valid only for a model in which water molecules are adsorbed by isolated non-interacting centres on the fiat rigid surface. Real protein solids are distinguished from such a model by three features. First, in a protein crystal the surface exposed to water is not a flat one but is a system of microcapillaries of great curvature. Considering that no more than a third of the protein surface is buried in the intermolecular contacts, one can estimate the specific area of the surface exposed to water in protein crystals to be 12" 103 m2/g protein, as in the best porous adsorbents. Second, the walls of these capillaries are capable to deform upon dehydration, which follows from the ability of protein crystals to shrink severely on dehydration, a feature known from the earliest works of Bernal et al. 2s. Third, as the result of deformation, the centres of binding of water may well be capable to interact with each other after dehydration to form new bonds. In view of these features, the total free energy of dehydration, AGo, must contain, apart from the dehydration energies of separate groups, AGh, several additional contributions inherent only in the aggregated state of the protein molecules: AGo = AGh + AG~ + AGd + AGw- AG~+ AGs + AGe
(1) Here, AGo is the change in the free energy caused by changes in the area of the water-vapour-protein interface, AGd is the change in the free energy expended for mechanical deformation of the crystal lattice and the protein molecules it consists of, AGw is the energy of uniform extension of water in capillaries under the action of capillary forces, AG, is the energy released during the formation of new bonds between the dehydrated centres of water binding. The latter two terms are inherent only in solid protein samples containing salts in the intracrystaUine liquid, AG~is the change in the free energy required for concentrating the intracrystalline salt solution, AGe is the energy spend for salt crystallization. The mechanosorptional effects which manifest themselves as swelling and shrinking of highly porous sorbents have long been known 29. However, until the present time they were not taken into account in the description of the sorption thermodynamics. Chernyak and Leonov a° were the first to stress recently the importance of taking into account the deformation of the sorbent in describing the sorption thermodynamics, and to analyse theoretically this complicated problem. However, up to now there was no experimental evidence
Int. J. Biol. Macromol., 1988, Vol. 10, December
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Interpretation of sorption isotherms: V. N. Morozov et al. for the importance of the mechanosorptional effects in energetics of real deformable sorbents. Using the data presented in the previous section, we shall show that protein solids are the objects in which the mechanosorptional effects are especially great.
Laplace's pressure as a major force inducing the shrinkage of solid protein samples upon dehydration Khachaturyan was the first to suggest that the deformation of a protein sample upon dehydration is induced by Laplace's pressure 31. This pressure arises from the difference in hydrostatic pressures between vapour and liquid under the concave meniscus. In a protein crystal, this pressure must result in an extension of water in capillaries and shrinking of the lattice of the protein globules. The Laplace's pressure can be calculated by the formula of Thomson (Kelvin):
RT In (P/Ps) Vm
PL = - - -
(3)
where Vmis the molar volume of water in the liquid phase, P is the pressure of water vapours at a given humidity; P~ is the pressure of saturated water vapours above the flat water surface at a given temperature. If the intracrystalline liquid is a salt solution, the pressure of vapours above the flat surface of the salt solution of the same composition, P~ must be used instead of P~ in equation (3). As the sample is dehydrated the composition of the intracrystalline liquid and, hence, the value of P~ in equation (3) would change. In order to estimate the salt concentration in the intracrystalline liquid at every humidity, we assumed that in a completely hydrated crystal, all the intracrystalline water has the same salt composition as the mother liquid has, except for the 'strongly' bound water which is inaccessible for salt. For the 'strongly' bound water we shall take here the water remaining in the crystal at A = 1.5 ~. The amount of the 'strongly' bound water thus calculated is 15-17 ~o of the total water in the crystal (see the water adsorption isotherms in Figure 1). This value is in a good agreement with the literature data indicating that about 20 ?/o of the total water in crystal is inaccessible for salt 32. In view of the aforesaid, the salt concentration in the intracrystalline liquid at humidity A can be calculated by the simple formula:
C(A )= Co[(ho - h 1)/(h(A)- h l)]
(4)
where ho is the amount of water in a completely hydrated crystal in the mother liquid, h(A) is the hydration level of the crystal at humidity A, h 1 is the hydration level at humidity A= 1.5 %, C o is the salt concentration in the mother liquid in g/100 g of water. After having calculated the value of C(A), one can find P'(A) from the tables and calculate the Laplace's pressure as a function of relative humidity, using equation (3). Given the Laplace's pressure, the volume strain in the crystal under the action of this pressure can be calculated and compared with the experimental value. To do this, one should know the value of the bulk modulus of the crystal, K. At the present time these data are lacking. However, K can be obtained from the relation for the moduli of isotropic solids: K =/~/3 (1 - 2#)
(5)
where /t is the Poisson coefficient, /~ is the Young's
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Int. J. Biol. Macromol., 1988, Vol. 10, December
modulus averaged over the three main crystallographic directions. The use of this relationship is justified by the negligible anisotropy of the studied protein crystals, the Young's modulus of which, according to our data, differ by no more than 30~o for different directions 33. Assume that the Poisson coefficient/~= 0.33, as in most polymer materials, and is independent of humidity. Since dehydration induces significant changes in the elastic properties of crystals, as it is seen in Figure 3, the volume strain of crystals can be calculated by integrating the parametric dependence K-1 versus Laplace's pressure:
~(A)=
_ (Pc,A)d p c ~o K
(6)
The results of the integration for lysozyme tetragonal crystals are presented in Table 1. The calculated values of the strain are seen to agree with the experimentally found within the limits of the error of measurement. This suggests that the dehydration-induced deformation of solid protein samples can actually be described as the result of the action of Laplace's pressure estimated by equation (3). Thus, the Laplace's pressure can be used for estimating the energy of mechanical deformation of crystal, AGdL.
Energy of dehydration-induced mechanical deformation of solid protein samples This can be estimated by two ways. The first method is integration of Laplace's pressure over the volume strain of crystal, e~, induced by dehydration: •
/%(m
AGdc= -..+",Vp Jo
PLd¢
(7)
where Vp is the volume of a unit cell per one protein molecule in a completely hydrated crystal, Xa is the Avogadro's number. Here and below the energy will be given per mole of protein. The second method of estimating AGa consists in the double integration of the bulk modulus, K, over the volume strain of the crystal:
AG~=.A/'~Vpf~A'fK(~,)de~d,
(8)
To do this, K(A) was calculated for every humidity by equation (5) and plotted in the form of the parametric dependence K(~,) against the volume strain ~,(A) at a corresponding humidity A.
Energy of concentraing the intracrystalline salt solution,
AG~ This was calculated by the expression:
AGs(A)=Mp- fh(A)A#dh
(9)
w Jh o
where Mp and Mw are the molecular weights of protein and water, respectively, Art = RT ln(P~/Ps) is the change in the chemical potential of water in the salt solution. P~(A) was calculated as described earlier when discussing the Laplace's pressure.
Integral changes in the free energy induced by dehydration of sample, AG Oper mole of protein These were calculated from water desorption isotherms by the expression:
Interpretation of sorption isotherms: V. N. Morozov et al. Table 2 Calculation of contributions of different processes to the total free energy change on dehydration of lysozyme tetragonal crystal= a (%)
AGo (ld/mol)
AGdL (kJ/mol)
AGd= (kJ/tool)
AGs (kJ/mol)
90 80 70 60 44 33
14 44 68 90 135 158
2.4 22 49 66 105 140
1.7 21 54 73
7 16 23 28 39 45
-
-
= All values of energy are given per mole of protein AGo is the total change of free energy induced by dehydration, calculated accordingto equation (10) AGs is the energy of concentrating the intracrystalline solution, calculated by equation (9) AGdL is the energy of crystal deformation calculated according to equation (7) as a work done by Laplace's pressure AGainis the sameenergycalculatedby equation(8) usingthe relaxation Young'smodulusand volumestrain on prolongedstorageof samplesat every humidity
Mp fh(A) A G o ( A ) = ~-~-. Jho
R T ln(P/P~)dh
(10)
Results and discussion The results of the calculations of AG o, AGs, AGdL and AGdm for tetragonal and triclinic lysozyme crystals are summarized in Table 2 and Fifure 5. The good agreement between the AGdLand AG~ values for tetragonal crystals calculated by the two different methods indicates a fairly high reliability of the estimates of AGd in spite of a few assumptions made independently in each method. This suggests also that similar calculation of the energy of deformation of a triclinic crystal under the action of the Laplace's pressure, AGdL, must yield a correct value of AGd. It should be noted that in calculating AGdLand AGdm one should use the values of the elastic properties and deformation of samples that were taken under the conditions similar to those under which water adsorption isotherms were taken. Since the samples are exposed to the long-term action of Laplace's pressure when taking isotherms, one should use the relaxation modulus, Er, and the strain obtained under prolonged stress, to calculate AGdm and AGdL. Otherwise, one can obtain erroneous results, as in calculation of AGdm of triclinic crystal for which the values of Er are lacking. It is seen from Figure 4 that substituting Ed (which may substantially exceed Er, as shown in Figure 4 for tetragonal crystals) for Er yields an overestimated AGain value. As a whole, comparing the value of AG Owith the sum AGd+AG~ for both triclinic and tetragonal crystals indicates that the sum of the two terms makes the main contribution to AGo throughout the humidity range for which the calculations are performed. Back to expression (2) for AGo, it may be concluded that the sum of the remaining terms of this equation is small. However, this does not necessarily mean that the terms AGh, AGa etc., are small by themselves, since they differ in sign. Such mutual compensation of dehydration energy of groups AGh and the energy of association of dehydrated groups AGa may be possible due to the ability of protein samples for deformation.
The great contribution of the energy of mechanical deformation of the lysozyme crystals and salt concentrating to the total change in the free energy upon dehydration suggests that their water sorption isotherm is also greatly dependent on the properties of the capillary system in protein sample, i.e. on its deformability, on hydrophobicity of capillary walls and on the composition and concentration of the intracrystalline solution. That is why the water uptake isotherm of the lysozyme crystals cannot be considered with in the framework of simple models based on water binding with isolated centres, as it has been commonly accepted 4'6'23. An essential question arises of whether and to what extent the conclusions drawn when dealing with lysozyme crystals are applicable to amorphous films and powders of lysozyme and to different solids of other proteins. As seen from Figures 2, 3 and 4, there are no fundamental differences between h(A), ~,(A) and Ed(A) dependences of lysozyme films and crystals. This means that the contribution of the energy of mechanical deformation to the total energy of dehydration of lysozyme films must be as great as in lysozyme crystals. Moreover, our experiments with crystalline and amorphous samples of eight different globular proteins have not shown any considerable differences of Ed(A) and ~,(A) dependences from those of lysozyme samples either 34'3s. Together with the well known similarity of hydration isotherms of different proteins, this suggests that the disjoining pressure substantiated here as the main factor inducing a humidity-dependent deformation, as well as the changes in the elasticity and energy of the lysozyme crystals must also act in all protein solids consisting of rigid native protein molecules which could not be packed without making a system of intermolecular capillaries filled with water. This water cannot leave the crystal 120 100
80 O
~E60
2o -i
0
0.1
0.2
0.3
h (g/g)
Figure 5 Contributions of different processes to free energy change upon dehydration of triclinic lysozyme crystals. (©), AGo, integral free energy of dehydration; (A), AGdL,energy of mechanical deformation of the crystal calculated as a work done by Laplace's pressure; (11), AGdm,the same energy calculated from the dynamic Young's modulus; (t~), AGs, the energy of concentrating the intracrystalline salt solution. All kinds of energy are given in kJ/mol protein. The calculations were made by formulae (10), (7), (8) and (9), respectively
Int. J. Biol. Macromol., 1988, Vol. 10, December
335
Interpretation of sorption isotherms: V. N. Morozov et al. without inducing the deformation of the crystal and its constituent molecules. The main difference between glassy and crystalline protein samples consists only in the absence of any translational and orientational long-range order in the arrangement of protein molecules as it follows from the data of neutron scattering 8 as well as from our unsuccessful attempts to discover any regularities in lysozyme and albumin films by low-angle X-ray scattering and by electron microscopy of protein film surface after fracturing. Unlike other inorganic and polymer glasses, protein films are amorphous at a supramolecular level only. As long as the protein globules retain their native rigid quasicrystalline structure and properties, such amorphous samples resemble rather polycrystalline materials or sintered powders. Apart from maintaining the capillary system, the rigidity of native protein globules generates the elastic restoring forces in amorphous samples as it does in crystalline ones, making the shrinkage, rigidity and water content changes reversible. The complete reversibility of the sorptiondesorption isotherms of chymotrypsin films has been recently demonstrated 2a. Thus, we can not see now any argument against the applicability of all the conclusions obtained on crystalline samples to amorphous protein samples. Suggesting protein powder to be a mixture of small particles of amorphous material the film consists of, we believe that the conclusion about the great contribution of the energy of the dehydration-induced deformation to the water desorption energetics is also valid for protein powders. As seen in Figure 5 and Table 2 in the hydration range between 0.15 and 0.22 g H20/g protein, the value of free energy of deformation per mole of protein becomes comparable with the energy of thermodynamic stability of proteins, and sufficient to induce perturbations in molecule structure. These perturbations may explain the change in the character of the dependence E(h) seen in Figure 4, the loss of enzymatic activity of lysozyme v' t 2.13 and other changes 5'8'9'16 discussed in detail in the introduction to this article. In conclusion, we should recognize that swelling and shrinkage of protein solids, when hydrated or dehydrated, influence water sorption isotherms greatly enough to make invalid any model description of hydration process that neglects the mechanosorptional effects.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Acknowledgements We are grateful to Drs Yu. M. L'vov, S. S. Khutsyan and A. G. Pogorelov for electron microscopy of our protein
films.
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Int. J. Biol. Macromol., 1988, Vol. 10, December
34 35
Finney, J. L. in 'Water: A Comprehensive Treatise', (Ed. F. Frank), Plenum, New York, 1979, Vol. 6, p. 47 Blake, C. C. F., Pulford, W. C. A. and Artymiuk, P. J. J. Mol. Biol. 1983, 167, 693 Edsall, J. T. and McKenzie, H. A. Adv. Biophys. 1983, 16, 53 Careri, G., Giansanti, A. and Gratton, E. Biopolymers 1979, 18, 1187 Poole, P. L. and Finney, J. L. Int. J. Biol. Macromol. 1983, 5, 308 Lfischer-Mattli, M. and R/iegg, M. Biopolymers 1982, 21,419 Careri, G., Gratton, E., Yang, P. H. and Rupley, J. A. Nature 1980, 284, 572 Finney, J. L. and Poole, P. L. Comments Mol. Cell. Biophys. 1984, 2, 129 Schinkel, J. E., Downer, N. W. and Rupley, J. A. Biochemistry 1985, 24, 352 Bone, S. and Pethig, R. J. Mol. Biol. 1985, 181,323 Kuntz, Jr, I. D. and Kauzmann, W. Adv. Protein Chem. 1974, 28, 239 Rupley, J. A., Yang, P.-H. and Tollin, U. in 'Water in Polymers', ACS Symposium Series, (Ed. S. P. Rowland), 1980, Vol. 127, p. 111 Rupley, J. A., Gratton, E. and Careri, G. Trends Biochem. Sci. 1983, 8, 18 Chirgadze, Yu. N. and Ovsepyan, A. M. Molec. Biol. (USSR) 1972, 6, 721 Yu, N.-T. and Jo, B. H. Arch. Biochem. Biophys. 1973, 156, 469 Poole, P. L. and Finney, J. L. Biopolymers 1983, 22, 255 Poole, P. L. and Finney, J. L. Biopolymers 1984, 23, 1647 Kachalova, G. S., Myachin, E. T., Morozov, V. N., Morozova, T. Ya., Vagin, A. A., Strokopitov, B. V. and Volkenstein, M. V. DAN USSR 1987, 293, 236 Steinrauf, L. K. Acta Crystallogr. 1959, 12, 77 Morozov, V. N. and Morozova, T. Ya. Biopolymers 1981,20, 451 Gevorkian, S. G. and Morozov, V. N. Biofizika (USSR) 1983, 28, 944 Morozov, V. N. and Gevorkian, S. G. Biopolymers 1985, 24, 1785 Lfischer-Mattli, M. and Riiegg, M. Biopolymers 1982, 21,403 Hnojewyi, W. S. and Reyerson, L. H. J. Phys. Chem. 1959, 63, 1653 Khurgin, Yu. I., Sherman, F. B. and Tusupkaliev, U. Biochemistry (USSR) 1977, 42, 490 Morozov, V. N., Morozova, T. Ya., Myachin, E. G. and Kachalova, G. S. Acta Crystallogr. 1985, IM1, 202 Sarvazyan, A. P. and Khrakoz, D. P. in 'Molecular and Cellular Biophysics', (Ed. G. M. Frank), Nauka, Moscow, 1977, p. 93 Bernal, J. D., Fankuchen, I., Perutz, M. Nature 1938, 141,523 Yates, D. J. C. in 'Adv. Catalysis and Related Subjects', (Eds D. D. Eley, P. B. Selwood and P. W. Weisz), Academic Press, New York, London, 1960, Vol. 12, p. 265 Chernyak, Yu. B. and Leonov, A. I. J. Colloid Interface Sci. 1986, 113, 504 Khachaturian, A, G. J. Exp. Theor. Phys. (USSR) 1977, 72, 1149 McMeekin, T. L. and Warner, R. C. J. Am. Chem. Soc. 1942, 64, 2393 Morozov, V. N. and Morozova, T. Ya. Biofizika (USSR) 1983, 28, 742 Morozova, T. Ya. PhD Thesis, Pushchino, Institute of Biol. Physics, USSR Academy of Science, 1983 Morozov, V. N. and Morozova, T. Ya. Molec. Biol. (USSR) 1983, 17, 577
(Received 4 August 1987; revised 15 March 1988) The interrelationship between water desorption isotherms and the humidity dependences of the Young's modulus and volume strains of different lysozyme crystals and films has been analysed. The strain of protein samples is shown to be dependent on their elastic properties and to be induced by Laplace' s pressure which can be calculated from the Thomson (Kelvin) relation. The energy of the mechanical deformation of protein samples expended for repacking and deformation of protein molecules considerably contributes to the integral change of free energy upon dehydration. Solid protein samples should be considered as deformable porous materials whose water sorption isotherms are determined not only by the number and properties of individual hydration centres but also by the macroscopic properties of protein solids. Keywords: Hydration; lysozyme;water content
Introduction The role of water in maintaining the native structure of proteins and their ability to function has been studied most intensively on solid protein samples with controlled water content, such as crystals 1-3, amorphous films 4-6, lyophilized powders 7-9, pressed lyophilized powders 1°. The energy of interaction of water with different groups on the protein surface is usually calculated from water sorption isotherms 4'6 thus assuming that no other processes contribute to changes in the free energy of the system. However, as early as 1974, Kuntz and Kausman claimed that 'the measured quantities are properties of the water-protein system as a whole and cannot be solely ascribed to the water' since they reflect protein conformational changes and swelling effects 11. Although some authors deny the possibility of significant structural changes on dehydration 7'12'x3, the occurrence of small changes in conformation may be considered well documented at present. Thus, Chirgadze and Ovsepyan observed by the c.d. method a deformation of ~-helices in molecules of some proteins on their dehydration 14. Using laser Raman spectroscopy Yu and Jo registered changes in the conformation of both the main chain and side residues of lysozyme molecules in dry powder compared with solution 15. Using various techniques, Poole and FinneyS.S,16,17 obtained evidence indicating the distortions of the lysozyme secondary structure in the hydration range 0.08-0.2 g water/g protein, namely, some distortions in 0t-helical conformation and shifts of the side chain tryptophan residues. At water content lower than h = 0.08 g water/g protein they observed a distortion of disulphide bridges, i.e. a deformation of valent bonds. Preliminary X-ray analysis of partially dehydrated lysozyme crystals indicated that dehydration induces small changes in the packing of molecules inside the crystals as well as rotation and approach of domains is and a decrease in the mean atom-atom distances in the molecule (unpublished data). Surely, all these processes 0141-8130/88/060329--08503.00 © 1988Butterworth & Co. (Publishers)Ltd
require expenditure of energy and must contribute to the total energetics of dehydration. In order to elucidate how great are these expenditures, we performed parallel studies of the Young's modulus, deformation and hydration as a function of humidity for different crystals and amorphous films of lysozyme. Analysis of the results indicates that the dehydration-induced deformation of crystals occurs under the action of capillary forces and depends on the elastic properties of samples. The energy of mechanical deformation of the crystal and its constituent protein molecules makes a significant contribution to the total free energy changes upon dehydration.
Materials and methods Materials
Hen egg-white lysozyme from the Olainen factory or from Sigma was used without additional purification; 25 % aqueous glutaraldehyde solution was obtained from Reanal, other reagents were from Reachim, all analytical grade. Triclinic (PI), monoclinic (P21) and tetragonal (P43212) crystals were grown according to the procedure of SteinrauP 9. All the measurements were done using lysozyme crystals and films cross-linked with glutaraldehyde. Glutaraldehyde cross-linking of the crystals and amorphous films and preparation of samples for measuring the Young's modulus were the same as in Ref. 20. Prior to measurements, the crystals and microtome sections of the crystals were stored in solutions identical with those in which they were grown: triclinic and monoclinic crystals and amorphous films in 0.05 MNa acetate buffer, pH 4.5, 2 % NaNO 3; tetragonal crystals in 0.05 M Na acetate buffer, pH 4.7, 5 % NaCI. Hydration
This was determined from the changes in resonance frequency of a tungsten or quartz microneedle with a
Int. J. Biol. Macromol., 1988, Vol. 10, December
329
Interpretation of sorption isotherms: V. N. Morozov et al. crystal or a piece of amorphous film on the top. The method enables the changes in the mass of a crystal (greater than 0.01 rag) to be recorded with an accuracy of o/ 0.1/o, and is described in detail elsewhere 21. The required relative humidity in the chamber was adjusted by CaC12 (A = 98-40 %) and LiC1 (A = 15 ~o) solutions or by passing through the chamber air-dried over melted CaC1z (A 1.5~) or silica gel (A~0.01%). To remove strongly bound water, the samples were dried at 130°C for 15 h.
application of the force to the parallel quartz rod (Z~ = Z ' I - Z ; ) were measured (see Figure 1). A simple calculation of the bending of the built-up cantilever beam with circular section of the quartz rod and rectangular section of the specimen yields the value of the relaxation modulus: Er =
37r" Zv" 13. D'*" /~q{16Z l • L3bh 3 [1 + 3(l/L)+ 3(ILL)2 - (alL} 3 - 3al(a + I)/L3] ~ -' ~1)
The method jbr measuring the dynamic Young's modulus, E d
This consists in analysing the transverse resonance vibrations (in a frequency range 1-100KHz) of a cantilever made of crystalline or amorphous samples clamped with micropincers, and placed into a humid thermostatically regulated chamber. The method and the construction of the improved chamber used in the study were described in detail earlier 2°'22. The accuracy of the measurements is approximately 5 °/0. Deformation of the crystalline and amorphous samples on dehydration This was measured directly by observing the changes in macroscopic dimensions of the samples under a microscope equipped with an eyepiece micrometer or by taking the X-ray patterns of (hk0), (hol) and (Okl) reciprocal-lattice sections with/~ = 15°. The accuracy of the first method was about 0.3 ~ for specimens 500/~m long. The lattice cell dimensions were measured with an accuracy of about 0.3-0.5 %. Microscopic measurements were performed in the humid chamber used for the Young's modulus and hydration measurements. For X-ray measurements a special cuvette, with two side inlets for changing CaC12 solution and vacuum drying crystals, was used that enabled one to vary the humidity inside the chamber by CaC12 solution without disturbing the adjustment of the crystal. The crystal was placed into a quartz capillary 10-15 mm from the CaC12 drop and sealed. X-ray patterns were taken daily at room temperature so long as there were changes in the lattice cell parameters at a given humidity. The method for measuring the relaxation Young's modulus at a constant load, Er This consists in analysing the transverse bending of a built-up cantilever beam designed as shown in Figure 1. It is made of the sample and a quartz rod 10-30#m in diameter, D. The sample, in the form of a rectangular plate 0.5-0.9mm long, b=20-40#m wide and h = 8 12 #m thick was dipped with one end into a drop of supercooled sulphur, 0.15-0.3 mm in diameter, and made it crystallize by touching with fine sulphur crystal seed. The solid sulphur drop with the sample was glued with cyanoacrylate adhesive to the quartz rod so that the specimen was parallel to the quartz rod, the free ends of the sample and the rod being at the same level. The construction was placed into the hermetically-sealed humid chamber described in Ref. 22. Using a second quartz rod mounted on a micromanipulator perpendicular to the cantilever beam, the latter was bent by loading the specimen. The deviation of the quartz rod along the line of action of the bending force (ZF) and the changes in the distance from the specimen at the point of
330
Int. J. Biol. Macromol., 1988, Vol. 10, December
Here Eo--63 G N m -2 is the Young's modulus of the quartz rod 22, L is the length of the quartz rod from the point of its attachment in the holder to the point of attachment of the specimen (usually 2-3 mm), l is the length of the specimen from the point of its attachment to the point of application of the force, a = 100-300 pm is the length of the rod that cannot bend due to the glue and sulphur drop. All distances and dimensions, except the thickness of the specimen, were measured with an eyepiece micrometer. The thickness was measured with a Linnik microinterferometer as described earlier 2°. The specimen was kept at room temperature under constant load for 15-24 h. The strain of the specimen reached the plateau within the first 6-8 h. The method is fairly simple but it does not provide a high accuracy, since the total contribution of the errors in determination of geometrical dimensions of the quartz rod, specimen, and their displacements under the action of load may cause a 203 0 ~ deviation of the result from the real value. All the measurements of hydration, Young's modulus and length were made at 25°C.
2
l,," 4
0
/,
II
3" i
/
4
Figure 1 Schematicrepresentation of the measurement of the relaxation Young's modulus Er by bending the built-up cantilever beam. 1, The sample; 2, quartz rod; 3, sulphur drops; 4, holders
Interpretation of sorption isotherms: V. N. Morozov et al. , I
", I
i
I
I
I 0.4
0.3
0.2
t
0.1
0
20
40
60
80
A (%)
Fisme 2 Water desorption isotherms of triclinic (--A--), monoclinic (--o--), tetragonal (--[3--) crystals and amorphous films (---O--) of hen egg-white lysozyme2t. Hydration is given as g water/g of dry protein sample. A is the relative humidity in ~o. The measurements were performed at 25°C. The samples are cross-linked with glutaraldehyde and soaked in the buffers the crystals were grown from. The films were soaked in 50 mM Na acetate, pH 4.5 with 2 ~ NaNOa. R.m.s. deviations of the mean values calculated from 5--15 experimental points on crystalline samples and from four points on amorphous ones are presented. The points without error bars are the mean values of two to three measurements
films (if we compared the data presented in Refs 4 and 21). Cross-linking of amorphous films may produce a considerable effect on swelling, elasticity and hydration only at a very high humidity where the cross-links will restrict an infinite swelling and transformation of the solid sample into solution. At A < 9 0 ~ all the properties of cross-linked crystals and amorphous films are mainly dependent upon the properties of protein molecules and direct van der Waals contacts between them 2°'21. The use of crystals as an object of hydration studies has the advantage over other solid protein samples in that it reveals the effect of packing of protein molecules on the form of water adsorption isotherms. Such a dependence is clearly seen when comparing the isotherms of monoclinic and triclinic crystals having the same amounts of intracrystalline water and grown from the same mother liquid. The different shape of the isotherm curves can be explained by no other reason than the different packing of molecules in these crystals. In reality (1) the different parts of the surface of the lysozyme molecule, i.e. different sites of water binding, are exposed to water in these two sorts of the crystals, and (2) the difference in the intermolecular contacts can determine different ability of protein molecules to change their arrangement within crystal, what, in turn, results in a different shrinkage of crystals on dehydration.
Deformation of crystals and films upon dehydration Figure 3 illustrates the results of equilibrium measurements, i.e. those made 1-3 days after keeping the
1.2
Results and discussion
Water desorption isotherms We will analyse only the results obtained upon dehydration of various solid specimens of lysozyme because they are more reproducible than those obtained on hydration of the same samples. The humidity dependence of the deformation, Young's modulus and hydration of crystal is well reproduced if the specimen is allowed to stand for a day in a corresponding buffer solution after drying. That the isotherm curves obtained on dehydration are closer to equilibrium that those obtained on hydration was demonstrated by LiischerMattli and Riiegg23. When studying the isotherms of ~chymotrypsin they showed that the hysteresis observed in the humidity range 0-100~o disappeared when the experiments were performed in the humidity range 1592 ~o, the isotherms in the latter case being coincident with the dehydration isotherms in the range 0--100~. The earlier obtained 2~ water desorption isotherms of different glutaraldehyde treated crystals and films of lysozyme soaked in salt solutions are given in Figure 2. It is clearly seen that the curves h(A) are similar to each other and to isotherms of powders and films of salt-free glutaraldehyde-untreated lysozyme obtained by other authors +'2+'25. An excess in the water content of our samples at A < 20 ~o is readily explainable by the presence of salt. The cross-linking itself was shown to change notably neither the total amount of water in lysozyme crystals 2~ nor the form of the isotherm curve of lysozyme
1.1
E o
1.0
0,9
0.8 o
20
40
60
80
100
A (%)
Figure 3 Humidity dependence of unit cell volume of triclinic (-A-), monoclinic ( - O - ) and tetragonal (-t3-) lysozyme crystals in cm3/g of protein. The volume was calculated from the X-ray data taking into account the number of molecules in the unit cell and the molecular weight of lysozyme of 14 300. The dehydration curves for triclinic and monoclinic crystals were obtained using one crystal in each case. The curve for the tetragonal crystal was obtained using five crystals with two to four measurement at different humidities for each crystal. In the top left comer, changes in the volume of amorphous films (in per cent of the volume of humid samples) calculated from the corresponding changes in linear dimensions measured under a microscope are given. R.m.s. deviations of the mean values calculated from four to eight points are presented. For other experimental conditions see the legend to Figure2
Int. J. Biol. Macromol., 1988, Vol. 10, December
331
Interpretation of sorption isotherms: V. N. Morozov et al. I Comparison between the experimental and calculated values of volume strain in the lysozyme tetragonal crystal at different humidities
Table
A (~)
PL (MPa)
97
0
90
9
80
22
70
36
60
54
0.01
-
E~ (GPa) 0.21 + 0.01 (8) 0.22+0.02 (9) 0.29 + 0.02 (6) 0.50+0.04 (5) 0.72+0.04 (5) 2.0 (2)
~v (%) Calcul. 0
~ (%) X-ray 0
-4.2
-2
- 9.4
- 7.9
- 13
- 15.2
- 16
- 19
-
- 32
~ (%) Optics 0 -3+2 (4) - 10 + 1.6 (7) - 15.3___+1.6 (6) - 17.4__+1 (7) - 28 + 1.2
(4)
Er relaxation Young's modulus averaged over the three main crystallographicdirections evis a volumestrain of the crystal in a slow (1-2 days at everyhumidity)dehydration process. The values werecalculatedaccording to (3) and (6) as a result of the effectof Laplace's pressure PL and were measured experimentallyby X-ray or optical methods. R.m.s. deviations of the mean values are presented together with the number of experimental points (in parenthesis)
samples at a given humidity, when the reflections in the Xray patterns ceased to shift. Earlier we have shown for tetragonal lysozyme crystals that the deformation of the crystal depends largely on the drying procedure 26. As the humidity was rapidly decreased to A=70-60~o the crystal could be converted to the metastable state from which it jumped spontaneously to the state which was equilibrium for the given humidity. On fast dehydration (15-20 min at each humidity value) the relative change in the volume of lysozyme tetragonal crystals at A = 7 0 ~ was ev = A V/V o = - 4.2 ~ whereas on slow dehydration (a day and more at each humidity value) ~ increased to -15.3 ~ at the same humidity. The shrinkage of the crystals is seen from Table 1 to be the same independent of whether the changes in the parameters of unit cell or in the dimensions of the sample were used to determine the shrinkage. It means that crystal defects of any kind do not contribute notably to the process. As seen in Fi#ure 3 and Table 1 the deformation of the crystals and films is great and occurs within the entire range of changes in the hydration level. This conflicts with the results of Golton (PhD thesis, London University, 1980), quoted in Ref 8, who noted that amorphous lysozyme films begin to swell markedly only at h > 0.3 g water/g protein. Despite the high value of deformation of the crystal unit cell which ranges from - 5 to - 15 ~o for different crystallographic directions, this shrinkage is reversible (on rehydration the cell dimensions are restored with an accuracy of 1 9/o) and retains unchanged the symmetry of space groups of the studied crystals. Comparison of the results presented in Figures 2 and 3 points to a correlation between the withdrawal of water from the crystal and its deformation, namely, the higher the ability of the crystal for deformation the more water it loses in the same humidity range. Comparison of the data for triclinic and monoclinic crystals shows that the deformation of crystals upon dehydration as well as hydration by itself depends on the packing of molecules in the crystal. However, it should be noted that the dehydrationinduced changes in the volume of the crystal do not
332
Int. J. Biol. Macromol., 1988, Vol. 10, December
coincide with the volume of the water withdrawn from lysozyme films and crystals (assuming that the partial specific volume of water in the crystal is equal to that in the bulk phase), as it is clear from comparison of the results presented in Figures 2 and 3. In the case of tetragonal crystals, these differences are particularly great. Thus, as the humidity is decreased to A = 85 ~o these crystals lose 0.15 g H 2 0 / g protein, i.e. about onethird of the total water present in the crystal whereas the specific volume of the crystal decreases by no more than 0.057cm3/g protein, which is 2.6-fold less than the volume of the withdrawn water in the bulk phase. With further decrease of humidity to 40 ~o the specific volume of the crystal changes by 0.28 cm3/g protein approaching the volume of the water lost is equal to 0.30 cma/g protein at this humidity. Such a behaviour indicates that the discrepancy between the volumes at A = 85 9/o is not an artefact which may result, for example, from evaporation of water from the surface or cracks of crystals, without changes in the volume of the unit cell. In other lysozyme crystals and films this discrepancy in the volumes also occurs, though it is not as great. The non-conformity of the volumes indicates convincingly that dehydration of lysozyme crystals and films, particularly at its early stages, induces a lowering of the packing density in the protein-water system. Simple estimates using the compressibility values know from the literature 27 have shown that the energy needed to homogeneously expand protein molecules and intracrystalline water would significantly exceed the total free energy of dehydration. Hence, the homogeneous expansion cannot account for this non-conformity of the volumes. It is assumed, therefore, that the lowering in the packing density is local and occurs, most likely, in water in the vicinity of waterexposed hydrophobic regions of the protein surface which may serve, in some way, as a nucleus for the vapour phase bubble. Surely, such a picture is not more than a macroscopic illustration of the phenomenon. The assumption of the lowering density of water near the hydrophobic regions at early stages of the dehydration is consistent with the modern conceptions of protein hydration according to which at h > 0.25-0.30 g water/g
Interpretation of sorption isotherms: K N. Morozov et al. I
I
I
I
6
hydrogen exchange of amide groups 9 and perturbations in the protein structure s'a'16,la are also observed. Since all these data point to the changes in the properties of the molecules one can relate the increase in the slope of E(h) at h < 0.22 g water/g protein to the increase in the rigidity of lysozyme molecules.
Thermodynamic of dehydration
Z ~4
Protein solid samples as deformable microporous materials
I.u
0
0.1
0.2
0.3
0.4
h (g/g)
Figure 4 Dehydration-induced changes in the elastic properties of differentsolid samples of lysozyme.(c3),dynamic Young's modulus, Ed, of tetragonal crystal along the direction [001] after long-term storage (1-2 days) at every humidity. (A), Ed of triclinic crystal along the [100] direction. (©), Ed of monoclinic crystal along the direction [010]. (e), Ed of amorphous films. (11) relaxation Young's modulus under constant load, Er, for the [001] direction of tetragonal crystal. R.m.s. deviations of the mean values calculated from 4-23 experimentsare presented. The points without error bars are the mean values of two to three measurements. For other experimental conditions see the legend to Figure 2 protein the hydration of polar groups comes to an end and the hydrophobic regions are getting covered with water due to the formation of water bridges between the water molecules which were earlier bound to polar groupsa' 1a.
Changes in the elastic properties of specimens on dehydration These are shown in Figure 4. It is seen that the value of the dynamic Young's modulus for tetragonal crystals is two to four times higher than the value of the relaxation modulus. Both relaxation and dynamic Young's moduli for all solid samples increase several times upon dehydration. The dehydration-induced increase in the Young's modulus of protein solids may be the result of both the shrinkage-induced increase in the surface and rigidity of intermolecular contacts and the increase in the rigidity of the protein globules themselves. As seen from Figure 4, E(h) consists of two linear parts with the break at h>0.17-0.22g water/g protein. At h>0.22g water/g protein different crystals and films show a similar Ed(h) dependence. In this range, solid protein samples behave like a composite material with the elastic properties depending on the protein-water ratio. Such a behaviour points to the independence of the elastic properties of lysozyme molecules on hydration in this range the changes in the intermolecular contacts being the main reason for Ed(h) dependence. The change in the character of the dependence occurs at h<0.22g water/g protein, i.e. a value at which, according to the literature data, a loss of the enzymic activity7'12'13, a significant decrease in the rate of
Water adsorption isotherms of protein samples are often used for estimating the energy of interaction of water with various groups on the protein surface4'6'11,23 It is assumed in these cases, directly or indirectly, that no other processes contribute to the energetics of water adsorption. However, this approach is valid only for a model in which water molecules are adsorbed by isolated non-interacting centres on the fiat rigid surface. Real protein solids are distinguished from such a model by three features. First, in a protein crystal the surface exposed to water is not a flat one but is a system of microcapillaries of great curvature. Considering that no more than a third of the protein surface is buried in the intermolecular contacts, one can estimate the specific area of the surface exposed to water in protein crystals to be 12" 103 m2/g protein, as in the best porous adsorbents. Second, the walls of these capillaries are capable to deform upon dehydration, which follows from the ability of protein crystals to shrink severely on dehydration, a feature known from the earliest works of Bernal et al. 2s. Third, as the result of deformation, the centres of binding of water may well be capable to interact with each other after dehydration to form new bonds. In view of these features, the total free energy of dehydration, AGo, must contain, apart from the dehydration energies of separate groups, AGh, several additional contributions inherent only in the aggregated state of the protein molecules: AGo = AGh + AG~ + AGd + AGw- AG~+ AGs + AGe
(1) Here, AGo is the change in the free energy caused by changes in the area of the water-vapour-protein interface, AGd is the change in the free energy expended for mechanical deformation of the crystal lattice and the protein molecules it consists of, AGw is the energy of uniform extension of water in capillaries under the action of capillary forces, AG, is the energy released during the formation of new bonds between the dehydrated centres of water binding. The latter two terms are inherent only in solid protein samples containing salts in the intracrystaUine liquid, AG~is the change in the free energy required for concentrating the intracrystalline salt solution, AGe is the energy spend for salt crystallization. The mechanosorptional effects which manifest themselves as swelling and shrinking of highly porous sorbents have long been known 29. However, until the present time they were not taken into account in the description of the sorption thermodynamics. Chernyak and Leonov a° were the first to stress recently the importance of taking into account the deformation of the sorbent in describing the sorption thermodynamics, and to analyse theoretically this complicated problem. However, up to now there was no experimental evidence
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Interpretation of sorption isotherms: V. N. Morozov et al. for the importance of the mechanosorptional effects in energetics of real deformable sorbents. Using the data presented in the previous section, we shall show that protein solids are the objects in which the mechanosorptional effects are especially great.
Laplace's pressure as a major force inducing the shrinkage of solid protein samples upon dehydration Khachaturyan was the first to suggest that the deformation of a protein sample upon dehydration is induced by Laplace's pressure 31. This pressure arises from the difference in hydrostatic pressures between vapour and liquid under the concave meniscus. In a protein crystal, this pressure must result in an extension of water in capillaries and shrinking of the lattice of the protein globules. The Laplace's pressure can be calculated by the formula of Thomson (Kelvin):
RT In (P/Ps) Vm
PL = - - -
(3)
where Vmis the molar volume of water in the liquid phase, P is the pressure of water vapours at a given humidity; P~ is the pressure of saturated water vapours above the flat water surface at a given temperature. If the intracrystalline liquid is a salt solution, the pressure of vapours above the flat surface of the salt solution of the same composition, P~ must be used instead of P~ in equation (3). As the sample is dehydrated the composition of the intracrystalline liquid and, hence, the value of P~ in equation (3) would change. In order to estimate the salt concentration in the intracrystalline liquid at every humidity, we assumed that in a completely hydrated crystal, all the intracrystalline water has the same salt composition as the mother liquid has, except for the 'strongly' bound water which is inaccessible for salt. For the 'strongly' bound water we shall take here the water remaining in the crystal at A = 1.5 ~. The amount of the 'strongly' bound water thus calculated is 15-17 ~o of the total water in the crystal (see the water adsorption isotherms in Figure 1). This value is in a good agreement with the literature data indicating that about 20 ?/o of the total water in crystal is inaccessible for salt 32. In view of the aforesaid, the salt concentration in the intracrystalline liquid at humidity A can be calculated by the simple formula:
C(A )= Co[(ho - h 1)/(h(A)- h l)]
(4)
where ho is the amount of water in a completely hydrated crystal in the mother liquid, h(A) is the hydration level of the crystal at humidity A, h 1 is the hydration level at humidity A= 1.5 %, C o is the salt concentration in the mother liquid in g/100 g of water. After having calculated the value of C(A), one can find P'(A) from the tables and calculate the Laplace's pressure as a function of relative humidity, using equation (3). Given the Laplace's pressure, the volume strain in the crystal under the action of this pressure can be calculated and compared with the experimental value. To do this, one should know the value of the bulk modulus of the crystal, K. At the present time these data are lacking. However, K can be obtained from the relation for the moduli of isotropic solids: K =/~/3 (1 - 2#)
(5)
where /t is the Poisson coefficient, /~ is the Young's
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modulus averaged over the three main crystallographic directions. The use of this relationship is justified by the negligible anisotropy of the studied protein crystals, the Young's modulus of which, according to our data, differ by no more than 30~o for different directions 33. Assume that the Poisson coefficient/~= 0.33, as in most polymer materials, and is independent of humidity. Since dehydration induces significant changes in the elastic properties of crystals, as it is seen in Figure 3, the volume strain of crystals can be calculated by integrating the parametric dependence K-1 versus Laplace's pressure:
~(A)=
_ (Pc,A)d p c ~o K
(6)
The results of the integration for lysozyme tetragonal crystals are presented in Table 1. The calculated values of the strain are seen to agree with the experimentally found within the limits of the error of measurement. This suggests that the dehydration-induced deformation of solid protein samples can actually be described as the result of the action of Laplace's pressure estimated by equation (3). Thus, the Laplace's pressure can be used for estimating the energy of mechanical deformation of crystal, AGdL.
Energy of dehydration-induced mechanical deformation of solid protein samples This can be estimated by two ways. The first method is integration of Laplace's pressure over the volume strain of crystal, e~, induced by dehydration: •
/%(m
AGdc= -..+",Vp Jo
PLd¢
(7)
where Vp is the volume of a unit cell per one protein molecule in a completely hydrated crystal, Xa is the Avogadro's number. Here and below the energy will be given per mole of protein. The second method of estimating AGa consists in the double integration of the bulk modulus, K, over the volume strain of the crystal:
AG~=.A/'~Vpf~A'fK(~,)de~d,
(8)
To do this, K(A) was calculated for every humidity by equation (5) and plotted in the form of the parametric dependence K(~,) against the volume strain ~,(A) at a corresponding humidity A.
Energy of concentraing the intracrystalline salt solution,
AG~ This was calculated by the expression:
AGs(A)=Mp- fh(A)A#dh
(9)
w Jh o
where Mp and Mw are the molecular weights of protein and water, respectively, Art = RT ln(P~/Ps) is the change in the chemical potential of water in the salt solution. P~(A) was calculated as described earlier when discussing the Laplace's pressure.
Integral changes in the free energy induced by dehydration of sample, AG Oper mole of protein These were calculated from water desorption isotherms by the expression:
Interpretation of sorption isotherms: V. N. Morozov et al. Table 2 Calculation of contributions of different processes to the total free energy change on dehydration of lysozyme tetragonal crystal= a (%)
AGo (ld/mol)
AGdL (kJ/mol)
AGd= (kJ/tool)
AGs (kJ/mol)
90 80 70 60 44 33
14 44 68 90 135 158
2.4 22 49 66 105 140
1.7 21 54 73
7 16 23 28 39 45
-
-
= All values of energy are given per mole of protein AGo is the total change of free energy induced by dehydration, calculated accordingto equation (10) AGs is the energy of concentrating the intracrystalline solution, calculated by equation (9) AGdL is the energy of crystal deformation calculated according to equation (7) as a work done by Laplace's pressure AGainis the sameenergycalculatedby equation(8) usingthe relaxation Young'smodulusand volumestrain on prolongedstorageof samplesat every humidity
Mp fh(A) A G o ( A ) = ~-~-. Jho
R T ln(P/P~)dh
(10)
Results and discussion The results of the calculations of AG o, AGs, AGdL and AGdm for tetragonal and triclinic lysozyme crystals are summarized in Table 2 and Fifure 5. The good agreement between the AGdLand AG~ values for tetragonal crystals calculated by the two different methods indicates a fairly high reliability of the estimates of AGd in spite of a few assumptions made independently in each method. This suggests also that similar calculation of the energy of deformation of a triclinic crystal under the action of the Laplace's pressure, AGdL, must yield a correct value of AGd. It should be noted that in calculating AGdLand AGdm one should use the values of the elastic properties and deformation of samples that were taken under the conditions similar to those under which water adsorption isotherms were taken. Since the samples are exposed to the long-term action of Laplace's pressure when taking isotherms, one should use the relaxation modulus, Er, and the strain obtained under prolonged stress, to calculate AGdm and AGdL. Otherwise, one can obtain erroneous results, as in calculation of AGdm of triclinic crystal for which the values of Er are lacking. It is seen from Figure 4 that substituting Ed (which may substantially exceed Er, as shown in Figure 4 for tetragonal crystals) for Er yields an overestimated AGain value. As a whole, comparing the value of AG Owith the sum AGd+AG~ for both triclinic and tetragonal crystals indicates that the sum of the two terms makes the main contribution to AGo throughout the humidity range for which the calculations are performed. Back to expression (2) for AGo, it may be concluded that the sum of the remaining terms of this equation is small. However, this does not necessarily mean that the terms AGh, AGa etc., are small by themselves, since they differ in sign. Such mutual compensation of dehydration energy of groups AGh and the energy of association of dehydrated groups AGa may be possible due to the ability of protein samples for deformation.
The great contribution of the energy of mechanical deformation of the lysozyme crystals and salt concentrating to the total change in the free energy upon dehydration suggests that their water sorption isotherm is also greatly dependent on the properties of the capillary system in protein sample, i.e. on its deformability, on hydrophobicity of capillary walls and on the composition and concentration of the intracrystalline solution. That is why the water uptake isotherm of the lysozyme crystals cannot be considered with in the framework of simple models based on water binding with isolated centres, as it has been commonly accepted 4'6'23. An essential question arises of whether and to what extent the conclusions drawn when dealing with lysozyme crystals are applicable to amorphous films and powders of lysozyme and to different solids of other proteins. As seen from Figures 2, 3 and 4, there are no fundamental differences between h(A), ~,(A) and Ed(A) dependences of lysozyme films and crystals. This means that the contribution of the energy of mechanical deformation to the total energy of dehydration of lysozyme films must be as great as in lysozyme crystals. Moreover, our experiments with crystalline and amorphous samples of eight different globular proteins have not shown any considerable differences of Ed(A) and ~,(A) dependences from those of lysozyme samples either 34'3s. Together with the well known similarity of hydration isotherms of different proteins, this suggests that the disjoining pressure substantiated here as the main factor inducing a humidity-dependent deformation, as well as the changes in the elasticity and energy of the lysozyme crystals must also act in all protein solids consisting of rigid native protein molecules which could not be packed without making a system of intermolecular capillaries filled with water. This water cannot leave the crystal 120 100
80 O
~E60
2o -i
0
0.1
0.2
0.3
h (g/g)
Figure 5 Contributions of different processes to free energy change upon dehydration of triclinic lysozyme crystals. (©), AGo, integral free energy of dehydration; (A), AGdL,energy of mechanical deformation of the crystal calculated as a work done by Laplace's pressure; (11), AGdm,the same energy calculated from the dynamic Young's modulus; (t~), AGs, the energy of concentrating the intracrystalline salt solution. All kinds of energy are given in kJ/mol protein. The calculations were made by formulae (10), (7), (8) and (9), respectively
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Interpretation of sorption isotherms: V. N. Morozov et al. without inducing the deformation of the crystal and its constituent molecules. The main difference between glassy and crystalline protein samples consists only in the absence of any translational and orientational long-range order in the arrangement of protein molecules as it follows from the data of neutron scattering 8 as well as from our unsuccessful attempts to discover any regularities in lysozyme and albumin films by low-angle X-ray scattering and by electron microscopy of protein film surface after fracturing. Unlike other inorganic and polymer glasses, protein films are amorphous at a supramolecular level only. As long as the protein globules retain their native rigid quasicrystalline structure and properties, such amorphous samples resemble rather polycrystalline materials or sintered powders. Apart from maintaining the capillary system, the rigidity of native protein globules generates the elastic restoring forces in amorphous samples as it does in crystalline ones, making the shrinkage, rigidity and water content changes reversible. The complete reversibility of the sorptiondesorption isotherms of chymotrypsin films has been recently demonstrated 2a. Thus, we can not see now any argument against the applicability of all the conclusions obtained on crystalline samples to amorphous protein samples. Suggesting protein powder to be a mixture of small particles of amorphous material the film consists of, we believe that the conclusion about the great contribution of the energy of the dehydration-induced deformation to the water desorption energetics is also valid for protein powders. As seen in Figure 5 and Table 2 in the hydration range between 0.15 and 0.22 g H20/g protein, the value of free energy of deformation per mole of protein becomes comparable with the energy of thermodynamic stability of proteins, and sufficient to induce perturbations in molecule structure. These perturbations may explain the change in the character of the dependence E(h) seen in Figure 4, the loss of enzymatic activity of lysozyme v' t 2.13 and other changes 5'8'9'16 discussed in detail in the introduction to this article. In conclusion, we should recognize that swelling and shrinkage of protein solids, when hydrated or dehydrated, influence water sorption isotherms greatly enough to make invalid any model description of hydration process that neglects the mechanosorptional effects.
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
Acknowledgements We are grateful to Drs Yu. M. L'vov, S. S. Khutsyan and A. G. Pogorelov for electron microscopy of our protein
films.
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34 35
Finney, J. L. in 'Water: A Comprehensive Treatise', (Ed. F. Frank), Plenum, New York, 1979, Vol. 6, p. 47 Blake, C. C. F., Pulford, W. C. A. and Artymiuk, P. J. J. Mol. Biol. 1983, 167, 693 Edsall, J. T. and McKenzie, H. A. Adv. Biophys. 1983, 16, 53 Careri, G., Giansanti, A. and Gratton, E. Biopolymers 1979, 18, 1187 Poole, P. L. and Finney, J. L. Int. J. Biol. Macromol. 1983, 5, 308 Lfischer-Mattli, M. and R/iegg, M. Biopolymers 1982, 21,419 Careri, G., Gratton, E., Yang, P. H. and Rupley, J. A. Nature 1980, 284, 572 Finney, J. L. and Poole, P. L. Comments Mol. Cell. Biophys. 1984, 2, 129 Schinkel, J. E., Downer, N. W. and Rupley, J. A. Biochemistry 1985, 24, 352 Bone, S. and Pethig, R. J. Mol. Biol. 1985, 181,323 Kuntz, Jr, I. D. and Kauzmann, W. Adv. Protein Chem. 1974, 28, 239 Rupley, J. A., Yang, P.-H. and Tollin, U. in 'Water in Polymers', ACS Symposium Series, (Ed. S. P. Rowland), 1980, Vol. 127, p. 111 Rupley, J. A., Gratton, E. and Careri, G. Trends Biochem. Sci. 1983, 8, 18 Chirgadze, Yu. N. and Ovsepyan, A. M. Molec. Biol. (USSR) 1972, 6, 721 Yu, N.-T. and Jo, B. H. Arch. Biochem. Biophys. 1973, 156, 469 Poole, P. L. and Finney, J. L. Biopolymers 1983, 22, 255 Poole, P. L. and Finney, J. L. Biopolymers 1984, 23, 1647 Kachalova, G. S., Myachin, E. T., Morozov, V. N., Morozova, T. Ya., Vagin, A. A., Strokopitov, B. V. and Volkenstein, M. V. DAN USSR 1987, 293, 236 Steinrauf, L. K. Acta Crystallogr. 1959, 12, 77 Morozov, V. N. and Morozova, T. Ya. Biopolymers 1981,20, 451 Gevorkian, S. G. and Morozov, V. N. Biofizika (USSR) 1983, 28, 944 Morozov, V. N. and Gevorkian, S. G. Biopolymers 1985, 24, 1785 Lfischer-Mattli, M. and Riiegg, M. Biopolymers 1982, 21,403 Hnojewyi, W. S. and Reyerson, L. H. J. Phys. Chem. 1959, 63, 1653 Khurgin, Yu. I., Sherman, F. B. and Tusupkaliev, U. Biochemistry (USSR) 1977, 42, 490 Morozov, V. N., Morozova, T. Ya., Myachin, E. G. and Kachalova, G. S. Acta Crystallogr. 1985, IM1, 202 Sarvazyan, A. P. and Khrakoz, D. P. in 'Molecular and Cellular Biophysics', (Ed. G. M. Frank), Nauka, Moscow, 1977, p. 93 Bernal, J. D., Fankuchen, I., Perutz, M. Nature 1938, 141,523 Yates, D. J. C. in 'Adv. Catalysis and Related Subjects', (Eds D. D. Eley, P. B. Selwood and P. W. Weisz), Academic Press, New York, London, 1960, Vol. 12, p. 265 Chernyak, Yu. B. and Leonov, A. I. J. Colloid Interface Sci. 1986, 113, 504 Khachaturian, A, G. J. Exp. Theor. Phys. (USSR) 1977, 72, 1149 McMeekin, T. L. and Warner, R. C. J. Am. Chem. Soc. 1942, 64, 2393 Morozov, V. N. and Morozova, T. Ya. Biofizika (USSR) 1983, 28, 742 Morozova, T. Ya. PhD Thesis, Pushchino, Institute of Biol. Physics, USSR Academy of Science, 1983 Morozov, V. N. and Morozova, T. Ya. Molec. Biol. (USSR) 1983, 17, 577