Thermodynamics of solution of lysozyme crystals

ARCHIVES

OF

BIOCHEMISTRY

AND

BIOPHYSICS

Thermodynamics

of Solution

JOAN BLYLER Department

130, 86-91 (1969)

of Lysozyme

COLE AND

of Chemistry,

Rosemont

MARY

Crystals

LEO BRYAN

College, Rosemont,

Pennsylvania

AND

WILLIA1\1 Department

of Chemistry,

Received

September

Boston

I’. BRYAN University,

23, 1968; accepted

Boston, October

Massachusetts 28, 1968

The solubilit,y of crystalline hen egg white lysozyme in 1.7 M (10%) NaCl has been studied in the pH range 2.5-5.0 and at temperatures of 21.7, 29.5, and 42.7”. The pH dependence of solubility can be used to evaluate the difference between the number of protons bound by a lysozyme molecule in the crystal and in solution. Differences were observed which do not appear to be due to intermolecular protein-protein interactions. These differences may indicate structural differences between enzyme in the crystal and in solution. Temperature dependence of solubility data were used to evaluate enthalpies and entropies of solution for the crystal. It can be shown that there is a negative cont,ribution to the entropy of solution when a crystal goes into solution. This suggests that crystalline phase solvent may be less ordered than bulk solvent in the solution phase.

Study of the solution of protein crystals is of interest for several reasons. Careful study of the solubility of crystalline proteins, whose structures have been determined by X-ray diffraction methods, may throw some light on the nature of the solution process and possible structural changes when a protein molecule passes from the crystalline to the solution phase. Such solubility data can be treated thermodynamically. Thus protein crystals can be considered as possible model systems for study of interactions between macromolecules in such biological systems as cell organelles. In principle, the detailed intermolecular interactions between protein molecules can be determined by X-ray methods and correlated with results of thermodynamic, chemical, and other studies. We have chosen to study the solubility of hen egg white lysozyme crystals in 1.7 M (10 %) NaCl in the acid pH region as a function of pH and of temperature. These conditions approximate those used by Blake et al. (1) in the preparation of the tetragonal

crystals used in their X-ray determination of lysozyme structure. Solubility data as a function of pH can be analyzed to give the difference in the number of protons bound by lysozyme in the crystalline and solution phases. Solubility data as a function of temperature can be used to get values for free energies, enthalpies, and entropies of solution of the protein. Butler and Rupley (2) have shown that the solubility of lysozyme in 5 % NaCl at pH 5.3 is unaffected by the presence of di- (N-acetylglucosamine). This indicates that the enzyme’s active site is equally accessible in crystalline and solution phases. EXPERIMENTAL Solutions of salt-free lysozyme (Worthington Biochemical Corp.) were prepared by drying samples of the protein to constant weight in a vacuum desiccator over anhydrous Mg(ClOa)n followed by dilution with pH 4.7 acetate buffer. These solutions were used to determine the molar extinction coefficient of lysoayme in pH 4.7 acetate

THER?rIOI~YPII’A?IlICS

OF LYSOZYME

buffer. A value of 3.58 X lo4 liters/mole~~m at 280 mp was used in our work. A stock solution of salt-free lysozyme in water was prepared and adjusted to the desired pII. It was then passed through a 0.2-p nlillipore filter in a Swinny Adapter to remove mold spores. Four to eight identical samples for solubilit,y determination were prepared by mixing filtered lysozyrne solution with NaCl solution srlch that each sample was 29; in enzyme and 10.0’;; ill NaCl. The pll of the mixture was taken. The samples xere thermostated at the desired temperature in a water bath and slowly rotated for at least 48 hr. This time was sllflicient to attain equilibrium at the lowest temperature used (21.7”) as judged by constant supernatarrt concentrattion with time and complete crystallinity of solid protein. Supernatant, was obtained free of crystals b> pressure filtration through a fine-porosit,y sintered glass disc. Aliquots of supernatant fluid were diluted with pH 4.7 acetate buffer and the absorbance at 280 rnp determined. Solubilit)y values were calculated from these data. At the end of t,he equilibration period the pH of the mixture was again determined. It was always greater than the initial pH and the difference was greater the higher the pH of the sample. These differences were quite marked and ranged from -0 pH units to 0.4 pH units at final pH values of 2.5 and 4.6 respectively. Data are reported in terms of equilibrium pH values. The crystals in equilibrium with the supernatant fraction were observed with a polarizing microscope. They were birefringent and had a needle-like habit. They are presumably tetragonal though direct demonstration of this supposition was not possible. Tetragonal bipyramids appear in unstirred solutions under the conditions of our experiments (3, 4) and correspond t,o the crystals used in the X-ray structure determination (1). A change to amorphous material was observed at pH vahles somewhat lower than those reported here. RESULTS

Figure 1 shows the results of mean solubility (s) determinations in moles/liter (mol w-t 14,600) at various pH and temperature values. Experiments outside of the indicated pH range gave amorphous precipitates and scattered results. Experiments at temperatures below 20” did not attain equilibrium. Solubility increases with increasing pH. Between pH values of 7 and 11 orthorhombic lysozyme crystals are formed (3, 5), but the

I O2 5

s7

SOLUTION

30

I 35

I 40

45

I 50

PH

FIG. 1. Solubility of lysozymc various values of pH and various indicated.

in 1.7 M NaCl temperatures

at, as

solubility of t’he orthorhombic form has not been measured. In Fig. 2 points taken from smooth curves drawn through the solubility data are plotted as log s vs. pH. The slopes of these curves increase with increasing pH. These slopes are related to the difference in the number of protons bound by protein in the crystal and protein in solution in equilibrium with protein crystal. Thermodynamic quant’ities for solution can be obt-ained from solubility data. We define each standard state of the protein rrystjal as t,he solid crystal at the specified conditions of temperature, pressure, pH, and salt concentration. The standard states of protein in solution are defined as hypothetical 1 molar solutions of the prot’ein under the same conditions. Then, with neglect of the activity coefficient of the protein, the standard free energy of solution of the protein is given by: Al?” = -RT

In s.

(1)

The variation of s with temperature can be used 00 obtain standard enthalpies and entropies of solution. Figure 3 shows points

88

COLE,

BRYAN,

taken from smooth curves drawn through the solubility data plotted as log s vs. l/T at various pH values. These points have been fitted by linear curves. Values of AH” have been calculated from the slopes of these straight lines. If AH” is temperature independent over a certain temperature range, AS” is also temnerature indenendent over the same range. -Values of AS” were calculated using the AH” values and the relationship :

AND

BRYAN TABLE

THERMODYN~\MIC PH

CL\.alues

AS0 = AH” - AF”

T

I

40-

A

29 5~

0

42.7Y

0

I

I

I

21 7oc

4.2 -

4.4 a 3 4.6 I

FIG. 2. Log solubility of lysoayme NaCl at various values of pH and various tures as indicated.

AH” (kcal/mole)

G.8 6.7 6.5 6.3 G.O 5.8

0.9 7.8 9.9 11.1 9.1 12.3

of AF”

OF TA;;W~y$‘/

0.1 1.1 3.4 4.8 3.1 6.5

SOLUTION ASO (gibbs/mole)

0.3 3.0 11.2 15.8 10.2 21

and TAS” at 30”.

(2)

-’

Values of t)hese thermodynamic quantities are given in Table I. As pH increases there is an upward trend in AH”. By itself this trend would tend to decrease solubility with increasing pH. The fact that solubility increases with pH is explained by the marked increase in AS” with increasing pH. Close examination of Fig. 3 indicates that constancy of AH’ over the temperature range of the measurements may be an oversimplification. At all pH values the points would be better fit by curves having slight’ 38

(kcal/ ~01~)~

AF"

3.00 3.30 3.60 3.90 4.20 4.10

I

QUANTITIES

in 1.7 M tempera-

negative curvature. Thus dAH”/dT or ACp’ becomes negative. The amount and accuracy of the data are not sufficient for numerical evaluat’ion of ACp”. IlISCUSSION

In the work reported here care was taken that the solubility values were thermodynamically meaningful. The protein crystalline phase was always the same and enough time was allowed to elapse so that’ solubility measurements gave constant values with time. Even though immediate precipitation is obtained upon mixing in many cases, the concentration in the supernatant fraction generally decreases with time as amorphous protein goes over into crystalline material. Below 20” very long times are necessary before constancy in solubility is obtained. Thus, Wetlaufer and Stahmann (6), in a study of dye-binding by lysozyme by means of precipitation curves, were never able to attain equilibrium in their measurements. If thermodynamically valid data are at, hand, thermodynamic analysis is possible. We shall first discuss the pH dependence of solubility. The pH dependence of protein solubility was discussed by LinderstromLang (7) who proposed a combination of solubility and titration measurements as a way of obtaining protein molecular weight. More recently the treatment has been extended by Shatkay and Michaeli (8) who derived more general relationships. The following equation is applicable to our measurements : d(log)s ~ d(pH)

=

-(

%- 5).

(3)

THERMODYNAMICS

OF LYSOZYME

I

I

1

3 20

3 30

3.40

IIT

ho.

3. Van’t

SOLUTION

Hoff plots of soluhility

Here 6 represents the average number of protons bound per molecule by protein, initially considered as having zero average charge due to proton binding, in the solution phase; and 5 represents the similar average number of protons bound per molecule by protein in the crystalline phase. Negative values of these quantities represent protons lost. The only important assumptions involved in deriving Eq. 3 are that the degree of polymerization of protein in solution is independent of pH and that the salt concentration is constant and large enough so that protein ion activity coefficients are independent of protein concentration and pH. The right hand side of Eq. 3 can, in principle, be experimentally determined and compared with solubility versus pH data in order to test the validity of the relationship. Here we merely calculate % - Z from solubility data and assume the validity of Eq. 3. It should be pointed out, that Eq. 3 has never been experimentally verified in a protein system. Plots of log s vs. pH are given in Fig. 2. The difference between t,he number of prot’ons bound by lysozyme in t,he crystal and

59

x IO3

at various

pH values

as indicated.

in solution in equilibrium with the crystal (3 - i) is given by the slope of such a curve. For example, the slope of the curve at 29.5” is 0.7 at pH 4.6 and about 0.2 at pH 3.0. Titration data for lysozyme in solution (9) indicate that about 10 prot’ons are bound at pH 5 and about 19 are bound at low pH. An obvious explanation for greater proton binding in the crystal might seem to be that pK values of acidic groups involved in intermolecular protein-protein interactions in the crystal could be higher than such values for the same groups in solution. However, this explanation is not consistent with the X-ray structure (1). The only interaction between molecules involving acidic groups which could give rise to such an effect involves a double salt bridge between a negatively charged terminal carboxyl group and a positively charged Lys 13 group of one molecule with the corresponding groups on the adjacent molecule. If the carboxyl group is normal in solution, t,his interaction would tend to lower the pK value in the crystal and 5 - i would be negative. Evidently this contribution to the difference in proton binding is either absent or outweighed

90

COLE,

BRYAN,

by contributions of opposite sign discussed below. There are two general ways of explaining our result’s. The first of these is in terms of specific structural interactions. Higher pK values in the crystal could be explained by specific interactions in solution, giving rise to abnormally low pK values, which are not present in the crystal where the pK values would be more normal. Alternatively specific interactions in the crystal could give rise to abnormally high pK values while those for protein in solution would be more normal. Presumably these interactions would not intermolecular protein-protein involve bonds. Changes in pK values could also be explained by environmental effects. Thus the environment around certain acidic groups in the crystal could be such that these groups would have higher pK values than in solution. We should note that we have interpreted specific interactions or environmental effects under t#he implicit assumption that the activity of hydrogen ion is the same in both phases. It may be that hydrogen ion activity in the crystalline phase is somewhat lower than in solution as a consequence of the over-all positive charge of the protein molecules. The exact significance of these results is still obscure, but there exists the possibility that they mirror structural differences between lysozyme in the crystal and in solution. For our discussion of the values of AH” and AS” in Table I, we shall postulate a simple model for solution of a protein crystal. We can consider AH” and AS” as being equal to the sum of three and four terms respectively. There must be contributions to both AH’ and AS” due to the breaking of proteinprotein intermolecular bonds. It is possible that intramolecular protein structural changes occur upon solution giving rise to contributions to AH” and AS”. Contributions to AH” and AS” can occur due to changes in the character and structure of the -33 y0 by weight (10) of solvent in the crystalline phase when it goes into solution, and in possible changes in solution solvent structure due to addition of protein and

ASI1

BRYAN

crystalline phase solvent. Finally we consider the increase in entropy (cratic entropy) which occurs when the protein molecules, initially close together in the crystal, expand to occupy a volume characteristic of the hypothetical 1 M protein solution. This has the well-known value of 8 gibbs/mole. We can therefore write: AH” = AH”intrrnmlecular

AS” = AS”intermolccular bonds

(5) + AS’;;,“,“,‘,“‘” + AS’soivent + 8 We shall discuss the various terms of Eqs. 4 and 5. The X-ray analysis of lysozyme (1) has revealed the nature and number of the intermolecular bonds in t’he crystal. Consideration of these clearly indicates that when these bonds are broken the side chain and peptide backbone groups involved should have more freedom of motion,. hence, ASDintcr,noiecu~ar bondsshould be positive. We can estimate the magnitude of this quantity. Scheraga (11) suggests a value of about 4 gibbs/mole for the breaking of a side chain hydrogen bond and about 4 gibbs/mole for the increase in entropy when the backbone due to an amino acid residue is released from rigid structural constraints. There are a total of eight intermolecular hydrogen bonds and one intermolecular salt bridge per lysozyme molecule in the crystal (1). These would account for about 36 gibbs/ mole. Increased freedom in t’he backbone would give an additional contribution. It is not unreasonable, therefore, to suggest a value of about 40 gibbs/mole for ASOintermolecular bonds. The value of ASostructureehangecan be approximated as being equal to 0. If anything, this quantity should be positive since the lysozyme molecule would be expected to have a higher structural entropy when released from contraints due to occupancy of positions in a crystal lattice. Reference to Table I shows that ASosoivent must be negative if the four quantities on

the right hand side of Eq. 3 are t’o add up to AS”. We t’herefore are led to t’he hypothesis that solvent in the prot,ein crystallme phase may, paradoxically, be less ordered than solvent in the solution phase. It seems reasonable to assign a positive sign t’o AH”interlnoleeu~nr bond., particularly because t’he broken bonds \vould not be expected t)o be strongly snlvated in a solution where salt, is also competing for water. We can set: AHostructurechanse= 0. If solvent is less ordered in the cry&al, then AHobolvrnt is negative. These quantities should add up to the values of AH” given in Table I. If w-e conclude that’ ASoholventis negative, some contributions to this quantity may be due to intermolecular hydrophobic int’eructions (1) (between Phe 34 and hrg 114 of one molecule and Tyr 23 of another molecule) and salt bridges (betlvcen Lys 13 and the terminal carboxyl group of anot’her molecule and Cl- salt bridge involving arg 114). The formation of such interactions would tend to release ordered water upon crystallization. Another possibility which should be seriously considered is t’hat since there are rather small spaces between protein molerules in protein crystals (la), the usual water clust’ers postulated present’ in bulk water (13) or salt solutions (14) may not always be accommodated. This would lead to greater disorder of solvent in these regions and to a higher entropy. X-ray results with lysozyme are consistent with such regions of disorder (1). We are thus led to suggest t’he possibility that in solid phases which can accommodat’e water in the spaces between macromolecules, such as protein crystals, or certain regions in cell organelles, a contribution t’o the stability of such phases may be made by the relative

disorder of t,he water in such spaces. Of course, there is a corresponding destabilization due to enthalpy. Until furt’her knowedge is available, we (bannot say whether the net effect is dominated by AS”,,l.,,, or AH’=so~vent.

The authors acklrowledge the help of Maryanne AIetz, Patricia Foster, Alice >IcL)ermott, and Sheila Catersoll in some of t,he work presented here. A11 esperimcntal work was carried out under NSF grant GY 431 for academic >.ear extension of work begun at Bosloll University. J:lSFEI:II‘UCI!X 1*

L

1. C. C. F. BL.\ICIG, el al., P/xx. R'o!/. Sot. London Ser. B 167, 3G5 (1967). 2. I,. G. Bu~r~lin, .\ND J. A. I~CPLI’Y, J. B’iol. Chern. 242, 1077 (196i). 3. G. ALDIXIXJS .LSD II. L. FM-OLD, J. Bid. Chem. 164, 1 (194(i). 4. F. T. JONM, J. ;Iw. Cherry. Sot. 68, 854 (1946). 5. K. J. PALMISX, AI. B.\LL.LNTYNE, AND J. A. G.ILVIN, J. :lVI. (:hCttl. SOC. 70, 906 (1948). G. I). B. WI,:,~L.\UPJX, .\SD hl. A. ST.\HMANN, J. by. Chenl. Sot. 80, l-193 (1958). 7. K. LINI~I~I~s,I~~~I-L.\N(:, -lrch. Biochenc. 11, 191 (19-8). 8. A. sH.\TIi.iY, AND I. RIICH.\I:IJ, J. Phys. Chem. 70, 3777 (1966). 9. C. TANFORD, ANuM.L. W.~ONER,J.~~~~. Chem. Sot. 76, 3331 (1954). 10. L. K. STMNR.XF, dcta Cry&. 12, 77 (1959). 11. 1-T.il. SCHER.XA in, “The Roteills” (H. Neurath, ed.). \‘ol. I, p. 477. Academic Press New, York (1963). 12. B. w. LO\\-, F. RI. 1:ICHAIlI>S, ANI> J. E. BI,SJGP:R, J. Anl. Chem. Sot. 78, 1107 (1956). 13. G. NEMIGTHY, ASID II. A. SCHCILAGA, J. Cheut. Phys. 36, 3382 (1962). 14. Ii. A. HORNK, .LND J. D. BII