Thermodynamic properties of the 11S globulin of Vicia faba-ovalbumin-aqueous solvent system: phase behaviour and light scattering

Food Hydrocolloids

Vol." 11 no. 3 pp. 327-337, 1997

Thermodynamic properties of the lIS globulin of Vicia faba-ovalbumin-aqueous solvent system: phase behaviour and light scattering L.A.Wasserman, M.G.Semenova 1 and E.N.Tsapkina

Institute of Food Substances of Russian Academy of Sciences,Vavilov Street 28, 117813 Moscow, Russia ITo whom correspondence should be addressed

Abstract The effect of pH on the thermodynamic properties of the mixed solution of the two different globular proteins, oligomeric globular protein-ll S globulin and monomeric globular protein-ovalbumin, has been studied. Thermodynamic incompatibility of the proteins was observed at pH 7.0 and 7.8, which are above the proteins' isoelectric points. Thermodynamic properties of the system were studied by phase analysis from moderate to high concentration and by light scattering on dilute solutions below the separation threshold. The rise of the concentration region of the protein immiscibility in the mixed protein solution was observed under a pH change from pH 7.8 to 7. O. Comparison of the alteration of the character of the interactions between all components of the solution with pH variation shows that the basic reason/or the rise in protein immiscibility with pH decrease (from 7.8 to 7.0) is intensification of the self-association of the mixed proteins, mainly of 11S globulin. It was established that the forces of electrostatic repulsion between both the similar and different protein molecules playa key role in the phase separation of the mixed protein solutions at pH 7.8. In contrast, the results obtained exhibit the determining role of the attractive forces acting between protein molecules and dictating features of the phase state of the mixed protein solution at pH 7.0.

Introduction Mixtures of proteins have wide applications in food formulations (1--4). In general, possible phase state and potential functional properties (ability to form homogeneous solutions, emulsifying capacity, gel-forming ability) of the mixtures of the proteins are impossible to predict only on the basis of the properties of individual components. In order to do this, evidently, information about the character of the intermolecular interactions between all components of the mixed protein systems is required. A thermodynamic approach can provide very valuable information about the nature and intensity of the intermolecular interactions in multicomponent systems as well as potential phase states of the systems under different experimental conditions. Immiscibility of proteins differing in nature is one of the basic phenomena in mixed solutions of proteins. This phenomenon can determine the structure of the mixed protein solutions as well as functional properties of the

© Oxford University Press

proteins in such solutions (5-7). To date, some experimental data on the phenomenology of the immiscibility of proteins have been gathered in the literature (8-10). At the time of this study, however, the nature of this phenomenon is not clearly understood. That is, the key physicochemical factors determining the peculiarities of the incompatibility of the different proteins in aqueous mixed solutions have not been adequately explored. From our point of view, one of the direct ways to examine the nature of the incompatibility of the proteins might be to study the nature and intensity of the intermolecular interactions between all the components of the system: protein I-protein 2-s01vent. The light-scattering method allows this possibility by values of the second virial coefficients which characterize the molar free energy of the pair interactions between all components of the polymer solutions (11). By this means, in order to elucidate the nature of the

328

L. A. Wasserman, M. G Semenova and E. N.Tsapkina

incompatibility of the proteins in the mixed solutions, we attempted to carry out a comparison of the features of the phase state of the mixed protein aqueous solutions with the character of the intermolecular pair interactions between all components of the solutions, namely protein-protein (for the same and different proteins) as well as protein-solvent. As the main objects of investigation we chose globular proteins with well-known properties, namely ovalbumin and lIS globulin of Viciafaba. The interest in studying this pair of proteins is due to both scientific and practical reasons. Proteins of leguminous plants are one of the most promising materials for formulating new forms of food products (12,13) and thus they, apparently, must be among the most important objects for systematic investigation. Protein of leguminous plants (soy, pea, broad bean, etc.) may be used as functional additives regulating the protein content in a given product and the food structure during processing and storage. For example, even today, isolates and concentrates of soy proteins are widely used in the preparation of mixtures for children's and medicinal feeding, and also for making new forms of salad seasonings, dressings, confectionery and meat products (12-14). lIS globulin of the broad bean is homologous in physical-chemical properties and biological function to 11S globulins, the main storage protein, of other leguminous plants (soy, pea, etc.) (13,15). Ovalbumin is the main protein of hen egg white (16,17), which is very widely used in food processing due to its whipping (18), gelling (19) and foaming (20) properties. Practical interest in studying the mixture of the proteins is induced, firstly, by the wide rate of occurrence of the protein mixtures in real biological systems and, secondly, by the goal to attain the most favourable balance of amino acid contents in the formulated food. The proteins chosen as objects of this study, apparently, might be promising components of formulated food due to the complementary amino acid composition of the proteins (15,21). From the scientific point of view, interest in studying the given pair of proteins is due to the fact that clarifying the factors controlling the thermodynamic incompatibility of the lIS globulin and ovalbumin in aqueous medium might explain some fundamental regularities of immiscibility of the globular proteins in aqueous medium, representing a wide class of the proteins of plant and animal origin.

Ovalbumin We used a lyophilizate of the ovalbumin (recrystallized five times) which was purchased from Bilar, Latvia. Preparation of solutions Double-distilled water was used in the preparation of solutions. The samples of proteins were dissolved in phosphate buffer (ionic strength 0.1 mol/dm", pH 7.0 or 7.8). Trace amounts (0.01%) of sodium azide ensured the prevention of bacteriological contamination. Mixed solutions of the proteins with given protein concentrations were prepared by mixing rated volumes of the individual protein stock solutions with predetermined concentrations. Concentration determination The concentration of lIS globulin of V.faba in the stock solutions was determined spectrophotometrically at 280 nm. The solution was stored in 8 mol/dm! urea for 24 h before measurement. The extinction coefficient Al%l em = 7.58 was used. The ovalbumin concentration in the stock solutions was determined using the refractive index increment predetermined for the light-scattering method. We did not use spectrophotometry in this case in order to avoid an additional calibrating experiment with the aim of extinction coefficient determination for a given ovalbumin sample. Sedimentation analysis Sedimentation analysis was performed in phosphate buffer (ionic strength 0.1, pH 7.0 or 7.8) by MOM 3170 B ultracentrifuge (Hungary). Refractive index increment determination The refractive index increments were determined on a Shimadzu differential refractometer (Japan) at A. = 436 nm. The following values were determined: u, lIS globulin of V.faba (0.2 ± 0.003) 10-3 m 3/kg; U, OVA (0.191 ± 0.003) 10-3 m 3/kg. Within experimental error, the protein refractive index increments are the same at pH 7.0 and 7.8.

=

=

Light scattering

Materials and methods 11S globulin of Viciafaba (legumin) lIS globulin was isolated from V.faba meal using the procedure described previously (22). A purified isolate was dialysed against double-distilled water at pH 8.0. Then the protein samples were lyophilized. The protein sample contained 95% of the main substance with a sedimentation coefficient of lIS, and -5% of a substance having a sedimentation coefficient of 15S, according to the sedimentation analysis (pH 7.0 and 7.8, I 0.1 mol/dm'),

=

The light-scattering measurements were made by the use of an FPS-3M nephelometer (Central Design Bureau for Unique Instruments, Academy of Sciences, Moscow, Russia) at T 25°C, A. 436 nm. The light-scattering measurements were carried out at a fixed scattering angle of 90° as no asymmetry was observed for both the proteins under consideration. The instrument was calibrated with dust-free benzene (R 4.74 X 10- 3 rrr', e 90°). Prior to the experiments, all solutions were filtered through membranes with a pore size of 0.45 urn (Sartorius) directly into the light-scattering cells.

=

=

=

=

Thermodynamics of Vfaba ovalbumin

The results obtained were used to plot the concentration dependencies of the ratio (KC;=2,3/flR90) for binary (proteinsolvent) solutions and the ratio (K'[C 2 + C3]/flR90) for ternary solutions (indexes included are: I, solvent; 2, lIS globulin; 3, ovalbumin), where K and K' are optical constants of the systems K =21t 2n2u 2/ N AI..4; K' = 21t 2n 2/ N AI..4; n is the refractive index of the solvent; N A is Avogadro's number; I.. is the wavelength of incident light in a vacuum; C is the concentration of biopolymers; and flR 90 is excess light scattering of biopolymer solutions over solvent. The second virial coefficients , characterizing the molar free energy of the pair interactions between the same individual proteins or between individual proteins with solvent (A 22 and A 33), were determined from the tangent of the slope of concentration dependencies of the ratio KC;=2.3/flR90 [equation (1)] for binary protein solutions: protein-solvent (see Figs 2 and 3) (11,23): i= 2, 3

(1)

where C; is protein concentration in the aqueous medium (g/ml); M wi is weight-average molecular weight of the protein (g/mol); and A 22, A 33 are second virial coefficients characterizing the molar free energy of the pair interaction between the same protein molecules in aqueous medium (in weight scale, cm-mol/g-). The cross second virial coefficient, characterizing the molar free energy of the pair interactions between the different proteins in aqueous medium (A 23), was determined from the tangent of the slope of the concentration dependence of the ratio [K'(C 2 + C 3)/flR90] (equation 2) for ternary solutions: protein l-protein 2-solvent (24) (see Fig. 4):

K' (C 2 + C3)/flR90 = 1/(ulM2wW2 + ulM3wW3) + 2 [(u lM2w2WlA 22 + 2 U2U3M2wM3wW2W3A23 + U3 2 M 3w2 W 32 A 33)/(ul M 2wW 2 + ul M 3wW 3)2] (C 2 + C 3) (2)

where An, A 33 are the second virial coefficients, characterizing the pair interactions between the same individual proteins or between individual proteins with the solvent; A 23 is the cross second virial coefficient characterizing the pair interactions between the different proteins (cm''rnol/g-) (in weight scale of protein concentra tion); U2, U3 are the refractive index increments of proteins (cmvg); W2, W 3 are the weight fractions of proteins, M 2w, M 3w are the weight-average molecular weights of the proteins (g/mol); and C2, C3 are the concentrations of the proteins (g/ml). Experimental error in the determination of the values of the protein molecular parameters is 10% for molecular weight and second virial coefficients (A 22, A 33), and 30% for the cross second virial coefficient (A 23). In order to calculate the spinodal and critical point coordinates, molal second virial coefficients were used (A 22*, A 33*, A 23*). Molal second virial coefficients were obtained by the following equations (25):

329

(3)

where A 22*, A 33*, A 23* are the second virial coefficients on a molal basis for pair interactions lIS globulin-lIS globulin, ovalbumin-ovalbumin and 11 S globulin-ovalbumin, respectively. We used the following equations for the calculation of critical point coordinates (26,27):

(4)

and for the spinodal the next equation (26,27): (5)

where m2, m3 are the concentrations of the proteins expressed in molal units; m2* and m3* are the concentrations of the proteins in the critical point. Determination of the phase diagram for the system llS globulin-ovalbumin-water

In order to determine the phase diagram (concentrations of each protein in co-existing phases in a wide concentration region of the mixed solution), we used the method of measuring the ratio between the co-existing phase volumes (28-30). In so doing, mixed solutions of the proteins with known concentrations were stirred and then centrifuged (30 min at 3500 g). As a result, mixed solutions of the proteins were separated into twoliquid phases reached by one of the proteins studied. The volumes of the co-existing phases were determined. The control of the individual protein concentrations in the co-existing phases was carried out by the method of measuring sedimentation areas on the sedimentograms determined by sedimentation analysis. Determination of the protein molecule charge in aqueous medium

Isoionic protein solution (1% w/v) was prepared by equilibrium dialysis against double-distilled water. Then NaCI was added to the protein isoionic solution up to 0.1 mol/dm- concentration in the solution. The original pH of this solution was determined. Measurement of pH was repeated after addition of a specific volume of the solution of HCl (0.1 mol/dm-) to the protein solution. In a parallel experiment, the solution of NaOH (0.1 mol/dm-) was added to the protein solution instead of acid. Two blank experiments, in which HCl (0.1 mol/dm') or NaOH (0.1 mol/dm') solution were added to a solution of NaCI (0.1 mol/dm'), were carried out in parallel. The pH was

L. A . Wasserman, M . G. Semenova and E. N Tsapkina

330

'coordiria'tes' ofihe critical points: . pH1.0 i " ; "' : . C 115YF.·=:7.8t:COVA=13.6% pH·I8 : . : .;. .- '.. :. .C..115.VE. = ~a4%. .C ; O.vA. = .18.9%

40

> ~

pH 7.0

30

.,


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4

UJ

Z

::;

a:

:::>

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0

-c

> 0

I.

pH 7.8 .

6

~

20

e

0

pH ,7.8

2

10

pH 7.0 0

0 0

10

20

30

40

0

1,0

.5 C . % w/v

C 115 V.F. % wlv

Figure 1 The experimental binodals of the ternary systems lIS globulin of Y.faba-ovalbumin--water at pH 7.8 and pH 7.0 (I =0.1 mol/drn-, t =25°C).

detected after each addition of HCl or NaOH. The number of hydrogen ions bound by protein was calculated on the basis of the difference between the pH observed for protein solution and blank solution during the titration. The number of hydrogen ions bound or dissociated with reference to the protein isoelectric point was identified with the number of the protein molecule charge. Determination of pH dependence of liS globulin solubility in aqueous medium

The protein solution with predetermined concentration (2%) was prepared at pH 8.0. Then the protein solution was titrated with a solution of HCl (0.1 mol/dm''). The protein lost solubility and precipitated at specific pH values. In order to estimate the protein solubility at specific pH, the protein solution was centrifuged (30 min at 3500 g) and then the protein concentration was determined in the supernatant. The protein solubility at distinct pH was evaluated relative to the initial protein concentration in the solution at pH 8.0.

Results and discussion Thermodynamic incompatibility was observed between lIS globulin and ovalbumin in aqueous medium at pH 7.0 and 7.8, which is higher than the pH of the protein isoelectric points [pI of 11S globulin 4.75 (15), pI of ovalbumin 4.8 (11)], namely, under the like negative sign of the net protein molecule charge. The mixed protein solutions separated into two co-existing phases reached by one of the proteins under specific sufficiently high concentrations of both proteins

1,5

Figure 2 Light-scattering data for 11 S globulin of Vf aba at pH 7.0 and 7.8 (I 0.1 mol/dm' , t 25°C).

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in the mixed solutions. Figure 1 exhibits experimentally obtained binodals with critical points describing concentration regions of homogeneity and heterogeneity of the mixed protein solutions at pH 7.0 and 7.8. Figure 1 shows a shift of the concentration region of the two phase existence in the mixed protein solutions towards lower concentrations of both proteins under a pH decrease from 7.8 to 7.0. This shift is expressed more for the right branch of the binodal relative to the critical point, i.e, co-solubility of the proteins became less, especially at high concentration of 11S globulin in the mixed solution at pH 7.0. In order to explain the regularities of the phase separation of the mixed protein solutions observed, we attempted to characterize quantitatively the change in the molecular and thermodynamic parameters of the proteins in the aqueous medium with pH variation by light scattering as well as alteration of the protein charge by acid/alkali titration of the protein solutions under pH change. Figures 2, 3 and 4 show light-scattering data for the llS globulin of Vfaba , ovalbumin and their mixed solutions accordingly at pH 7.0 and 7.8. Concentration dependencies of KCI!1R 90 for individual proteins and K(C2 + C 3)/!1R90 for equimass mixed protein solutions are linear. This circumstance raises the accuracy of the concentration dependence extrapolations toward zero protein concentration in the solutions and , therefore, the precision of the determination from the concentration dependencies of both protein weight-average molecular weights (M2w , M 3w ) and second virial coefficients (A 22 , A 33, A 23) . The numerical results obtained from light-scattering data are given in Tables 1 and 2. Table 1 shows that the weight-average molecular weights

331

Thermodynamics of V.faba ovalbumin

3

6

b.

e

pH 7.0 pH 7.8

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I e*

pH 7.81 pH 7.0

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ill

ill

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c . % wlv

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1.0

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1.5

2.0

C. % wlv

Figure 3 Light-scattering data for ovalbumin at pH 7.0 and 7.8 (I = 0.1 mol/dm'', t =25°C).

Figure 4 Light-scattering data for equimass mixed solutions of lIS globulin of Vfaba with ovalbumin at pH 7.0 and 7.8 (I = 0.1 mol/dm', t = 25°C).

Table I Molecular weight and thermodynamic parameters of the 11S globulin of Vjaba and ovalbumin in aqueous medium at different pH and 1= 0.1 mol/dm''

Protein

Second virial coefficient, A*ii x 104 m3/mol) Experimental A*ii

Theoretical The excluded volume term (equation 11) A*ii exe

The electrostatic term A*iie1ectr = A *iiexp - A *;;exel

The ideal Donnan Correction factor term (equation 13) to the ideal Donnan term A*iiD r;=

Coefficient activity of counter ions (equation 14) Yeo

A*lie1ectr/A*IP

pH7.8 11S globulin (Mw = 330 kDa) Ovalbumin (Mw=44kDa) pH 7.0 11S globulin (Mw = 350 kDa) Ovalbumin (Mw = 44 kDa)

174.2

25.2

149.0

2205.0

0.068

0.23

22.5

5.5

17.0

31.9

0.534

0.64

-39.2

25.2

6.5

5.5

0.046

0.189

1531.3 1.0

of 11S globulin (330 kDa) and ovalbumin (44 kDa) obtained at pH 7.8 are in agreement, within experimental accuracy, with the values determined by other techniques (11,15). Under a pH decrease from 7.8 to 7.0, the weight-average molecular weight of 11S globulin increases from 330 to 350 kDa, suggesting that there is some association of the protein molecules in aqueous medium at pH 7.0. It was established

23.1

that the weight-average molecular weight of the ovalbumin does not change with pH alteration. With pH reducing from 7.8 to 7.0, the values of the protein second virial coefficients (A 22, A 33) decrease significantly, especially in the case of the lIS globulin, when the value of the second virial coefficient changes from positive to negative (see Table 1).

L. A. Wasserman, M. G. Semenova and E. N. Tsapkina

332

Table 2 Thermodynamic parameters of the pair interactions of 11S globulin with ovalbumin in aqueous solution at different pH and I = 0.1 mol/dnr' Cross second virial coefficient, A*23 x 104 m 3/mol

pH

Experimental

Theoretical The excluded volume The electrostatic interaction term term (equation 11) A*23 exc

A23theor

=

The ideal Donnan term (equation 13)

A*23 D

A*23 e1ectr(theor) = A*23 DxrI

A*23 exp = A*23 exc + A*23 DX fl

(I': = 0.245)

A*23 exp - A*23 exc

70.0 7.3

7.8 7.0

57

13 13

265.1 199.4

The values of the cross second virial coefficient, A 23, are positive and also decrease considerably with pH reducing from 7.8 to 7.0 (see Table 2). Table 3 presents both values of the cross second virial coefficients obtained experimentally by the light-scattering method and values of the cross second virial coefficient calculated from coordinates of the critical points of the binodals on the basis of the second virial coefficients of individual proteins (A 22* ii A 33*) obtained experimentally by the spinodal equation (5). [The critical point is the common point of the binodal and spinodal curves (31).] The closeness of the experimental and calculated cross second virial coefficient values, within experimental error, apparently indicates the certainty of the cross second virial coefficient values determined by light scattering. Going to the examination of the change in the experimental second virial coefficients with pH variation, we would like to point out that, in general, the sign and value of the second virial coefficient carry information about initial deviation of the macromolecular solutions from the ideal state at small macromolecular concentrations, and reflect the character and intensity of the intermolecular pair interactions in the solution. There is a direct relationship between the second virial coefficients and free energy of the polymer solutions. The molar free energy (chemical potential) of the components in solutions may be expressed in terms of the second virial coefficients. So, for example, the chemical potential of the protein in the binary solution (protein-solvent) may be expressed by the following equation (II): i

=2, 3

(6)

and chemical potentials of the components in the ternary solutions (protein-protein-solvent) may be expressed by the following equations (32): 1-11

=1-11° - (RT/mI) x (m2 +m3 + (A 22*mi 2 + A 23* m2m3)

+ A 33*m32)/ (7)

64.9

77.9

Table 3 Thermodynamic parameters of the pair interaction of 11S globulin with ovalbumin obtained experimentally by light scattering and calculated from coordinates of the critical point obtained experimentally pH

7.8 7.0

Cross second virial coefficient, A*23 x 104 (m 3/mol) Experimentally obtained by light scattering

Calculated

70.0 7.3

73.04 6.56

where I-1P and m, are the standard chemical potential and concentration (molal scale) of components (i = 1, 2, 3), respectively; mO is the standard-state molality of the components; R is the gas constant; and T is the absolute temperature. From the above equations (6-9), it might be assumed that positive values of A 22*, A 33* and A 23* lead both to the increase in the chemical potentials of the polymer components of a solution and to a decrease in the solvent chemical potential. That is, positive values of the second virial coefficients A 22*, A 33* and A 23*, obtained experimentally for the system studied, manifest thermodynamically unfavourable interactions between proteins and opposite thermodynamically favourable interactions between the proteins and solvent (see Tables 1 and 2). It is well known from the literature that there is a strong tendency towards phase separation in the mixed polymer solutions if the contacts of two polymers are energetically unfavourable, and/or when the two polymer types differ in their affinity towards the solvent (33,34). By this means, in order to draw the right conclusions about the main reasons for the protein miscibility change observed, it seems necessary to compare it with change in the character of the interactions between all components of the solution with pH variation. Tables 1 and 2 show that interactions between protein molecules became more thermodynamically favourable with a decrease in the pH from 7.8 to 7.0. So, in the case of the ovalbumin positive value of the molal second virial coefficient (A 33*, m 3/mol)

333

Thermodynamics of Vfaba ovalbumin

(a)

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400 r-~~~------~~~~---..,

experimental data Rterature data

20

100

200 75

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N

50

-20

-200

-400

25

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2.5 pH

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5.0

7.5

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10.0

pH

Figure 5 pH dependencies of the protein charge: (a) for ovalbumin (1) obtained experimentally; (2) taken from the literature (10); (b) for lIS globulin (1) obtained experimentally; (2) pH dependence of the protein solubility.

decrease from 2.25 x 10-3 to 6.5 X 10--4, the value of the molal second virial coefficient of the llS globulin (A 22*, m 3/mol) varies from positive 1.742 x 10-2 to negative -3.92 x 10-3, and the value of the molal cross second virial coefficient (A 23*, m3/mol) decreases, practically, in order of the value from 7.0 x 10-3 to 7.3 X 10--4. As this takes place, the pH dependencies of the protein charge indicate a reduction of the negative charge of the proteins under a pH decrease from 7.8 to 7.0 (Fig. 5a and b). In this manner, an increase in the thermodynamic affinity between the same and different protein molecules under a decrease in pH can result, probably from diminution of the electrostatic repulsion between like-sign charged protein molecules. In the case of the lIS globulin, the negative value of the second virial coefficient, together with the increase in the weight-average molecular weight, manifests the protein molecule associate formation at pH 7.0. Probably, in this case, the balance of the forces acting between protein molecules shifts from electrostatic repulsion towards hydrophobic attraction in the aqueous medium as a result of the diminution of the protein negative charge. In fact, pH dependence of the lIS globulin solubility in aqueous medium also confirms the data obtained (see Fig. 5b). Thus, from the solubility curve, it follows that pH 7.0 is the end point of the protein solubility in aqueous medium, following which a sharp fall in protein solubility begins towards the pH of the protein isoelectric point. Let us compare alteration of phase diagrams with change in the values of the second virial coefficients. Such a comparison allows one to assume that protein incompatibility increase, developing in the binodal shift towards the low protein concentration region, is caused by a decrease in the protein affinity for solvent. The most significant shift of the right binodal branch relative to the critical point

towards the protein concentration axis is mainly due to thermodynamic affinity of the llS globulin for solvent decrease attending 11 S globulin molecule self-association. As this takes place, it is interesting to note that weakening of the mutual repulsion forces between the different protein molecules, manifesting in a decrease in the value of the cross second virial coefficient under pH reduction from 7.8 to 7.0, is not, apparently, the deciding factor in the phase state of the mixed protein solution modification under pH variation for this protein pair. Thus, as a consequence of this, we do not see a decrease in the concentration area of the two phase existence in the mixed protein solutions. Probably, the more significant diminution in magnitude of the protein thermodynamic affinity relative to solvent occurs more governing factor causing the increase in the concentration area of the phase separation of the mixed solutions of the proteins studied under pH variation from 7.8 to 7.0. Direct relationships between the second virial coefficient determined experimentally with the chemical potential, i.e. with the molar free energy, show in their turn that the value and sign of the second virial coefficient are also a reflection of the sum of both entropy (in particular structural) and enthalpy (in particular energy of different types of interactions) factors controlling the nature of the interactions of the components in the system. The analysis of the nature of the factors controlling interactions between all components of the system and, as a consequence of this, the conclusions about the nature of the deciding factors determining the phase state of the mixed polymer solutions may be carried out by determination and comparison of the nature of the constituents of the second virial coefficient value. Current theories of the second virial coefficient attest that in the case of the polyelectrolytes, among which are proteins,

L.A. Wasserman, M. G. Semenova and E.N Tsapkina

334

the value of the second virial coefficient is mainly determined by the contribution of the value of the thermodynamically excluded volume of the macroion (measure of the volume occupied by the macroion and modified by intermolecular interactions), as well as by the contribution of the electrostatic forces acting between macroions (11,23).The equation for the second virial coefficient may thus be written as: A"

lJ

=A lJ..exe + A lJ..electr

(10)

i =j for the case of interactions of the same macroions, where the first term is the contribution of the thermodynamically excluded volume of the polyion to the experimental second virial coefficient, A ire. Let us assume in the first approximation that the thermodynamically excluded volume is defined only by the physical volume occupied by one protein molecule which is inaccessible for other protein molecules (11):

where N A is Avogadro's number; U =41t/3 (R, + Rj )3 in the case of the interaction between hard spheres (an approximation which is acceptable under interactions of the globular proteins); R, and R, are equivalent solid-sphere radii of protein molecules; R 1IS globulin v.F. =5 nm (35); ROVA =3 nm (11,36); and M i , M, are weight molecular weights of the proteins. The second term of equation (10) is the contribution of the electrostatic interactions in the system to the value of the experimental second virial coefficient, A;fteetr. Let us suppose in the first approximation that Aijeleetr is the product of the ideal Donnan term (Al; this is the term which stems from the condition that the electric neutrality is fulfilled in the theory of Debye and Huckel) and the correction factor for the electrostatic interaction between ions (I' I)' In the case of the globular protein, it is possible to assume that polyion as a rigid sphere may be presented as a point particle having (-2) charges and does not take into account the chain character of the polyion (11): A ..eleetr lJ

=A lJ..0

xrl

(12)

where (13) in which Zi' Zj are protein molecule charges; VI is partial specific volume of the solvent; m3 is the molal concentration of supporting electrolyte in the solution; and M i , M, are molecular weights of the polyelectrolytes.

where Yso is the activity coefficient of added salt without

polyelectrolytes, Yso =0.778 (39); Yeo is the activity coefficient of counterions in the salt-free polyelectrolyte solution averaged over the range of polymer concentration used. In order to analyse the nature of the second virial coefficients determined experimentally, firstly, we tried to estimate what contribution of thermodynamically excluded volume or electrostatic forces determines the character of the pair interactions between protein molecules under the experimental conditions. The contribution of excluded volume to the magnitude of a second virial coefficient was calculated by equation (11) both at pH 7.8 and pH 7.0. In so doing, we assumed that the size of the protein molecules is constant in the pH region studied. The contribution of the electrostatic component to the magnitude of a second virial coefficient was calculated by subtraction of the excluded volume contribution from the magnitude of a second vidal coefficient obtained experimentally. The data obtained exhibit substantial change in the nature of the intermolecular interactions, between both the same and different protein molecules under pH variation from 7.8 to 7.0 (see Tables 1 and 2). So, at pH 7.8, interaction between protein molecules is determined by electrostatic repulsion in preference. The contribution of the electrostatic interactions exceeds the excluded volume contribution several times. In contrast, at pH 7.0 the contribution of the excluded volume either defines the character of the protein molecule interaction, as in the case of ovalbumin, or exceeds the magnitude of the experimental second virial coefficient essentially both as in the case of lIS globulin and in the case of the interaction between ovalbumin and lIS globulin molecules. In this way, at pH 7.0 attractive forces, probably of a hydrophobic nature, begin to prevail over electrostatic repulsions between protein molecules in aqueous medium as a result of like-sign charge diminution on the protein molecules. As a consequence of this, either attractive forces compensate the excluded volume effect as well as forces of the electrostatic repulsion (as in the case of the interaction between lIS globulin molecules themselves and with ovalbumin molecules), or the excluded volume effect begins to determine interactions between protein molecules as a result of a compensating effect of electrostatic repulsion by attractive forces (as in the case of the interactions between ovalbumin molecules). The certainty of the electrostatic contribution obtained experimentally to the magnitude of the second virial coefficient was estimated by correlating experimental data with theoretical calculations on the basis of the protein molecule charges, which were determined experimentally. The comparison of the values of the electrostatic contribution defined experimentally (A;fleetr) with the ideal Donnan term (AijD), calculated by equation (13) manifests the essential exceed ideal Donnan term contribution over electrostatic contribution obtained experimentally to the magnitude of the second virial coefficient. At the time of this

Thermodynamics of Vfaba ovalbumin

study, this result was observed both in the case of the interactions of the same protein molecules and the different protein molecules (see Tables I and 2). The result gained is typical for real, as general, non-ideal solutions of the polyelectrolytes (11,23). For example, in extremely non-ideal systems such as linear polyelectrolyte solutions, the experimental second virial coefficient is about onehundredth as low as the Donnan term. This disagreement between theory and experiments points out the necessity of considering electrostatic interactions under theoretical calculation of electrostatic contribution to the magnitude of the second virial coefficient (11). Thus, it can be seen that the Donnan term of the second virial coefficient of polyelectrolyte solutions should be modified by both the electrostatic interaction among ions and the chain character of polyion (23). Using the values of A;fleJ:.tr obtained experimentally and the calculated values of Al, we attempted to evaluate the electrostatic interaction term F I. The values of r l thus obtained and also the values of Yeo calculated by using equation (14) are listed in Table 1. The values of r l and Yeo obtained for lIS globulin at pH 7.8 are close to the theoretical values expected, which are typical for polyions (23,39). Higher values of r l and Yeo in the case of ovalbumin are apparently specified by the smaller charge of ovalbumin molecules as compared with the charge of the 11 S globulin molecules (see Fig. 5a and b). The average activity coefficient of counterions in the mixed protein solution was calculated on the basis of the values of the activity coefficients of counterions estimated in the solutions of individual proteins. In so doing, the principle of additivity relative to activity coefficients was taken into account (11 ,37,38). Namely: Yemix = (YellS

+ Yeov~/2 = (0.23 + 0.64)/2 = 0.44

(15)

The correction factor r l [equation (14)] for mixed protein solutions was calculated on the basis of "(cmix• Then the value of the electrostatic term of the cross second virial coefficient was counted on the basis of this correction factor by equation (12). Within 10% experimental error, this calculated electrostatic term agrees nicely with electrostatic term of the cross second virial coefficient determined experimentally (see Table 2). The results observed obviously manifest the certainty of the experimentally determined electrostatic contributions to the magnitudes of the second virial coefficients, characterizing pair interactions of both the similar protein molecules and the different protein molecules at pH 7.8, and consequently the reliability of the conclusions about the determining role of the electrostatic repulsion in interactions between protein molecules in the system studied at pH 7.8. It is known from the literature that the character of interactions between the components of a solution defines the phase state of the solution (27,33,34,40). Relying on this knowledge, it is possible to assume that the forces of electrostatic repulsion between both the similar and different

335

protein molecules playa key role in the phase separation of the mixed protein solutions at pH 7.8. The compensation effect of the attractive forces between both the same and the different protein molecules leads to the impossibility of adequate theoretical estimation of the forces of the electrostatic interaction between protein molecules at pH 7.0. It is thus possible that this circumstance might explain unexpected reduced values of both the correction factor to the ideal Donnan term and the activity coefficient of counterions in the case of ovalbumin at pH 7.0 (see Table 1). However, the results obtained clearly exhibit the determining role of attractive forces, which are apparently hydrophobic in nature, acting between protein molecules and dictating both the character of the interaction between protein molecules in aqueous medium and features of the phase state of the mixed protein solutions at pH 7.0. In such a manner, it is possible to suppose that intensification of the mutual attraction between protein molecules and the consequent decrease in the thermodynamic affinity of the protein molecules in relation to solvent are the main reasons for the increase in the concentration area of phase separation in the mixed protein solutions under pH variation from 7.8 to 7.0. Also pointed out is the necessity of considering the translational entropy of the contribution of counterions to the free energy of the system under examination factors controlling the phase separation in the solutions of the polyelectrolytes (41,42). The contribution of the translational entropy of counterions leads to a significant increase in the mixing entropy of the system and, as a result, to the enhancement of miscibility of the polyions (41,42). However, in the case of the mixed protein system studied, the change in the phase state of the mixed protein solution under pH variation is hardly possible to explain by tran slational entropy of counterion alteration since it was clearly established in the literature that the presence of salt suppresses significantly the compatibility enhancement effect described above. There is a rather large amount of salt (0.1 mol/dm! NaCl) in the mixed protein solution studied and , moreover, the protein total charge does not change dramatically under pH variation from 7.0 to 7.8 (see Fig. 5). Consequently, the number of dissociated counterions also does not alter dramatically. A significant increase in the miscibility of polymers was observed in the literature under charge density rise on polymer molecule, as a rule, in the case of the mixtures of the ionic polymer with unionic polymer. On the other hand, it has also been indicated in the literature that in the case of like-signed ionic polymer mixtures, in general, a substantial increase in the density of dissociating groups on one of the polyelectrolytes leads to a dramatic decrease in the miscibility of the polyelectrolytes independently of the contribution of the counterions to the mixing entropy of the system (41,42). In our case, reduction of the like-signed charge density on protein molecules did not lead to a rise of protein compatibility but , on the contrary, caused an increase in

L. A. Wasserman, M. G Semenova and E. N.Tsapkina

336

(~)

40

.. ~

cooidina\esof the critical points: (experimentaO . C11SVF.,,1.8%: C OVA = 13.6%

coordinates of thecritical points: experimental C 115 V.F. ~8.5 %: C OVA. 18.9 % calculated; C 115 V.F.. 18.9 %.C OVA.. 11.9 %

40

. ~

30

30

6::;; ::::>

CIl

--' -c

> 0

20

0

10

10 C 115 V.F.. % wlv

20

30

40

C 115 V.F.. % wlv

Figure 6 The experimental binodals with spinodals calculated theoretically for the ternary system lIS globulin-ovalbumin-water (I == 0.1

mol/dm'' NaCl, t =25°C). (a) at pH 7.8; (b)at pH 7.0.

protein immiscibility. Consequently, it is possible to assume that the basic reason for the protein immiscibility rise with pH decrease (from 7.8 to 7.0) is intensification of the self-association of the mixed proteins, mainly of the lIS globulin, as indicated by comparison of the second virial coefficients, characterizing the pair interactions of both similar and different protein molecules. Generally, alteration of the chemical potentials in one process to another characterizes the thermodynamic behaviour of the system in passing from one equilibrium state to another. So, for example, it is possible to predict the concentration region of the phase separation in mixed polymer solutions by calculation through the use of chemical potentials (27,32,40,43). The equations describing coordinates both of the critical point (equation 4) and of spinodal (equation 5) were developed on the basis of the chemical potentials of the components of the ternary system (equations 7-9). In so doing, all these equations are based on values of the second virial coefficients characterizing the nature and intensity of the pair interactions of both the same and different macromolecules. The advantage of the chemical potentials expression of the polymer solution components using values of the second virial coefficients is universality and independence on one or another theory of polymer solutions. So, we attempted to calculate spino dais as well as coordinates of the critical points by equations (4) and (5) on the basis of the second virial coefficients obtained experimentally. Figure 6a and b shows binodals determined experimentally as well as spinodals calculated theoretically. The shift in the calculated area of phase separation both at pH 7.8 and 7.0 in mixed protein solutions has been determined experimentally and, supposedly, can manifest the

impossibility of an absolute exact prediction of the phase separation area of the system on the basis of the values of the second virial coefficients, i.e. on the basis only of the pair interactions between components of the solution, firstly, without consideration of the higher order interactions between molecules, and secondly, without taking into account any possible change in the second virial coefficient values with protein concentration increase in the solutions. By this means, from the results obtained in this investigation, it is possible to conclude that on the basis of the second virial coefficients, both examination of the nature of the key factors controlling the phase state of the mixed biopolymer solutions and approximate estimation of the concentration area of the phase separation in the mixed biopolymer solutions are conceivable.

Acknowledgement The research described in this paper was made possible in part by grant no. MLNOOO from the International Science Foundation.

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Thermodynamics of V.faba ovalbumin

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Received on December 21, 1994; accepted on March 22, 1996