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A surface equation of state for globular proteins at the air-water interface
A Surface Equation of State for Globular Proteins at the Air-Water Interface 1 FAROOQ URAIZEE AND GANESAN NARSIMHAN 2 Department of Agricultural Engineering, Purdue University, West Lafayette, Indiana 47907 Received July 2, 1990; accepted February 21, 1991 A surface equation of state for globular proteins at the air-water interface accounting for the structure of the protein molecule, its degree of unfolding, and segment-segment, segment-solvent, and electrostatic interactions is proposed. The proposed lattice model employs the simplifying assumption that all the adsorbed segments are present in the form of trains. Results obtained by fitting the equation of state to the experimental data indicate that the average degree of unfolding of bovine serum albumin (BSA) is greater than that of lysozyme. The number of segments adsorbed per molecule of BSA is found to vary linearly with the surface concentration, whereas the segments of lysozyme adsorbed at the interface are fairly independent of surface concentration. The segment-solvent interactions of the adsorbed segments of BSA and lysozyme are found to be unfavorable (X > 0.5) due to the exposure of hydrophobic functional groups resulting from unfolding. The maximum surface pressure and surface concentration for monolayer coverage are highest at p I and their predicted variation with pH is in good agreement with the experimental data.
© 1991 Academic Press, Inc.
INTRODUCTION
Investigation of protein adsorption at fluidfluid interfaces is necessary for a proper understanding of its ability to stabilize foams and emulsions in a variety of applications. Adsorption of proteins at the gas-liquid interface leads to a lowering of the surface tension or an increase in the surface pressure. The relationship between the surface pressure and the surface concentration is usually referred to as the surface equation of state. Although this relation is determined experimentally for various proteins ( 1), a satisfactory mathematical model for the determination of the surface equation of state does not exist in the literature because the behavior of adsorbed protein at the interface has not yet been fully understood. Proteins are complex macromolecules formed by the association of a large number of amino acid residues. The number, type, and sequence Paper No. 12715, Agricultural Experiment Station, Purdue University, West Lafayette, IN 47907. 2 To whom correspondence should be addressed.
of amino acids present in a protein molecule determine its size, shape, and properties in aqueous solutions as well as at interfaces. In globular proteins, the amino acid residues are folded compactly into spherical or globular shapes in aqueous solutions. Upon adsorption at an interface these proteins tend to unfold and the degree of unfolding depends on the nature of protein, the interaction between the adsorbed segments and the protein molecule, and the surface concentration. Thus, the behavior of proteins at interfaces is very complex compared with the behavior of polymers. Extensive work has been done on the adsorption of flexible polymers at the air-liquid interface. Singer (2), on the basis of the approach of statistical thermodynamics, derived an expression for the surface pressure of flexible homopolymers assuming that all segments were adsorbed at the interface and that there were no interactions between them. This expression was valid only for low surface pressure. Singer's model has been extended to account for segment-segment interactions (3, 4)
169 0021-9797/91 $3.00 Journal of Colloid and Interface Science, VoI. 146, No. 1, October 1, 1991
Copyright © i991 by Academic Press, Inc. All rights of reproduction in any form reserved
170
URAIZEE AND NARSIMHAN
as well as for the formation of loops and trains (5). The number and size of the loops and trains formed due to the adsorption of a polymer have been shown to depend on the energy configuration of the polymer and are independent of its molecular weight (6). Although the existing models for polymers may find limited application in the description of the surface equation of state for flexible, random coil proteins such as t-casein, they are not likely to be applicable to the adsorption of globular protein. The objective of the present paper is to develop a surface equation of state for globular proteins accounting for the structure of the protein molecule, the extent of unfolding, and the interactions among the adsorbed segments, as well as for the pH and ionic strength. The salient features of the model are given in the next section. This is followed by the comparison o f model predictions with the experimental data for model systems of BSA and lysozyme.
Moreover, the extent of unfolding is hindered by the presence o f disulfide bonds within the protein molecule. Consider a two-dimensional surface lattice consisting of Ns lattice sites. The area of each lattice site is assumed to be equal to the area occupied by an adsorbed protein segment at the interface. It is customary to assume that this is also equal to the area occupied by a solvent molecule. Let n segments of a protein molecule be adsorbed and N2 protein molecules be placed at the surface. The total number of adsorbed segments, therefore, is N2n. It is assumed that the adsorbed segments are present only in the form o f trains at the interface. Since only a certain fraction of segments in a protein molecule is adsorbed with the rest, more or less maintaining the original conformation, the adsorbed segments are connected to the protein molecules protruding into the aqueous medium and therefore cannot be iocated anywhere in the lattice. In order to calculate the configurational entropy, we will first MODEL FOR SURFACE EQUATION OF STATE calculate the number of ways in which the protein molecules themselves can be placed A globular protein molecule in aqueous so- on the lattice, followed by the number o f ways lution tends to assume a tertiary structure in of mixing the adsorbed segments belonging to which most of the hydrophobic functional a protein molecule. groups are buried inside the protein molecule Since n adsorbed segments belonging to a and the hydrophilic functional groups are ex- protein molecule are interconnected and loposed to the aqueous medium at the surface calized in an "island" on the lattice, the numsince such a conformation is energetically ber of ways of placing the protein molecules most favorable. Adsorption of globular protein can be evaluated by placing them on a "super at the air-water interface results in partial lattice" whose lattice site can accommodate a penetration of the molecule while the rest o f protein molecule (i.e., n lattice sites). The total the molecule retains more or less its original number of super lattice sites is equal to N's structure. Upon penetration, the molecule ( = U s / n ) . unfolds so that the hydrophobic functional The n u m b e r of ways of placing the first progroups are exposed to the air and the hydro- tein molecule on the super lattice is N'~; the philic groups are exposed to the aqueous me- number o f ways of placing the second protein dium. T h e extent of penetration and subse- molecule is (N's - 1 ). Similarly, the number quent unfolding of the molecule depends on of ways of placing the (i + 1 ) th protein molthe surface pressure (i.e., surface concentra- ecule is (N" - i). tion) and segment-segment interactions of the The segmems belonging to an adsorbed molecule. For example, a t lower surface con- protein molecule can, in turn, be placed in centrations, the adsorbed globular protein many ways within the island of n lattice sites. molecule tends to penetrate and unfold more The number of ways of placing the first segthan at higher surface concentrations (1). ment is n. If z is the coordination number of Journal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
PROTEINS
AT THE
AIR-WATER
the lattice, the number of ways of placing the second segment is z. The number of ways of placing any subsequent segment is (z - 1 )f, where the flexibility parameter f can take values between 0 and 1. Therefore, the total number of ways w , ( z ) in which the n adsorbed segments can be placed on the lattice is given by 1 ) f } n-z,
wn(z) = l n z { ( z -
[1]
where the factor 2 is included to avoid double counting. For completely flexible molecules, the number of ways of placing the segments wU(z) is given by w~(z)
= lnz(z
-
1) "-2.
[2]
For a completely inflexible protein molecule, however, the adsorbed segments can be placed only in one way. In this case, the problem reduces to that of evaluating the number of ways of placing the molecules on the super lattice. It is to be pointed out, however, that the unfolding of the penetrated segments does require some flexibility of the segments so the flexibility parameter is never quite equal to zero. Hence, the total number of ways ft of placing N2 protein molecules in the lattice is given by a =
~-IN201 ( N s / n N2~
i) w"(z}
[31
As pointed out earlier, the number of segments adsorbed per protein molecule (the extent of penetration and unfolding) depends on the surface concentration. The relationship between the number of adsorbed segments n and the surface concentration I" can be formally expressed as n -- = g(P/I'max), no
[4]
where no is the total number of segments in the protein molecule and Pmax is the maxim u m surface concentration corresponding to monolayer coverage. The function g is monotonically decreasing with surface concentration so that n -* no as r --~ 0; i.e., complete
INTERFACE
171
unfolding of the protein molecule occurs at very low surface concentrations. The secondary and tertiary structures of globular proteins are held together by hydrogen bonds (a-helices and /3-pleated sheets), hydrophobic interactions, and ionic bonds (7). Even though the tertiary structure of the adsorbed globular protein may be somewhat altered because of the unfolding of adsorbed segments, experimental observation of the structure of a foamed protein (8) indicates that the secondary structure (a-helices and 13pleated sheets) is preserved. The local ordering of amino acid residues due to the formation of a-helices and/3-sheets, therefore, results in the loss of flexibility of the adsorbed segments. Furthermore, the adsorbed segments which belong to the interior of the globular protein experience an additional loss of flexibility because of (i) strong segment-segment interactions and (ii) the presence of disulfide bonds. Consequently, the average flexibility of adsorbed segments is likely to be lower if the fraction of adsorbed segments belonging to the interior of the globular protein molecule is higher. As a result, the flexibility of adsorbed segments depends on the extent of penetration of the protein molecule and therefore on the number of segments adsorbed. When the number of adsorbed segments is large, i.e., the extent of penetration of the globular protein is large, the flexibility of the segments is likely to be low since the fraction of adsorbed segments buried inside the protein molecule is high. On the other hand, segments can unfold more easily (and hence are more flexible) if the extent of penetration is small since most of the adsorbed segments will be on the surface. The exact relationship between the number of adsorbed segments and their flexibility is not known and is likely to be infuenced by the type of amino acid residues and the segment-segment interactions. Since the flexibility of the segments would become smaller as a greater number of segments are adsorbed, the number of ways of arranging the adsorbed segments w, (z) will be a relatively weak function of n, as can be seen from Eq. [1 ]. ConJournal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
172
URAIZEE AND NARSIMHAN
sequently, w,(z) can be replaced by an average value, if(z), in Eq. [ 3] and therefore
~
IIN~=oI (N~/ n - i) ~ )
[51
N2~
The entropy of mixing AS is therefore given
tration of the electrolyte, Kis the Debye length parameter, e is the elementary charge, 3, is the valence number of the electrolyte, and ¢ is the potential of the interfacial protein layer. This surface potential can be related to the surface charge density {7through
by
. h_r[
2kT = -~
AS=klng=kff
{7
]
l(8kZl~Eo)l/2J
,
[11]
~ In 1 i=0
Expanding the logarithmic term in a Taylor series, we get
kw
s,n
+
[12]
{7 = Fqe.
The free energy of the surface lattice when the adsorbed protein molecules are charged is given by
T
+ kN2ff:ln(-~)-
where e is the dielectric constant of the medium and e0 is the permittivity of the vacuum. The surface charge density {7is, in turn, related to the charge on the protein molecule q and the surface concentration F via
kN21nN2.
[7]
The enthalpy of mixing can be written following Flory's treatment as N2n N
z2XI-I = XON1 = X - - - ~ s
1,
(OAF) H
OA
[14] N2,T
where the total area of the surface lattice A is N, ao. Therefore, I~ {7O
_{
l ONs
JN2,T
[9]
where AS and M-/are given by Eqs. [ 7 ] and [ 8 ], respectively. When the pH of the medium is other than pI, the interfacial protein layer will be charged and consequently an electrical double layer will be set up next to the interface. The free energy of the unit area of the double layer ZSaWDLis given by (9) AFDL---8kTm[c°sh(~2-~T)--K - 1} ,
where {70is the area of a lattice site. The surface pressure II is related to the free energy AF via
[8]
where X is the Hory-Huggins parameter, 0 is the fraction of the surface occupied by adsorbed segments, and N~ is the number of solvent molecules. The free energy of the surface lattice when the adsorbed protein molecules are uncharged is therefore given by AF, = Mt - TAS,
T A S + Z~WDLNs{70, [13]
AT" = M 4 -
[10]
where k is Boltzmann's constant, T is the absolute temperature, m is the number concenJournalof Colloidand InterfaceScience, Vol. 146, No. 1, October 1, 1991
+[
iN2,A-d-f] -g- d"
Evaluating the above we get X [ ~2( l + r
-II- = kT
ao X (70
+ --
if0
[r ~ o ( 1
o"o~-ll 20n']oF]j
nr{7o) - r - : - ~
n
On
r2{7o ~-f ( 1 - nr{7o) - ¢ 2 r % o
+ ~I" 1 + ~ (r{7on) + ~ (r{7on) 2
0n 1
173
PROTEINS AT THE AIR-WATER INTERFACE
+ ¼ (I'~ron)3 q - ~ (I'cron)4 + ' ' ' ]
20-
ff~p2On On[2 1 n or + ~r3a° or + ~ (raon)
+ ~, ( r~on)2 + ~1 ( r ~ o n ) 3 +-
+
• . .
]
Surface Pressure
HxlO3 N/m
8m[ (ze ) ] cosh
10-
- 1
K
8m r
c~rz[l + clr/¢1 + (clr) 2] ~ I ' + ~/1 + - ( q - ~
J ' [16]
where
Surface Concentration
qe C1
(8kTrmeo) u2
~b2 = nFa0.
r mg/m2
FIG. 1. Effect of variation in parameter a on the predicted surface equation of state. Values for parameter a are 0.68 for curve 1, 0.7 for curve 2, 0.709 for curve 3, 0.72 for curve 4, and 0.85 for curve 5. Other parameter values are those for BSA given in Table I.
RESULTS
The following functional relationship for the dependence of the number of protein segments adsorbed at different surface concentrations was employed in the calculations:
of state (Eq. [16]) was fitted to the experimental data for BSA and lysozyme using nonlinear optimization (10). a, b, x, and # ( z ) are the independent parameters that are fitted. Fma x is obtained from experimental data. The n___= 1 - a(XVrmax) b. [17] optimization routine was run for a wide range no of initial guesses for the parameter values in The parameter a is related to the average order to ensure a unique set of fitted parameter degree of unfolding of the protein molecule. values. The values of the parameters a, b, ×, Smaller (larger) values of parameter a corre- and # ( z ) for BSA and lysozyme are given in spond to protein molecules that unfold more Table I. Analysis of the sensitivity of the surface (less) upon adsorption. The derived equation equation of state (Eq. [ 16 ]) to the parameters a, b, x, and v~(z) was performed and the reTABLE I sults of this analysis are shown in Figs. 1-4, respectively. The effect of parameter a on the BSA Lysozyrne surface equation of state is shown in Fig. 1. The surface pressure for high surface concenMolecular weight 68,000 14,400 trations is found to be very sensitive to the no 606 147 pI 5.5 9.2 value of a (Fig. 1 ). On the other hand, there ~7(z) 67.54 24.72 is negligible variation in the surface pressure x 0.605 0.695 for smaller surface concentrations (see Fig. 1 ). a 0.709 0.816 As can be seen in Fig. 1, the predicted values b 1 -0.05 Fma,~(mg/m 2) (pH 7) 2.22 5.00 of IImax decrease as parameter a increases beII~x (N/m) (pH 7) 17 X 10-3 21 X 10-3 cause of the decrease in the degree of unfoldo-0 (m 2) 17 X 10-20 17 X 10-20 ing. The effect of parameter b on the surface Journal of Colloid and lnterface Science, VoL
146, No. 1, October 1, 1991
174
URAIZEE A N D N A R S I M H A N
3020-
251520Surface Preasure
Surface Pressure ,5-
H x 103 N/m
II x ,03 N/m
,0-
,0-
5-
0-
'
J
I
;.s
~
2~
J
3~
Surface Concentration
Surface Concentration
F mg/m2
i ~ iltg/m 2
FIG. 2. Effect of variation in parameter b on the predicted surface equation of state. Values for parameter b are 1.5 for curve 1, 1.1 for curve 2, 1.0 for curve 3, 0.8 for curve 4, and 0.5 for curve 5. Other parameter values are those for BSA given in Table I.
FIG. 4. Effect of variation in parameter if(z) on the predicted surface equation of state. Values for parameter ,7(z) are 75 for curve 1, 70 for curve 2, 67-54 for curve 3, 60 for curve 4, and 55 for curve 5. Other parameter values are those for BSA given in Table I.
equation of state is shown in Fig. 2. The surface pressure is found to be very sensitive to the values of parameter b and increases for larger values of b over the whole range of sur-
face concentrations. This can be attributed to the fact that the number of adsorbed segments (and therefore the degree of unfolding) increases for larger values of b (see Eq. [ 17 ]). The predicted surface equation of state is not as sensitive to the Flory-Huggins X parameter
20-
185 1515-
Surface Pressure 17 x 103 N/m
12,0Surface Pressure Flx 103 N/m
9-
6-
30-
0Surface Concentration r mf~ Surface Concentration
FIG. 3. Effect of variation in parameter X on the predicted surface equation of state. Values for parameter x are 0,8 for curve 1, 0.7 for curve 2, 0.605 for curve 3, 0.5 for curve 4, and 0.3 for curve 5. Other parameter values are those for BSA given in Table I. Journal of Colloid and Interface Science, V o l .
146, N o . 1, O c t o b e r 1, 1991
]" IIig/m2
FIG. 5. Plot of surface pressure versus surface concentration of BSA; solid curve refers to model predictions; ( n ) is the experimental data of G r a h a m and Phillips ( 1 ).
175
PROTEINS AT THE AIR-WATER INTERFACE 24-
21-
18-
15. Surface Pressure
12 -
FIx 103 N/m
/ ~
9:
62 32
0~
/
A
Surface Concentration F mg/m2
FIG. 6. Plot of surface pressure versus surface concentration of lysozyme; solid curve refers to model predictions; (A) is the experimental data of Graham and Phillips ( 1 ).
as to the other two parameters, as can be seen in Fig. 3. For higher surface concentrations, surface pressure is found to increase for larger X values (see Fig. 3 ). For smaller surface concentrations, however, the opposite trend is observed (Fig. 3). The effect of parameter ~ ( z ) on the surface equation of state is shown in Fig. 4. Increasing the number of ways of placing the protein segments [ # ( z ) ] at the gasliquid interface leads to higher surface pressure, as can be seen in Fig. 4. It is found that parameter a for BSA (0.709) is lower than that (0.86) for lysozyme (see Table I), implying thereby that the average degree of unfolding for lysozyme is lower than that for BSA. Moreover, from the values of parameter b, it can be said that the number of segments of BSA adsorbed at the interface bear a linear relationship with the surface concentration, whereas the number of adsorbed segments oflysozyme is more or less independent of the surface concentration. These are in accordance with the experimental observation that lysozyme is more condensed than BSA, thereby implying that it unfolds less than BSA ( 1 ). It can be seen from Table I that the FloryHuggins X parameters for BSA and for lysozyme are 0.605 and 0.695, respectively, im-
plying thereby that the segment solvent interactions are unfavorable (i.e., the solvent is " p o o r " ) . This unfavorable interaction results from the exposure of more hydrophobic functional groups due to the unfolding of the protein molecule. The comparison between the experimental data and the fit for the surface equation of state for BSA and lysozyme is shown in Figs. 5 and 6, respectively. At monolayer coverage, the neutral adsorbed interfacial protein layer consists of close-packed islands of segments connected to the part of the protein molecule that extends into the solution. Charging this neutral film leads to a decrease in the cohesiveness of the adsorbed segments because o f electrical interactions and consequently to a reduction in the surface concentration. This reduction in the surface concentration can also be viewed as a consequence of the increase in the excluded area of the segments due to electrical interactions. The reduction in the maximum surface concentration for monolayer coverage can be related to the change in the free energy of a segment due to electrical charge via the Boltzmann factor as
( ol 1
= e -n°l~°/kr,
[181
\ Fneutral/max
18 -
pl pH 7
15 -
pH 9
12Surface Pressure H x l 0 3 Nhn
9-
6-
3-
0-
'
.;
i
1;
~
2;
;
;.5
Surface Concentration F mgtm2
FIG. 7. Predicted surface equation o f state for BSA at different pH. Journal of Colloid and lnterface Science,
V o t . 146, N o . t, O c t o b e r 1, 1991
176
URAIZEE AND NARSIMHAN
where
kT
t
~
JN,,T --~
jN,,r\-O--~/
[19]
and AFDL is given by Eq. [10]. The maxim u m surface concentration corresponding to monolayer coverage Fmax at any p H is evaluated using Eq. [18] and the dependence of charge on pH for BSA ( 11 ) and lysozyme (12). Figure 7 shows the plot of II versus P for BSA at p H values of 5.5, 7, and 9. The effect of charge is negligible at lower surface concen-
trations, becoming significant only at surface concentrations near rmax, and is consistent with the experimental observations of Graham and Phillips ( 1 ). ° Figure 8 shows a comparison between the experimental and the predicted dependence of maximum surface pressure on pH for BSA and lysozyme. As the charge on BSA changes considerably with pH, the effect of pH on maximum surface pressure is more pronounced, with IImax being highest at the isoelectric point. The predicted variation of Ilmax with pH for BSA agrees fairly well with the experimental data in the pH range of 2 to 7. For higher pH values (7-12), however, very little variation of IImax is observed, whereas
30,
X
25
X x []
20 Maximum Surface Pressure
÷++ a
15
+
+
+
a
A
+
÷
+
+
rlm~ N/m x
+A
A
103 10
I 2
I 4
I 6
I 8
[ 10
I 12
pH
FIG. 8. Plot of maximum surface pressure versus pH for BSA and lysozyme.(A) and ([~) refer to the experimental data ( 1) for BSA and lysozyme,respectively,and (+) and (×) refer to model predictionsfor BSA and lysozyme,respectively. Journal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
PROTEINS AT THE AIR-WATER INTERFACE the predicted values exhibit a slight decrease with pH (Fig. 8). On the other hand, for lysozyme the variation of charge with pH is not significant, except very near the isoelectric point. This is reflected in a very weak dependence of IImax on p H away from the p I (pH 9.2 ) and a sharp variation near the isoelectric point. Unfortunately, no experimental data are available to show this dramatic increase in the surface pressure of lysozyme near its isoelectric point. Experimental and predicted maximum surface concentrations corresponding to monolayer coverage for BSA are shown in Fig. 9. As expected, predicted Fmax is m a x i m u m at the isoelectric point. The experimental variation of Fmax with pH is found to be larger than predicted, as can be seen from Fig. 9.
177
CONCLUSIONS A surface equation of state for globular proteins at the air-water interface accounting for the structure of the protein molecule, its degree of unfolding, and segment-segment, segmentsolvent, and electrostatic interactions has been proposed. The lattice model assumed that all the adsorbed segments are present in the form of trains, and the variation in the number of adsorbed segments (degree of unfolding) with the surface concentration is represented by the relationship n/no = 1 - a ( £ / r m a x ) b . From the results obtained by fitting this equation of state to experimental data it is found that the average degree of unfolding of BSA is more than that of lysozyme and that the number of segments of BSA adsorbed at the interface
2.5 [] []
p~xx ~
Maximum Surface Concentration F max
x
x
[] []
1.5
mg/m 2
1-
.5
O-
I 2
I 4
I 6
I 8
I I0
I 12
pH
FIG. 9. Plot of maximum surfaceconcentrationversuspH for BSA; ([5) refersto experimentaldata ( 1) and (×) refersto model predictions. Journal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
178
URAIZEE AND NARSIMHAN
varies linearly with the surface concentration, whereas the segments o f lysozyme adsorbed at the interface are m o r e or less independent o f the surface concentration. For both BSA a n d lysozyme, it is f o u n d that the parameter X is greater than 0.5, suggesting that the solvent segment interactions are unfavorable at the interface for the adsorbed protein molecule. The dependence o f m a x i m u m surface pressure a n d m a x i m u m surface concentration on p H has been evaluated and is f o u n d to agree well with the experimental observations. It is found that both the surface pressure and the surface concentration for BSA are m a x i m u m at the isoelectric point and decrease with an increase in the charge o n the protein molecule. For lysozyme, the m a x i m u m surface pressure is m o r e or less independent o f p H at p H other than the isoelectric point. The results obtained here are in g o o d agreement with the experimental data.
Journal of Colloid and Interface Science, Vot. 146, No. 1, October 1,1991
REFERENCES 1. Graham, D. E., and Phillips, M. C., J. Cotloidlnte(ace Sci. 70, 427 (1979). 2. Singer, S. J., J. Chem. Phys. 16, 872 (1948). 3. Davies, J. T., and Lopis, J. L., Proc. R. Soc. London A 227, 537 (1955). 4. Motomura, K., and Matuura, R., J. Colloid Sci. 18, 52 (1963). 5. Frisch, H. L., and Simha, R., J. Chem. Phys. 27, 702 (t957). 6. Silberberg, A., J. Phys. Chem. 66, 1872 (1962). 7. Lehninger,A. L., "Biochemistry,"2nd ed. Worth, New York, t975. 8. Clark, D. C., Smith, L. J., and Wilson, D. R., J. Colloid Interface Sci. 121, 136 (1988). 9. Verwey, E. J. W., and Overbeek, J. Th. G., "Theory of the Stability of Lyophobic Colloids." Elsevier, New York, 1948. 10. Procedure NL1N. SAS Release, 6.03 Edition. SAS Institute, Cary, NC, 1988. 11. Tanford, C., Swanson, S. A., and Shore, W. S., J. Am. Chem. Soc. 77, 6414 (1955). 12. Devereux, J., Haeberli, P., and Smithies, O., Nucleic Acids Res. 12( 1), 387 (1984).
© 1991 Academic Press, Inc.
INTRODUCTION
Investigation of protein adsorption at fluidfluid interfaces is necessary for a proper understanding of its ability to stabilize foams and emulsions in a variety of applications. Adsorption of proteins at the gas-liquid interface leads to a lowering of the surface tension or an increase in the surface pressure. The relationship between the surface pressure and the surface concentration is usually referred to as the surface equation of state. Although this relation is determined experimentally for various proteins ( 1), a satisfactory mathematical model for the determination of the surface equation of state does not exist in the literature because the behavior of adsorbed protein at the interface has not yet been fully understood. Proteins are complex macromolecules formed by the association of a large number of amino acid residues. The number, type, and sequence Paper No. 12715, Agricultural Experiment Station, Purdue University, West Lafayette, IN 47907. 2 To whom correspondence should be addressed.
of amino acids present in a protein molecule determine its size, shape, and properties in aqueous solutions as well as at interfaces. In globular proteins, the amino acid residues are folded compactly into spherical or globular shapes in aqueous solutions. Upon adsorption at an interface these proteins tend to unfold and the degree of unfolding depends on the nature of protein, the interaction between the adsorbed segments and the protein molecule, and the surface concentration. Thus, the behavior of proteins at interfaces is very complex compared with the behavior of polymers. Extensive work has been done on the adsorption of flexible polymers at the air-liquid interface. Singer (2), on the basis of the approach of statistical thermodynamics, derived an expression for the surface pressure of flexible homopolymers assuming that all segments were adsorbed at the interface and that there were no interactions between them. This expression was valid only for low surface pressure. Singer's model has been extended to account for segment-segment interactions (3, 4)
169 0021-9797/91 $3.00 Journal of Colloid and Interface Science, VoI. 146, No. 1, October 1, 1991
Copyright © i991 by Academic Press, Inc. All rights of reproduction in any form reserved
170
URAIZEE AND NARSIMHAN
as well as for the formation of loops and trains (5). The number and size of the loops and trains formed due to the adsorption of a polymer have been shown to depend on the energy configuration of the polymer and are independent of its molecular weight (6). Although the existing models for polymers may find limited application in the description of the surface equation of state for flexible, random coil proteins such as t-casein, they are not likely to be applicable to the adsorption of globular protein. The objective of the present paper is to develop a surface equation of state for globular proteins accounting for the structure of the protein molecule, the extent of unfolding, and the interactions among the adsorbed segments, as well as for the pH and ionic strength. The salient features of the model are given in the next section. This is followed by the comparison o f model predictions with the experimental data for model systems of BSA and lysozyme.
Moreover, the extent of unfolding is hindered by the presence o f disulfide bonds within the protein molecule. Consider a two-dimensional surface lattice consisting of Ns lattice sites. The area of each lattice site is assumed to be equal to the area occupied by an adsorbed protein segment at the interface. It is customary to assume that this is also equal to the area occupied by a solvent molecule. Let n segments of a protein molecule be adsorbed and N2 protein molecules be placed at the surface. The total number of adsorbed segments, therefore, is N2n. It is assumed that the adsorbed segments are present only in the form o f trains at the interface. Since only a certain fraction of segments in a protein molecule is adsorbed with the rest, more or less maintaining the original conformation, the adsorbed segments are connected to the protein molecules protruding into the aqueous medium and therefore cannot be iocated anywhere in the lattice. In order to calculate the configurational entropy, we will first MODEL FOR SURFACE EQUATION OF STATE calculate the number of ways in which the protein molecules themselves can be placed A globular protein molecule in aqueous so- on the lattice, followed by the number o f ways lution tends to assume a tertiary structure in of mixing the adsorbed segments belonging to which most of the hydrophobic functional a protein molecule. groups are buried inside the protein molecule Since n adsorbed segments belonging to a and the hydrophilic functional groups are ex- protein molecule are interconnected and loposed to the aqueous medium at the surface calized in an "island" on the lattice, the numsince such a conformation is energetically ber of ways of placing the protein molecules most favorable. Adsorption of globular protein can be evaluated by placing them on a "super at the air-water interface results in partial lattice" whose lattice site can accommodate a penetration of the molecule while the rest o f protein molecule (i.e., n lattice sites). The total the molecule retains more or less its original number of super lattice sites is equal to N's structure. Upon penetration, the molecule ( = U s / n ) . unfolds so that the hydrophobic functional The n u m b e r of ways of placing the first progroups are exposed to the air and the hydro- tein molecule on the super lattice is N'~; the philic groups are exposed to the aqueous me- number o f ways of placing the second protein dium. T h e extent of penetration and subse- molecule is (N's - 1 ). Similarly, the number quent unfolding of the molecule depends on of ways of placing the (i + 1 ) th protein molthe surface pressure (i.e., surface concentra- ecule is (N" - i). tion) and segment-segment interactions of the The segmems belonging to an adsorbed molecule. For example, a t lower surface con- protein molecule can, in turn, be placed in centrations, the adsorbed globular protein many ways within the island of n lattice sites. molecule tends to penetrate and unfold more The number of ways of placing the first segthan at higher surface concentrations (1). ment is n. If z is the coordination number of Journal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
PROTEINS
AT THE
AIR-WATER
the lattice, the number of ways of placing the second segment is z. The number of ways of placing any subsequent segment is (z - 1 )f, where the flexibility parameter f can take values between 0 and 1. Therefore, the total number of ways w , ( z ) in which the n adsorbed segments can be placed on the lattice is given by 1 ) f } n-z,
wn(z) = l n z { ( z -
[1]
where the factor 2 is included to avoid double counting. For completely flexible molecules, the number of ways of placing the segments wU(z) is given by w~(z)
= lnz(z
-
1) "-2.
[2]
For a completely inflexible protein molecule, however, the adsorbed segments can be placed only in one way. In this case, the problem reduces to that of evaluating the number of ways of placing the molecules on the super lattice. It is to be pointed out, however, that the unfolding of the penetrated segments does require some flexibility of the segments so the flexibility parameter is never quite equal to zero. Hence, the total number of ways ft of placing N2 protein molecules in the lattice is given by a =
~-IN201 ( N s / n N2~
i) w"(z}
[31
As pointed out earlier, the number of segments adsorbed per protein molecule (the extent of penetration and unfolding) depends on the surface concentration. The relationship between the number of adsorbed segments n and the surface concentration I" can be formally expressed as n -- = g(P/I'max), no
[4]
where no is the total number of segments in the protein molecule and Pmax is the maxim u m surface concentration corresponding to monolayer coverage. The function g is monotonically decreasing with surface concentration so that n -* no as r --~ 0; i.e., complete
INTERFACE
171
unfolding of the protein molecule occurs at very low surface concentrations. The secondary and tertiary structures of globular proteins are held together by hydrogen bonds (a-helices and /3-pleated sheets), hydrophobic interactions, and ionic bonds (7). Even though the tertiary structure of the adsorbed globular protein may be somewhat altered because of the unfolding of adsorbed segments, experimental observation of the structure of a foamed protein (8) indicates that the secondary structure (a-helices and 13pleated sheets) is preserved. The local ordering of amino acid residues due to the formation of a-helices and/3-sheets, therefore, results in the loss of flexibility of the adsorbed segments. Furthermore, the adsorbed segments which belong to the interior of the globular protein experience an additional loss of flexibility because of (i) strong segment-segment interactions and (ii) the presence of disulfide bonds. Consequently, the average flexibility of adsorbed segments is likely to be lower if the fraction of adsorbed segments belonging to the interior of the globular protein molecule is higher. As a result, the flexibility of adsorbed segments depends on the extent of penetration of the protein molecule and therefore on the number of segments adsorbed. When the number of adsorbed segments is large, i.e., the extent of penetration of the globular protein is large, the flexibility of the segments is likely to be low since the fraction of adsorbed segments buried inside the protein molecule is high. On the other hand, segments can unfold more easily (and hence are more flexible) if the extent of penetration is small since most of the adsorbed segments will be on the surface. The exact relationship between the number of adsorbed segments and their flexibility is not known and is likely to be infuenced by the type of amino acid residues and the segment-segment interactions. Since the flexibility of the segments would become smaller as a greater number of segments are adsorbed, the number of ways of arranging the adsorbed segments w, (z) will be a relatively weak function of n, as can be seen from Eq. [1 ]. ConJournal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
172
URAIZEE AND NARSIMHAN
sequently, w,(z) can be replaced by an average value, if(z), in Eq. [ 3] and therefore
~
IIN~=oI (N~/ n - i) ~ )
[51
N2~
The entropy of mixing AS is therefore given
tration of the electrolyte, Kis the Debye length parameter, e is the elementary charge, 3, is the valence number of the electrolyte, and ¢ is the potential of the interfacial protein layer. This surface potential can be related to the surface charge density {7through
by
. h_r[
2kT = -~
AS=klng=kff
{7
]
l(8kZl~Eo)l/2J
,
[11]
~ In 1 i=0
Expanding the logarithmic term in a Taylor series, we get
kw
s,n
+
[12]
{7 = Fqe.
The free energy of the surface lattice when the adsorbed protein molecules are charged is given by
T
+ kN2ff:ln(-~)-
where e is the dielectric constant of the medium and e0 is the permittivity of the vacuum. The surface charge density {7is, in turn, related to the charge on the protein molecule q and the surface concentration F via
kN21nN2.
[7]
The enthalpy of mixing can be written following Flory's treatment as N2n N
z2XI-I = XON1 = X - - - ~ s
1,
(OAF) H
OA
[14] N2,T
where the total area of the surface lattice A is N, ao. Therefore, I~ {7O
_{
l ONs
JN2,T
[9]
where AS and M-/are given by Eqs. [ 7 ] and [ 8 ], respectively. When the pH of the medium is other than pI, the interfacial protein layer will be charged and consequently an electrical double layer will be set up next to the interface. The free energy of the unit area of the double layer ZSaWDLis given by (9) AFDL---8kTm[c°sh(~2-~T)--K - 1} ,
where {70is the area of a lattice site. The surface pressure II is related to the free energy AF via
[8]
where X is the Hory-Huggins parameter, 0 is the fraction of the surface occupied by adsorbed segments, and N~ is the number of solvent molecules. The free energy of the surface lattice when the adsorbed protein molecules are uncharged is therefore given by AF, = Mt - TAS,
T A S + Z~WDLNs{70, [13]
AT" = M 4 -
[10]
where k is Boltzmann's constant, T is the absolute temperature, m is the number concenJournalof Colloidand InterfaceScience, Vol. 146, No. 1, October 1, 1991
+[
iN2,A-d-f] -g- d"
Evaluating the above we get X [ ~2( l + r
-II- = kT
ao X (70
+ --
if0
[r ~ o ( 1
o"o~-ll 20n']oF]j
nr{7o) - r - : - ~
n
On
r2{7o ~-f ( 1 - nr{7o) - ¢ 2 r % o
+ ~I" 1 + ~ (r{7on) + ~ (r{7on) 2
0n 1
173
PROTEINS AT THE AIR-WATER INTERFACE
+ ¼ (I'~ron)3 q - ~ (I'cron)4 + ' ' ' ]
20-
ff~p2On On[2 1 n or + ~r3a° or + ~ (raon)
+ ~, ( r~on)2 + ~1 ( r ~ o n ) 3 +-
+
• . .
]
Surface Pressure
HxlO3 N/m
8m[ (ze ) ] cosh
10-
- 1
K
8m r
c~rz[l + clr/¢1 + (clr) 2] ~ I ' + ~/1 + - ( q - ~
J ' [16]
where
Surface Concentration
qe C1
(8kTrmeo) u2
~b2 = nFa0.
r mg/m2
FIG. 1. Effect of variation in parameter a on the predicted surface equation of state. Values for parameter a are 0.68 for curve 1, 0.7 for curve 2, 0.709 for curve 3, 0.72 for curve 4, and 0.85 for curve 5. Other parameter values are those for BSA given in Table I.
RESULTS
The following functional relationship for the dependence of the number of protein segments adsorbed at different surface concentrations was employed in the calculations:
of state (Eq. [16]) was fitted to the experimental data for BSA and lysozyme using nonlinear optimization (10). a, b, x, and # ( z ) are the independent parameters that are fitted. Fma x is obtained from experimental data. The n___= 1 - a(XVrmax) b. [17] optimization routine was run for a wide range no of initial guesses for the parameter values in The parameter a is related to the average order to ensure a unique set of fitted parameter degree of unfolding of the protein molecule. values. The values of the parameters a, b, ×, Smaller (larger) values of parameter a corre- and # ( z ) for BSA and lysozyme are given in spond to protein molecules that unfold more Table I. Analysis of the sensitivity of the surface (less) upon adsorption. The derived equation equation of state (Eq. [ 16 ]) to the parameters a, b, x, and v~(z) was performed and the reTABLE I sults of this analysis are shown in Figs. 1-4, respectively. The effect of parameter a on the BSA Lysozyrne surface equation of state is shown in Fig. 1. The surface pressure for high surface concenMolecular weight 68,000 14,400 trations is found to be very sensitive to the no 606 147 pI 5.5 9.2 value of a (Fig. 1 ). On the other hand, there ~7(z) 67.54 24.72 is negligible variation in the surface pressure x 0.605 0.695 for smaller surface concentrations (see Fig. 1 ). a 0.709 0.816 As can be seen in Fig. 1, the predicted values b 1 -0.05 Fma,~(mg/m 2) (pH 7) 2.22 5.00 of IImax decrease as parameter a increases beII~x (N/m) (pH 7) 17 X 10-3 21 X 10-3 cause of the decrease in the degree of unfoldo-0 (m 2) 17 X 10-20 17 X 10-20 ing. The effect of parameter b on the surface Journal of Colloid and lnterface Science, VoL
146, No. 1, October 1, 1991
174
URAIZEE A N D N A R S I M H A N
3020-
251520Surface Preasure
Surface Pressure ,5-
H x 103 N/m
II x ,03 N/m
,0-
,0-
5-
0-
'
J
I
;.s
~
2~
J
3~
Surface Concentration
Surface Concentration
F mg/m2
i ~ iltg/m 2
FIG. 2. Effect of variation in parameter b on the predicted surface equation of state. Values for parameter b are 1.5 for curve 1, 1.1 for curve 2, 1.0 for curve 3, 0.8 for curve 4, and 0.5 for curve 5. Other parameter values are those for BSA given in Table I.
FIG. 4. Effect of variation in parameter if(z) on the predicted surface equation of state. Values for parameter ,7(z) are 75 for curve 1, 70 for curve 2, 67-54 for curve 3, 60 for curve 4, and 55 for curve 5. Other parameter values are those for BSA given in Table I.
equation of state is shown in Fig. 2. The surface pressure is found to be very sensitive to the values of parameter b and increases for larger values of b over the whole range of sur-
face concentrations. This can be attributed to the fact that the number of adsorbed segments (and therefore the degree of unfolding) increases for larger values of b (see Eq. [ 17 ]). The predicted surface equation of state is not as sensitive to the Flory-Huggins X parameter
20-
185 1515-
Surface Pressure 17 x 103 N/m
12,0Surface Pressure Flx 103 N/m
9-
6-
30-
0Surface Concentration r mf~ Surface Concentration
FIG. 3. Effect of variation in parameter X on the predicted surface equation of state. Values for parameter x are 0,8 for curve 1, 0.7 for curve 2, 0.605 for curve 3, 0.5 for curve 4, and 0.3 for curve 5. Other parameter values are those for BSA given in Table I. Journal of Colloid and Interface Science, V o l .
146, N o . 1, O c t o b e r 1, 1991
]" IIig/m2
FIG. 5. Plot of surface pressure versus surface concentration of BSA; solid curve refers to model predictions; ( n ) is the experimental data of G r a h a m and Phillips ( 1 ).
175
PROTEINS AT THE AIR-WATER INTERFACE 24-
21-
18-
15. Surface Pressure
12 -
FIx 103 N/m
/ ~
9:
62 32
0~
/
A
Surface Concentration F mg/m2
FIG. 6. Plot of surface pressure versus surface concentration of lysozyme; solid curve refers to model predictions; (A) is the experimental data of Graham and Phillips ( 1 ).
as to the other two parameters, as can be seen in Fig. 3. For higher surface concentrations, surface pressure is found to increase for larger X values (see Fig. 3 ). For smaller surface concentrations, however, the opposite trend is observed (Fig. 3). The effect of parameter ~ ( z ) on the surface equation of state is shown in Fig. 4. Increasing the number of ways of placing the protein segments [ # ( z ) ] at the gasliquid interface leads to higher surface pressure, as can be seen in Fig. 4. It is found that parameter a for BSA (0.709) is lower than that (0.86) for lysozyme (see Table I), implying thereby that the average degree of unfolding for lysozyme is lower than that for BSA. Moreover, from the values of parameter b, it can be said that the number of segments of BSA adsorbed at the interface bear a linear relationship with the surface concentration, whereas the number of adsorbed segments oflysozyme is more or less independent of the surface concentration. These are in accordance with the experimental observation that lysozyme is more condensed than BSA, thereby implying that it unfolds less than BSA ( 1 ). It can be seen from Table I that the FloryHuggins X parameters for BSA and for lysozyme are 0.605 and 0.695, respectively, im-
plying thereby that the segment solvent interactions are unfavorable (i.e., the solvent is " p o o r " ) . This unfavorable interaction results from the exposure of more hydrophobic functional groups due to the unfolding of the protein molecule. The comparison between the experimental data and the fit for the surface equation of state for BSA and lysozyme is shown in Figs. 5 and 6, respectively. At monolayer coverage, the neutral adsorbed interfacial protein layer consists of close-packed islands of segments connected to the part of the protein molecule that extends into the solution. Charging this neutral film leads to a decrease in the cohesiveness of the adsorbed segments because o f electrical interactions and consequently to a reduction in the surface concentration. This reduction in the surface concentration can also be viewed as a consequence of the increase in the excluded area of the segments due to electrical interactions. The reduction in the maximum surface concentration for monolayer coverage can be related to the change in the free energy of a segment due to electrical charge via the Boltzmann factor as
( ol 1
= e -n°l~°/kr,
[181
\ Fneutral/max
18 -
pl pH 7
15 -
pH 9
12Surface Pressure H x l 0 3 Nhn
9-
6-
3-
0-
'
.;
i
1;
~
2;
;
;.5
Surface Concentration F mgtm2
FIG. 7. Predicted surface equation o f state for BSA at different pH. Journal of Colloid and lnterface Science,
V o t . 146, N o . t, O c t o b e r 1, 1991
176
URAIZEE AND NARSIMHAN
where
kT
t
~
JN,,T --~
jN,,r\-O--~/
[19]
and AFDL is given by Eq. [10]. The maxim u m surface concentration corresponding to monolayer coverage Fmax at any p H is evaluated using Eq. [18] and the dependence of charge on pH for BSA ( 11 ) and lysozyme (12). Figure 7 shows the plot of II versus P for BSA at p H values of 5.5, 7, and 9. The effect of charge is negligible at lower surface concen-
trations, becoming significant only at surface concentrations near rmax, and is consistent with the experimental observations of Graham and Phillips ( 1 ). ° Figure 8 shows a comparison between the experimental and the predicted dependence of maximum surface pressure on pH for BSA and lysozyme. As the charge on BSA changes considerably with pH, the effect of pH on maximum surface pressure is more pronounced, with IImax being highest at the isoelectric point. The predicted variation of Ilmax with pH for BSA agrees fairly well with the experimental data in the pH range of 2 to 7. For higher pH values (7-12), however, very little variation of IImax is observed, whereas
30,
X
25
X x []
20 Maximum Surface Pressure
÷++ a
15
+
+
+
a
A
+
÷
+
+
rlm~ N/m x
+A
A
103 10
I 2
I 4
I 6
I 8
[ 10
I 12
pH
FIG. 8. Plot of maximum surface pressure versus pH for BSA and lysozyme.(A) and ([~) refer to the experimental data ( 1) for BSA and lysozyme,respectively,and (+) and (×) refer to model predictionsfor BSA and lysozyme,respectively. Journal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
PROTEINS AT THE AIR-WATER INTERFACE the predicted values exhibit a slight decrease with pH (Fig. 8). On the other hand, for lysozyme the variation of charge with pH is not significant, except very near the isoelectric point. This is reflected in a very weak dependence of IImax on p H away from the p I (pH 9.2 ) and a sharp variation near the isoelectric point. Unfortunately, no experimental data are available to show this dramatic increase in the surface pressure of lysozyme near its isoelectric point. Experimental and predicted maximum surface concentrations corresponding to monolayer coverage for BSA are shown in Fig. 9. As expected, predicted Fmax is m a x i m u m at the isoelectric point. The experimental variation of Fmax with pH is found to be larger than predicted, as can be seen from Fig. 9.
177
CONCLUSIONS A surface equation of state for globular proteins at the air-water interface accounting for the structure of the protein molecule, its degree of unfolding, and segment-segment, segmentsolvent, and electrostatic interactions has been proposed. The lattice model assumed that all the adsorbed segments are present in the form of trains, and the variation in the number of adsorbed segments (degree of unfolding) with the surface concentration is represented by the relationship n/no = 1 - a ( £ / r m a x ) b . From the results obtained by fitting this equation of state to experimental data it is found that the average degree of unfolding of BSA is more than that of lysozyme and that the number of segments of BSA adsorbed at the interface
2.5 [] []
p~xx ~
Maximum Surface Concentration F max
x
x
[] []
1.5
mg/m 2
1-
.5
O-
I 2
I 4
I 6
I 8
I I0
I 12
pH
FIG. 9. Plot of maximum surfaceconcentrationversuspH for BSA; ([5) refersto experimentaldata ( 1) and (×) refersto model predictions. Journal of Colloid and Interface Science, Vol. 146, No. 1, October 1, 1991
178
URAIZEE AND NARSIMHAN
varies linearly with the surface concentration, whereas the segments o f lysozyme adsorbed at the interface are m o r e or less independent o f the surface concentration. For both BSA a n d lysozyme, it is f o u n d that the parameter X is greater than 0.5, suggesting that the solvent segment interactions are unfavorable at the interface for the adsorbed protein molecule. The dependence o f m a x i m u m surface pressure a n d m a x i m u m surface concentration on p H has been evaluated and is f o u n d to agree well with the experimental observations. It is found that both the surface pressure and the surface concentration for BSA are m a x i m u m at the isoelectric point and decrease with an increase in the charge o n the protein molecule. For lysozyme, the m a x i m u m surface pressure is m o r e or less independent o f p H at p H other than the isoelectric point. The results obtained here are in g o o d agreement with the experimental data.
Journal of Colloid and Interface Science, Vot. 146, No. 1, October 1,1991
REFERENCES 1. Graham, D. E., and Phillips, M. C., J. Cotloidlnte(ace Sci. 70, 427 (1979). 2. Singer, S. J., J. Chem. Phys. 16, 872 (1948). 3. Davies, J. T., and Lopis, J. L., Proc. R. Soc. London A 227, 537 (1955). 4. Motomura, K., and Matuura, R., J. Colloid Sci. 18, 52 (1963). 5. Frisch, H. L., and Simha, R., J. Chem. Phys. 27, 702 (t957). 6. Silberberg, A., J. Phys. Chem. 66, 1872 (1962). 7. Lehninger,A. L., "Biochemistry,"2nd ed. Worth, New York, t975. 8. Clark, D. C., Smith, L. J., and Wilson, D. R., J. Colloid Interface Sci. 121, 136 (1988). 9. Verwey, E. J. W., and Overbeek, J. Th. G., "Theory of the Stability of Lyophobic Colloids." Elsevier, New York, 1948. 10. Procedure NL1N. SAS Release, 6.03 Edition. SAS Institute, Cary, NC, 1988. 11. Tanford, C., Swanson, S. A., and Shore, W. S., J. Am. Chem. Soc. 77, 6414 (1955). 12. Devereux, J., Haeberli, P., and Smithies, O., Nucleic Acids Res. 12( 1), 387 (1984).