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Enzymes entrapped into reversed micelles in organic solvents
Enzymes Entrapped into Reversed Micelles in Organic Solvents Sedimentation Analysis of the Protein-Aerosol OT-H20-Octane System1 A N D R E Y V. L E V A S H O V , Y U R I I L. K H M E L N I T S K Y , N A T H A L I A L. K L Y A C H K O , V I C T O R YA. C H E R N Y A K , AND K A R E L M A R T I N E K 2 Department o f Chemistry, Lomonosov State University, Moscow 117234, USSR R e c e i v e d J u l y 17, 1981; a c c e p t e d N o v e m b e r 2, 1981
Ultracentrifugation was used to study the systems of reversed Aerosol OT micelles in octane that contain solubilized protein (a-chymotrypsin, lysozyme, trypsin, egg albumin, horse liver alcohol dehydrogenase, ?-globulin). Changes in the sedimentation coefficients of reversed micelles upon protein entrapment into the latter were found to correlate solely with the molecular weight of solubilized protein in a wide range of experimental conditions, such as the surfactant hydration degree or protein concentration. Proceeding from this, a simple model of solubilization was suggested according to which a protein molecule is entrapped into a reversed micelle in a stoichiometric ratio of 1:1 rendering therewith no significant effect on the size of the reversed micelle. The conditions were found by the example of a-chymotrypsin under which the sedimentation properties of the system deviate from those of the model. The deviationsoccur at rather low hydrationdegrees of the surfactant when the inner cavity of a reversed micelle is less than the effective size of the solubilized protein molecule. In the latter case the protein "creates" around itself a new micelle of a required (bigger) size. is that the quantity of water in microenvironment of enzyme molecule inside a reversed micelle can be monitored with a high accuracy (1, 3, 8). Apart from solving the fundamental problems, micellar systems could be applied in fine organic synthesis as they make controlling the equilibrium of chemical reactions in a wide range possible (9). To understand the mode of action of enzymes entrapped into reversed micelles, it is important to know the structural organization of such systems. So, we studied the structural properties of enzyme-containing reversed micelles and, primarily the structural changes occurring in the micelle upon entrapment of a protein molecule into it. The enzyme-micellar system we created (3, 4) may well help to gain a deeper insight into the structure of biological membranes, par-
INTRODUCTION
Molecules of many surfactants in nonpolar organic solvents form reversed micelles, capable of solubilizing large amounts of water and other polar compounds (2) and, what is more, aqueous solutions of enzymes in catalytic quantities (3). Water-soluble enzymes solubilized by reversed micelles in organic solvents usually retain their catalytic activity and specifity, as was first found by us (3, 4) and then supported by other authors (5, 6, 7). Systems of reversed micelles in organic solvents offer fundamentally novel possibilities of studying mechanisms of enzyme catalytic action (1, 3, 4, 7) as well as the role water plays in enzymatic catalysis. The point i For previous p a p e r see (1). 2 To w h o m c o r r e s p o n d e n c e s h o u l d be addressed. 444 0021-9797/82/080444-14502.00/0 Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal
of Colloid and Interface Science, Vol. 88, No. 2, August 1982
445
P R O T E I N S IN R E V E R S E D M I C E L L E S
ticularly in the vicinity of protein molecules incorporated into them. Up to now, the published information has been devoted solely to the structure of reversed micelles containing no enzyme molecules. We shall dwell upon one of the beststudied systems of this type, i.e., on the system with bis(2-ethylhexyl)sodium sulfosuccinate (called Aerosol OT or AOT) as surfactant and with a hydrocarbon as organic solvent. These systems arouse interest due to their capability of solubilizing large amounts of water (up to 50 to 60 molecules per AOT molecule in some hydrocarbons, such as octane or decane) to form optically transparent and stable solutions (2). The structural properties of AOT reversed micelles in hydrocarbon solutions, such as size, aggregation number, and symmetry, were studied by the methods of neutron scattering (10), ultracentrifugation ( 11-14), viscosimetry (11, 15, 16, 19), light scattering (10, 13, 15, 17-19), and by use of the Kerr effect (16). The structure of the reversed AOT micelles is only slightly dependent on the nature of hydrocarbon solvent and AOT concentration and is largely influenced by water content in the system, i.e., by the molar concentration ratio Hz0/AOT (15). With increasing hydration degree, the molecular weight, aggregation number, and size of reversed micelles markedly grow. So, as was shown by Eicke and Rehak (12), at H 2 0 / AOT ,,, 0 the aggregation" number of AOT micelles is 15 to 20 (the molecular weight about 104), whereas at H 2 0 / A O T = 40 to 50 the aggregation number amounts some hundreds (the molecular weight about 106). At present, the generally acknowledged viewpoint is that the reversed AOT micelles, being slightly asymmetrical at low water content (a few H20 molecules per AOT molecule), become essentially spherical with rising hydration degree. However, according to the results obtained by Rouviere et al. (16) the reversed AOT micelles in heptane and decane become spherical at neither H20/AOT ratios but are ellipsoidal with an axes ratio of about 1:2.
As to the protein-containing reversed AOT micelles, their structure up to now has not been studied by physicochemical methods. The subject of this paper is the structural properties of protein-containing reversed AOT micelles in n-octane studied by the ultracentrifugation. MATERIALS AND METHODS
Trypsin and egg albumin were purchased from Sigma. a-Chymotrypsin, egg white lysozyme (grade B) and -y-globulin were obtained from the Olaine plant of chemical reagents (USSR). Horse liver alcohol dehydrogenase (crystal suspension) was a product of Reanal. a-Chymotrypsin and ~,-globulin were purified by gel filtration on Biogel P-2 and Sephadex G-75 columns, respectively, with the following lyofllization. According to the data of the a-chymotrypsin active center titration by N-transcinnamoylimidazole (20), the content of the active enzyme in the resultant preparation was 80%. The preparation of egg albumin was electrophoretically pure. Other proteins were used without further purification. Bis(2 - ethylhexyl)sodium sulfosuccinate (AOT) purchased from Merck was not further purified. We also used AOT purified by crystallization and by treatment with activated charcoal as described in Ref. (22). The results of experiments performed using purified and commercial AOT preparations showed practically no difference, if the presence of some water in commercial AOT had been taken into account. According to irspectroscopy data, the water content in the preparation from Merck was 2.5 mole per mole AOT (this value was taken into account during quantification of the overall water in reversed micellar systems). AOT solutions were prepared in commercial n-octane (Soyuzkhimreactiv). Buffer solutions were made with Tris from Reanal. Preparation o f micellar protein solutions. Stock protein solutions ( 1 0 -4 t o 10 -2 M ) were prepared in 0.05 M Tris HC1 buffer at Journal of Colloid and Interface Science,
Vol. 88, No. 2, August 1982
446
LEVASHOV ET AL.
pH 8.0. To prepare micellar solution, to 0.1 M AOT in octane was added the necessary amount of the stock protein solution and the mixture was then intensively shaken for 1 to 2 min to a homogeneous (optically transparent) state. Before the sedimentation experiments, the micellar solutions were incubated at 20°C for at least 2 hr. The systems investigated were stable for at least one day, i.e., during this time we were not able to establish any change in sedimentation properties. Sedimentation coefficients of reversed AOT micelles were determined at 20°C using a Beckman E analytical ultracentrifuge at 20,000 to 48,000 rpm. The determination was performed by a traditional technique, see, for instance (21). Depending on the aim of the experiment, scanning was carried out at various wavelengths. In the systems containing no solubilized protein, 20 to 50/zM 2,4-dinitrophenol was added to the micellar solution to stain micelles (22) which were traced in the absorption band of the indicator (405 nm). In protein-containing systems use was also made of a second indicator, picric acid (2,4,6-trinitrophenol), at the same concentration to record micelles at 400 nm. It should be noted that the sedimentation coefficient values of both "unfilled" (not containing a protein molecule) and "filled" (protein-containing) micelles were independent of the nature of the dye used. Furthermore, the sedimentation coefficients of protein-containing micelles, determined by tracing the dye as label, were identical with those in the dye-free systems scanned at 280 nm (the wavelength of protein absorption); in these conditions unfilled micelles are not detectable. This implies that to determine the sedimentation characteristics of reversed micellar systems, only one of the above tracing procedures, fit for a particular case, can suffice in most cases. The surfactant, involved in the formation of protein-containing reversed micelles, is preferably quantified using picric acid. Picric acid, as well as 2,4-dinitrophenol, allow a detection of various micelle fractions; yet Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
P..4
234
I
4.0
0.5
S FIG. 1. The typical sedimenting boundaries in the system of reversed micelles A O T - o c t a n e - H 2 0 at various c~-chymotrypsin concentrations. H 2 0 / A O T = 12.5. Concentrations of a-chymotrypsin (in the introduced aqueous solution) are 1, 0; 2, 1.8 × 10 3 M; 3, 5 × 10 -3 M; 4, 6.5 × 10 -3 M.
unlike the latter it has a lower pKa value (0.7 and 4.1, respectively). This permits an unhampered use of picric acid in systems with lowered pH (in concentrated aqueous a-chymotrypsin solutions pH is about 4 to 5), i.e., in the conditions when the extinction coefficient of 2,4-dinitrophenol markedly falls because of protonation of this indicator. RESULTS AND DISCUSSION
Dispersity of protein-containing micelles. A typical sedimenting boundary of reversed AOT micelles in octane in the absence of solubilized protein is schematically shown in Fig. 1 (curve 1, the molar ratio H 2 0 / A O T = 12.5). The sedimentograms obtained at various AOT hydration degrees show in all cases only one distinct boundary, which is indicative of the monodispersity of micelles (i.e., all micelles are characterized by the same sedimentation coefficient). The sedimentation coefficient of unfilled micelles as a function of their hydration degree is given in Fig. 2 (curve 1). The found values of sedimentation coefficients agree in order of magnitude with published data obtained in some other conditions (11, 13, 14). When protein (a-chymotrypsin) is solubilized in the system of reversed micelles, a second boundary appears on the sedimentogram (see, for instance, curves 2-4, Fig.
447
P R O T E I N S IN R E V E R S E D M I C E L L E S Mox 10-4
~,
~p
2o
As
80
,,so
/ / / // /
60
3 / //
/ /II / / // / / / / ///i//11 2 .~/.~--4 ~/
40
I
i//111~ /.1
o
40
20
30
40
I.IzO/AOT
FIG. 2. The sedimentation coefficient of reversed A O T micelles in octane as a function of H 2 0 / A O T . The experimental results: curve 1, unfilled micelles; 2, the micelles containing a-chymotrypsin. The theoretically calcu.lated curves: 3, hypothetical double unfilled micelles; 4, 5, the double micelles containing two c~-chymotrypsin molecules. Curve 4 describes the case with additive volumes of unfilled micelle and protein molecule and 5 refers to the case with unchanging volume of the micelle upon enzyme entrapment. Plotted against the upper axis are the molecular weights of unfilled single micelles (from (12)).
1). It is noteworthy that the slow sedimenting fraction of micelles is therewith characterized by the sedimentation coefficient equal to that of micelles of the protein-free system (at the same hydration degree). The micelles of this light fraction are evidently identical with" those of the protein-free system and are in fact unfilled micelles. The quickly sedimenting heavy fraction consists then of protein-containing micelles. The latter are also expressed on sedimentogram by only one distinct boundary (see, for instance, curves 2-4, Fig. 1). They are therefore also monodispersed. We arrived at the same conclusion while analyzing the sedimentation characteristics we obtained for other proteins (lysozyme, trypsin, egg albumin, horse liver alcohol dehydrogenase, ~/-globulin). a-Chymotrypsin solubilization limit. Figure 1 shows that with increasing concentration of the solubilized enzyme there occurs
• a regular growth in optical density characterizing the light fraction of micelles (unfilled micelles) (segment y). Its value is presumably directly proportional to concentration of the micelles that remain unfilled. The amount of surfactant remained in unfilled micelles can be calculated from sedimentation results (Fig. 1) as [ A O T ] . y / ( x + y). From the data on the aggregation numbers of unfilled micelles by Eicke and Rehak (12), one can find a dependence of the quantity of unfilled micelles, remained after achymotrypsin solubilization, on the overall enzyme concentration in the system. This dependence is shown in Fig. 3 for various H 2 0 / A O T ratios. We failed to attain higher concentrations of a-chymotrypsin than is shown in Fig. 3 because the system becomes turbid at enzyme concentration marked by arrows. It is seen that at the moment of appearance of turbidity in the micellar system, a large quantity of unfilled micelles remains unused. The amount o f surfactant needed to solubilize one enzyme molecule. Figure 3 shows that at every given hydration degree of AOT (curves 1 to 3) the number of unfilled mi-
400
~Z
80
=~
60
40
-
r
-
e-4 0-2 i- 5
"L~,t~.
z
20
[ CHYMOTRYPSlN].ro.rA,x t0 S, M
FIG. 3. The relative number of reversed unfilled AOT micelles in octane, left after a-chymotrypsin solubilization, as a function of the overall enzyme concentration in the system at various H 2 0 / A O T ratios: 1, 12.5; 2, 16.4, and 3, 22.5. Arrows show the c~-chymotrypsin concentration values corresponding to the solubilization limit at a given H ~ O / A O T ratio. Journal of Colloid and Interface Science, Vol, 88, No. 2, August 1982
448
LEVASHOV ET AL.
celles decreases with growing enzyme concentration. We succeeded in quantitation of this qualitatively evident regularity. To this end, the amount of surfactant, involved in the formation of protein-containing micelles, can be conveniently presented on the basis of sedimentation data (Fig. 1) in the form [AOT]. x/(x + y). Then, since the concentration of solubilized protein is known, one can determine the number of AOT molecules per protein molecule in a protein-containing micelle. Finally, using the published data on aggregation numbers of unfilled micelles (12), one can find the number of initial unfilled micelles N, involved in solubilization of one a-chymotrypsin molecule. The N value as a function of the overall achymotrypsin concentration in the system is shown in Fig. 4. Figure 4 shows that at not too high enzyme concentrations, N = 1 irrespective of AOT hydration degree (points 1 to 3). In other words, one enzyme molecule is solubilized by the amount of surfactant contained in one unfilled micelle. At medium values of H 2 0 / A O T (points 1 and 2) this regularity holds up to the limit enzyme concentration (marked by arrows 1 and 2), when the micellar system becomes turbid. At a higher value of H 2 0 / A O T (points 3), however, the N value falls with growing enzyme concentration and becomes equal to 0.5. This implies that the amount of surfactant contained in one micelle is capable in principle of solubilizing two enzyme molecules. Unfortunately, the sedimentation method is not sensitive enough to determine the N value at low hydration degrees of micelles (H20/AOT ~ 12.5, where H20/AOT = 12.5 corresponds to points 1 in Figs. 3 and 4). This is due to the fact that the limit concentration of solubilized a-chymotrypsin in the system of reversed AOT micelles in octane decreases with the molar ratio H 2 0 / AOT (Fig. 3) andhence, a portion of the overall surfactant amount involved in the formation of protein-containing micelles falls. Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
N 4.0
3 ,r.~.
0,5
o-4 0-2
m-3
t0
20
30
[ CI.IYMOTRYPSIN] .rorAtx 40s, M FIG. 4. The number of initial unfilled AOT micelles in octane necessary to solubilize an a-chymotrypsin molecule as a function of the overall concentration of the enzyme in the system at various hydration degrees of AOT. H20/AOT: 1, 12.5; 2, 16.4, and 3, 22.5. The limit concentrations of a-chymotrypsin, over which the system becomes turbid, are indicated by arrows.
In practice this leads to decrease in the x segment (Fig. 1) to the value experimentally undeterminable. Nevertheless, at not too low hydration degrees of AOT (H20/AOT ~- 12, Figs. 3 and 4, points 1) the analysis of sedimenting boundaries of protein-containing micelles and of sedimentation coefficients of the micelles remaining unfilled still enabled us to determine the stoichiometric ratio A O T / protein in protein-containing micelles. It should be noted that even if N is constant and equal to 1 (Fig. 4), the stoichiometric ratio AOT/protein alters with AOT hydration degree. This is due to the fact that with increasing H 2 0 / A O T ratio, the aggregation number of reversed micelles grows (12). Since one protein molecule is solubilized by the amount of surfactant contained in one micelle (N = 1, Fig. 4), the number of AOT molecules involved in protein solubilization at every given hydration degree of AOT will be different. The stoichiometric ratio of AOT/protein found by us does not permit a determination of absolute quantity of protein molecules contained in one micelle. In other words, it cannot be used to discriminate the cases
PROTEINS
IN REVERSED
when a protein-containing micelle is formed, for instance, by one unfilled micelle and one protein molecule or by two unfilled micelles and two protein molecules, and so on. To discern these "multiple" molecular mechanisms of solubilization and to decide on how the protein-containing micelle is constructed, one should analyze the sedimentation coefficients of the protein-containing reversed micelles proper (see below).
Hydration degree of protein-containing micelles. It has been shown above that on protein solubilization in the system of reversed micelles, the sedimentation coefficient of the micelles remaining unfilled does not alter (Fig. 1). On the other hand, the sedimentation coefficient of unfilled micelles depends on their hydration degree (Fig. 2, curve 1). Hence, on protein solubilization the hydration degree of unfilled micelles does not change. This implies that the protein solubilization does not cause redistribution of water in the system of reversed micelles, i.e., unfilled and filled micelles are characterized by the same H 2 0 / A O T ratio. This inference holds solely for not too low H 2 0 / A O T ratios. The fact is, the amount of surfactant involved in the formation of protein-containing micelles is too low at low H 2 0 / A O T ratios (Fig. 3, curve i). So, the hydration degree of unfilled micelles should alter only slightly even at significant change in the hydration degree of protein-containing micelles and hence, the experimentally determined sedimentation coefficient of unfilled micelles will hardly change. The accuracy of the experiment ensures a record of a change in the sedimentation coefficient only at a change of the H 2 0 / A O T ratio not less than by unity. Let us try to assess on this basis the lowest H 2 0 / A O T ratio starting from which one can be sure that the hydration degrees of unfilled and filled micelles are equal. So, at H 2 0 / A O T = 12.5 (Fig. 3, points 1) the maximal possible amount of AOT involved in the formation of proteincontaining reversed micelles is about 15% of the overall AOT amount. So, a change in
MICELLES
449
the H 2 0 / A O T ratio of unfilled micelles even by 1 (an accuracy limit of the sedimentation experiment, see above) would raise the hydration degree of protein-containing micelles by 6 H20 molecules per AOT molecule, i.e., by about 30%. This is the minimal error in determining the hydration degree of proteincontaining micelles at H 2 0 / A O T = 12.5. At H 2 0 / A O T = 16.4 and 22.5 (Figs. 3 and 4, points 2 and 3), the minimal error is 18 and 4%, respectively. It is evident that the experimental error decreases with increasing H / O / A O T ratio and conversely. So, the invariability of the sedimentation coefficient of unfilled micelles which we observed experimentally on protein solubilization (Fig. 1), can be indicative of equality of hydration degrees of filled and unfilled micelles only at fairly high H 2 0 / A O T ratios. To decide on the hydration degree of protein-containing micelles at low H20/AOT, we shall try to analyze below the sedimentation coefficients of the protein-containing micelles proper.
Sedimentation coefficients of reversed micelles containing a-chymotrypsin. The sedimentation coefficient of reversed micelles containing a-chymotrypsin as a function of AOT hydration degree is shown in Fig. 2 (curve 2). In this paper we shall analyze in detail the sedimentation results solely for the systems with not too high enzyme concentrations (when N = 1, Fig. 4). In these conditions the experimentally observed sedimentation coefficient is independent of the enzyme concentration. Account should be taken here that the sedimentation coefficient values of proteincontaining micelles at all H 2 0 / A O T ratios exceed the sedimentation coefficients of unfilled micelles (curve 1). Discrepancies between the sedimentation coefficients of unfilled and filled micelles are greater, the smaller the surfactant hydration degree. The sedimentation coefficient of a proteincontaining micelle can in principle be calculated theoretically (see Appendix), proceeding from a certain model of its construcJournal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
450
L E V A S H O V ET AL.
tion. Below we shall try to choose an appropriate model of protein-containing micelles comparing theoretical values of sedimentation coefficients (calculated for different models) with experimental results. Model o f "'multiple" micelles. In the above discussion on the stoichiometric A O T / protein ratio found experimentally (see Fig. 4) we concluded that a possible model of protein-containing micelles at N = 1 (in the region of H 2 0 / A O T ~ 12) can be "multipie" micelles, i.e., the micelles formed of two, three, and more initial unfilled micelles and containing two, three, and more protein molecules, respectively. The theoretically calculated curve of the sedimentation coefficient of hypothetical unfilled double micelles as a function of H 2 0 / A O T is shown in Fig. 2 (curve 3). On entrapment of a protein molecule into a reversed micelle two extreme cases can, in principle, be realized: the size of the micelle can either remain practically unaltered (curve 5), or equal to a sum of volumes of the unfilled micelle and the protein molecule (curve 4). The curves corresponding to an intermediate change in the micelle size will evidently lie between curves 4 and 5 describing these two extreme cases. It is seen in Fig. 2 that none of the theoretical curves coincides with the experimental (curve 2). This moreover refers, as was confirmed by calculations, to the protein-containing micelles with a greater aggregation degree, whose curves lie still higher. The model of multiple micelles cannot therefore describe the sedimentation properties of real protein-containing micelles. Other models should be considered. In choosing the model, account should be taken of the fact that the size of the inner cavity of reversed micelles increases with the H 2 0 / A O T ratio (Fig. 5, upper axis). Hence, depending on the H 2 0 / A O T ratio, the cavity radius can be bigger or smaller than the effective size of a solubilized protein molecule. The molecular mechanism of solubilization in the two cases will expectedly be different and so we shall discuss them separately. Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
40
2!,5 30
40
50
40+
60
70
///
/j7 //
30
(// /
#1 //~ / o~ 3 / Z~¢71 // / I
i l-j.i~;'.s
/
/11
8
40 9 "-\\! I I
~o,I
~o
3o
io
RIO/hOT FIG. 5. Comparison of theoretically calculated and experimental (dotted line) dependencies of the sedimentation coefficient of c~-chymotrypsin-containing reversed A O T micelles on H 2 0 / A O T ratio. Curves 1-5: the aggregation n u m b e r and the hydration degree of micelle do not alter upon entrapment of an enzyme molecule. Changes in the micelle volume upon protein entrapment: 1, no change; 2, 3, 4, increases by 10, 20, and 30% of the a-chymotrypsin molecular volume, respectively; 5, the additivity of the micelle and c~-chymotrypsin molecular volumes. Curves 6 - 9 refer to the model 2.3 (Table I). The micelle inner cavity volume is equal: curve 6, to the a-chymotrypsin molecular volume; curves 7, 8, to the c~-chymotrypsin molecular volu m e plus 10 and 30% of its volume, respectively; curve 9, to the s u m of volumes of an a-chymotrypsin molecule and of water present in the micelle. T h e vertical broken line is plotted at H 2 0 / A O T = 11.6. Plotted against the upper axis are the radius values of the unfilled micelle inner cavity (see Appendix).
Solubilization model involving the micelles, with their inner cavity larger than the effective size o f the protein molecule or equal to it. The size of an ~-chymotrypsin molecule is 40 × 40 × 50 ,~ (23). Being approximated by the sphere of equal volume, the molecule will have a radius of 21.5 /~. The inner cavity of reversed micelle has the same radius at H 2 0 / A O T = 11.6 (Fig. 5, vertical broken line). First, we shall consider the a-chymotrypsin solubilization in systems of reversed micelles with H g O / A O T ~> 11.6 (Fig. 5, to the right of the vertical broken line), when the size of the micelle inner cav-
P R O T E I N S IN REVERSED MICELLES
ity exceeds the effective size of an o~-chymotrypsin molecule. To determine the model in further detail account should be taken of the above-established fact that the protein-containing micelles in the studied range of H 2 0 / A O T ratios differ from initial unfilled micelles neither in aggregation numbers, nor in the hydration degree; i.e., entrapment of protein into a reversed micelle does not change the composition of the latter. So, Fig. 5 shows theoretical curves of the sedimentation coefficient of protein-containing micelles as a function of the surfactant hydration degree (broken lines) calculated particularly for such a solubilization model. On entrapment of a protein molecule into a reversed micelle, two extreme cases can, in principle, be realized: the micelle volume can (a) practically remain unchanged (curve 1) or (b) turn out equal to the sum of volumes of the unfilled micelle and the protein molecule (curve 5). Intermediate cases are described by curves 2 to 4, i.e., when the inner cavity volume of a protein-containing micelle is equal to the volume of the unfilled micelle plus 10, 20, and 30% of the volume of the entrapped enzyme molecule, respectively. Figure 5 shows that the experimental points lie between curves 1 and 2. This implies that on entrapment of an a-chymotrypsin molecule into a reversed micelle, the volume of the latter increases only by a volume not exceeding 10% of the volume of the protein molecule. This astonishing fact may be accounted for by redistribution of water inside the micelle on entrapment of a protein molecule. So, the sedimentation data agree with the model according to which entrapment of an a-chymotrypsin molecule into a reversed AOT micelle in octane (at H z O / A O T > 11.6) does not significantly alter the size of the initial unfilled micelle with its aggregation number and hydration degree remaining unchanged.
Solubilization model involving micelles with their inner cavity smaller than the effective size o f the protein molecule. At H 2 0 / A O T < 11.6 (Fig. 5, to the left of the
451
vertical broken line) an a-chymotrypsin molecule is bigger than the inner cavity of a reversed micelle (Fig. 5, upper axis). So, a protein-containing micelle should inevitably greatly differ from unfilled micelles in size and presumably in the aggregation number and/or the hydration degree. In other words, entrapment of a protein molecule into a reversed micelle should be accompanied by structural rearrangement of the latter, or to be more precise, a protein molecule will "create" around itself a new micelle. This agrees with the conclusion arrived at by Menger and Yamada (5) by means of enzyme kinetics. In this case (i.e., in the presence of small micelles incapable of direct entrapment of an enzyme molecule) a protein molecule seems to get coated with a monolayer of hydrated surfactant molecules. As the effective radius of an ~-chymotrypsin molecule (21.5 A) equals to the radius of the inner cavity of an unfilled micelle at H 2 0 / A O T = 11.6, one may suppose that the mode of formation of this monolayer is, to some extent, determined by the regularities that govern the formation of unfilled micelles precisely at this boundary value of the hydration degree, i.e., at H 2 0 / A O T = 11.6. The characteristics of the models of protein-containing micelles we analyzed are given in Table I and the relevant calculated theoretical curves for the sedimentation coefficient of the micelles as a function of H z O / A O T are shown in Fig. 6. The experimental points are given for comparison. In all sections of Fig. 6 one curve represents the extreme case, when the volumes of the mieelle inner cavity and of a-chymotrypsin molecule are equal, and another refers to a second extreme, when the volume of the micelle inner cavity is equal to the sum of volumes of the o~-chymotrypsin molecule and the water residing in the micelle. The curves for intermediate values of the inner cavity volume of the protein micelle should evidently lie in the area between a pair of these curves. It is obvious that a model of a protein-containing micelle cannot
452
L E V A S H O V ET AL.
describe experimental results if the experimental points lie beyond this area. Figure 6 shows that this formal requirement is met by only two models, precisely by models 2.3 and 2.2, shown in Table I. The patterns of curves both 2.2.1 and 2.2.2 (and therefore of all "intermediate" curves between the two) does not correspond, however, to the experimental curve. For this reason model 2.2 is presumably inadequate to describe experimental results.
The curves, corresponding to model 2.3, the only model capable of describing the experimental results, are shown in enlarged scale in Fig. 5 (curves 6 and 9). Figure 5 shows the curves corresponding to intermediate values of the micelle inner cavity volume equal to 1.1 (curve 7) and 1.3 (curve 8) of the a-chymotrypsin molecular volume. Figure 5 shows that the experimental points lie between curves 6 and 7. This implies that the volume of the protein-containing micelle
TABLE I Structural Parameters of the Models of Protein-Containing Micelles for H 2 0 / A O T < 11.6" Aggregation
1
2
nfoT = n~,OT
f __ o nAox -nAOT at
Hydration
1.1
nf20 = n~i20 (or wf = Wo)
1.2
f _ o nH2o - nn2o at wo = 11.6
1.3
wf = 11.6
2.1
nf~o = n~2o
2.2
nfn2o=n~2oatWo = 11.6
2.3
(or wf = 11.6) wf = Wo
3.1
nf2o = n~2o
3.2
n~2o = n~2o at Wo = 11.6
3.3
w~ = wo
3.4
wf = 11.6
4.1
nf~o = n~2o
4.2
nf:o = n~2o at Wo = 11.6
4.3
wf = Wo
Wo = 11.6
3
4
f~,oT = f~,or
f o r = f~oT at Wo = 11.6
4.4
wf = 11.6
Volume of inner cavity
1.1.1
lip
1.1.2
Vp + V.~o
1.2.1 1.2.2 1.3.1 1.3.2
Vp Vp + V.2o Vp
2.1.1" 2.1.2 2.2.1"* 2.2.2 2.3.1'** 2.3.2
Vp Vp + VH2o lip Vp + V.2o Vp Vp + Vn~o
3.1.1 3.1.2 3.2.1 3.2.2 3.3.1 3.3.2 3.4.1 3.4.2
Vp Vp + V.2o Vp Vp + V.2o Vp Vp Vp + VH2o
4.1.1" 4.1.2 4.2.1"* 4.2.2 4.3.1"** 4.3.2 4.4.1"* 4.4.2
Vp lip Vp Vp lip Vp II0 Vp
Vp +
VH20
Vp + Vn2o
+ Vn~o + Vn2o + VH2o + VH20
"Designations used: nAOT, nH20, fAOT, and w are the aggregation number, a number of water molecules present in micelle, area per A O T molecule on the surface of a micelle, and A O T hydration degree ( H 2 0 / A O T ) , respectively. Subscripts " f " and "0" refer to "filled" and "unfilled" micelles, respectively. Vp is the volume of an a-chymotrypsin molecule, Vn20 is the volume of water present in a micelle. Asterisks mark equivalent models; equal models are marked by an equal number of asterisks. Journal o f Colloid and Interface Science, Vol. 88, No. 2, August 1982
40-
~-~ Ii /1.4.t
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H20/AOT FIG. 6. The sedimentation coefficient of a-chymotrypsin-containing reversed AOT micelles in octane as a function of H20/AOT ratio theoretically calculated for the models given in Table I. The corresponding model numbers are shown in the upper-left corner of each section. Dots show the experimental sedimentation coefficient values. The vertical broken lines are plotted at HzO/AOT = 11.6, Journal of Colloid and Interface Science, Vol. 88, No. 2, August
453
1982
454
LEVASHOV
inner cavity is not over 1.1 of the a-chymotrypsin molecular volume. So, analysis of sedimentation coefficients of reversed AOT micelles in octane (at H 2 0 / AOT < 11.6), containing solubilized a-chymotrypsin, results in the following model of protein-containing micelles (model 2.3, Table I): (a) the size of the inner cavity of the protein-containing micelle is close to that of a-chymotrypsin molecule; (b) the aggregation number of such a micelle is constant and equal to the aggregation number of unfilled micelles at H 2 0 / A O T = 11.6, and (c) the surfactant hydration degree in the filled micelle is the same as in unfilled micelles existing at H 2 0 / A O T < 11.6. Solubilization of other proteins. Along with a-chymotrypsin we studied by the sedimentation method solubilization of some other proteins, such as lysozyme, trypsin, horse liver alcohol dehydrogenase, -r-globulin, and egg albumin, considerably differing in their molecular weights: 14,300, 23,000, 80,000 (23), 150,000 (24), and 44,000 (25), respectively. The experiment for each protein was conducted at a fairly high surfactant hydration degree, i.e., at such a fairly big volume of the micelle inner cavity which, in principle, can house a protein molecule. On the other hand, for the maximal simplicity of the experiment, the cavity size should not greatly exceed the effective size of the protein molecule, to rule out a possible entrapment into micelle of protein aggregates. So, for lysozyme and trypsin with their molecular dimensions 45 X 30 × 30 A and 50 × 40 × 40 A, respectively (23), use was made of the system characterized by H 2 0 / A O T = 12.5 in which the micelle inner cavity diameter is 50 A (Fig. 4, upper axis); for egg albumin (molecular dimensions are 33 X 33 × 96 A (25)), the system characterized by H 2 0 / A O T = 30.5 (the cavity diameter 100 A); for alcohol dehydrogenase and ~/-globulin (dimensions of the former are 45 × 55 × 110 A (23), the latter is approximated by a sphere with a diameter of about 110 to 120 Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
E T AL.
/ /
60 ¸
4O
/
/
/
/
/
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/
/
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¢)eAL' $ FIG. 7. Correlation between e x p e r i m e n t a l (S~xp) and theoretically calculated (scat) s e d i m e n t a t i o n coefficients of protein-containing reversed A O T micelles in octane: 1, lysozyme ( H 2 0 / A O T = 12.5); 2, trypsin ( H e O / A O T = 12.5); 3, a - c h y m o t r y p s i n ( H 2 0 / A O T = 12.5); 4, egg a l b u m i n ( H e O / A O T = 30.5); 5, horse liver alcohol deh y d r o g e n a s e ( H 2 0 / A O T = 39.5); 6, "y-globulin ( H 2 0 / A O T = 39.5).
(26)), the system characterized by H 2 0 / AOT = 39.5 (the cavity diameter 130 A). Fig. 7 shows a correlation between the sedimentation coefficients of protein-containing micelles found experimentally (Sexp) and those calculated theoretically assuming that a micelle does not practically alter on protein entrapment into it (Sc~l). A broken line with a slope equal to 1 corresponds to a precise performance of the model. As seen, the calculated results satisfactorily agree with experimental findings. This implies that on entrapment of any of the studied proteins (greatly differing in their molecular weights) into a reversed AOT micelle (with a fairly large inner cavity size), its shape and volume do not appreciably alter with the aggregation number and the initial hydration degree unchanged. CONCLUSION
The results obtained by the sedimentation analysis enable us to only indirectly conjecture about the structural properties of protein-containing reversed AOT micelles. So,
PROTEINS IN REVERSED MICELLES
455
TABLE II Parameters of Reversed AOT Micelles in Aliphatic Hydrocarbons
H20 AO--'-T= w°
Molecular weight, /14o*
Aggregation number, n~or b
Radius R~ (A) ~
Radius of inner cavity, r o (A) a
Thickness of surfactant layer, / = Ro - ro (A)
5 7 9 12 16 20 25 30 40
25,670 38,270 54,440 86,350 145,530 226,980 365,530 551,370 1,092,730
48 67 90 131 199 282 408 560 938
20.9 24.9 26.9 31.4 37.5 43.7 51.3 59.0 74.3
11.7 14.7 17.7 22.1 28.0 33.9 41.4 48.9 64.1
9.2 9.2 9.2 9.3 9.5 9.8 9.9 10.1 10.2
Area per A O T molecule on the surface of micelle, f~,or (A 2)"
Partial specific volume, rio (cm3/g) f
Volume of an H20 molecule, v (A 3) g
36.0 40.5 43.7 46.8 49.5 51.3 52.7 53.7 55.0
0.8905 0.8969 0.9009 0.9050 0.9149 0.9225 0.9302 0.9363 0.9461
28.4 28.6 28.8 28.9 29.1 29.2 29.3 29.4 29.6
Molecular weights were calculated using empirical formula Mo = (19 + 2.1Wo)3, which well describes the experimental data (12). b n~,or = Mo/(MAoT + MH2oWo), where MAOTand Mmo are the molecular weights of AOT (445) and water, respectively. c Calculated from Eq. [5] (see Appendix). dr o = ((3/4~r)n°AOTWoV) I/3, where v is the volume of an H20 molecule at a given H20/AOT ratio. e f~.or = 47r~/n~,oT. YFrom Refs. (13, 14). g From Ref. (11). to verify the inferences m a d e f r o m the sedimentation analysis, a direct physical m e t h o d should be used t h a t provides a direct information on the structure of particles in solution, for instance the m e t h o d of X - r a y lowangle scattering. Studies in this direction are in progress. APPENDIX
Df -Mf -o S°'Do'M
1 - ~fp
o 1 -- f;oP
[2]
where " f " and " o " denote filled and unfilled micelles, respectively. T h e diffusion coefficients of reversed micelles in Eq. [2] can be expressed by the S t o k e s - E i n s t e i n equation [ 3 ] with the assumption of the micelle sphericity3: kT
T h e sedimentation coefficients of reversed micelles were theoretically calculated according to the Svedberg equation D s = R - ~ M ( 1 - ~p),
Sf
[1]
where s is the sedimentation coefficient of particles with molecular weight M and the partial specific volume fi in the solvent with density p, D is the diffusion coefficient, R is the gas constant, and T is the absolute temperature. C o m b i n a t i o n of two types-[ 1 ] equations, written for filled and unfilled micelles, gives
D = f(CAoT) 67rr/R M
[3]
where k is the B o l t z m a n n constant, n is the viscosity of solvent, RM is the micelle radius, f(CAoT) is a function of A O T concentration, f(CAoT) ~ 1 at CAOT ---' 0, f(CAoT) < 1 at CAOT ~ 0 (14). W i t h regard to Eq. [3], Eq. [2] transforms into M f 1 - Dfp Rf Mo 1 - V o p "
Ro
sf=So
[4]
Calculations show that the conclusions of the present paper remain operative also in the case if micelles are not spheres but ellipsoids of revolution with not too large ratio of semiaxes (about 1:2). Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
456
L E V A S H O V E T AL.
Equation [4] was used to calculate the sedimentation coefficients of protein-containing reversed micelles. It is important to emphasize that Eq. [4] does not contain f(CAoT) which is a measure of the system's nonideality and whose view is unknown. The values of Mo and Vo in Eq. [4] are known from literature (12-14) for any H 2 0 / AOT ratios (Table II gives the parameters of unfilled reversed micelles used for calculations). The so was determined experimentally (Fig. 2, curve 1). The Ro can be expressed using the known values of 3/o and Voif we take into consideration that Vo is the parameter equal to the reciprocal of the density of unfilled micelles. Then 4~r R3NA --, 3 Mo
[51
where NA is Avogadro's number. If upon entrapment of a protein molecule into a micelle the aggregation number and the hydration degree of the micelle do not alter, then Mf = Mo + Mp, where Mp is the protein molecular weight. The Rf can be determined as Rf = rf + l, where rf is the radius of the inner cavity of the protein-containing micelle that is given by the volumes of the protein molecule and water present in the micelle with regard to the assumption on the relation between these volumes, and l is the thickness of the reversed micelle outer layer formed by "tails" of AOT molecules. The l value at every H 2 0 / A O T ratio was determined as the difference l = Ro - ro, where ro is the inner cavity radius of unfilled reversed micelles. The ro value was taken equal to the radius of the water drop formed by the number of water molecules present in the micelle with regard to the density of "micellar" water as a function of H 2 0 / A O T ratio (11). The number of water molecules present in the unfilled micelle was determined from the equation o
BH20 :
Mowo M A O T -I- M H 2 o W o '
where Wo= H20/AOT, MAOT, and MH=Oare Journal o f Colloid and Interface Science, VoL 88, No. 2, August 1982
the molecular weights of AOT and H20, respectively. The l value thus determined alters from 9.2 to 10.2 A. depending on H 2 0 / AOT ratio (Table II), which agrees with the literature value of the length of an AOT molecule equal to 11 A (15). The vf value, reciprocal to the density of protein-containing micelles, was determined from the found Mf and Rf values according to the equation analogous with Eq. [5]. The described approach was used to calculate the sedimentation coefficients of reversed micelles containing a-chymotrypsin in the range H 2 0 / A O T ~ 11.6, other proteins and also to calculate the sedimentation coefficients of protein-containing multiple micelles.4 In calculations of the sf values of reversed micelles, containing a-chymotrypsin, in the range H 2 0 / A O T < 11.6 use was made of the parameters given in Table I. The characteristics of protein-containing micelles presented in Eq. [4] were determined from the relations Mf=
f 2 o M H 2 0 d- M p HfA o T M A o T -{- n H
Rf = (3Vf/47r) 1/3 + l, where ngoT, f nn20,fand Vf are the number of AOT molecules, the number of water molecules in a protein-containing micelle, and the volume of its inner cavity, respectively (Table I). All the models given in Table I are based on the assumption that the outer layer of protein-containing reversed micelles is formed by the monolayer of surfactant molecules. Accordingly, nfgoT in models 3 and 4 (Table I) was determined from the relation 4 rg n oT - A o T ' where rf is the inner cavity radius of a pro4 In the case of unfilled multiple micelles Eq. [4] transforms into s" = nsoRo/R', where s" and R" are the sedimentation coefficient and the radius of an n-multiple unfilled micelle. R" is determined as the radius of the sphere, whose volume equals the volume of n initial unfilled micelles.
PROTEINS IN REVERSED MICELLES
tein-containing reversed micelle. In models 3.3.2, 3.4.2, 4.3.2, and 4.4.2 the rf value is the real root of the cubic equation
47rr~ _ fAOT
4 7 r r~ -
3
3
rp
Wfl)
'
where rp is the effective radius of protein molecule (a-chymotrypsin), and v is the volume of an H20 molecule at a given hydration degree of surfactant. The vr value was determined from the equation, analogous with Eq. [5]. The used values of / and density of the micellar water in each model corresponded to the hydration degree of proteincontaining micelles given by this model. ACKNOWLEDGMENTS We are pleased to acknowledge the constant attention to our work and invaluable comments of Professor I. V. Berezin. We also thank Professor P. L. Luisi for sending us a preprint of his paper (27) describing another structural model of protein-containing micelle. REFERENCES 1. Martinek, K., Levashov, A. V., Klyachko, N. L., Pantin, V. I., and Berezin, I. V., Biochim. Biophys. Acta 657, 277 (1981). 2. Fendler, J. H., and Fendler, E. J., "Catalysis in Micellar and Macromolecular Systems." Academic Press, New York, 1975. 3. Martinek, K., Levashov, A. V., Klyachko, N. L., and Berezin, I. V., Dokl. Akad. Nauk. S S S R 236, 920 (1977). [Russ.] 4. Levashov, A. V., Klyachko, N. L., and Martinek, K., Bioorg. Khim. 7, 679 (1981). [Russ.] 5. Menger, F. M., and Yamada, K., J. Amer. Chem. Soc. 101, 6731 (1979). 6. Wolf, R., and Luisi, P. L., Biochem. Biophys. Res. Commun. 89, 209 (1979). 7. Balny, C., and Douzou, P., Biochimie 61, 445 (1979).
457
8. Martinek, K., Levashov, A. V., Pantin, V. I., and Berezin, I. V., Dokl. Akad. Nauk S S S R 238, 626 (1978). [Russ.] 9. Martinek, K., Khmelnitsky, Yu. L., Levashov, A. V., Klyachko, N. L., Semenov, A. N., and Berezin, I. V., Dokl. Akad. Nauk S S S R 256, 1423 (1981). [Russ.] 10. Cabos, C., and Delord, D., J. Appl. Crystallogr. 12, 502 (1979). 11. Mathews, M. B., and Hirschhorn, E., J. Colloid Sci. 8, 86 (1953). 12. Eicke, M. F., and Rehak, J., Helv. Chim. Acta 59, 2883 (1976). 13. Zulauf, J. M., and Eicke, H. F., J. Phys. Chem. 83, 480 (1979). 14. Robinson, B. H., Steytler, D. C., and Tack, R. D., Z Chem. Soc. Faraday Trans. I 75, 481 (1979). 15. Ekwall, P., Mandell, L., and Rontell, K., J. Colloid Interface Sci. 33, 215 (1970). 16. Rouviere, J., Couret, J.-M., Lindheimer, M., Dejardin, J.-L., and Marrony, R., J. Chim. Phys. Phys. Chim. Biol. 76, 289 (1979). 17. Frank, S. G., and Zografi, G., J. Pharm. Sci. 58, 993 (1969). 18. Menger, F. M., Donohue, J. A., and Williams, R. F., J. Amer. Chem. Soc. 95, 286 (1973). 19. Day, R. A., Robinson, B. H., Clarke, J. H. R., and Doherty, J. V., J. Chem. Soc. Faraday Trans 1 75, 132 (1979). 20. Schonbaum, G. R., Zerner, B., and Bender, M. L., J. Biol. Chem. 236, 2430 (1961). 21. Freifelder, D., "Physical Biochemistry. Application to Biochemistry and Molecular Biology," Chap. 11. Freeman, San Francisco, 1976. 22. Levashov, A. V., Pantin, V. I., and Martinek, K., Kolloidn. Z. 41, 453 (1979). [Russ.] 23. Squire, P. G., and Himmel, M. E., Arch. Biochem. Biophys. 196, 165 (1979). 24. Pilz, I., Schwarz, F., and Palm, W., Eur. J. Biochem. 75, 195 (1977). 25. Haurowitz, F., "The Chemistry and Function of Proteins." Academic Press, New York, 1963. 26. Munn, E. A., Bachmann, L., and Feinstein, A., Biochim. Biophys. Acta 625, 1 (1980). 27. Bonner, E. J., Wolf, R., and Luisi, P. L., J. Solid Phase Biochem. 5, 255 (1980).
Journal of Colloid and Interface Science, VoI.88, No. 2, August1982
Ultracentrifugation was used to study the systems of reversed Aerosol OT micelles in octane that contain solubilized protein (a-chymotrypsin, lysozyme, trypsin, egg albumin, horse liver alcohol dehydrogenase, ?-globulin). Changes in the sedimentation coefficients of reversed micelles upon protein entrapment into the latter were found to correlate solely with the molecular weight of solubilized protein in a wide range of experimental conditions, such as the surfactant hydration degree or protein concentration. Proceeding from this, a simple model of solubilization was suggested according to which a protein molecule is entrapped into a reversed micelle in a stoichiometric ratio of 1:1 rendering therewith no significant effect on the size of the reversed micelle. The conditions were found by the example of a-chymotrypsin under which the sedimentation properties of the system deviate from those of the model. The deviationsoccur at rather low hydrationdegrees of the surfactant when the inner cavity of a reversed micelle is less than the effective size of the solubilized protein molecule. In the latter case the protein "creates" around itself a new micelle of a required (bigger) size. is that the quantity of water in microenvironment of enzyme molecule inside a reversed micelle can be monitored with a high accuracy (1, 3, 8). Apart from solving the fundamental problems, micellar systems could be applied in fine organic synthesis as they make controlling the equilibrium of chemical reactions in a wide range possible (9). To understand the mode of action of enzymes entrapped into reversed micelles, it is important to know the structural organization of such systems. So, we studied the structural properties of enzyme-containing reversed micelles and, primarily the structural changes occurring in the micelle upon entrapment of a protein molecule into it. The enzyme-micellar system we created (3, 4) may well help to gain a deeper insight into the structure of biological membranes, par-
INTRODUCTION
Molecules of many surfactants in nonpolar organic solvents form reversed micelles, capable of solubilizing large amounts of water and other polar compounds (2) and, what is more, aqueous solutions of enzymes in catalytic quantities (3). Water-soluble enzymes solubilized by reversed micelles in organic solvents usually retain their catalytic activity and specifity, as was first found by us (3, 4) and then supported by other authors (5, 6, 7). Systems of reversed micelles in organic solvents offer fundamentally novel possibilities of studying mechanisms of enzyme catalytic action (1, 3, 4, 7) as well as the role water plays in enzymatic catalysis. The point i For previous p a p e r see (1). 2 To w h o m c o r r e s p o n d e n c e s h o u l d be addressed. 444 0021-9797/82/080444-14502.00/0 Copyright © 1982 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal
of Colloid and Interface Science, Vol. 88, No. 2, August 1982
445
P R O T E I N S IN R E V E R S E D M I C E L L E S
ticularly in the vicinity of protein molecules incorporated into them. Up to now, the published information has been devoted solely to the structure of reversed micelles containing no enzyme molecules. We shall dwell upon one of the beststudied systems of this type, i.e., on the system with bis(2-ethylhexyl)sodium sulfosuccinate (called Aerosol OT or AOT) as surfactant and with a hydrocarbon as organic solvent. These systems arouse interest due to their capability of solubilizing large amounts of water (up to 50 to 60 molecules per AOT molecule in some hydrocarbons, such as octane or decane) to form optically transparent and stable solutions (2). The structural properties of AOT reversed micelles in hydrocarbon solutions, such as size, aggregation number, and symmetry, were studied by the methods of neutron scattering (10), ultracentrifugation ( 11-14), viscosimetry (11, 15, 16, 19), light scattering (10, 13, 15, 17-19), and by use of the Kerr effect (16). The structure of the reversed AOT micelles is only slightly dependent on the nature of hydrocarbon solvent and AOT concentration and is largely influenced by water content in the system, i.e., by the molar concentration ratio Hz0/AOT (15). With increasing hydration degree, the molecular weight, aggregation number, and size of reversed micelles markedly grow. So, as was shown by Eicke and Rehak (12), at H 2 0 / AOT ,,, 0 the aggregation" number of AOT micelles is 15 to 20 (the molecular weight about 104), whereas at H 2 0 / A O T = 40 to 50 the aggregation number amounts some hundreds (the molecular weight about 106). At present, the generally acknowledged viewpoint is that the reversed AOT micelles, being slightly asymmetrical at low water content (a few H20 molecules per AOT molecule), become essentially spherical with rising hydration degree. However, according to the results obtained by Rouviere et al. (16) the reversed AOT micelles in heptane and decane become spherical at neither H20/AOT ratios but are ellipsoidal with an axes ratio of about 1:2.
As to the protein-containing reversed AOT micelles, their structure up to now has not been studied by physicochemical methods. The subject of this paper is the structural properties of protein-containing reversed AOT micelles in n-octane studied by the ultracentrifugation. MATERIALS AND METHODS
Trypsin and egg albumin were purchased from Sigma. a-Chymotrypsin, egg white lysozyme (grade B) and -y-globulin were obtained from the Olaine plant of chemical reagents (USSR). Horse liver alcohol dehydrogenase (crystal suspension) was a product of Reanal. a-Chymotrypsin and ~,-globulin were purified by gel filtration on Biogel P-2 and Sephadex G-75 columns, respectively, with the following lyofllization. According to the data of the a-chymotrypsin active center titration by N-transcinnamoylimidazole (20), the content of the active enzyme in the resultant preparation was 80%. The preparation of egg albumin was electrophoretically pure. Other proteins were used without further purification. Bis(2 - ethylhexyl)sodium sulfosuccinate (AOT) purchased from Merck was not further purified. We also used AOT purified by crystallization and by treatment with activated charcoal as described in Ref. (22). The results of experiments performed using purified and commercial AOT preparations showed practically no difference, if the presence of some water in commercial AOT had been taken into account. According to irspectroscopy data, the water content in the preparation from Merck was 2.5 mole per mole AOT (this value was taken into account during quantification of the overall water in reversed micellar systems). AOT solutions were prepared in commercial n-octane (Soyuzkhimreactiv). Buffer solutions were made with Tris from Reanal. Preparation o f micellar protein solutions. Stock protein solutions ( 1 0 -4 t o 10 -2 M ) were prepared in 0.05 M Tris HC1 buffer at Journal of Colloid and Interface Science,
Vol. 88, No. 2, August 1982
446
LEVASHOV ET AL.
pH 8.0. To prepare micellar solution, to 0.1 M AOT in octane was added the necessary amount of the stock protein solution and the mixture was then intensively shaken for 1 to 2 min to a homogeneous (optically transparent) state. Before the sedimentation experiments, the micellar solutions were incubated at 20°C for at least 2 hr. The systems investigated were stable for at least one day, i.e., during this time we were not able to establish any change in sedimentation properties. Sedimentation coefficients of reversed AOT micelles were determined at 20°C using a Beckman E analytical ultracentrifuge at 20,000 to 48,000 rpm. The determination was performed by a traditional technique, see, for instance (21). Depending on the aim of the experiment, scanning was carried out at various wavelengths. In the systems containing no solubilized protein, 20 to 50/zM 2,4-dinitrophenol was added to the micellar solution to stain micelles (22) which were traced in the absorption band of the indicator (405 nm). In protein-containing systems use was also made of a second indicator, picric acid (2,4,6-trinitrophenol), at the same concentration to record micelles at 400 nm. It should be noted that the sedimentation coefficient values of both "unfilled" (not containing a protein molecule) and "filled" (protein-containing) micelles were independent of the nature of the dye used. Furthermore, the sedimentation coefficients of protein-containing micelles, determined by tracing the dye as label, were identical with those in the dye-free systems scanned at 280 nm (the wavelength of protein absorption); in these conditions unfilled micelles are not detectable. This implies that to determine the sedimentation characteristics of reversed micellar systems, only one of the above tracing procedures, fit for a particular case, can suffice in most cases. The surfactant, involved in the formation of protein-containing reversed micelles, is preferably quantified using picric acid. Picric acid, as well as 2,4-dinitrophenol, allow a detection of various micelle fractions; yet Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
P..4
234
I
4.0
0.5
S FIG. 1. The typical sedimenting boundaries in the system of reversed micelles A O T - o c t a n e - H 2 0 at various c~-chymotrypsin concentrations. H 2 0 / A O T = 12.5. Concentrations of a-chymotrypsin (in the introduced aqueous solution) are 1, 0; 2, 1.8 × 10 3 M; 3, 5 × 10 -3 M; 4, 6.5 × 10 -3 M.
unlike the latter it has a lower pKa value (0.7 and 4.1, respectively). This permits an unhampered use of picric acid in systems with lowered pH (in concentrated aqueous a-chymotrypsin solutions pH is about 4 to 5), i.e., in the conditions when the extinction coefficient of 2,4-dinitrophenol markedly falls because of protonation of this indicator. RESULTS AND DISCUSSION
Dispersity of protein-containing micelles. A typical sedimenting boundary of reversed AOT micelles in octane in the absence of solubilized protein is schematically shown in Fig. 1 (curve 1, the molar ratio H 2 0 / A O T = 12.5). The sedimentograms obtained at various AOT hydration degrees show in all cases only one distinct boundary, which is indicative of the monodispersity of micelles (i.e., all micelles are characterized by the same sedimentation coefficient). The sedimentation coefficient of unfilled micelles as a function of their hydration degree is given in Fig. 2 (curve 1). The found values of sedimentation coefficients agree in order of magnitude with published data obtained in some other conditions (11, 13, 14). When protein (a-chymotrypsin) is solubilized in the system of reversed micelles, a second boundary appears on the sedimentogram (see, for instance, curves 2-4, Fig.
447
P R O T E I N S IN R E V E R S E D M I C E L L E S Mox 10-4
~,
~p
2o
As
80
,,so
/ / / // /
60
3 / //
/ /II / / // / / / / ///i//11 2 .~/.~--4 ~/
40
I
i//111~ /.1
o
40
20
30
40
I.IzO/AOT
FIG. 2. The sedimentation coefficient of reversed A O T micelles in octane as a function of H 2 0 / A O T . The experimental results: curve 1, unfilled micelles; 2, the micelles containing a-chymotrypsin. The theoretically calcu.lated curves: 3, hypothetical double unfilled micelles; 4, 5, the double micelles containing two c~-chymotrypsin molecules. Curve 4 describes the case with additive volumes of unfilled micelle and protein molecule and 5 refers to the case with unchanging volume of the micelle upon enzyme entrapment. Plotted against the upper axis are the molecular weights of unfilled single micelles (from (12)).
1). It is noteworthy that the slow sedimenting fraction of micelles is therewith characterized by the sedimentation coefficient equal to that of micelles of the protein-free system (at the same hydration degree). The micelles of this light fraction are evidently identical with" those of the protein-free system and are in fact unfilled micelles. The quickly sedimenting heavy fraction consists then of protein-containing micelles. The latter are also expressed on sedimentogram by only one distinct boundary (see, for instance, curves 2-4, Fig. 1). They are therefore also monodispersed. We arrived at the same conclusion while analyzing the sedimentation characteristics we obtained for other proteins (lysozyme, trypsin, egg albumin, horse liver alcohol dehydrogenase, ~/-globulin). a-Chymotrypsin solubilization limit. Figure 1 shows that with increasing concentration of the solubilized enzyme there occurs
• a regular growth in optical density characterizing the light fraction of micelles (unfilled micelles) (segment y). Its value is presumably directly proportional to concentration of the micelles that remain unfilled. The amount of surfactant remained in unfilled micelles can be calculated from sedimentation results (Fig. 1) as [ A O T ] . y / ( x + y). From the data on the aggregation numbers of unfilled micelles by Eicke and Rehak (12), one can find a dependence of the quantity of unfilled micelles, remained after achymotrypsin solubilization, on the overall enzyme concentration in the system. This dependence is shown in Fig. 3 for various H 2 0 / A O T ratios. We failed to attain higher concentrations of a-chymotrypsin than is shown in Fig. 3 because the system becomes turbid at enzyme concentration marked by arrows. It is seen that at the moment of appearance of turbidity in the micellar system, a large quantity of unfilled micelles remains unused. The amount o f surfactant needed to solubilize one enzyme molecule. Figure 3 shows that at every given hydration degree of AOT (curves 1 to 3) the number of unfilled mi-
400
~Z
80
=~
60
40
-
r
-
e-4 0-2 i- 5
"L~,t~.
z
20
[ CHYMOTRYPSlN].ro.rA,x t0 S, M
FIG. 3. The relative number of reversed unfilled AOT micelles in octane, left after a-chymotrypsin solubilization, as a function of the overall enzyme concentration in the system at various H 2 0 / A O T ratios: 1, 12.5; 2, 16.4, and 3, 22.5. Arrows show the c~-chymotrypsin concentration values corresponding to the solubilization limit at a given H ~ O / A O T ratio. Journal of Colloid and Interface Science, Vol, 88, No. 2, August 1982
448
LEVASHOV ET AL.
celles decreases with growing enzyme concentration. We succeeded in quantitation of this qualitatively evident regularity. To this end, the amount of surfactant, involved in the formation of protein-containing micelles, can be conveniently presented on the basis of sedimentation data (Fig. 1) in the form [AOT]. x/(x + y). Then, since the concentration of solubilized protein is known, one can determine the number of AOT molecules per protein molecule in a protein-containing micelle. Finally, using the published data on aggregation numbers of unfilled micelles (12), one can find the number of initial unfilled micelles N, involved in solubilization of one a-chymotrypsin molecule. The N value as a function of the overall achymotrypsin concentration in the system is shown in Fig. 4. Figure 4 shows that at not too high enzyme concentrations, N = 1 irrespective of AOT hydration degree (points 1 to 3). In other words, one enzyme molecule is solubilized by the amount of surfactant contained in one unfilled micelle. At medium values of H 2 0 / A O T (points 1 and 2) this regularity holds up to the limit enzyme concentration (marked by arrows 1 and 2), when the micellar system becomes turbid. At a higher value of H 2 0 / A O T (points 3), however, the N value falls with growing enzyme concentration and becomes equal to 0.5. This implies that the amount of surfactant contained in one micelle is capable in principle of solubilizing two enzyme molecules. Unfortunately, the sedimentation method is not sensitive enough to determine the N value at low hydration degrees of micelles (H20/AOT ~ 12.5, where H20/AOT = 12.5 corresponds to points 1 in Figs. 3 and 4). This is due to the fact that the limit concentration of solubilized a-chymotrypsin in the system of reversed AOT micelles in octane decreases with the molar ratio H 2 0 / AOT (Fig. 3) andhence, a portion of the overall surfactant amount involved in the formation of protein-containing micelles falls. Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
N 4.0
3 ,r.~.
0,5
o-4 0-2
m-3
t0
20
30
[ CI.IYMOTRYPSIN] .rorAtx 40s, M FIG. 4. The number of initial unfilled AOT micelles in octane necessary to solubilize an a-chymotrypsin molecule as a function of the overall concentration of the enzyme in the system at various hydration degrees of AOT. H20/AOT: 1, 12.5; 2, 16.4, and 3, 22.5. The limit concentrations of a-chymotrypsin, over which the system becomes turbid, are indicated by arrows.
In practice this leads to decrease in the x segment (Fig. 1) to the value experimentally undeterminable. Nevertheless, at not too low hydration degrees of AOT (H20/AOT ~- 12, Figs. 3 and 4, points 1) the analysis of sedimenting boundaries of protein-containing micelles and of sedimentation coefficients of the micelles remaining unfilled still enabled us to determine the stoichiometric ratio A O T / protein in protein-containing micelles. It should be noted that even if N is constant and equal to 1 (Fig. 4), the stoichiometric ratio AOT/protein alters with AOT hydration degree. This is due to the fact that with increasing H 2 0 / A O T ratio, the aggregation number of reversed micelles grows (12). Since one protein molecule is solubilized by the amount of surfactant contained in one micelle (N = 1, Fig. 4), the number of AOT molecules involved in protein solubilization at every given hydration degree of AOT will be different. The stoichiometric ratio of AOT/protein found by us does not permit a determination of absolute quantity of protein molecules contained in one micelle. In other words, it cannot be used to discriminate the cases
PROTEINS
IN REVERSED
when a protein-containing micelle is formed, for instance, by one unfilled micelle and one protein molecule or by two unfilled micelles and two protein molecules, and so on. To discern these "multiple" molecular mechanisms of solubilization and to decide on how the protein-containing micelle is constructed, one should analyze the sedimentation coefficients of the protein-containing reversed micelles proper (see below).
Hydration degree of protein-containing micelles. It has been shown above that on protein solubilization in the system of reversed micelles, the sedimentation coefficient of the micelles remaining unfilled does not alter (Fig. 1). On the other hand, the sedimentation coefficient of unfilled micelles depends on their hydration degree (Fig. 2, curve 1). Hence, on protein solubilization the hydration degree of unfilled micelles does not change. This implies that the protein solubilization does not cause redistribution of water in the system of reversed micelles, i.e., unfilled and filled micelles are characterized by the same H 2 0 / A O T ratio. This inference holds solely for not too low H 2 0 / A O T ratios. The fact is, the amount of surfactant involved in the formation of protein-containing micelles is too low at low H 2 0 / A O T ratios (Fig. 3, curve i). So, the hydration degree of unfilled micelles should alter only slightly even at significant change in the hydration degree of protein-containing micelles and hence, the experimentally determined sedimentation coefficient of unfilled micelles will hardly change. The accuracy of the experiment ensures a record of a change in the sedimentation coefficient only at a change of the H 2 0 / A O T ratio not less than by unity. Let us try to assess on this basis the lowest H 2 0 / A O T ratio starting from which one can be sure that the hydration degrees of unfilled and filled micelles are equal. So, at H 2 0 / A O T = 12.5 (Fig. 3, points 1) the maximal possible amount of AOT involved in the formation of proteincontaining reversed micelles is about 15% of the overall AOT amount. So, a change in
MICELLES
449
the H 2 0 / A O T ratio of unfilled micelles even by 1 (an accuracy limit of the sedimentation experiment, see above) would raise the hydration degree of protein-containing micelles by 6 H20 molecules per AOT molecule, i.e., by about 30%. This is the minimal error in determining the hydration degree of proteincontaining micelles at H 2 0 / A O T = 12.5. At H 2 0 / A O T = 16.4 and 22.5 (Figs. 3 and 4, points 2 and 3), the minimal error is 18 and 4%, respectively. It is evident that the experimental error decreases with increasing H / O / A O T ratio and conversely. So, the invariability of the sedimentation coefficient of unfilled micelles which we observed experimentally on protein solubilization (Fig. 1), can be indicative of equality of hydration degrees of filled and unfilled micelles only at fairly high H 2 0 / A O T ratios. To decide on the hydration degree of protein-containing micelles at low H20/AOT, we shall try to analyze below the sedimentation coefficients of the protein-containing micelles proper.
Sedimentation coefficients of reversed micelles containing a-chymotrypsin. The sedimentation coefficient of reversed micelles containing a-chymotrypsin as a function of AOT hydration degree is shown in Fig. 2 (curve 2). In this paper we shall analyze in detail the sedimentation results solely for the systems with not too high enzyme concentrations (when N = 1, Fig. 4). In these conditions the experimentally observed sedimentation coefficient is independent of the enzyme concentration. Account should be taken here that the sedimentation coefficient values of proteincontaining micelles at all H 2 0 / A O T ratios exceed the sedimentation coefficients of unfilled micelles (curve 1). Discrepancies between the sedimentation coefficients of unfilled and filled micelles are greater, the smaller the surfactant hydration degree. The sedimentation coefficient of a proteincontaining micelle can in principle be calculated theoretically (see Appendix), proceeding from a certain model of its construcJournal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
450
L E V A S H O V ET AL.
tion. Below we shall try to choose an appropriate model of protein-containing micelles comparing theoretical values of sedimentation coefficients (calculated for different models) with experimental results. Model o f "'multiple" micelles. In the above discussion on the stoichiometric A O T / protein ratio found experimentally (see Fig. 4) we concluded that a possible model of protein-containing micelles at N = 1 (in the region of H 2 0 / A O T ~ 12) can be "multipie" micelles, i.e., the micelles formed of two, three, and more initial unfilled micelles and containing two, three, and more protein molecules, respectively. The theoretically calculated curve of the sedimentation coefficient of hypothetical unfilled double micelles as a function of H 2 0 / A O T is shown in Fig. 2 (curve 3). On entrapment of a protein molecule into a reversed micelle two extreme cases can, in principle, be realized: the size of the micelle can either remain practically unaltered (curve 5), or equal to a sum of volumes of the unfilled micelle and the protein molecule (curve 4). The curves corresponding to an intermediate change in the micelle size will evidently lie between curves 4 and 5 describing these two extreme cases. It is seen in Fig. 2 that none of the theoretical curves coincides with the experimental (curve 2). This moreover refers, as was confirmed by calculations, to the protein-containing micelles with a greater aggregation degree, whose curves lie still higher. The model of multiple micelles cannot therefore describe the sedimentation properties of real protein-containing micelles. Other models should be considered. In choosing the model, account should be taken of the fact that the size of the inner cavity of reversed micelles increases with the H 2 0 / A O T ratio (Fig. 5, upper axis). Hence, depending on the H 2 0 / A O T ratio, the cavity radius can be bigger or smaller than the effective size of a solubilized protein molecule. The molecular mechanism of solubilization in the two cases will expectedly be different and so we shall discuss them separately. Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
40
2!,5 30
40
50
40+
60
70
///
/j7 //
30
(// /
#1 //~ / o~ 3 / Z~¢71 // / I
i l-j.i~;'.s
/
/11
8
40 9 "-\\! I I
~o,I
~o
3o
io
RIO/hOT FIG. 5. Comparison of theoretically calculated and experimental (dotted line) dependencies of the sedimentation coefficient of c~-chymotrypsin-containing reversed A O T micelles on H 2 0 / A O T ratio. Curves 1-5: the aggregation n u m b e r and the hydration degree of micelle do not alter upon entrapment of an enzyme molecule. Changes in the micelle volume upon protein entrapment: 1, no change; 2, 3, 4, increases by 10, 20, and 30% of the a-chymotrypsin molecular volume, respectively; 5, the additivity of the micelle and c~-chymotrypsin molecular volumes. Curves 6 - 9 refer to the model 2.3 (Table I). The micelle inner cavity volume is equal: curve 6, to the a-chymotrypsin molecular volume; curves 7, 8, to the c~-chymotrypsin molecular volu m e plus 10 and 30% of its volume, respectively; curve 9, to the s u m of volumes of an a-chymotrypsin molecule and of water present in the micelle. T h e vertical broken line is plotted at H 2 0 / A O T = 11.6. Plotted against the upper axis are the radius values of the unfilled micelle inner cavity (see Appendix).
Solubilization model involving the micelles, with their inner cavity larger than the effective size o f the protein molecule or equal to it. The size of an ~-chymotrypsin molecule is 40 × 40 × 50 ,~ (23). Being approximated by the sphere of equal volume, the molecule will have a radius of 21.5 /~. The inner cavity of reversed micelle has the same radius at H 2 0 / A O T = 11.6 (Fig. 5, vertical broken line). First, we shall consider the a-chymotrypsin solubilization in systems of reversed micelles with H g O / A O T ~> 11.6 (Fig. 5, to the right of the vertical broken line), when the size of the micelle inner cav-
P R O T E I N S IN REVERSED MICELLES
ity exceeds the effective size of an o~-chymotrypsin molecule. To determine the model in further detail account should be taken of the above-established fact that the protein-containing micelles in the studied range of H 2 0 / A O T ratios differ from initial unfilled micelles neither in aggregation numbers, nor in the hydration degree; i.e., entrapment of protein into a reversed micelle does not change the composition of the latter. So, Fig. 5 shows theoretical curves of the sedimentation coefficient of protein-containing micelles as a function of the surfactant hydration degree (broken lines) calculated particularly for such a solubilization model. On entrapment of a protein molecule into a reversed micelle, two extreme cases can, in principle, be realized: the micelle volume can (a) practically remain unchanged (curve 1) or (b) turn out equal to the sum of volumes of the unfilled micelle and the protein molecule (curve 5). Intermediate cases are described by curves 2 to 4, i.e., when the inner cavity volume of a protein-containing micelle is equal to the volume of the unfilled micelle plus 10, 20, and 30% of the volume of the entrapped enzyme molecule, respectively. Figure 5 shows that the experimental points lie between curves 1 and 2. This implies that on entrapment of an a-chymotrypsin molecule into a reversed micelle, the volume of the latter increases only by a volume not exceeding 10% of the volume of the protein molecule. This astonishing fact may be accounted for by redistribution of water inside the micelle on entrapment of a protein molecule. So, the sedimentation data agree with the model according to which entrapment of an a-chymotrypsin molecule into a reversed AOT micelle in octane (at H z O / A O T > 11.6) does not significantly alter the size of the initial unfilled micelle with its aggregation number and hydration degree remaining unchanged.
Solubilization model involving micelles with their inner cavity smaller than the effective size o f the protein molecule. At H 2 0 / A O T < 11.6 (Fig. 5, to the left of the
451
vertical broken line) an a-chymotrypsin molecule is bigger than the inner cavity of a reversed micelle (Fig. 5, upper axis). So, a protein-containing micelle should inevitably greatly differ from unfilled micelles in size and presumably in the aggregation number and/or the hydration degree. In other words, entrapment of a protein molecule into a reversed micelle should be accompanied by structural rearrangement of the latter, or to be more precise, a protein molecule will "create" around itself a new micelle. This agrees with the conclusion arrived at by Menger and Yamada (5) by means of enzyme kinetics. In this case (i.e., in the presence of small micelles incapable of direct entrapment of an enzyme molecule) a protein molecule seems to get coated with a monolayer of hydrated surfactant molecules. As the effective radius of an ~-chymotrypsin molecule (21.5 A) equals to the radius of the inner cavity of an unfilled micelle at H 2 0 / A O T = 11.6, one may suppose that the mode of formation of this monolayer is, to some extent, determined by the regularities that govern the formation of unfilled micelles precisely at this boundary value of the hydration degree, i.e., at H 2 0 / A O T = 11.6. The characteristics of the models of protein-containing micelles we analyzed are given in Table I and the relevant calculated theoretical curves for the sedimentation coefficient of the micelles as a function of H z O / A O T are shown in Fig. 6. The experimental points are given for comparison. In all sections of Fig. 6 one curve represents the extreme case, when the volumes of the mieelle inner cavity and of a-chymotrypsin molecule are equal, and another refers to a second extreme, when the volume of the micelle inner cavity is equal to the sum of volumes of the o~-chymotrypsin molecule and the water residing in the micelle. The curves for intermediate values of the inner cavity volume of the protein micelle should evidently lie in the area between a pair of these curves. It is obvious that a model of a protein-containing micelle cannot
452
L E V A S H O V ET AL.
describe experimental results if the experimental points lie beyond this area. Figure 6 shows that this formal requirement is met by only two models, precisely by models 2.3 and 2.2, shown in Table I. The patterns of curves both 2.2.1 and 2.2.2 (and therefore of all "intermediate" curves between the two) does not correspond, however, to the experimental curve. For this reason model 2.2 is presumably inadequate to describe experimental results.
The curves, corresponding to model 2.3, the only model capable of describing the experimental results, are shown in enlarged scale in Fig. 5 (curves 6 and 9). Figure 5 shows the curves corresponding to intermediate values of the micelle inner cavity volume equal to 1.1 (curve 7) and 1.3 (curve 8) of the a-chymotrypsin molecular volume. Figure 5 shows that the experimental points lie between curves 6 and 7. This implies that the volume of the protein-containing micelle
TABLE I Structural Parameters of the Models of Protein-Containing Micelles for H 2 0 / A O T < 11.6" Aggregation
1
2
nfoT = n~,OT
f __ o nAox -nAOT at
Hydration
1.1
nf20 = n~i20 (or wf = Wo)
1.2
f _ o nH2o - nn2o at wo = 11.6
1.3
wf = 11.6
2.1
nf~o = n~2o
2.2
nfn2o=n~2oatWo = 11.6
2.3
(or wf = 11.6) wf = Wo
3.1
nf2o = n~2o
3.2
n~2o = n~2o at Wo = 11.6
3.3
w~ = wo
3.4
wf = 11.6
4.1
nf~o = n~2o
4.2
nf:o = n~2o at Wo = 11.6
4.3
wf = Wo
Wo = 11.6
3
4
f~,oT = f~,or
f o r = f~oT at Wo = 11.6
4.4
wf = 11.6
Volume of inner cavity
1.1.1
lip
1.1.2
Vp + V.~o
1.2.1 1.2.2 1.3.1 1.3.2
Vp Vp + V.2o Vp
2.1.1" 2.1.2 2.2.1"* 2.2.2 2.3.1'** 2.3.2
Vp Vp + VH2o lip Vp + V.2o Vp Vp + Vn~o
3.1.1 3.1.2 3.2.1 3.2.2 3.3.1 3.3.2 3.4.1 3.4.2
Vp Vp + V.2o Vp Vp + V.2o Vp Vp Vp + VH2o
4.1.1" 4.1.2 4.2.1"* 4.2.2 4.3.1"** 4.3.2 4.4.1"* 4.4.2
Vp lip Vp Vp lip Vp II0 Vp
Vp +
VH20
Vp + Vn2o
+ Vn~o + Vn2o + VH2o + VH20
"Designations used: nAOT, nH20, fAOT, and w are the aggregation number, a number of water molecules present in micelle, area per A O T molecule on the surface of a micelle, and A O T hydration degree ( H 2 0 / A O T ) , respectively. Subscripts " f " and "0" refer to "filled" and "unfilled" micelles, respectively. Vp is the volume of an a-chymotrypsin molecule, Vn20 is the volume of water present in a micelle. Asterisks mark equivalent models; equal models are marked by an equal number of asterisks. Journal o f Colloid and Interface Science, Vol. 88, No. 2, August 1982
40-
~-~ Ii /1.4.t
40
40
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I/ "/ .I/" "//
co 10le.
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/
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,~,~i .-,~J4 "/
•el
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'x,J\ 2.1.2
\
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" [~
t
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t
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I
t
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40- [ ~ ] i I 30-
,31
I / I/
///
!
20-
I /
2
|././
~
3O
£0-
!,,2d / !" ~ "// / ' . "/ 4 Z //
./
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3O
20 ¸
/ / l~
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\ ~'•.." . ~.
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-._~2.4
I I I
40-
3.2.2
~ ] '~ I '/ • 14.1.1/ //4.1.2 II // / 30
I I I I
~,1 "¢'"
"ZI
I
I I
l
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40
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//:'~'3"4
20
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H20/AOT FIG. 6. The sedimentation coefficient of a-chymotrypsin-containing reversed AOT micelles in octane as a function of H20/AOT ratio theoretically calculated for the models given in Table I. The corresponding model numbers are shown in the upper-left corner of each section. Dots show the experimental sedimentation coefficient values. The vertical broken lines are plotted at HzO/AOT = 11.6, Journal of Colloid and Interface Science, Vol. 88, No. 2, August
453
1982
454
LEVASHOV
inner cavity is not over 1.1 of the a-chymotrypsin molecular volume. So, analysis of sedimentation coefficients of reversed AOT micelles in octane (at H 2 0 / AOT < 11.6), containing solubilized a-chymotrypsin, results in the following model of protein-containing micelles (model 2.3, Table I): (a) the size of the inner cavity of the protein-containing micelle is close to that of a-chymotrypsin molecule; (b) the aggregation number of such a micelle is constant and equal to the aggregation number of unfilled micelles at H 2 0 / A O T = 11.6, and (c) the surfactant hydration degree in the filled micelle is the same as in unfilled micelles existing at H 2 0 / A O T < 11.6. Solubilization of other proteins. Along with a-chymotrypsin we studied by the sedimentation method solubilization of some other proteins, such as lysozyme, trypsin, horse liver alcohol dehydrogenase, -r-globulin, and egg albumin, considerably differing in their molecular weights: 14,300, 23,000, 80,000 (23), 150,000 (24), and 44,000 (25), respectively. The experiment for each protein was conducted at a fairly high surfactant hydration degree, i.e., at such a fairly big volume of the micelle inner cavity which, in principle, can house a protein molecule. On the other hand, for the maximal simplicity of the experiment, the cavity size should not greatly exceed the effective size of the protein molecule, to rule out a possible entrapment into micelle of protein aggregates. So, for lysozyme and trypsin with their molecular dimensions 45 X 30 × 30 A and 50 × 40 × 40 A, respectively (23), use was made of the system characterized by H 2 0 / A O T = 12.5 in which the micelle inner cavity diameter is 50 A (Fig. 4, upper axis); for egg albumin (molecular dimensions are 33 X 33 × 96 A (25)), the system characterized by H 2 0 / A O T = 30.5 (the cavity diameter 100 A); for alcohol dehydrogenase and ~/-globulin (dimensions of the former are 45 × 55 × 110 A (23), the latter is approximated by a sphere with a diameter of about 110 to 120 Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
E T AL.
/ /
60 ¸
4O
/
/
/
/
/
5~// /
/
,o 2O /
/
/
4° ~ / / /, / 2
2'o
410
'
60
¢)eAL' $ FIG. 7. Correlation between e x p e r i m e n t a l (S~xp) and theoretically calculated (scat) s e d i m e n t a t i o n coefficients of protein-containing reversed A O T micelles in octane: 1, lysozyme ( H 2 0 / A O T = 12.5); 2, trypsin ( H e O / A O T = 12.5); 3, a - c h y m o t r y p s i n ( H 2 0 / A O T = 12.5); 4, egg a l b u m i n ( H e O / A O T = 30.5); 5, horse liver alcohol deh y d r o g e n a s e ( H 2 0 / A O T = 39.5); 6, "y-globulin ( H 2 0 / A O T = 39.5).
(26)), the system characterized by H 2 0 / AOT = 39.5 (the cavity diameter 130 A). Fig. 7 shows a correlation between the sedimentation coefficients of protein-containing micelles found experimentally (Sexp) and those calculated theoretically assuming that a micelle does not practically alter on protein entrapment into it (Sc~l). A broken line with a slope equal to 1 corresponds to a precise performance of the model. As seen, the calculated results satisfactorily agree with experimental findings. This implies that on entrapment of any of the studied proteins (greatly differing in their molecular weights) into a reversed AOT micelle (with a fairly large inner cavity size), its shape and volume do not appreciably alter with the aggregation number and the initial hydration degree unchanged. CONCLUSION
The results obtained by the sedimentation analysis enable us to only indirectly conjecture about the structural properties of protein-containing reversed AOT micelles. So,
PROTEINS IN REVERSED MICELLES
455
TABLE II Parameters of Reversed AOT Micelles in Aliphatic Hydrocarbons
H20 AO--'-T= w°
Molecular weight, /14o*
Aggregation number, n~or b
Radius R~ (A) ~
Radius of inner cavity, r o (A) a
Thickness of surfactant layer, / = Ro - ro (A)
5 7 9 12 16 20 25 30 40
25,670 38,270 54,440 86,350 145,530 226,980 365,530 551,370 1,092,730
48 67 90 131 199 282 408 560 938
20.9 24.9 26.9 31.4 37.5 43.7 51.3 59.0 74.3
11.7 14.7 17.7 22.1 28.0 33.9 41.4 48.9 64.1
9.2 9.2 9.2 9.3 9.5 9.8 9.9 10.1 10.2
Area per A O T molecule on the surface of micelle, f~,or (A 2)"
Partial specific volume, rio (cm3/g) f
Volume of an H20 molecule, v (A 3) g
36.0 40.5 43.7 46.8 49.5 51.3 52.7 53.7 55.0
0.8905 0.8969 0.9009 0.9050 0.9149 0.9225 0.9302 0.9363 0.9461
28.4 28.6 28.8 28.9 29.1 29.2 29.3 29.4 29.6
Molecular weights were calculated using empirical formula Mo = (19 + 2.1Wo)3, which well describes the experimental data (12). b n~,or = Mo/(MAoT + MH2oWo), where MAOTand Mmo are the molecular weights of AOT (445) and water, respectively. c Calculated from Eq. [5] (see Appendix). dr o = ((3/4~r)n°AOTWoV) I/3, where v is the volume of an H20 molecule at a given H20/AOT ratio. e f~.or = 47r~/n~,oT. YFrom Refs. (13, 14). g From Ref. (11). to verify the inferences m a d e f r o m the sedimentation analysis, a direct physical m e t h o d should be used t h a t provides a direct information on the structure of particles in solution, for instance the m e t h o d of X - r a y lowangle scattering. Studies in this direction are in progress. APPENDIX
Df -Mf -o S°'Do'M
1 - ~fp
o 1 -- f;oP
[2]
where " f " and " o " denote filled and unfilled micelles, respectively. T h e diffusion coefficients of reversed micelles in Eq. [2] can be expressed by the S t o k e s - E i n s t e i n equation [ 3 ] with the assumption of the micelle sphericity3: kT
T h e sedimentation coefficients of reversed micelles were theoretically calculated according to the Svedberg equation D s = R - ~ M ( 1 - ~p),
Sf
[1]
where s is the sedimentation coefficient of particles with molecular weight M and the partial specific volume fi in the solvent with density p, D is the diffusion coefficient, R is the gas constant, and T is the absolute temperature. C o m b i n a t i o n of two types-[ 1 ] equations, written for filled and unfilled micelles, gives
D = f(CAoT) 67rr/R M
[3]
where k is the B o l t z m a n n constant, n is the viscosity of solvent, RM is the micelle radius, f(CAoT) is a function of A O T concentration, f(CAoT) ~ 1 at CAOT ---' 0, f(CAoT) < 1 at CAOT ~ 0 (14). W i t h regard to Eq. [3], Eq. [2] transforms into M f 1 - Dfp Rf Mo 1 - V o p "
Ro
sf=So
[4]
Calculations show that the conclusions of the present paper remain operative also in the case if micelles are not spheres but ellipsoids of revolution with not too large ratio of semiaxes (about 1:2). Journal of Colloid and Interface Science, Vol. 88, No. 2, August 1982
456
L E V A S H O V E T AL.
Equation [4] was used to calculate the sedimentation coefficients of protein-containing reversed micelles. It is important to emphasize that Eq. [4] does not contain f(CAoT) which is a measure of the system's nonideality and whose view is unknown. The values of Mo and Vo in Eq. [4] are known from literature (12-14) for any H 2 0 / AOT ratios (Table II gives the parameters of unfilled reversed micelles used for calculations). The so was determined experimentally (Fig. 2, curve 1). The Ro can be expressed using the known values of 3/o and Voif we take into consideration that Vo is the parameter equal to the reciprocal of the density of unfilled micelles. Then 4~r R3NA --, 3 Mo
[51
where NA is Avogadro's number. If upon entrapment of a protein molecule into a micelle the aggregation number and the hydration degree of the micelle do not alter, then Mf = Mo + Mp, where Mp is the protein molecular weight. The Rf can be determined as Rf = rf + l, where rf is the radius of the inner cavity of the protein-containing micelle that is given by the volumes of the protein molecule and water present in the micelle with regard to the assumption on the relation between these volumes, and l is the thickness of the reversed micelle outer layer formed by "tails" of AOT molecules. The l value at every H 2 0 / A O T ratio was determined as the difference l = Ro - ro, where ro is the inner cavity radius of unfilled reversed micelles. The ro value was taken equal to the radius of the water drop formed by the number of water molecules present in the micelle with regard to the density of "micellar" water as a function of H 2 0 / A O T ratio (11). The number of water molecules present in the unfilled micelle was determined from the equation o
BH20 :
Mowo M A O T -I- M H 2 o W o '
where Wo= H20/AOT, MAOT, and MH=Oare Journal o f Colloid and Interface Science, VoL 88, No. 2, August 1982
the molecular weights of AOT and H20, respectively. The l value thus determined alters from 9.2 to 10.2 A. depending on H 2 0 / AOT ratio (Table II), which agrees with the literature value of the length of an AOT molecule equal to 11 A (15). The vf value, reciprocal to the density of protein-containing micelles, was determined from the found Mf and Rf values according to the equation analogous with Eq. [5]. The described approach was used to calculate the sedimentation coefficients of reversed micelles containing a-chymotrypsin in the range H 2 0 / A O T ~ 11.6, other proteins and also to calculate the sedimentation coefficients of protein-containing multiple micelles.4 In calculations of the sf values of reversed micelles, containing a-chymotrypsin, in the range H 2 0 / A O T < 11.6 use was made of the parameters given in Table I. The characteristics of protein-containing micelles presented in Eq. [4] were determined from the relations Mf=
f 2 o M H 2 0 d- M p HfA o T M A o T -{- n H
Rf = (3Vf/47r) 1/3 + l, where ngoT, f nn20,fand Vf are the number of AOT molecules, the number of water molecules in a protein-containing micelle, and the volume of its inner cavity, respectively (Table I). All the models given in Table I are based on the assumption that the outer layer of protein-containing reversed micelles is formed by the monolayer of surfactant molecules. Accordingly, nfgoT in models 3 and 4 (Table I) was determined from the relation 4 rg n oT - A o T ' where rf is the inner cavity radius of a pro4 In the case of unfilled multiple micelles Eq. [4] transforms into s" = nsoRo/R', where s" and R" are the sedimentation coefficient and the radius of an n-multiple unfilled micelle. R" is determined as the radius of the sphere, whose volume equals the volume of n initial unfilled micelles.
PROTEINS IN REVERSED MICELLES
tein-containing reversed micelle. In models 3.3.2, 3.4.2, 4.3.2, and 4.4.2 the rf value is the real root of the cubic equation
47rr~ _ fAOT
4 7 r r~ -
3
3
rp
Wfl)
'
where rp is the effective radius of protein molecule (a-chymotrypsin), and v is the volume of an H20 molecule at a given hydration degree of surfactant. The vr value was determined from the equation, analogous with Eq. [5]. The used values of / and density of the micellar water in each model corresponded to the hydration degree of proteincontaining micelles given by this model. ACKNOWLEDGMENTS We are pleased to acknowledge the constant attention to our work and invaluable comments of Professor I. V. Berezin. We also thank Professor P. L. Luisi for sending us a preprint of his paper (27) describing another structural model of protein-containing micelle. REFERENCES 1. Martinek, K., Levashov, A. V., Klyachko, N. L., Pantin, V. I., and Berezin, I. V., Biochim. Biophys. Acta 657, 277 (1981). 2. Fendler, J. H., and Fendler, E. J., "Catalysis in Micellar and Macromolecular Systems." Academic Press, New York, 1975. 3. Martinek, K., Levashov, A. V., Klyachko, N. L., and Berezin, I. V., Dokl. Akad. Nauk. S S S R 236, 920 (1977). [Russ.] 4. Levashov, A. V., Klyachko, N. L., and Martinek, K., Bioorg. Khim. 7, 679 (1981). [Russ.] 5. Menger, F. M., and Yamada, K., J. Amer. Chem. Soc. 101, 6731 (1979). 6. Wolf, R., and Luisi, P. L., Biochem. Biophys. Res. Commun. 89, 209 (1979). 7. Balny, C., and Douzou, P., Biochimie 61, 445 (1979).
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8. Martinek, K., Levashov, A. V., Pantin, V. I., and Berezin, I. V., Dokl. Akad. Nauk S S S R 238, 626 (1978). [Russ.] 9. Martinek, K., Khmelnitsky, Yu. L., Levashov, A. V., Klyachko, N. L., Semenov, A. N., and Berezin, I. V., Dokl. Akad. Nauk S S S R 256, 1423 (1981). [Russ.] 10. Cabos, C., and Delord, D., J. Appl. Crystallogr. 12, 502 (1979). 11. Mathews, M. B., and Hirschhorn, E., J. Colloid Sci. 8, 86 (1953). 12. Eicke, M. F., and Rehak, J., Helv. Chim. Acta 59, 2883 (1976). 13. Zulauf, J. M., and Eicke, H. F., J. Phys. Chem. 83, 480 (1979). 14. Robinson, B. H., Steytler, D. C., and Tack, R. D., Z Chem. Soc. Faraday Trans. I 75, 481 (1979). 15. Ekwall, P., Mandell, L., and Rontell, K., J. Colloid Interface Sci. 33, 215 (1970). 16. Rouviere, J., Couret, J.-M., Lindheimer, M., Dejardin, J.-L., and Marrony, R., J. Chim. Phys. Phys. Chim. Biol. 76, 289 (1979). 17. Frank, S. G., and Zografi, G., J. Pharm. Sci. 58, 993 (1969). 18. Menger, F. M., Donohue, J. A., and Williams, R. F., J. Amer. Chem. Soc. 95, 286 (1973). 19. Day, R. A., Robinson, B. H., Clarke, J. H. R., and Doherty, J. V., J. Chem. Soc. Faraday Trans 1 75, 132 (1979). 20. Schonbaum, G. R., Zerner, B., and Bender, M. L., J. Biol. Chem. 236, 2430 (1961). 21. Freifelder, D., "Physical Biochemistry. Application to Biochemistry and Molecular Biology," Chap. 11. Freeman, San Francisco, 1976. 22. Levashov, A. V., Pantin, V. I., and Martinek, K., Kolloidn. Z. 41, 453 (1979). [Russ.] 23. Squire, P. G., and Himmel, M. E., Arch. Biochem. Biophys. 196, 165 (1979). 24. Pilz, I., Schwarz, F., and Palm, W., Eur. J. Biochem. 75, 195 (1977). 25. Haurowitz, F., "The Chemistry and Function of Proteins." Academic Press, New York, 1963. 26. Munn, E. A., Bachmann, L., and Feinstein, A., Biochim. Biophys. Acta 625, 1 (1980). 27. Bonner, E. J., Wolf, R., and Luisi, P. L., J. Solid Phase Biochem. 5, 255 (1980).
Journal of Colloid and Interface Science, VoI.88, No. 2, August1982