J. Phys. Chem. 1991, 95, 1799-1811 Such a substantial difference in the molecular deformation caused by the tensile stress is attributed to the difference in the symmetry of Mon and Orth 11. The point groups isomorphous to the factor groups of the crystals of Mon and Orth I1 are C,, and Da, respectively. Therefore, the deformation, which is related to cjj, has to belong to the Ag species in both cases. For Mon the gear-type rotation of two dimers adjacent in the stacking direction around the a axis is forbidden because the two dimers belong to the different unit cells. As a result, the two dimers must rotate in the same direction. However, this kind of rotation increases the interlamellar strain energy so that the strain energy of the molecule should be relaxed through the intramolecular deformations. On the other hand, the gear-type rotation is allowed in Orth I1 because the two rotating dimers of Orth I1 belong to the same unit cell. Consequently, the strain energy of the molecule can be relaxed through this rotation, which is governed by weak intermolecular interactions.
1799
Conclusion The elastic behavior of two polytypes of stearic acid B form was studied by Brillouin spectroscopy. It was found that the diagonal terms are greater in Mon than in Orth 11, particularly cj3, which expresses the elastic property of the lamellar stacking direction. It was nearly doubled in Mon. This large difference in c33was attributed to the difference of symmetries of the polytype structures of Mon and Orth 11, based on theoretical calculations using intra- and intermolecular force fields. Acknowledgment. We thank Professor K. Sat0 of Hiroshima University for providing us single crystals of stearic acid B form. This work was supported by a Grant-in-Aid for Scientific Research on Priority Areas, New Functional Materials-Design, Preparation and Control, The Ministry of Education, Science and Culture, Japan (No. 63604014). Registry No. Stearic acid, 57-1 1-4.
Structural Characterization of cw-Chymotrypsin-Containing A 0 1 Reversed Micelles Reza S. Rahaman and T. Alan Hatton* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39 (Received: January 2, 1990; In Final Form: July 31, 1990)
A thermodynamic model is developed for the prediction of the sizes of protein-containingand non-protein-containing reversed micelles as a function of system parameters such as ionic strength, protein net charge and size, and protein concentration and water content in the micellar phase, for systems produced by both the phase-transfer and injection methods. Excellent agreement is obtained between model predictions and small-angle neutron scattering data on micellar sizes for the system a-chymotrypsin in AOT/isooctane reversed micelles. The model provides some new insights into the nature of protein-micelle complexes; it indicates that filled micelles may be larger or smaller than empty micelles and that it is the energetics of the filled micelles that are usually the dominant contribution to the free energy of the reversed micellar system. The model identifies the free energy associated with simple charge interactions within micelles and between proteins and micelles as the major electrostatic driving force responsible for protein solubilization in these charged microemulsion systems. Screening of across-micelle surfactant interactions by the presence of a low-dielectric body (the protein) in the micellar core lowers the electrostatic free energy sufficiently that even unfavorably charged proteins may be solubilized.
Introduction The solubilization of polar solutes such as amino acids, nucleic acids, and proteins in reversed micellar media has attracted considerable interest over the past decade or so.’ These surfactant-stabilized, nanometer-scale water droplets in an oil continuum are potentially attractive as media for the biosynthetic production of fine chemicals and pharmaceuticals? as extractants for the separation and purification of a range of biological product^,^ and as membrane-mimetic media for the analysis of membrane transport ~haracteristics.~While much work has been done on characterizing the properties of reversed micelles, both in terms of fundamental scientific interest and from the perspective of developing practical applications, still not much is known about the actual structural characteristics of protein-containing reversed micellar solution^.^ A theoretical understanding of how and why micellar sizes change with system conditions could provide information about micellar structure, address issues such as size exclusion of proteins from reversed micelles: and contribute to an understanding of the partitioning behavior of proteins between bulk aqueous and reversed micellar solutions. Moreover, a better understanding of the nature of the protein-micelle complex, and how the sizes of empty and protein-filled reversed micelles change with overall water content, could provide some insight into the reasons for the accompanying changes in reaction rates frequently observed in reversed micellar biocatalysis studies.’ These issues are addressed in this paper, where we present a model capable
* Author to whom all correspondence should be addressed.
of predicting, almost quantitatively, experimentally observed sizes of empty and protein-filled micelles, and use these results to provide insight into reversed-micellar-specific factors affecting protein partitioning and biocatalysis. (1) (i) Luisi, P. L.; Magid, L. J. CRC Crir. Rev. Biochem. 1986,20,409. (ii) Luisi, P. L.; Giomini, M.; Pileni, M. P.; Robinson, B. H. Biochim. Biophys. Acta 1988, 947, 209. (2) (i) Luthi, P.; Luisi, P. L. J . Am. Chem. Soc. 1984, 106, 7285. (ii) Shield, J. W.; Ferguson, H. D.; Gleason, K. K.; Hatton, T. A. In ACS Symposium Series; Burrington, J. D., Clark, D. S., Eds.; American Chemical Society: Washington, DC, 1989; No. 392, Chapter 7. (3) (i) Dekker, M.; Baltussen, J. W. A.; Van’t Riet, K.; Bijsterbosch, B. H.; Laane, C.; Hilhorst, R. In Biocatalysis in Organic Media; Laane, C., Tramper, J., Lilly, M. D., Eds.;Elsevier: Amsterdam, 1987; p 285. (ii) Goklen, K. E.; Hatton, T. A. Sep. Sci. Techno/. 1987, 22,831. (iii) Hatton, T. A. In Surfactant-Based Separation Processes; Scamehorn, J. F., Harwell, J. H., Eds.; Marcel Dekker: New York, 1989; p 55. (iv) Leser, M.; Luisi, P. L. Biotechnol. Bioeng. 1989, 34, 1140. (4) (i) Martinek, K.; Klyachko, N. L.; Kabanov, A. V.; Khmelnitsky, Y. L.; Levashov, A. V. Biochim. Biophys. Acta 1989,981, 161. (ii) Vacher, M.; Waks, M.; Nicot, C. J . Neurochem. 1989,52, 117. ( 5 ) Pileni, M.-P., Ed. Srrucrure and Reactivity in Reversed Micelles; Elsevier: Amsterdam, 1989. (6) Kelley, B. D.; Rahaman, R. S.; Hatton, T. A. In Analytical Chemistry in Organized Media: Reversed Micelles; Hinze, W. L., Ed.; JAI Press: Greenwich, CT, in press. (7) (i) Luisi, P. L. Angew. Chem. 1985, 24, 439. (ii) Luisi, P. L.; Steinmann-Hofmann, B. In Methods in Enzymology: Immobilized Enzymes and Cells-Part C; Mosbach, K., Ed.; Academic Press: New York, 1987; p 188. (iii) Martinek, K.; Berezin, I. V.; Khmelnitski, Y.L.; Klyachko. N. L.; Levashov, A. v. Collect. Czech. Chem. Commun. 1987,52,2589. (iv) Martinek, K.; Levashov, A. V.; Klyachko, N.; Khmelnitski. Y. L.; Berezin, I. V. Eur. J. Biochem. 1986, 155, 453.
0022-3654/91/2095-1799%02.50/0 0 1991 American Chemical Societv
1800 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991 Models of Protein Solubilization in Reversed Micelles There have been relatively few studies on the modeling of protein-containing reversed micellar systems. Bonner et aL8 were the first to consider this problem, basing their analysis on the simple hypothesis that when a protein is encapsulated within a reversed micelle the micelle expands by a volume equal to that of the protein, Le., that a noninteger number, n, of empty micelles combine to form a filled micelle, where n is determined by a volume balance on water and protein and by an area balance on the surfactant headgroups in the micellar shell. No account was taken of the physicochemical interactions occurring in the system that might be responsible for the formation of a protein-micelle complex. Woll and Hatton9 used a similar idea with extensions to relate the complex size to protein size and charge, and surfactant concentration, in the development of a phenomenological model which adequately correlated experimental results on the partitioning of the proteins ribonuclease A and concanavalin A between bulk aqueous and Aerosol-OT/isooctane reversed micellar solutions. The model is, however, correlative and not predictive in nature and it does not provide detailed insight into the fundamentals of the protein/reversed micellar system. The simple thermodynamic model of Caselli et a1.I0 for the prediction of the sizes of filled and empty micelles comes closer to this goal. It is based on the minimization of an approximate expression for the system free energy incorporating contributions from the electrostatic interaction between the protein and the charged micellar wall, evaluated in terms of a simple microcapacitor model, the entropy change due to the change of micellar sizes on protein injection, and the entropy change as mobile ions rearrange themselves in the micellar cores after protein injection. However, this model appears to be inconsistent in the limit of complete occupancy of micelles, where the radius of the filled micelles produced is the same as that of the micelles initially present before protein uptake. Given their assumption of constant surfactant headgroup coverage, this implies that there is the same number of filled micelles as there were empty micelles initially. Since each micelle now hosts a protein molecule, this appears to result in a violation of the constraint of constant water volume in the system. Bratko et al." studied the thermodynamics of protein solubilization in reversed micelles from bulk aqueous solutions using a shell and core model for the protein-micelle complex. Their model, which assumes that electrostatic interactions and the ideal mixing of proteins into the micellar solution are the important model constituents, appears to capture the experimentally observed trends in protein solubilization as a function of salt concentration and pH. However, this result is a direct consequence of their use of a Langmuir-type isotherm for the solubilization and does not reflect any inherent quantitative predictive capability of the model. Indeed, their model assumes that filled and empty micelles are the same size, independent of salt strength and pH, while experimental evidence suggests that it is precisely the changes in these micelle sizes with changes in ionic strength that are responsible for the observed partitioning behavior.6 It is evident that to date no consistent theory has been developed for the characterization of protein-containing reversed micellar media, either from the perspective of elucidating the distribution of water and surfactant over the two classes of micelles or from the point of view of predicting protein-partitioning behavior. In this paper, we present a thermodynamic model capable of predicting the sizes of AOT reversed micelles over a range of salt conditions, pH, and surfactant concentrations for both the phase-transfer and the injection technique. This development is extended further elsewhereT2to allow the quantitative prediction (8) Bonner, F. J.; Wolf, R.; Luisi, P. L. J. Solid-PhaseEiochem. 1980,5, 255. (9) Woll, J. M.; Hatton, T. A. Eioprocess Eng. 1989, 4 , 193. (10) Caselli, M.; Luisi, P. L.; Maestro, M.; Roselli, R. J. Phys. Chem. 1988. 92, 3899. ( 1 1 ) Bratko, D.; Luzar, A.; Chen, S . H. J. Chem. Phys. 1988, 89, 545. ( I 2) Rahaman, R. S.PhD Thesis, Massachusetts Institute of Technology, 1989.
Rahaman and Hatton of protein-partitioning behavior over a wide range of experimental conditions.
Experimental Results on Reversed Micellar Sizes in the Presence of Proteins A number of different analytical techniques have been used in an attempt to estimate the sizes of filled and empty reversed micelles; these have included various forms of ultracentrifugation,8qT3J4quasi-elastic light scattering (QELS),15 fluorescence recovery after fringe pattern photobleaching (FRAPP),I6 and small-angle neutron scattering (SANS).17J8 None of these is totally without its ambiguities, however, and there is still some uncertainty as to the relative and absolute distributions of water and surfactants over the filled and empty micelles. One of the earliest studies on the sizes of protein-containing reversed micelles was that of Bonner et ale8 They analyzed ultracentrifugation results in terms of their simple model discussed above, in which it is assumed that empty micelles combine to form a filled micelle in such a manner that the net water-to-surfactant ratio, wo, in the filled micelle is the same as that of the reversed micellar solution as a whole. While it is now recognized that this is not the case, this pioneering effort was nonetheless an important contribution, paving the way for other, more detailed studies. Levashov et al.I3 used a water-soluble indicator probe, picric acid, to observe the sedimentation behavior of a mixture of filled and empty reversed micelles in an analytical ultracentrifuge. They concluded that the water-to-surfactant ratio, wo,was the same in both micelle types and that the micelle sizes were unaffected by the presence of the protein. It has been p ~ i n t e d l ~out . ' ~that this violates the area and volume constraints imposed on the system by the predetermined water, protein, and surfactant concentrations, and their results may have been an artifact of the experimental and analysis procedure adopted. This argument has been countered by the Soviet group who contend that their proposed scenario is consistent with a deeper penetration of the surfactant headgroup region by water owing to the presence of the protein in the micelle ~ 0 r e . l ~ Zampieri et sought to circumvent the problems inherent in the earlier sedimentation studies by employing two different dyes, one water-soluble and the other strongly interfacially active, to monitor independently the association of the water and of the surfactant with the empty and filled micelles. Thus they were able to determine the individual wovalues for the two micelle types, and on the basis of water, surfactant, and protein balances they were able to estimate the sizes of the filled and empty micelles. Their conclusions were in sharp contrast to those of Levashov et al. in that they found that both the filled and empty micelles increased in size with overall wo and that neither the filled nor the empty micelle size subsequent to the injection of protein into the micellar solution was the same as the empty micelle size prior to the introduction of the protein. A key assumption in the double-dye technique of Zampieri et al., however, is that the two dyes distribute between the micelles in proportion to the water and surfactant, respectively, in these micelles. Recent analyses of the substrate distribution effects in these systems suggest that this assumption may not be true and that the statistical distribution of solutes over the micelle population may be skewed to one or the other of the two micelle types.*O Again, there is a level of (13) Levashov, A. V.; Khmelnitsky, Y. L.; Klyachko, N. L.; Chernyak, V. Y.; Martinek, K. J. Colloid Interface Sci. 1982, 88, 444. (14) Zampieri, G. G.;Jackle, H.; Luisi, P. L. J . Phys. Chem. 1986, 90, 1849. (15) Chatenay, D.; Urbach, W.; Cazabat, A. M.; Vacher, M.; Waks, M. Eiophys. J . 1985, 48, 893. (16) Chatenay, D.; Urbach, W.; Nicot, C.; Vacher, M.; Waks, M. J. Phys. Chem. 1987. 91. 2198. (17) Fletcher, P. D. I.; Howe, A. M.; Perrins,.N. M.; Robinson, B. H.;
Toprakcioglu, C.; Dore, J. C. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum: New York, 1984; p 1745. (18) Sheu, E.; Gddcn, K. E.; Hatton, T. A.; Chen, S.-H. Eiotechnol. Prog. 1986, 2, 175. (19) Shapiro, Y. E.; Budanov, N. A.; Levashov, A. V.;Klyachko, N. L.; Khmelnitsky, Y. L.; Martinek, K. Collect. Czech. Chem. Commun. 1989,54, 1126.
a-Chymotrypsin-Containing AOT Reversed Micelles ambiguity in the reported results. Chatenay et al.I5 used Banner's* model in the analysis of QELS data on protein-containing reversed micellar solutions. Thus their conclusions are limited by the constraints imposed by this model, which is now recognized as being too restrictive in the manner in which system components are redistributed over the filled and empty micelles. These limitations were lifted in subsequent work using FRAPP to obtain translational diffusion coefficients, and hence apparent hydrodynamic radii, of empty and filled reversed micelles.I6 However, it was not possible to measure these radii simultaneously as the probe used to label the empty micelles distributed over both micelle types. Thus, the empty micelle sizes were measured in the absence of the protein, and it was implicitly assumed that this size was unchanged in the presence of the protein. This assumption is challenged by results obtained by using techniques which allow simultaneous determination of both micellar radii.I4 Fletcher et al.” performed SANS studies on a-chymotrypsin-containing AOT-in-heptane reversed micellar systems, observing little change in the scattering profiles when the proteincontaining systems were compared to non-protein-containing systems of the same wo. They concluded that no quantitative interpretation concerning enzyme location or filled micelle size was possible using their approach, but that the number and shape of the reversed micelles were largely unperturbed by the addition of the a-chymotrypsin. Sheu et al.,’* on the other hand, in the only study conducted on phase-transferred proteins, did find significant differences in the SANS spectra as the composition of the protein-containing system was varied. They used a shell and core model for the protein/reversed micelle complex in the analysis of their data. However, there is now significant evidence that the protein used in their work, cytochrome c, associates with the AOT micellar interface,21and this has two important implications with regard to their data analysis. First, the shell and core model was not an appropriate description of the protein/reversed micelle complex, and second, the assumption of the conservation of micellar surface area implicit in their model was incorrect because the protein also occupied portions of the interface. Thus our earlier results must be viewed with some caution. In summary, measurements of the sizes of protein-filled and empty micelles by a range of techniques are not without their ambiguities, either because of limitations in models used for data analysis, or because of artifacts introduced by the experimental approach. In this work, we present results of a SANS study that appear to be self-consistent and, to a large extent, unambiguous. The results are, however, restricted to the solubilization of CYchymotrypsin, which is known to reside in the water pool of the reversed micelles, and may not extend to proteins which are associated with the surfactant interface.
Theory Model Assumptions and Approach. We assume that the reversed micellar population is bidisperse, consisting of empty micelles containing only aqueous salt solution, and filled micelles hosting, in addition, concentrically located protein molecules. The possibility of multiple protein occupancy in a micelle is disregarded. The charges on the protein and the micellar surfactant interface are taken to be uniformly distributed over the respective surfaces. All of the surfactant is assumed to be aggregated in micellar form and none lost to the bulk aqueous solution. The electrostatic interactions within the micelles, and between the protein and the inner micellar wall, are represented by the nonlinear PoissonBoltzmann equation. Micellemicelle interactions are neglected. We model two systems. The first consists of a reversed micellar organic solution in equilibrium with an excess protein-containing aqueous phase, corresponding to conditions typically encountered in protein extraction studies. Here, the water transferred into the micellar phase is not constrained by material balance restrictions (20) Hatton, T. A. Manuscript in preparation. (21) Brochette, P.; Petit, C.; Pileni, M. P. J . Phys. Chem. 1988, 92, 3505.
The Journal of Physical Chemistry, Vol. 95, NO.4, I991
1801
but is determined by thermodynamic equilibrium constraints. In contrast, in the second system considered, the injection technique used predominantly in the study of biocatalysis in reversed micelles, a known amount of a concentrated protein solution is introduced into the micellar phase, so that the concentrations of the aqueous solution and the protein in this phase are predetermined. These constraints on the salt, water and protein present in the micellar solution must be heeded in the model development; the system is not in thermodynamic equilibrium with a second, aqueous phase. The equilibrium micellar radii are assumed to be those that minimize the total system free energy. In two-phase systems we specify the protein concentrations in the reversed micellar phase and allow for the exchange of water and ions between this phase and the bulk aqueous solution. Standard-state chemical potentials for all aqueous solution components are assumed to be the same in both the water pools and the bulk aqueous phase, and it is assumed that the small amount of water transferred between the two phases does not result in a significant change in the chemical potential of the protein in the bulk aqueous phase. That part of the total free energy that changes as the sizes of the two classes of reversed micelle change, for a given protein concentration in the reversed micellar phase, is then composed of contributions from electrostatic interactions, both protein-surfactant and surfactantsurfactant, given by Gel, the ideal mixing of the two classes of micelles into the organic continuum, G ~and,steric interactions between adjacent surfactant tails, Gtaik,which all vary as the sizes of the two classes of micelles are varied. Thus the total system free energy can be written as where contributions that are assumed to be invariant with changes in the micelle sizes have been dropped. The evaluation of these different contributions to the system free energy is considered below, where it is argued that the mixing entropy of the ions as a result of ordering in the electrical double layers associated with the micelles is included implicitly in Gel. Electrostatic Term. The electrostatic interactions within the empty and filled reversed micelles are represented by the nonlinear Poisson-Boltzmann equation 1 dz(nC.)
r
dr2
2Ne sinh ( e + / k T ) D
+
where is the electrostatic potential at the radial position r within the micelle, N is the reference salt concentration in the bulk aqueous phase, e is the unit electronic charge, k is Boltzmann’s constant, and D is the dielectric constant of the aqueous micellar core, which is assumed to be that of bulk water. The boundary conditions are (3)
for both empty and filled micelles, where R, is the micellar radius d+/dr = 0
at r = 0
(4)
for empty micelles, and
for filled micelles, where R, is the protein radius. The equations were solved numerically by using centered finite differences and a Newton’s iteration convergence scheme. The electrostatic free energy contribution to the total system free energy is that associated with the development of the electrostatic potential profiles as the system is charged and ions are brought from an infinite reservoir to their positions in the double layer. We assume a constant surface charge density boundary condition, which is equivalent to specifying that the surfactant and protein counterions do not act as potential determining ions; i.e., the level of dissociation does not vary during the charging process, although the surface charge density does. This should be a very good approximation for the system under consideration.
1802 The Journal of Physical Chemistry, Vol. 95, No. 4 , 1991
The physical picture represented by the charging process is as follows. The mobile ions in solution, including the surfactant counterions, always possess their final charge. All the ions on the surface are present but are completely uncharged in their initial state. As the charge on the surface ions is incremented at each stage of the charging process, the mobile ions in solution are allowed to respond to the change in surface charge, and the potential is recalculated at the new equilibrium condition. Thus the calculation of free energy implied by the charging process also includes the contribution due to the entropy loss of the mobile ions as they are fixed in position in the electric field. At each stage of the charging process, the free energy that is gained by the movement of a mobile ion into a more favorable electrostatic environment is exactly balanced by the free energy required to hold the mobile ion in its new average position against thermal motion. Thus, we do not need to evaluate the entropy of ions explicitly, as was done, for instance, by Bratko et al.lI For the constant surface charge density boundary conditions, Stigter and OverbeekZ2show that where F’is the Helmholtz free energy per unit surface area, which is identical to G’,the Gibbs free energy per unit area, if charging of the double layer has no influence on the volume; this is a good assumption. G i I is the electrical contribution to the free energy, and G;,,,, includes both electrical and chemical terms. u is the surface charge density, and q0 is the surface electrical potential. OverbeekZ3also shows that, for our case,
Combining (6) and (7) we obtain the very simple relation that
The electrical free energy per unit surface area is thus the integral of the surface electrostatic potential with respect to the surface charge density on that surface. The total electrical contribution to the free energy is therefore obtained by integrating over the total system area and can be expressed in the form I
Gel =: 4nN,(R:upi
+ R$J,~’$(R~;X) dh) +
$(Rp;X) dh
Rahaman and Hatton as evidenced by SANS spectra, were discarded in subsequent analyses. Tail Interaction Term. There is a free energy component owing to the steric interactions of the tail groups of adjacent surfactant molecules on the same micelle with one another. A large class of theories on droplet microemulsibns, known as curvature-based models, postulate that the elastic free energy of the surfactant interface plays a dominant role in determining aggregate size;25 these models all introduce various phenomenological parameters, the most important being the natural radius of curvature, and various elasticity moduli. The natural radius of curvature is not a well-defined concept but is generally taken to be the radius for which bending stresses disappear. In an analogous fashion, we envision the normal swept volume as the volume available to the surfactant tails above which tail bending stresses disappear. If we assume that the region around a micelle, in the volume outside of the surfactant headgroups, but within the shell defined by the maximum length of the surfactant tails, is the volume shared by all the surfactant molecules of that micelle, then at small micelle radii, and hence large curvature, each surfactant molecule has the volume that its tails normally sweep out avilable to it within this shell. As micelle radius increases, however, the curvature decreases, and the full swept volume of the surfactant tails is no longer available to each surfactant molecule. This gives rise to an unfavorable steric interaction between the tails of neighboring surfactant molecules on the micelle shell. The energetic pentalty to be paid for the surfactant tails not being able to access their full swept volume is assumed to depend on the ratio of the natural swept volume of the surfactant tails, V,,, to the accessible volume, Vsh, which will depend on the interfacial curvature. Thus we assume
and restrict this function to be zero for V,, 5 V,,,. A number of forms can be assumed for the function f. We select a simple polynomial expression truncated at the second-order term, which imposes the additional restriction that the function is smooth (i.e., has a continuous first derivative) at V,, = vsh. This gives an expression of the form
I
4rNeR:omJ
#(&;A) dh (9)
where X is the charging parameter and represents the fraction of the final charge attained on the protein and micellar surfaces at any stage in the charging process. Ideal Mixing Term. Meroni et al.24 have shown that the entropy of mixing of spheres of different diameters calculated by using an ideal mixing term is in good agreement with more rigorous calculations using Monte Carlo simulation and the Mansoori-Carnahan-Starling equation of state. We therefore take the free energy due to mixing to be given by Gmi, = k T E x i In xi (10) i
where the summation extends over the components i, Le., over filled micelles, empty micelles, and solvent molecules. This ideal mixing assumption is a reasonable approximation at temperatures close to the lower temperature phase boundary, corresponding to the two-phase system in which the reversed micellar solution is in equilibrium with an excess aqueous solution, since here the AOT stabilized water droplets interact only weakly. However, the droplets become attractive at temperatures close to the upper temperature phase boundary, and this will affect the validity of the ideal mixing calculation. It is assumed that the injection samples studied in this work do not, in general, fall in this regime. Indeed, samples that exhibited significant intermicelle interactions, (22) Overbeek, J. Th. G.; Stigter, D . Recueil 1956, 75, 1263. (23) Overbeek, J. Th.G . In Colloid Science: Kruyt, H. R., Ed.: Elsevier: Amsterdam, 1952; Vol. 1, p 142. (24) Meroni, A.; Pimpinelli, A.; Reatto, L. J. Chem. Phys. 1987, 87, 3644.
Gtails = 0
for Vsw 5 Vsh (12) where L,3 is an empirical constant to be determined later. Vsh is simply the volume of the concentric shell between the outer radius of the surfactant headgroups, R a, and the outer region of the surfactant shell, R 1, divided by the number of surfactants in the shell. R is the radius of the water pool, a is the thickness of the surfactant headgroup layer, and 1 is the length of the entire surfactant molecule, Le., the headgroup thickness plus the extended tail length of the surfactant. The number of surfactants in the shell is given by
+
NAOT
=
+
4nR2
f*or
wherefAoT is the surfactant headgroup coverage at micellar radius R. Thus we obtain
where u = V,,/lfAoT is a surfactant packing parameter similar to that defined by Mitchell et a1.26 (25) (i) Langevin, D.; Guest, D.; Meunier, J. Colloids SurJ 1986,19, 159. (ii) Miller, C. A. J . Dispersion Sci. Technol. 1983, 6, 159.
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
a-Chymotrypsin-Containing AOT Reversed Micelles Thus the total tail interaction energy for the system is
I2 where cSiis the concentration of surfactant forming micelles of type i, where i extends over empty and filled micelles. There are a number of forms of tail term dependence that would give essentially equivalent results. Overbeek et ala?' for example, as part of a comprehensive thermodynamic theory of droplet-type microemulsions, note that an important determinant of droplet size in microemulsion systems is the effect of curvature on the interfacial tension, Le., on the free energy of the double layer, and on the degree of crowding of the hydrophobic tails of the surfactant. The free energy component that arises from the effect of steric hindrance of the surfactant tails is proportional to the interfacial area and was modeled in terms of the exponential of the negative of the curvature. Although our tail interaction term is different from the Overbeek treatment, it is clear that the general form of the dependence has the same trend; the free energy contribution approaches zero as micellar radius tends to zero and increases in a monotonic fashion as micellar radius increases. At small values of micellar radius, the exponential and squared dependence of the two models match well. Evaluation of Micelle Radii. For the phase-transfer technique, there are no constraints on the protein, ions, or water that can be transferred into the reversed micellar solution. There is, however, a constraint on the total surfactant head area coverage that must be incorporated in the model calculations as this will limit the total number of micelles of each type that can form. We assume that the surfactant headgroup area, fAOT, varies with micellar size in a manner suggested by the data of EickeZ8and that this behavior is the same for both filled and empty micelles, viz. 62.3R, fAoT = 6.39 R,
+
where fAor is in A2 and R,, the micelle radius, is in A. With this restriction, the pair of empty and filled micelle radii that minimizes the total free energy of the reversed micellar solution was determined by a gradient search technique. For the phase-transfer method, the salt concentration used for comparison to experimental data is that of the excess bulk aqueous solution. The length, I, of the surfactant tail was taken to be 8.3 A, while the thickness of the surfactant head layer, a, was assumed to be 3.5 A. The normal swept volume was estimated as the difference between the measured partial molar volume of approximately 660 A3,29for the surfactant molecule, and an assumed head volume of 230 A3, and was thus taken to be 430 A3. This value is larger than the actual molecular volume of the two tails calculated by using group contribution methods to be 320 A3. There are two constraints to be satisfied in the injection method, balances on the surfactant head area coverage (as for the phase-transfer case) and on the total volume contained within the filled and empty micelles, which must equal the volume of protein and aqueous solution injected into the micellar phase. To satisfy both constraints requires that, for a given surfactant concentration, water content, and protein content in the micellar solution, there must be a unique value of empty micelle radius for each value of filled micelle radius. This reduces the problem to a one-di(26) Mitchell, D. J.; Ninham, B. W. J . Chem. Soc., Faraday Trans. 2
1803
mensional optimization which is readily accomplished by using any one of the many optimization techniques available. The effective salt concentration within the reversed micellar solution used for comparison with experimental data was found by volume integration of the concentration profiles over the filled and empty micelles. Experimental Section Materials. The surfactant sodium bis(2-ethylhexyl) sulfosuccinate, more commonly known as Aerosol-OT or AOT, was obtained from Pfalz and Bauer, Stamford, CT, and was 99% purity, the highest grade available. The organic solvent isooctane was spectrophotometric grade and was supplied by Mallinckrodt, Inc., Paris, KY. Micellar solutions consisted of 25-400 mM solutions of AOT in isooctane. a-Chymotrypsin from bovine pancreas, three times crystallized and lyophilized (C4129), was supplied by the Sigma Chemical Co., St. Louis, MO. Buffers consisted of mono- and dibasic sodium phosphate and carbonate salts. These salts were all analytical reagent grade and were obtained from Mallinckrodt. All aqueous solutions were prepared in distilled water filtered through a Millipore Milli-Q system, except those for the SANS measurements, which were prepared in deuterium oxide (D20) of 99.9% purity supplied by Cambridge Isotope Laboratories, Woburn, MA. Protein solutions typically consisted of 2 mg/mL of a-chymotrypsin in 0.1-1.0 M solutions of the sodium buffers, the relative proportions of which were altered to provide the desired PH. Preparation of Transfer Samples. Equal volumes of the micellar and protein solutions were contacted in a beaker under conditions of intense agitation. Typically 5 mL of each of the solutions were mixed for 5 min in a 30-mL beaker at approximately 750 rpm, producing a protein-containing micellar phase and a protein-depleted aqueous or raffinate phase. The resulting dispersion was centrifuged at 2000 rpm for 5 min to obtain a distinct phase boundary and then incubated in a constant temperature water bath at 25 OC for 2 days to ensure complete equilibration at the desired temperature. For the vast majority of our samples, the phase boundary obtained was completely clean, that is, free of interfacial precipitate. No samples with more than the lighest dusting at the interface were used in this work. After incubation, the phases were separated and each phase assayed. Assays. The protein concentration in the aqueous phase was measured by UV absorbance at 280 nm on a Perkin-Elmer Lambda 3B dual beam UV/vis spectrophotometer. The readings were corrected for turbidity by subtraction of the absorbance at 310 nm. Presaturation of the salt solutions with AOT prior to adding the protein showed that, while both the 280- and 310-nm reading were increased by the presence of AOT, the calibration curves based on 280 minus 310 readings were unaffected. This suggests that the presence of small amounts of AOT in the aqueous solutions after contact with the micellar phase led to only a small amount of nonspecific solution turbidity which could be adequately accounted for by subtraction of the absorbance at 310 nm. A modified form of the Lowry assay30 was used as a further measurement of protein concentration. Only samples that exhibited negligible interfacial precipitate were analyzed, to prevent errors due to protein or surfactant loss at the interface. The total protein content remaining in the aqueous phase was obtained from the concentration measurements after accounting for the reduction in aqueous volume due to water transfer into the organic phase. The protein transferred to the organic phase was then calculated by difference from the initial protein present in the aqueous phase. The pH of the aqueous phase in equilibrium with the micellar phase was measured by using a Fisher Accumet pH meter, Model 825MP, equipped with a Fisher combination polymer-body/ gel-filled pencil electrode. The water content of the organic phase
1981, 77, 601.
(27) Overbeek, J. Th. G.; Verhoeckx, G. J.; de Bruyn, P. L.;Lekkerkerker, H.N. W. J. Colloid Interface Sci. 1987, I 19, 422. (28) Eicke, H.F.; Rehak, J. Helu. Chim. Acta 1976, 59, 2883. (29) Goklen, K. E. PhD Thesis, Massachusetts Institute of Technology, 1986.
(30) (i) Waterborg, J. H.;Matthew, H.R. In Methods of Molecular Biology; Walker, J. M., Ed.; Humana: Clifton, NJ, 1984; Chapter 1. (ii) Hanson, R. S.;Philip, J. A. In Manual of Methods for General Bacteriology; Gerhardt, P., Ed.; American Society of Microbiology: Washington, DC,1981; Chapter 17.
Rahaman and Hatton
1804 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
was determined with a Mettler DL18 Karl Fmher titrator. These readings were corrected for evaporation from the test tubes, which were rubber stoppered and covered with parafilm during the 2day incubation period. Preparation of Injection Samples. Solutions were prepared by the direct injection of a measured amount of concentrated protein/salt solution into 10 ml of the reversed micellar solution, such that predetermined concentrations of both protein and the aqueous solution were produced in the micellar phase. The samples were then incubated in a constant temperature water bath at 25 OC for 2 days. The volume of the organic solution was measured before and after incubation to account for the small amount of solvent evaporation, typically less than 5%, which occurred during the 2-day period. The water content of the micellar solution was also checked by using Karl Fischer titration; no evaporation of water was detected over the equilibration period. The protein content of the micellar phase was assumed to be equal to protein injected; no samples with evidence of protein precipitation were used. SANS Analysis. The small-angle neutron scattering experiments were carried out at the high flux beam reactor of the Brookhaven National Laboratory; the low-angle spectrometer used in these studies has been described in detail by Schneider and Schoenborn.” Cold neutrons, produced by a liquid hydrogen source at 20 K, passed through a series of guides to the spectrometer beamline, through a cold Be filter to remove neutrons of wavelength shorter than 4 A, and then through a monochromator and three collimators to produce a 6 mm diameter circular beam of wavelength X = 4.95 A with an average wavelength spread of about 5%. The beam (which ranged in intensity between 3.0 X I O6 and 4.1 X IO6 neutrons/cm2) impinged on a flat cylindrical sample cell, and the scattered neutrons were detected by a 50 cm X 50 cm two-dimensional detector consisting of 128 X 128 pixels, each with dimensions 3.9 mm X 3.925 mm. The sample to detector distance of 145 mm and the beam stop of radius 20 mm used in our experiments provided a scattering angle range of 0.9O-12.3O (or alternatively, a Bragg wave number ( Q ) measurement range of 0.02-0.27 Samples were housed innflat quartz cells with window thickness= of 1 mm and a path length of 2 mm. Measurement times ranged from 1 to 4 h. The raw scattering data were corrected for the background, incoherent scattering of the solvent, and quartz cell contributions, in the manner suggested by Chen and Bended~uch.’~A separate transmission measurement was made for each sample to account for attenuation of the neutron beam in the sample, and the reduced data were then standardized by dividing by data from a standard sample of a 1 mm thick quartz cell of H 2 0 . This standardization corrected for any variations in sensitivity between pixels in the detector. The model employed to interpret the SANS data from the protein-containing reversed micellar solutions is that described by Sheu et a1.I8 Since the samples were isotropic, the scattering intensity I, was a function of the scattering angle t9 only. The intensity was reported as a function of the Bragg wave number, Q, defined by 4x e Q = - sin - (A-1) A 2 For a collection of monodisperse spherical particles of number density N, in solution, the normalized intensity can be written as3’ I ( Q ) = N$(Q) S(Q) (18) where P(Q) and S(Q) are the intra- and interparticle structure factors, respectively. S(Q)is in general an oscillatory function of Q, with period a/R, where R is the radius of the particle in solution. If the volume (31) Schneider, D. K.; Schoenborn, B. P. In Neutrom in Biology; Schoenborn, B. P., Ed.; Plenum: New York, 1984; p 119. (32) Chen, S.H.; Bendedouch, D. In Merhods in Enzymology: Enzyme Sfrucrure;Hirs, C. H., Timasheff, S.N., Eds.; Academic Press: New York. (33) Kotlarchyk, M.; Chen, S.H. J . Chem. Phys. 1983, 79, 2461.
i-Octane
I-OCtaM
F i i 1. Geometric models of reversed micelles used for SANS analysis.
fraction of particles in solution is low, then the interparticle structure factor is approximately unity at finite Q and deviates from unity only as Q 0. Sheu et a1.18 have shown that, for a protein-containing 50 mM AOT in isooctane reversed micellar solution, the deviation of S(Q) from unity is less than 2% even at Q = 0, and therefore S(Q) can be taken to be unity for all Q. This assumption will fail a t temperatures close to the upper temperature phase boundary, where the droplets will become attractive. The particle structure factor P(Q) is defined as
-
P(Q) =
(J d3r [p(r)- pSl exp(iQr))l
(19)
“P
where p(r) is the scattering length density of the particle at position r and ps is the scattering length density of the solvent, which is taken to be a constant. For a spherically symmetric distribution of scattering length density, eq 19 becomes
This integral can be evaluated analytically for the scattering length distributions used to describe the protein-filled and empty AOT reversed micelles shown in Figure 1. The empty micelle was considered to be a homogeneous spherical water core of scattering length density p I , surrounded by a shell consisting of the polar surfactant headgroups with scattering length density p2. The surfactant tails were assumed to have the same scattering length density as the isooctane solvent ps, as is shown in Figure 1. For this geometry, eq 20 reduces to
where RI is the radius of the water core, R2 is the radius of the sphere containing the water core and the surfactant head region, and j , is the spherical Base1 function of the first rank. The protein-containing micelle was modeled as a spherical protein of scattering length density p,, concentrically located within the micellar water pool, which was in turn surrounded by the surfactant head layer, as shown in Figure 1. The particle structure factor for this geometry is
where V, is the volume of the protein, V2 is the volume of the water, and V , is the volume of the polar surfactant headgroup shell.
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991 1805
a-Chymotrypsin-Containing AOT Reversed Micelles TABLE I: Transfer Data Summary
[salt], M
[AOT], m M
[protein], PM
pH
0.1 0.175 0.2 0.2 0.3 0.5 0.5 0.75 I .o 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0. I 0. I 0.2 0.3 0.5 0.75 0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.5
100
76.6 86.2 86.9 85.8 89.5 40.1 53.1 87.5 1.4 4.8 9.8 10.8 20.7 24.4 42.4 92.5 179.5 56.6 56.6 25.2 22.7 22.6 20.6 85.7 85.7 74.2 74.2 72.7 42.5 42.5 14.9
6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 9.2 9.2 9.2 9.2 9.2 9.2 7.7 7.7 7.7 7.7 7.7 7.7 7.7 7.7
w, (overall) 46.6 36.8 29.6 37.6 21.9 18.7 21.5 21.4 15.4 21 .o 27.4 21.8 25.3 21.7 26.9 21.2 26.8 49.5 49.5 32.7 26.9 20.9 17.6 55.8 55.8 36.2 36.2 27.3 24.3 24.3 21.2
IO0 100 100
IO0 IO0 100
IO0 100 100 100 100 100 100 100 100
IO0 100 100 100 100 100 100 100 100
IO0 100 100 100 100 100
R.. 8, SANS theory 74 64 43 49 39 32 37 35 27 35 43 36 41 36 43 37 45 77 76 45 40 35 32 84 84 51 50 44 40 40 37
Rt. 8, ~
I 7
SANS
theory
% occupancy
75.0 52.9 46.5 46.5 38.1 31.9 31.9 28.0 26.1 38.4 38.4 38.4 38.3 38.3 38.2 38.1 37.7 75.0 75.0 46.9 38.3 31.9 28.2 75.1 75.1 46.4 46.4 37.9 34.1 34.1 31.7
36 34 32 33 30 33 33 36 31 33 34 34 33 33 33 33 33 56 55 39 34 34 34 50 50 35 36 32 33 33 33
35.1 35.0 34.5 34.5 33.1 31.2 31.2 29.8 28.9 33.1 33.1 33.1 33.1 33.1 33.1 33.1 33.0 49.1 49.1 44.4 40.4 36.3 33.6 42.8 42.8 40.3 40.3 37.3 35.4 35.4 34.1
49.7 43.6 25.7 37.8 22.3 7.2 12.4 19.9 0.2 1.1 4.0 2.4 7.9 5.6 17.1 21.8 60.7 55.1 46.0 9.1 6.5 4.9 3.8 71.5 71.7 35.3 35.4 28.2 14.9 14.9 4.9
% occupancy 11.9 11.4 12.2 12.4 12.0 12.1 11.2 7.8 14.5 14.5 15.9 16.5 16.9 15.6 16.3 4.8 8.8 33.3 45.4 46.9 35.6 2.9 0.8 11.7 9.6 2.9 5.7 25.0
TABLE II: Injection Data Summary
Rf,A
Re, 8,
[salt], M
[AOT], m M
[protein], pM
pH
wo (overall)
SANS
theory
SANS
theory
0.1 0.1 0.2 0.2 0.3 0.3 0.5
100 100 100 100 100 100 100 100 100 100 100 100 100 100
44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 44.3 11.1 22.1 88.5 132.7 132.7 44.3 44.3 44.3 44.3 44.3 11.1 22.1 88.5
6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 6.4 9.2 9.2 6.4 6.4 6.4
15.1 15.1 16.0 16.0 16.4 16.4 14.8 11.4 19.0 19.0 20.5 20.8 22.2 23.2 23.2 23.3 23.6 23.8 23.8 23.8 17.5 8.7 4.9 15.3 13.8 14.9 17.1 15.5
34 33 34 34 34 33 33 26 38 38 40 41 42 40 41 44 42 43 43 44 45 22 16 33 29 33 33 35
32.4 32.4 33.9 33.9 34.5 34.5 32.2 27.1 38.3 38.3 40.5 39.3 43.0 44.5 44.5 42.5 43.5 42.1 45.1 45.1 38.6 22.4 17.6 32.2 30.4 31.3 34.7 34.5
33 31 33 33 33 36 31 31 32 32 35 34 33 33 33 33 33 33 31 33 34 30 27 33 34 33 33 34
34.1 34.1 33.6 33.6 32.8 32.8 31.2 29.1 34.3 34.3 34.4 32.4 34.6 34.4 34.4 34.3 34.4 34.4 34.5 34.5 32.3 31.4 30.2 37.7 34.6 32.9 33.8 33.1
1 .o
0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.5 0.2 0.2 0.2
IO0 IO0 100 100
IO0 100 50 200 400 100
IO0 IO0 100 100
The respective radii are R for the protein, R, for the water pool, and R2 for the water pool plus surfactant head layer. The normalized intensity f(Q) is the simple number density weighted average of the scattering intensities of the two classes of particles. The molecular volumes of water, protein, and the surfactant headgroup were assumed to be 30.15, 45 830, and 230 A3, respectively. The model incor rated material balances on water, protein, and surfactant an assumed that the surfactant headgroup area was the same for both types of micelles. These
r
choices reduced the degrees of freedom in the system to two and allowed the determination of the two micellar radii by a nonlinear least-squares regression fit of the model to the SANS spectra. Results and Discussion SANS Analysis. The empty and protein-filled reversed micellar sizes obtained from the analysis of the SANS spectra are presented in Tables I and I1 for the phase-transfer and injection techniques, respectively. In almost all cases the quality of fit of the model
1806 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
l5K--Rahaman and Hatton
1
-
25
10
15
r---
-
50
20
-
-
15
---
30
d
2-
0.00
0.05
0.25
0.20
0.15
0.10
20
I
i .-
--E
lo
C
0 0.00
0.05
0.10
0.15
0.20
0 25
Momentum Transfer. 0 i A - ' l
Figure 2. SANS spectra and associated model fits for reversed micellar solutions produced by phase transfer from 2 mg/mL a-chymotrypsin solutions at pH 7.7 into a 100 mM AOT/isooctane solution. Salt concentrations are (a) 0.2 M, (b) 0.3 M, (c) 0.4 M, and (d) 0.5 M. Note the change in intensity scale as the salt concentration increases.
to the normalized SANS intensity spectra was good to excellent, as shown in Figure 2, which was anticipated as an analysis of the scattering patterns on a Guinier plot (In [Z(Q)] vs @) yielded two intersecting straight lines for most of the samples, indicating the validity of the bidisperse micelle population. Exceptions were noted for transfer samples under low salt conditions with surfactant concentrations higher than 200 mM, where large discrepancies occurred in the low Q region. At these high micellar concentrations the assumption of no interparticle interaction, and hence the use of an interparticle structure factor of unity, was probably invalid. For the large micelles formed under these conditions, deviations from sphericity owing to surface fluctuations could also account for the type of spectra observed. The adjustable model parameter, 0, was estimated by reconciling the model predictions with a single datum point corresponding to the size of empty micelles in equilibrium with protein-containing micelles a t 0.5 M salt and 100 mM AOT concentrations. The value of 10 kJ/mol surfactant obtained represents an energy contribution of about 0.4kT per surfactant molecule for the tail contribution to the free energy of the system when the volume available to the tails is 75% of the swept volume of the tail region; this corresponds to a micellar radius of 80 A. Transfer Results. Figure 3 shows the variation with salt concentration of the radii of filled and empty micelles produced by the transfer of a-chymotrypsin at two different pHs into a 100 mM AOT/isooctane micellar phase. The results for a third pH are given in Table 1. In all cases the agreement between the model predictions and experimental data was found to be good to excellent. For all salt concentrations, the size of the empty micelles produced was found to be independent of the pH of the aqueous protein solution, suggesting that changes in the amount of surfactant and water associated with the filled micelles are not reflected in changes in the empty micelle size, but rather in the number of these empty micelles. Thus it would appear that it is the intramicellar electrostatic and steric (tail) interactions that determine the micelle characteristics and that entropic effects associated with the mixing of the micelles into the oil continuum are not important. As salt concentration decreased, the size of the empty micelles increased dramatically. At pHs significantly below the isoelectric point of a-chymotrypsin (PI 8.2-8.6). where the protein was positively charged and there was an attractive electrostatic interaction with the anionic surfactant headgroups, little effect of salt concentration on filled micelle size was observed, With increasing pH, corresponding
201 0.00
.
'
'
' 0.20
'
'
'
'
'
'
'
0.40
' 0.60
'
'
'
'
0.80
Salt CoKentration (M)
Figure 3. Micellar radii as a function of salt concentration for phase transfer into 100 m M AOvisooctane solutions: empty micelles (0), filled micelles at pH 6.4 (A),filled micelles at pH 9.2 ( 0 ) .
to a weakening electrostatic attraction between the protein and the surfactants, the salt concentration effect on the filled micelle size became more pronounced, particularly at the low ionic strengths. It is remarkable that even at a pH above the PI of the protein, where electrostatic repulsions between the protein and the surfactants would be anticipated to inhibit solubilization or to result in filled micelles larger than the empty aggregates, significant solubilization at low salt concentrations was still observed and the filled micelles were found to be smaller than their empty counterparts. This variation in micellar sizes with changes in salt concentration can be attributed to different levels of screening of the electrostatic interactions within the individual empty and filled micelles as salt concentration is changed. For empty micelles there is a repulsive electrostatic interaction a c r w the water pool between the surfactant headgroups as a result of overlapping electrical double layers. With a lowering of the salt concentration, screening of the electrostatic interaction is reduced, and the empty micelle tends to grow in response to the increasing electrostatic repulsion. For the filled micelle at a pH < PI, on the other hand, these across-micelle interactions are for the most part screened by the presence of the protein in the micelle core, and it is the attractive interactions between the protein and the surfactants that determine
a-Chymotrypsin-Containing AOT Reversed Micelles w
El + Empty
E i
- t -Filled
- 5 0 : 4
. 40:
T
O
1 A0
30:
20
T
The Journal of Physical Chemistry, Vol. 95, No. 4, 1991 1807 60 1
- 1 5
50
0
T
y
1
0
T
+__; ----_--___--2
-----
0
1......................
A
t
I
Protein
2 0 1 ' ' ' ' 0~ -10 -5
'
~
"
"
0
'
"
"
"
'
5
"
"
"
'
'
10
Protein Charge (wltiples of
" ' " ~ " " " ' " " " " ' ' ' ' ' ' ' ~
~
15
20
el
Figure 5. Model predictions for micelle sizes as a function of protein charge for phase transfer from 0.2 M sodium buffers into 1 0 0 mM AOT/isooctane for a protein of radius 22.2 A. 60
1
20'
I
I
.
'
"
18 20 22 24 26
"
"
"
28 30 32 34 36 38 4 0
Protein Radius ( A )
Figure 6. Model predictions for the variation of micellar radii with protein size for a fixed protein surface charge density of 1.55 X C/m2. Solid lines are empty micelles; broken lines are filled micelles for (a) 0.2 M, (b) 0.5 M, and (c) 1.0 M salt concentration.
electrostatic interaction causes the micellar shell to contract as the protein charge increases; this would eventually lead to its collapse onto the protein. However, because of the disparity between the surface charge densities on the micellar and protein surfaces, a significant number of counterions must be accommodated in the water pool to maintain electrical neutrality. As the micellar shell contracts, the volume available to the counterions shrinks, increasing the ion concentration in the water pool and creating an osmotic pressure driving force for more water to be transferred into the filled micelle. It is the balancing of the electrostatic attraction and the osmotic pressure effect that causes the asymptotic behavior as protein charge is increased. The variation of filled and empty micellar radii with protein size predicted for different salt concentrations and for a fixed protein surface charge density is shown in Figure 6. These results are in direct contradiction of the early reversed micellar literature. The suggestion that a protein taken up by the micellar solution displaces a volume of water equal to its own volume, leaving the micelle unchanged," is not supported by the present results. Neither is the model proposed that the solubilized protein simply increases the micellar volume by its own volume, leaving the volume of water in the micelle unchanged.* If this were the case, the filled micelle sizes would converge to the protein radius for the larger proteins as the volume represented by the fixed amount of water in the filled micelle would represent a smaller and smaller shell between the protein and the micelle as radius increased. Instead, as protein size increases, at a constant surface charge density and for a favorable electrostatic interaction the distance between the micellar shell and the protein remains essentially constant. This distance is a function of salt concentration and represents a balance between electrostatic attraction and the osmotic effect. An analogy can be made to the electrostatic interaction between two flat plates, for which there will be an optimum separation for each combination of given surface charge densities on the plates' surfaces, and for which the optimum separation will depend on the level of screening of the medium separating the plates, Le., on the salt concentration. As expected, empty micelle radius does not vary with protein radius, but decreases as salt concentration increases. These results also indicate that, under conditions where there is a strong electrostatic at-
1808 The Journal of Physical Chemistry, Vol. 95, No. 4, 1991
Rahaman and Hatton
1
60 [
20'I"
"
"
"
"
'
18 20 22 24 26 20 30 32 34 36 38 40 Protein Radius ( A )
Figure 7. Predicted effects of protein surface charge density on micelle radii for 0.2 M salt concentration. Values of protein surface charge C/m2, density are (a) -5.2 X lo-' C/m2, (b) 0 C/m2, (c) 1.55 X C/m2. and (d) 3.9 X
-
45 r
--b
p
al
35
5
I
;/
.
30 2.5
__----
_______________----------,
e
e
3.0
e
3.5
e
e .
4.0
4.5
Percent Water in Mcellar Phase
Figure 8. Micelle radii as a function of organic phase water content for injection of a-chymotrypsin in 0.2 M buffer at pH 6.4 into 100 mM
AOT/isooctane solution. traction between the protein and the micellar shell, the prime determinant of micellar size as protein size is varied is provided by the electrostatic interactions in the reversed micellar system, and that the entropic contributions associated with the mixing of the micelles into the organic continuum do not play a major role. Figure 7 shows the model predictions for the variation of micellar radii with protein size as a function of the surface charge density on the protein surface for a fixed salt concentration. As protein radius increases, the curves for the filled micelle for all protein surface charge densities asymptote to a series of lines parallel to that for the protein radius; as the surface charge density on the protein surface becomes less positive, and the electrostatic interaction less favorable, the separation between the protein and the micellar shell increases. With a decrease in protein radius, however, the filled micelles containing uncharged and negatively charged proteins exhibit an increase in the distance between the protein and the micellar shell. Since the protein is able to screen a smaller fraction of the across-micelle electrostatic interactions as the protein size decreases, the filled micelle grows to minimize both across-micelle and protein-micelle repulsion. Injection Results. The experimental and theoretical results for sizes of reversed micelles obtained by using the injection technique are summarized in Table 11. The value of the ,8 parameter obtained from the single transfer datum point and used in the analysis of all the transfer data was also used for the analysis of the injection results. Figure 8 shows the variation of filled and empty micelle radii with overall water content in the reversed micellar solution for an overall protein concentration of 1 mg/mL. As the water content in the micellar solution increased, there was essentially no change in the filled micelle radius, while the empty micelle radius increased steadily. These data are in contrast to the results of the Caselli et a1.I0 model which predicts that both filled and empty micelles increase in size with wo and that the larger change occurs in the filled micelles.
10
15
20
25
wo
Figure 9. Variation of micellar radii with wo as a function of protein concentration in the organic phase for the injection of a-chymotrypsin in 0.2 M buffer at pH 6.4 into 100 mM AOT/isooctane solution; protein loadings are (a) 3 mg/mL, (b) 1 mg/mL, and (c) 0.25 mg/mL.
There appears to be an optimum size for the filled micelle for a given combination of pH and salt concentration (the system parameters that determine the electrostatic interaction between the protein and the micellar shell), as was also observed for samples produced by the phase-transfer technique. As the overall water content was varied, the empty micelle size changed to satisfy the material balance constraints on water and surfactant in the system. The model calculations indicate that, except a t very low wo, the energetics of the filled micelles are the dominant contribution to the free energy of the reversed micellar solution produced by the injection method and that changes in filled micelle size produce the largest variations in the electrostatic free energy of the system. The model predictions for the variation of micellar sizes over a wider range of wo values for different protein loadings presented in Figure 9 confirm that the variation of filled micelle size with wo is the same for all three values of protein loading in the organic considered and indicate that there is no variation of filled micelle size with wo, except at low w
