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The influence of the ionic strength on enzyme solubilization in water-in-oil microemulsions
291
Bioe:ec~whemist~~ and BiaenergeHcs, 20 (1988; 291-2% A section ol J. Ekwroanaf Chem., and constituting Vol. 254 (1988) Ekvier Scquch S-A., Lausanne - Printtd in The Netherlands
-
The influence of the ionic streq$h cbnemyme solubilization iu water-in-oil microeuudsions * D. Bratko Depcurmenr of Physic& Chemistg, I&b&no (Yugoslavia)
Fucu&v of Natural Sciences, Universi& E. Karde@, Muraikuva 6.
A. Pnaru IJW~W#~ of Micr~biofo~, Medical Facu@, University E. Ku&e&, L#b&ana (Yugoslavia) S.H. Chen Deparfmen! qf Nuciear Engineering Massachusetts fnstitute of Tech,roiogy. Cambridge, MA 02139 (U.S.A.) (Received 23 member
1987; in foal
form 15 Seplcmber
1988)
Solubilization of enzymes in water&-oil microemulsions [l-9] is important in various biotechnological processes ranging from selective protein extraction [7] to biocatalyzed synthesis [S]. It is of particular interest that the activity of enzyme.~ accomodated in the aqueous core of inverted micelles often remains similar to that in pure aqueous solution [4]. The solubility of ionizing proteins in the microemulsion can be regulated by varying different parameters like the detergent concentration, the detergent-to-water ratio, the temperature, the pH, and the simple electtolyte activity in the system [4,8]. In the present study, the influence of the ionic strength is analyzed in terms of electrostatic contributions to the thkmodynamics of enzyme/inverted mkeilc complexation. The shell-and-core model [1,3,8] for the inverted micelle is used in &e Poisson-Bohzmann approximation [lo] to calculate the free energy of transfer of the enzyme from the bulk aqueous solution to the aqueous core of an inverted micelIe. The mechanism of the enzyme solubilizatik in the microemulsion is shown k Fig. 1, The shell-and-core model pictures the inverted micelles as spherical tintities consisting of the aqueous core and of the detergent shell of radius rM_ The ionizing miceEed detergent contributes to the ‘micelle charge zM spread over the idealized smooth micek surface, the surface charge
* Presented al the 9th l-5 September, 1987.
BES Symposium
0 1988 E&&r
on Bioeltctrochemist~y
Sequoia
S.A.
and Biwnergetics,
Szeged
(Hungary),
Fig. 1. ‘I%e model for aqueous enzyme sAtion (l-i&?).
(left! and for the enzyme-containing
microemulsion
The water pool in the micelle may host a density being (JM = tMe0/(4mRt,). hydrophilic enzyme which is assumed to lie in the centre of the micelle. The globular enzyme is modelled as a uniformly charged sphere of radius rE, charge za, and The aqueous solution of the enzyme surface charge density on = zEe0/(47&. maintaining equilibrium with the microemulsion is represented by the spherical cell model of colloidal solutions [ll-13j. According to this model, the solution is represented by a large number of equal spherical cells, each containing an enzyme molecule and the neutralizing simple ions. The volume of the cell V, and its radius rC depend on the enzyme concentration cE = l/(N,&) where V, = 47r&3. Water in the cell as well as that in the micellar core is treated as a dielectric continuum of permittivity t. For the sake of simplicity, the image interactions [14] and the structural changes of water at the interfaces [15] are not taken into account. The electric field and the distribution of the simple ions are determined via the Poisson-Boltzmann (PB) equation v23,=
-f-f&inS i
exp -F (
eo\l, 1
(1)
where $J is the local electrostatic potential, e. the proton charge, k the Bokmann constant and T the absolute temperaiure. Further, np is the number density of the z,-valent. simple ion at the surface of the cell, r = rc, or for the micelle, r = rM, where the potential is set equal to zero for convenience. The boundary conditions = (d\t/dr).= = 0, (d+/dr),, = -GE/C and (d#/dr)r, = CM/c follow (dWdr),=o directly from the Gauss theorem. The choice of the appropriate values of the reference number densities n p and the numerical solution of the PB equation (I),
293
WEBanalogous to that described earlier [121 in copaection with the modified PI3 equation A more deraikd description will be given in the forthcoming study [16]. The free energy of the enzyme/inverted micclle complexation, AG is defined as the change is the free energy due to the transfer of an enzyme mokcute from the bulk aqueous solution to the water pool of an inverted micelle. During this process, A&.4, molecules of the simple electrolyte MX move from the micelle to the aqueous solution irl order to satisfy the equilibrium requirement that the electrolyte activity, aMx = c+c_y& in both the water pool of the enzyme-free inverted micelle and in the enzyme/tnicelle complex remain equal to that in the bulk solution. Here, c+ and c_ are the cation and the anion concentrations. The activity coeffitient of the electrolyte, y *, in each of the three different subsystems is approximated by 1171: y,(k)
= I
(2)
where the angular brackets denote the volume average, k = 1 corresponds to the enzyme-free inverted micelle, k = 3 to the eIlzy_me-containingelementary cell of the bulk solution, k = 3 to the same ceil after removal of thr: enzyme, and k = 4 to the enzyme/ inverted micelle complex. The free energy of complexation is then approximately given by: AG = G(4) + G(3) - G(2) - G(1)
(3) where ‘G(k) is the free energy of the subsystem k as specified above. Following the approach of ref. 17, the free energy of the system k, G(k), is estima?ag as the sum of the pure coulombic term and the configurational entropy term
as described in full detail elsewhere 117,181.Here, p is the local charge density due to the presence of all ionized species of local Ilumber densities nj, and the sum is
over all solutes, including the protein. The standard chemical potential terms C, = c i~i(k)Crp were not taken into account in the calculations since they cancel when the difference AG of eqn. (3) is formed. The energy of enzyme/inverted micelle complexation AU is defined in an anologous manner as AG in cqn, (3), i.e. term of the AU = U(4) - U(2) - U(1). Here, U(k) is equal to the coulombic subsystem k, eqn. (4), multiplied by the factor (1 -k d In E/d In T) [17], and U(3) = 0 in the present approach. Jn Fig. 2 we show the ionic strength dependence of the calculated energy and the free energy of’ the enzyme/inverted micelle compiexation, AU and AG. &Themodel parameters usr:d in these calculations were chosen to mimic the system involving cytochrome c in water at cn = 0.0OOlti hJ and in the ~utionic detergent sodium di-2-ethylhexyl sulfosuccinate (AOT) water-in-isooctane microemulsion at 25 o C. This system has been character&d re:ently by small angle neutron diffraction measurements IS]. The rounded radii of ‘rhe enzyme and of the inverted micelle were taken to be rE = 1.5 nm and pM = 3.0 nm, while r, was 13.5 nm. The charge of the ionized enzyme zE = + 10 [I!!] and that of the detergent shell in the inverted micelle
,
0.2
0.4
,
,
0.6
,
,
0.0
Ilm01dm'~
l’ig. 2. The dependence of the energy AU (- -- --) and free energy AG (micelle complexation on the ionic strength I of the bulk aqueow sohtion.
) of enzyme/inverted
-20. This value is consistent with the apparent degree of ionization of ACT micelles in aqueous solution [20]. The polydispersity and the micellar growth or shrinking that may accompany the addition of the electrolyte or polyelectrolyte such as the ionized enqme [4,6,gj were disregarded in the present, preliminary study. As shown in Fig. 2, the calculated energy of complexation AU is negative over the whole range OF the ionic strength I of the aqueous enzyme solution in contact with the microemulsion, hence the process is exothermic at all conditions. With increasing ionic sPrength AU tends to zero due to the increasing shielding effects in the ionic atmosphere next to the charged colloidal particles. The calculated AG grows with I from strongly negative values at low ionic strength to positive values at high electrolyte concentration. The enzyme solubility in the microemulsion is therefore high at ionic strengths I below 0.18 M but drops almost to zero at I > 0.35 M where AG is already highly positive. The coulombic contribution to AG is proportional to the energy of complexation AW from which it differs by the factor (i-t d ln c/d ln T). As (1+ d ln c/d In T) = -0.372 in water at room temperature we note that the coulombic term in AG is positive over tha whole range of I in the system studied. The negative free cncrgy of compJexation bG is therefore due mainly to the considerable increase in the configurational eatropy of the simple ions that leave the water goal of the inverted micelle during complexation. Clearly, qon entrapment of the positively charged enzyme in the water pool of the inverted mice-de, an equivalent number of positively charged counterions move to the aqueous solution since they are no more bound to the interior of the micelle by the electroneutrality condition. This process is entropically favorable as long as the corlnterion concentration in the micelJe exceeds that in the bulk aqueous phase. A quantitative estimate of the enzyme distribution between the bulk aqueous phase and the microemulsion is a.Jso of interest. Considering that there are (E) .ways Z,=
295
0
0.2
0.4
0.6
Fig. 3. The fraction of the enzyme-containing inverted micelles in the microemulsion equilibrated with the aqueous solution of the enzyme as a function of its ionic strength I at zE = 10, zM = - 20, r, = 1.5 nm, rM= 3.0 nm and r, = 13.5 nm or with the same parameters but with rE = 1.g nm (11, zM = - 45 (Z), RM = 2.4 nm (3), and ZM= - 180 (4).
of distributing N enzyme molecules in the microemulsion contianing M available inverted micelles, the additional configurational entropy is equal to kT In(!). Following closely the derivation of the Langmuir adsorption isotherm [21,22], the equilibrium fraction 8 = N/M of the inverted micelles occupied by the enzyme can be related to the free energy of complexation of a single enzyme, AG: 8_
exp(-AG/kT)._ 1+ exp( - AG/kT)
(5)
Here, the enzyme concentration cE has already been taken into account in the determination of AG. In Fig. 3, the calculated fractions of enzyme-containing inverted micelles in a microemulsion equilibrated with aqueous enzyme solutions of different ionic strengths are shown. In order to estimate the effect of varying the characteristic parameters of the model, a few curves for different sizes and charges of the reverse micelle and the enzyme are included. The solid curve describes the model system *OT *zater-in-oil microemulsion spe.&ed above. which mimics the cytochrome c i.n d. in accordti~ti with recent small angle neutron diffraction measurements [S], a high solubility of this enzyme is predicted at low concentration of the simple electrolyte, I +z 0.15 M, whereas the enzyme is only poorl, v soluble at I B 0.35-0.4 M, Although the model calculations correspond to a somewhat different physical situation than considered in the experiment, the substantial agreement between the measurement and the calculation appears to justify the thFaretica1 approach proposed above. It is particularly important that the observed enzyme solubilization may be interpreted satisfactorily solely in terms of non-specific, coulombic interactions. Possible refinements of the model and the calculation will be discussed later [he] but further applications of the proposed treatment to other protein/microemulsion systems are claerly encouraged in view of the present results.
Jm!cNOWLEDoEMENT
This pork wfts supparted by 13SF tirrough the I3Jiotechnology Process Engineering Center at M.I.T. and through the United States-Yugoslav Joint Fund for Scientific Cooperation under Grant No. 8711845. Support from the Research Community of Slovenia is also acknowledged. REFERENCES 1 F.J. Bonncr. R Wolf and P.L. Luisi, J. Solid Phase Kochem., 5 (1980) 255. 2 A.V. Levasbov, Y.L. Kht~elnitsky, N.L. Klyachko. V.Y. Chemyak and 1;. Martin&, 3. Colbid ;‘ntcrface Sci., 88 (1982) 444. 3 P.L. L&i and R Wolf in K.L. Mittal and J.H. Fendler (Ws.), Solution Behaviour of Surfactants, vol. 2, Plenum, New York 1982, p. 867. 4 J.H. Fendlcr, Membrane Mimetic Chemistry, Wiley, New York, 19S2, p. 259. 5 P. Luthi and P.L. Luisi, J. Am. Chem. Sot., 106 (1984) 7285. 6 M.P. Pile& T. Zemb and C. Petit, Chcm. Phys. Lett, 118 (1985) 414. 7 ICE GoHen and T.A. Hatton, BiotechnoL Rag., 1 (1985) 69. 8 BY. Shcu, ICE Golden, T.A. Hatton and S.H. Chen, Biotechnol. Prog.. 1 (1986) 175. 9 D. Cbatenay, W. Urbach; C. Nicot, M. Vacher and M. Waks, J. Phys. Chem., 91 (1987) 2198. 10 R Kubii H.F. Eicke and 8. Jonsson, Helv. Chim. Acti, 65 (1982) 170. 11 G.M. Bell and AJ. Dunniug. Trans. Faraday See.. 66 (1970) 500. 12 M. Mille and Cr. Vanderkoci, -7. Colloid Interface Sci., 59 (1977) 211. 13 D. Bra&r, Bioelectrochem. Bioenerg., 13 (1984) 459. 14 D. Bratka, B. J&xson and H. Wennerstram, Chem. Phys. Lett., 128 (1986) 449. 15 A. Luzar, S. Svetina and B. &k& Bioelectrochem. Biceuerg., 13 (1984) 473, 16 D. Bratko, A. Lwar and S.H. Chen, to be published. 17 RA. Marcus, J. Chcm. Phys., 23 (1954) 1057. 18 D. Bratko and D. Dolar, J. Chem. Phys., 80 (1984) 5782. 19 A.L. Lehninger, Biochemistry, Worth Publishers, New York, 1975, p. 102. 20 E.Y. Sheu. S.H. Chm and J.S. Huang, J. Phys. Chem., 91 (1987) 3306. 21 T.L. Hill, An Introductior: to Statistical Thermodynamics, Addison-Wesley, Reading, MA, 1962,124. 22 A.W. Adamson, Physical Chemistry of Surfaces, Wiley, New York, 1976, p. 554.
Bioe:ec~whemist~~ and BiaenergeHcs, 20 (1988; 291-2% A section ol J. Ekwroanaf Chem., and constituting Vol. 254 (1988) Ekvier Scquch S-A., Lausanne - Printtd in The Netherlands
-
The influence of the ionic streq$h cbnemyme solubilization iu water-in-oil microeuudsions * D. Bratko Depcurmenr of Physic& Chemistg, I&b&no (Yugoslavia)
Fucu&v of Natural Sciences, Universi& E. Karde@, Muraikuva 6.
A. Pnaru IJW~W#~ of Micr~biofo~, Medical Facu@, University E. Ku&e&, L#b&ana (Yugoslavia) S.H. Chen Deparfmen! qf Nuciear Engineering Massachusetts fnstitute of Tech,roiogy. Cambridge, MA 02139 (U.S.A.) (Received 23 member
1987; in foal
form 15 Seplcmber
1988)
Solubilization of enzymes in water&-oil microemulsions [l-9] is important in various biotechnological processes ranging from selective protein extraction [7] to biocatalyzed synthesis [S]. It is of particular interest that the activity of enzyme.~ accomodated in the aqueous core of inverted micelles often remains similar to that in pure aqueous solution [4]. The solubility of ionizing proteins in the microemulsion can be regulated by varying different parameters like the detergent concentration, the detergent-to-water ratio, the temperature, the pH, and the simple electtolyte activity in the system [4,8]. In the present study, the influence of the ionic strength is analyzed in terms of electrostatic contributions to the thkmodynamics of enzyme/inverted mkeilc complexation. The shell-and-core model [1,3,8] for the inverted micelle is used in &e Poisson-Bohzmann approximation [lo] to calculate the free energy of transfer of the enzyme from the bulk aqueous solution to the aqueous core of an inverted micelIe. The mechanism of the enzyme solubilizatik in the microemulsion is shown k Fig. 1, The shell-and-core model pictures the inverted micelles as spherical tintities consisting of the aqueous core and of the detergent shell of radius rM_ The ionizing miceEed detergent contributes to the ‘micelle charge zM spread over the idealized smooth micek surface, the surface charge
* Presented al the 9th l-5 September, 1987.
BES Symposium
0 1988 E&&r
on Bioeltctrochemist~y
Sequoia
S.A.
and Biwnergetics,
Szeged
(Hungary),
Fig. 1. ‘I%e model for aqueous enzyme sAtion (l-i&?).
(left! and for the enzyme-containing
microemulsion
The water pool in the micelle may host a density being (JM = tMe0/(4mRt,). hydrophilic enzyme which is assumed to lie in the centre of the micelle. The globular enzyme is modelled as a uniformly charged sphere of radius rE, charge za, and The aqueous solution of the enzyme surface charge density on = zEe0/(47&. maintaining equilibrium with the microemulsion is represented by the spherical cell model of colloidal solutions [ll-13j. According to this model, the solution is represented by a large number of equal spherical cells, each containing an enzyme molecule and the neutralizing simple ions. The volume of the cell V, and its radius rC depend on the enzyme concentration cE = l/(N,&) where V, = 47r&3. Water in the cell as well as that in the micellar core is treated as a dielectric continuum of permittivity t. For the sake of simplicity, the image interactions [14] and the structural changes of water at the interfaces [15] are not taken into account. The electric field and the distribution of the simple ions are determined via the Poisson-Boltzmann (PB) equation v23,=
-f-f&inS i
exp -F (
eo\l, 1
(1)
where $J is the local electrostatic potential, e. the proton charge, k the Bokmann constant and T the absolute temperaiure. Further, np is the number density of the z,-valent. simple ion at the surface of the cell, r = rc, or for the micelle, r = rM, where the potential is set equal to zero for convenience. The boundary conditions = (d\t/dr).= = 0, (d+/dr),, = -GE/C and (d#/dr)r, = CM/c follow (dWdr),=o directly from the Gauss theorem. The choice of the appropriate values of the reference number densities n p and the numerical solution of the PB equation (I),
293
WEBanalogous to that described earlier [121 in copaection with the modified PI3 equation A more deraikd description will be given in the forthcoming study [16]. The free energy of the enzyme/inverted micclle complexation, AG is defined as the change is the free energy due to the transfer of an enzyme mokcute from the bulk aqueous solution to the water pool of an inverted micelle. During this process, A&.4, molecules of the simple electrolyte MX move from the micelle to the aqueous solution irl order to satisfy the equilibrium requirement that the electrolyte activity, aMx = c+c_y& in both the water pool of the enzyme-free inverted micelle and in the enzyme/tnicelle complex remain equal to that in the bulk solution. Here, c+ and c_ are the cation and the anion concentrations. The activity coeffitient of the electrolyte, y *, in each of the three different subsystems is approximated by 1171: y,(k)
= I
(2)
where the angular brackets denote the volume average, k = 1 corresponds to the enzyme-free inverted micelle, k = 3 to the eIlzy_me-containingelementary cell of the bulk solution, k = 3 to the same ceil after removal of thr: enzyme, and k = 4 to the enzyme/ inverted micelle complex. The free energy of complexation is then approximately given by: AG = G(4) + G(3) - G(2) - G(1)
(3) where ‘G(k) is the free energy of the subsystem k as specified above. Following the approach of ref. 17, the free energy of the system k, G(k), is estima?ag as the sum of the pure coulombic term and the configurational entropy term
as described in full detail elsewhere 117,181.Here, p is the local charge density due to the presence of all ionized species of local Ilumber densities nj, and the sum is
over all solutes, including the protein. The standard chemical potential terms C, = c i~i(k)Crp were not taken into account in the calculations since they cancel when the difference AG of eqn. (3) is formed. The energy of enzyme/inverted micelle complexation AU is defined in an anologous manner as AG in cqn, (3), i.e. term of the AU = U(4) - U(2) - U(1). Here, U(k) is equal to the coulombic subsystem k, eqn. (4), multiplied by the factor (1 -k d In E/d In T) [17], and U(3) = 0 in the present approach. Jn Fig. 2 we show the ionic strength dependence of the calculated energy and the free energy of’ the enzyme/inverted micelle compiexation, AU and AG. &Themodel parameters usr:d in these calculations were chosen to mimic the system involving cytochrome c in water at cn = 0.0OOlti hJ and in the ~utionic detergent sodium di-2-ethylhexyl sulfosuccinate (AOT) water-in-isooctane microemulsion at 25 o C. This system has been character&d re:ently by small angle neutron diffraction measurements IS]. The rounded radii of ‘rhe enzyme and of the inverted micelle were taken to be rE = 1.5 nm and pM = 3.0 nm, while r, was 13.5 nm. The charge of the ionized enzyme zE = + 10 [I!!] and that of the detergent shell in the inverted micelle
,
0.2
0.4
,
,
0.6
,
,
0.0
Ilm01dm'~
l’ig. 2. The dependence of the energy AU (- -- --) and free energy AG (micelle complexation on the ionic strength I of the bulk aqueow sohtion.
) of enzyme/inverted
-20. This value is consistent with the apparent degree of ionization of ACT micelles in aqueous solution [20]. The polydispersity and the micellar growth or shrinking that may accompany the addition of the electrolyte or polyelectrolyte such as the ionized enqme [4,6,gj were disregarded in the present, preliminary study. As shown in Fig. 2, the calculated energy of complexation AU is negative over the whole range OF the ionic strength I of the aqueous enzyme solution in contact with the microemulsion, hence the process is exothermic at all conditions. With increasing ionic sPrength AU tends to zero due to the increasing shielding effects in the ionic atmosphere next to the charged colloidal particles. The calculated AG grows with I from strongly negative values at low ionic strength to positive values at high electrolyte concentration. The enzyme solubility in the microemulsion is therefore high at ionic strengths I below 0.18 M but drops almost to zero at I > 0.35 M where AG is already highly positive. The coulombic contribution to AG is proportional to the energy of complexation AW from which it differs by the factor (i-t d ln c/d ln T). As (1+ d ln c/d In T) = -0.372 in water at room temperature we note that the coulombic term in AG is positive over tha whole range of I in the system studied. The negative free cncrgy of compJexation bG is therefore due mainly to the considerable increase in the configurational eatropy of the simple ions that leave the water goal of the inverted micelle during complexation. Clearly, qon entrapment of the positively charged enzyme in the water pool of the inverted mice-de, an equivalent number of positively charged counterions move to the aqueous solution since they are no more bound to the interior of the micelle by the electroneutrality condition. This process is entropically favorable as long as the corlnterion concentration in the micelJe exceeds that in the bulk aqueous phase. A quantitative estimate of the enzyme distribution between the bulk aqueous phase and the microemulsion is a.Jso of interest. Considering that there are (E) .ways Z,=
295
0
0.2
0.4
0.6
Fig. 3. The fraction of the enzyme-containing inverted micelles in the microemulsion equilibrated with the aqueous solution of the enzyme as a function of its ionic strength I at zE = 10, zM = - 20, r, = 1.5 nm, rM= 3.0 nm and r, = 13.5 nm or with the same parameters but with rE = 1.g nm (11, zM = - 45 (Z), RM = 2.4 nm (3), and ZM= - 180 (4).
of distributing N enzyme molecules in the microemulsion contianing M available inverted micelles, the additional configurational entropy is equal to kT In(!). Following closely the derivation of the Langmuir adsorption isotherm [21,22], the equilibrium fraction 8 = N/M of the inverted micelles occupied by the enzyme can be related to the free energy of complexation of a single enzyme, AG: 8_
exp(-AG/kT)._ 1+ exp( - AG/kT)
(5)
Here, the enzyme concentration cE has already been taken into account in the determination of AG. In Fig. 3, the calculated fractions of enzyme-containing inverted micelles in a microemulsion equilibrated with aqueous enzyme solutions of different ionic strengths are shown. In order to estimate the effect of varying the characteristic parameters of the model, a few curves for different sizes and charges of the reverse micelle and the enzyme are included. The solid curve describes the model system *OT *zater-in-oil microemulsion spe.&ed above. which mimics the cytochrome c i.n d. in accordti~ti with recent small angle neutron diffraction measurements [S], a high solubility of this enzyme is predicted at low concentration of the simple electrolyte, I +z 0.15 M, whereas the enzyme is only poorl, v soluble at I B 0.35-0.4 M, Although the model calculations correspond to a somewhat different physical situation than considered in the experiment, the substantial agreement between the measurement and the calculation appears to justify the thFaretica1 approach proposed above. It is particularly important that the observed enzyme solubilization may be interpreted satisfactorily solely in terms of non-specific, coulombic interactions. Possible refinements of the model and the calculation will be discussed later [he] but further applications of the proposed treatment to other protein/microemulsion systems are claerly encouraged in view of the present results.
Jm!cNOWLEDoEMENT
This pork wfts supparted by 13SF tirrough the I3Jiotechnology Process Engineering Center at M.I.T. and through the United States-Yugoslav Joint Fund for Scientific Cooperation under Grant No. 8711845. Support from the Research Community of Slovenia is also acknowledged. REFERENCES 1 F.J. Bonncr. R Wolf and P.L. Luisi, J. Solid Phase Kochem., 5 (1980) 255. 2 A.V. Levasbov, Y.L. Kht~elnitsky, N.L. Klyachko. V.Y. Chemyak and 1;. Martin&, 3. Colbid ;‘ntcrface Sci., 88 (1982) 444. 3 P.L. L&i and R Wolf in K.L. Mittal and J.H. Fendler (Ws.), Solution Behaviour of Surfactants, vol. 2, Plenum, New York 1982, p. 867. 4 J.H. Fendlcr, Membrane Mimetic Chemistry, Wiley, New York, 19S2, p. 259. 5 P. Luthi and P.L. Luisi, J. Am. Chem. Sot., 106 (1984) 7285. 6 M.P. Pile& T. Zemb and C. Petit, Chcm. Phys. Lett, 118 (1985) 414. 7 ICE GoHen and T.A. Hatton, BiotechnoL Rag., 1 (1985) 69. 8 BY. Shcu, ICE Golden, T.A. Hatton and S.H. Chen, Biotechnol. Prog.. 1 (1986) 175. 9 D. Cbatenay, W. Urbach; C. Nicot, M. Vacher and M. Waks, J. Phys. Chem., 91 (1987) 2198. 10 R Kubii H.F. Eicke and 8. Jonsson, Helv. Chim. Acti, 65 (1982) 170. 11 G.M. Bell and AJ. Dunniug. Trans. Faraday See.. 66 (1970) 500. 12 M. Mille and Cr. Vanderkoci, -7. Colloid Interface Sci., 59 (1977) 211. 13 D. Bra&r, Bioelectrochem. Bioenerg., 13 (1984) 459. 14 D. Bratka, B. J&xson and H. Wennerstram, Chem. Phys. Lett., 128 (1986) 449. 15 A. Luzar, S. Svetina and B. &k& Bioelectrochem. Biceuerg., 13 (1984) 473, 16 D. Bratko, A. Lwar and S.H. Chen, to be published. 17 RA. Marcus, J. Chcm. Phys., 23 (1954) 1057. 18 D. Bratko and D. Dolar, J. Chem. Phys., 80 (1984) 5782. 19 A.L. Lehninger, Biochemistry, Worth Publishers, New York, 1975, p. 102. 20 E.Y. Sheu. S.H. Chm and J.S. Huang, J. Phys. Chem., 91 (1987) 3306. 21 T.L. Hill, An Introductior: to Statistical Thermodynamics, Addison-Wesley, Reading, MA, 1962,124. 22 A.W. Adamson, Physical Chemistry of Surfaces, Wiley, New York, 1976, p. 554.