J. Phys. Chem. 1982,86,5015-5018
5015
Quantitative Characterization of Micellar Equilibria by Sedimentation Equilibrium. Micelle Size and Association Constant for Chlorpromazine Lawrence W. Nichol,‘ Ellsabeth A. Owen, Department of Physical Biochemistry, John Curtin School of Medical Research, Australian National University, Canberra, A.C.T. 260 1, Australia
and Donald J. Wlnzor Department of Biochemistry, University of Queensland, St. Lucia, OM. 4067, Australia (Received: May 28, 1982, I n Final Form: August 12, 1982)
Sedimentation equilibrium results obtained with chlorpromazine hydrochloride in 0.154 M NaCl at 20 OC are analyzed to show that the system comprises essentially two states, monomer in equilibrium with a 35-mer, the L ” / p . The experiments were conducted micelle formation being governed by an association constant of 5.4 x to encompass the region of the critical micelle concentration, where the concentration of micelle increases steeply with increase of total concentration. This feature, common to other micellizing systems, leads to unusual forms of plots conventionally used to determine the weight fraction of monomer in self-associating systems subjected to sedimentation equilibrium. Three different types of analysis are considered, particular attention being paid to interpolation or extrapolation procedures required in the evaluation of monomer weight fractions. Guided by the results obtained with chlorpromazine together with numerical simulations, we conclude that all methods of analysis examined offer potential in the thermodynamic characterization of micellar systems.
Introduction The recent interpretation1*2of binding results for the interaction of chlorpromazine with brain tubulin3 in terms of the preferential binding of the micellar state of the tranquilizer required assessment of the micelle size and the equilibrium association constant governing its formation. This is not an isolated example of the need for the thermodynamic elucidation of small molecule micellization because several diverse biochemical systems have been studied in which a self-associating ligand of this type interacts with a macromolecular a~ceptor.”~A characteristic feature of micelle formation is the rapid increase in the concentration of the micelle in a region termed the “critical micelle concentration”, which has been utilized in studies to estimate thermodynamic parameters.g10 However, the definition and use of the critical micelle concentration for this purpose has recently been questionedll and attention drawn to the paucity of studies in which micelle formation has been characterized by well-established methods such as sedimentation equilibrium. In this area, two basic approaches exist for the analysis of interacting systems, one centered on the use of molecular weight averages12J3and the other on the direct determi(1)M.J. Sculley, L. W. Nichol, and D. J. Winzor, J . Theor. Biol., 90, 365 (1981). (2)J. R. Cann, L. W. Nichol, and D. J. Winzor, Mol. Pharmacol., 20, 244 (1981). (3)N. D. Hinman and J. R. Cann, Mol. Pharmacol., 12, 769 (1976). (4)L.W. Nichol, G. D. Smith, and A. G. Ogston, Biochim. Biophys. Acta, 184, l(1969). (5) N. C. Robinson and C. Tanford, Biochemistry, 14, 369 (1975). (6)P. W. Kuchel, D. G. Campbell, A. N. Barclay, and A. F. Williams, Biochem. J., 169,411 (1978). (7)G.M. Donn6-Op den Kelder, J. D. R. Hille, R. Dijkman, G. H. de Haas, and M. R. Egmond, Biochemistry, 20, 4074 (1981). 51,561 (1955). (8)J. N. Phillips, Trans. Faraday SOC., (9)C. Tanford, ‘The Hydrophobic Effect: Formation of Micelles and Biological Membranes”, Wiley, New York, 1973. Reu., 6 , 25 (1977). (10)L.R. Fisher and D. G. Oakenfull, Chem. SOC. (11)L.W.Nichol and A. G. Ogston, J. Phys. Chem., 85,1173 (1981). 86,3454 (12)E. T. Adams, Jr., and J. W. Williams, J.Am. Chem. SOC., (1964). (13)E. T. Adams, Jr., L.-H. Tang, J. L. Sarquis, G. H. Barlow, and W. M. Norman in ‘Physical Aspects of Protein Interactions”, N. Catsimpoolas, Ed., Elsevier/North-Holland Publishing Co., New York, 1978,p 1.
nation of the activity distribution of m0n0mer.l~ While different, each of these approaches utilizes an extrapolation procedure, the nature of which is largely unexplored in relation to micellar systems, where forms of curves may well exhibit unusual features due to the rapid change of micelle concentration over a relatively narrow region of total concentration. The purpose of this work is to explore this question and others which arise in analysis of sedimentation equilibrium results obtained with micellizing systems. The particular system chosen for experimental illustration is chlorpromazine hydrochloride a t 20 OC in 0.154 M NaC1, for which the reported15 critical micelle concentration of 4.56 mM (1.6 g/L) occurs in a concentration range that is eminently suited for analysis by the Rayleigh optical system of the ultracentrifuge. Experimental Section Chlorpromazine hydrochloride (monomer molecular weight 355.4) obtained from Sigma Chemical Co., St. Louis, MO, was dissolved directly in 0.154 M NaC1, the molar concentration of the resulting solution being determined spectrophotometrically on the basis of a molar absorptivity of 4400 at 300 nm.I6 Since it is not possible to dialyze such solutions by conventional or alternative m e a d 7 due to small monomeric size and absorption characteristic^,^ the Donnan equation was used to calculate the composition of diffusate appropriate for use as the reference solvent in all experiments.18J9 Sedimentation equilibrium experiments were conducted at 20 O C in a Spinco Model E ultracentrifuge equipped with electronic speed control and Rayleigh interference optics. Interferograms recorded after 24 h were measured (14)B.K.Milthorpe, P. D. Jeffrey, and L. W. Nichol, Biophys. Chem., 3, 169 (1975). (15) A. T. Florence and R. T. Parfitt, J. Phys. Chem., 75,3554(1971). (16)E. W. Neuhoff and H. Auterhoff, Arch. Pharm. Ber. Dtsch. Pharm. Ges., 288,400 (1955). (17)W. E.Ferguson, C. M. Smith, E. T. Adams, Jr., and G. H. Barlow, Biophys. Chem., 1, 325 (1974). (18)E. F. Casassa and H. Eisenberg, Adu. Protein Chem., 19, 287 (1964). (19)C. Tanford, ‘Physical Chemistry of Macromolecules”,Wiley, New York, 1961.
0022-3654/82/2086-50 15$01.25/0 0 1982 American Chemical Society
5016
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982
Nichol et al.
Results and Discussion Figure l a presents results obtained in a sedimentation equilibrium experiment conducted with an initial loading concentration of 1.356 g/L of chlorpromazine hydrochloride (Scatchard component). It is evident that a portion of the plot of In J ( r ) vs. rz is linear, with slope 0.0550, determined by least-squares regression. Consideration of this quantity in terms of its conventional identification as M(l - Op)w2/(2RT)for a single solute yields a value of 319 for M which corresponds closely to the calculated molecular weight of 326 for the Scatchard monomeric component. This is not unexpected since the concentration range spanned in this region is below the critical micelle concentration. Moreover, it is noteworthy that the experimental value of 0 was determined at a concentration (9.22 g/L) well above the critical micelle concentration, and hence the close agreement of the mo-
nomer molecular weight values provides the first experimental indication that no measurable volume change occurs on micellization. Slopes of tangents to the curve shown in Figure l a define $M,(r) where $ = (1 - 0p)w2/ (2RT) and MJr) is the weight-average molecular weight: in these terms the limiting slope of 0.0550 specifies $MI, the subscript denoting monomer. It was on this basis that Figure l b was constructed, which includes, also, points in a higher range of total concentration determined from a second sedimentation equilibrium experiment conducted with an initial loading concentration of chlorpromazine hydrochloride of 1.658 g/L. The essential superposition of the two sets of data over the common range of total concentration supports the view that no significant volume change accompanies micelle formation. The first type of analysis to which results of the type shown in Figure l b may be subjected is that recently suggested by Nichol and Ogston" which assumes an insignificant population of polymers with size intermediate between those of monomer and micelle. The analysis is aided when the size of the micelle may be assessed independently. To this end a third sedimentation equilibrium experiment was performed with a loading concentration of 9.22 g/L and a speed of 20000 rpm, the results being recorded by the schlieren optical system and analyzed by the Lamm procedure.zz The plot of In [(l/r)(dn/dr)]vs r2was linear, giving a z-average molecular weight of 11100, which corresponds to a value of 34.9 f 0.3 for the ratio MJM,. Since this experiment was conducted in a concentration range well above the critical micelle concentration and was deliberately analyzed in terms of a z average weighted toward polymeric species, a value of 35 may reasonably be inferred for the micelle size, n. Use of this value of n permits the calculationll of the values of M,(r)/M1 a t which the second and third derivatives of the curve shown in Figure l b are zero, and also the calculation" of the monomer weight fractions, cl(r)/t(r), at these points, 0.989, 0.906, and 0.799 for points 1, 2, and 3 in Figure lb. It is now possible from the experimental results to find by interpolation the corresponding values of the total concentrations, C(r),shown in Figure lb, and hence the concentrations of monomer and micelle at each point. The corresponding values of the apparent association equilibrium constant, K , obtained by this means were 7.9 X 5.2 X lom7,and 5.0 X lo-' L34/g34. It would be unwise to comment further at this stage on this first experimental application of the Nichol and Ogston procedure" because it does not encompass the possibility that other intermediate polymers may also coexist in significant amounts. Figure 2a presents the results of the sedimentation equilibrium experiments conducted with the lower initial loading concentrations in terms of the function Q ( r )defined by Milthorpe et al.14 In this analysis procedure, the weight fraction of monomer at a selected reference value of total concentration, E(+), is determined as the value of Q(r)at infinite dilution. While it has been shown that this extrapolation is not complicated by the existence of critical points,14 the matter of interest with the micellar system is the ease with which it may be made. Computer simul a t i ~ of n ~the ~ sedimentation equilibrium distribution of a system with n = 35 and K = 5 x lo-' L34/g34and subsequent analysis of the simulated results by the Q ( r )method revealed that horizontal extrapolation was appropriate. It is seen from Figure 2a that the experimental
(20) E. G. Richards, D. C. Teller, and H. K. Schachman, Biochemistry, 7, 1054 (1968). (21) G.Scatchard, J . A m . Chem.SOC.,68,2315 (1946).
(22) 0. Lamm, Ark. Mat.,Astron. Fys.,21B, 1 (1929). (23) G. J. Howlett, P. D. Jeffrey, and L. W. Nichol, J . Phys. Chem., 74, 3607 (1970).
"0"
1.2
1.4
1.6
1.8
c(r)
(mg/ml)
2.0
2.2
2.4
Figure I. Evaluation of the weight-average molecular weight of chlorpromazine hydrochloride in 0.154 M NaCl at 20 OC. (a) Solute distribution resulting from a sedimentation equlllbrlum experiment conducted at 52 000 rpm w'W an initial loading concentration of 1.356 g/L and fa = 6.9077 cm, r b = 7.2052 cm, denoting the radial meniscus and base positins, respectively. (b) Concentration dependence of the weight-average molecular weight, M&), from the experiment conducted at 52 000 rpm (0)and a second experiment (0)performed at 40 000 rpm with loading concentration 1.658 g/L and r a = 6.8596 cm, r b = 7.1839 cm. Results are expressed relative to the monomeric molecular weight, M,,deduced from the slope of the broken line in part a. Interpolations in the plot are those suggested by the analysis procedure of Nichol and Ogston" (see text).
according to the method of Richards, Teller, and Schachman,20which led to the basic experimental results in terms of plots of interference fringes, J(r), as a function of radial distance, r. A synthetic boundary cell was employed to determine initial loading concentrations expressed in terms of fringes where 1g/L corresponds to 5.96 fringes. The partial specific volume was estimated by using an Anton Paar DMA 60/602 precision density meter as 0.713 mL/g, this value being based on the concentration scale defined in terms of the Scatchard componentz1 of calculated molecular weight 326.
The Journal of Physical Chemistty, Vol. 86, No. 25, 1982 5017
Sedimentation Studies of Chlorpromazine Miceliization
:
c
4
'
/ - I
+
0
1 . 1 1
0.9
1
0'51
0.12
0.4
0.13
I
I
0.14
0.15
I 0.16 Log cl(r)
I 0.17
i 0.18
0.19
Figure 3. Test of the chlorpromazine results for conformity with a two-state system comprising monomer in equilibrium with a 35-mer micelle. Concentrations of monomer, c,(r),and micelle, E ( r ) - c , ( r ) , were deduced from the sedimentation equilibrium experiments conducted at angular veloclties of 52 000 (0)and 40 000 ( 0 )rpm.
LI'
results do contain the onset of this horizontal region to guide the required extrapolation. Accordingly, the Q ( r ) method offers no difficulty in determining the weight fraction of monomer a t the reference concentration and hence a t all concentrations encompassed by the sedimentation equilibrium experiment^.'^ Indeed, the method gives the distribution of thermodynamic activity of monomer, which may be of importance in relation to systems where marked nonideality must be considered in the present instance, we shall equate activity with concentration as an approximation in view of the relatively low concentration range (1-2 g/L) studied. The same information on the weight fraction of monomer as a function of total concentration is potentially available from the method of Steiner26developed by Adams12 in which d r ) = [(Ml/Mw(r)) - 1]/Wis plotted against E(r),as in Figure 2b. In this method, extrapolation of the plot to infinite dilution is again required, followed by determinations of areas under the curve a t successive values of C(r). I t has been shown previo~sly'~ by numerical example that, for systems with n > 2 and with small populations of intermediate polymers, a maximum arises in this curve, a feature clearly evident in Figure 2b. Nevertheless, it is fair to note that for the micellar system under discussion the extrapolation procedure to infinite dilution is not difficult since the ordinate intercept, K , is indistinguishable from zero. It would indeed suffice, for the required area de-
terminations, to extrapolate the plot to an abscissa value as shown in Figure 2b. Although both analyses shown in Figure 2 may be used to determine the weight fraction of monomer as a function of total concentration, we choose the former as it is more direct and avoids errors inherent in area determinations. Evaluation of the concentration distribution of monomer, cl(r), from the Q(r)plot makes it possible to examine the postulate that micellization approximates closely a two-state system, a view with both theoreticalz7 and experimenta128i29 justification in globular micelle formation. The procedure is to substract cl(r) from E(r) found at each r , and to plot the logarithm of the difference against the logarithm of cl(r), as in Figure 3. From the logarithmic form of the definition of K , such a plot should be linear with slope n and ordinate intercept log K for a two-state system. The solid line in Figure 3 has been constructed with a slope of 35 and a value of 5.4 X lo-' L34/g34for the best-fit estimate of K. Clearly, the fit of the experimental points to this line justifies the two-state hypothesis for this system. In conclusion, four points merit further comment. First, the reported critical micelle concentration for this system of 4.56 mM (1.49 g/L of Scatchard component), derived from nuclear magnetic resonance studies,15is only in fair agreement with the value that might be deduced from Figure lb. This observation emphasizes the inadvisability of basing thermodynamic characterization on the notion of a critical micelle concentration, a quantity whose value may well depend on the method used to estimate it. Secondly, since it has now been established that the chlorpromazine system essentially comprises monomer and 35-mer, comment is possible on the values of K obtained by the Nichol and Ogston procedure,'l illustrated in Figure lb. Clearly, the value obtained by interpolation with respect to point 1is the least accurate, which is not unexpected; but the value found from points 2 and 3 (an avL'/g3") is in very close agreement with erage of 5.1 X that of 5.4 X lo-'' L34/g34found from Figures 2a and 3. Thirdly, computer simulation of both sedimentation
(24) C. J. Biaselle and D. B. Millar, Biophys. Chem., 3, 355 (1975). (25) P. R. Wills, L. W. Nichol, and R. J. Siezen, Biophys. Chem., 11, 71 (1980). (26) R. F. Steiner, Arch. Biochem. Biophys., 39, 333 (1952).
(27) J. N. Israelachvili, D. J. Mitchell, and B. W. Ninham, J. Chem. Soc., Faraday T r a m . 2, 72, 1525 (1976). (28) P. Mukerjee, J. Phys. Chem., 7 6 , 565 (1972). (29) G. Kegeles, J.Phys. Chem., 83, 1728 (1979).
0.1
O 0
1.1
L
1.3
4
1.5
1 7
-
1 9
d
2 1
2.3
d
2.5
?(r) (mg/ml)
Figure 2. Graphical methods for evaluating the weight fraction of monomeric chlorpromazine. (a) The n ( r ) analysls" for a reference Concentration, E ( r F ) , of 1.739 g/L. (b) A plot of -q(r) = [l - (MI/ M J r ) ) ] / E ( r )vs. the total solute concentration, E & ) , according to the basic formulatlon suggested by Steiner: the solM line descrlbes the theoretical relationship for a micellizing system with n = 35 and K = 5.4 x io-' L V g ?
J. Phys. Chem. 1982,86,5018-5023
SO18
equilibrium experiments on which Figures 1-3 are based, and with the determined values of n and K , permitted a final test of the thermodynamic characterization: over the entire range of total concentration examined, the standard deviation of theoretical and experimental distributions was *15 Mm in terms of fringe displacement, an acceptable deviation for sedimentation equilibrium measurementam Finally, it is noted that, while the extrapolation procedures (30) P. D. Jeffrey, B. K. Milthorpe, and L. W. Nichol, Biochemistry, 15, 4660 (1976).
involved in the analysis of micellar systems do exhibit unusual features, already mentioned in relation to Figure 2, a and b, this work has established that no real difficulty exists in performing them and that accordingly characterization of micellar systems is indeed possible by sedimentation equilibrium.
Acknowledgment. The technical assistance of C. J. Leeder is gratefully acknowledged, as is the partial support of this investigation by the Australian Research Grants Scheme.
Cesium-133 Nuclear Magnetic Resonance Study of the Complexation of Cesium Salts by 18-Crown-6 in Methylamine. 1. 1:l Complex Formation Sadegh Khazaeli, Alexander I. Popov, and James L. Dye* Department of Ctmmistty, Michigan State University, East Lansing, Michigan 48824 (Recelved: June 16, 1982; In Final Form: August 18, 1982)
The variation of the 133Cschemical shift (6) with the temperature and with the (18-crown-G)/(Cs+)mole ratio in methylamine solutions indicated the formation of both 1:l and 2:l complexes. The concentration and temperature dependence of 6 for the 1:l complex in methylamine is described by the equilibria cs++ c
KC .Wac
KA csc+ csc++ x- e csc+.x- cs+.x-+ c M O A
KX
m x
csc+.x
where C and X- are the ligand and the anion, respectively. Free energies, enthalpies, and entropies of the complexation reactions were obtained on the basis of the above equilibria and with previously determined ion-pair formation constants. The ion-pair formation constants of both the 1:l complexes and the salts are of similar magnitude, which suggests that both the salts and the 1:l complexes form mainly noncontact ion pairs and that only small relative concentrations of contact ion pairs are present in methylamine solutions. The value of Kx depends on the anion and varies in the order SCN- < I- < BPh4-which indicates a competition between ion-pair formation and complex formation.
Introduction The complexation of the cesium cation by 18-crown-6 in aqueous and methanolic solutions as well as in mixtures of these solvents has been studied by potentiometric' and calorimetric2p3techniques. Mei et al.475used 133CsNMR to study the complexation of cesium tetraphenylborate by 18-crown-6 in six nonaqueous solvents. In all cases the formation of the 1:l complex (crown/Cs+) was followed by the addition of a second molecule of the ligand to form a "sandwich" 2:l complex. The use of solvents with high solvating ability, such as liquid ammonia and methylamine, to study alkali-metal solutions in the presence of macrocylic ligands6 motivated us to investigate the complexation of cesium salts by 18crown-6 in these solvents. Although the most interesting species in alkali-metal solutions are anionic, it is the complexation of alkali cations by crown ethers and cryptands which enhances the solubility of the metals. Consequently, studies of the thermodynamics of complexation of simple (1) Christensen, J. J.; Eatough, D. J.; Izatt, R. M. Chem. Reu. 1974, 74, 351.
(2) Izatt, R. M.; Terry, R. E.; Haymore, B. L.; Hanson, L. D.; Dalley, N. K.; Avondet, A. G.; Christensen, J. J. J. Am. Chem. SOC.1976,98,6720. (3) Izatt, R. M.; Terry, R. E.; Nelson, D. P.; Chan, Y.; Eatough, D. J.; Bradshaw, J. S.; Hansen, L. D.; Christensen, J. J. J. Am. Chem. SOC.1976, 98, 7626. (4) Mei, E.; Dye, J. L.; Popov, A. I. J . Am. Chem. SOC.1977,99, 5308. (5) Mei, E.; Popov, A. I.; Dye, J. L. J. Phys. Chem. 1977, 81, 1677. ( 6 ) Dye. J. L. J. Phys. Chem. 1980, 84, 1084.
salts with macrocycles can be used to predict the behavior of alkali-metal solutions. In the course of the study of the complexation of cesium salts with 18-crown-6 in methylamine it became clear, because of the low dielectric constant (D= 9.0 at 25 "C), that many equilibria are involved in the complexation process. Therefore, an extensive study of the system was carried out to obtain the thermodynamic formation constants of the 1:l and 2:l complexes. We present here the results for the formation of 1:l complexes of cesium salts by 18-crown-6 in methylamine solutions. The data for 2:l complex formation in methylamine as well as in liquid F m o n i a will be discussed in another paper.' Experimental Section Chemicals. Cesium salts were purified and dried by previously described techniques.s The ligand 18-crown-6 (Parish) was purified by several crystallizations from acetonitrileg and sublimed under high vacuum. Methylamine was dried as previously described.8 Solutions were prepared in 10-mm 0.d. precision NMR tubes (Wilmad) with a wall thickness of 0.5 mm. All samples were prepared under high vacuum (
