Triton X-305 system

ARCHIVES OF IBIOCHEMISTRY AND BIOPHYSICS Vol. 240, Nso. 1, July, pp. 191-200, 1985

Organization and Structure of Two Mixed Micellar Phases of the Sphingomyelin/Triton X-305 System SAUL YEDGAR’ DeparWent

of Biochemistry, Received

Hebrew July

AND

GERALD

University-Hadassah 16, 1984, and in revised

V. COOPER Medical

form

School, Jerusalem

March

91010, Israel

6, 1985

Properties of mixed dispersions of sphingomyelin and the nonionic detergent, Triton X-305, were investigated by analytical ultracentrifugation and by autocorrelation spectroscoply of scattered laser light. These properties were compared with those of the sphingomyelin/Triton X-100 mixed micellar system reported previously [S. Yedgar, Y. Barenholz, and V. G. Cooper (1974) Biochim. Biophys. Acta 363, 98-1111. The substitution of the 30-unit ethylene oxide chain of Triton X-305 for the lo-unit chain of the Triton X-100 resulted in the appearance of two micellar phases at all detergent/ lipid mixture ratios studied, whereas only a single mixed micellar phase was observed using Triton X-100. Despite this difference, the properties of the mixed lipid/detergent micelles obtained using Triton X-100 have been verified in the following respects: The detergent aggregation numbers in the mixed micelles are quite constant over a wide range of detergent molar fractions, being about 70 and 400 for the lighter and heavier mixed micellar phases, respectively. The detergent aggregation numbers are larger in the mixed micelle than in the pure detergent micelle. Very large sphingomyelin aggregation numbers can be accommodated within the mixed micelles, apparently by the critical intervention of the detergent molecules to produce a stable micellar structure. 0 is85 Academic PWS,

Inc.

In earlier work (1, 2) we reported a study of mi.xed micelles of the nonionic detergent, Triton X-100 (TXlOO)? and the phospholipid sphingomyelin (SPM), and models for the mixed micelle structure were derived. The main conclusions of the earlier work were as follows: (i) Over a wide range of TX100 to SPM ratios, a single mixeld micellar phase is formed. The number of TX100 molecules in the micelles was constant at about 200, and variation in the concentration ratio was manifested in changes in the SPM aggregation number. (ii) At low TX100 mole fractions the micelle was highly oblate. In this oblate structure, the SPM mole-

cules aggregate in a quasibilayer on the opposite surfaces of low curvature, and the TX100 molecules are located primarily around the high-curvature periphery of the micelle. At high TX100 mole fractions the micelle was highly hydrated and spherical. Although TX100 is the most commonly used nonionic detergent in the study of biological systems, other Tritons are widely used as well (3). Their properties as solubilizers depend on both the hydrocarbon and polar moieties, which determine the hydrophilic-lipophilic balance (4). The present work was undertaken to determine whether the behavior observed with TX100 is applicable when the length of the polar head group is increased. This was examined by replacing TXlOO, which contains 10 ethylene oxide (EO) units, by TX305, which is composed of the same

1 To whom correspondence should be addressed. ’ Abbreviatio.~ used: EO, ethylene oxide; SPM, sphingomyelin; TX-100, Triton X-100; TX-305, Triton x-305. 191

0003-9861185 $3.00 Copyright 0 1985 by Academic Press, Inc. All rights of reproduction in any form reserved.

192

YEDGAR

AND

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hydrophobic part (octyl phenyl) but has a larger polar part containing 30 EO units (5). MATERIALS

AND

METHODS

TX305 was obtained from Sigma (St. Louis, MO.). SPM was prepared from bovine brain according to Gatt et al. (6). Mixed micelles of SPM and TX305 were prepared as described by Yedgar et al (2): The SPM and TX305, each in chloroform-methanol (21) solutions were combined in the desired ratio. The solvent was evaporated under nitrogen. Sodium acetate buffer (0.1 M), pH 5.0, was then added. The solution was warmed to the cloud point, stirred on a cyclomixer, and cooled. Hydrolysis of SPM by rat brain sphingomyelinase was assayed as described by Yedgar and Gatt (7). Sedimentation and diffusion coefficients were determined by analytical centrifugation and autocorrelation spectroscopy, respectively. The experimental techniques used in the present work were as described previously (1, 2). Departures in technique are described in the results where relevant. RESULTS

Sedimentation Composition of the mixtures. Sedimentation studies were performed on a wide range of TX305/SPM ratios. All ratios showed two distinct phases. Of these ratios, four representative values were chosen for detailed study of concentration dependence of S for extrapolation to S,. We shall denote concentration ratios according to the mass fraction of TX305 in the solute, X,,. The four ratios studied were 0.36, 0.45, 0.62, and 0.77, as well as pure TX305. Traces at the four fractions, X,,, and for pure TX305 are shown in Fig. 1. The traces are for roughly equal sedimentation times (about 40 min). We shall designate the slower sedimenting (lighter) phase (Y, and the faster, heavier phase p. A clear trend is evident from these traces. Phase CY is dominant at high X,,, and becomes relatively weaker with decreasing X,, . The areas of the Schlieren peaks were measured to determine the relative concentrations of the two phases. Schlieren peak area is proportional to concentration and to dn/dC, the change in solution refractive index per unit concentration of the sedimenting phase (8). We measured

FIG. 1. Schlieren traces, at an elapsed sedimentation time of about 40 min, for four TX305-SPM concentration ratios, and pure TX305 (X,, = 1). For the four mixtures, the left-hand (slower sedimenting) peak is phase a, and the right-hand peak is phase /3.

dn/dC for pure TX305, and for pure SPM dispersed by sonication, as shown in Fig. 2. The slope of the graph of n vs. C is 0.17 ml/g for both constituents, to within a few percent. Therefore, dn/dC was taken to have this same value for all ratios of TX305 to SPM in the two phases, and we may take the concentration of the phases as simply proportional to the peak areas. Areas of the Schlieren peaks were determined graphically from enlargement of the traces. In all instances the fraction of phase (Y was apparently enhanced at higher solute concentrations. This is a manifestation of the Johnston-Ogston effect (8), wherein molecules of the lighter phase which are above the interface of the heavier phase sediment faster than those below the interface. A “piling-up” of phase LY on the gradient of phage P occurs. It has been corrected for by extrapolation to zero solute concentration. The fraction of the total solute concentration appearing in phase cr-@,-is given in Table I. Sedimentation coeficients. The sedimentation coefficient (S) was examined as a function of total solute concentration S for phase (Y showed negligible dependence on total concentration. On the other hand, S for phase fl was concentration dependent, being about 0.02 S mg-’ ml-‘. Ex-

TWO

PHASES

OF

SPHINGOMYELIN/TRITON

X-305

The dependence of the form (9)

193

MICELLES

of the density

on C is

P = PO + (1 - VPo>C,

I

I 0

I

05

C (gm/ml) FIG. 2. Index of refraction as a function concentration for pure TX305 (open circles) SPM (solid points).

of solute and pure

trapolated values at zero solute concentration, S,, are given in Table I. Both phases shovv a slight increase in S,, with decreasing I%, . Sedimentation coefficients were determined for four solutions of pure TX305 at different concentrations. The results were all close to 1. S, independent of concentration. Thus, it seems fairly certain that phase LY is not a phase of pure TX305, since its sedimentation coefficient is about double this value and, moreover, varied with X,,. Partial SpeciJic Volume

Densities were measured for various concentrations of solutes, from pure TX305 to pure SPM (dispersed by sonication). TABLE

PI

where po is the solvent density, and G is the partial specific volume of the solute. For each X,,, p was measured at six concentrations. The results were fit to a linear function of C, and the factor (1 - Vpo) for each X& (the slope) was determined. For convenience we shall express the term (1 - Vpo) as 6. The values of 6 are plotted with respect to X,, in Fig. 3. The five points in Fig. 3 show little departure from a linear function. This indicates that TX305 and SPM retain their respective partial specific volumes on mixing, for in that event (from the definition of 6) the value of this parameter for any mixture of TX305 and SPM is the simple massweighted average of &, and aspm, the limiting values of 6 for the pure constituents. That is, 6 at any fraction X,, is given by

zz 6spm+ x,,(fL

- &pm),

PI

which provides the linear dependence of d on Xt, presented in Fig. 3. The intercept of the line at X,, = 0, which is identical to &ml, is 0.025. The intercept at X,, = 1, which is &, is 0.17. These limiting values of 6 are used in subsequent calculations (see Appendix).

I

FRACTION OF S,DLUTE IN PHASE a, +a, SEDIMENTATION COEFFICIENTS, S,, FOR PHASES LY AND p, AND OVERALL DIFFUSION CONSTANT, Do, FOR THE MIXED MICELLAR SYSTEM

s x,X 1.0 0.77 0.62 0.45 0.36

Oa

4

a

P 1.0

0.75 0.42 0.30 0.20

2.1 2.2 2.2 2.4

5.8 6.1 6.1 7.5

(X10’

cm/s) 5.0 2.0 1.7 1.5 1.5

0'

0 ‘TX

FIG. 3. The flotation factor 6 = (1 - VpO) as a function of the TX305 fraction, X,,. The intercept at Xt, = 0 equals S,,,; the intercept at X,, = 1 equals 6,,.

194 Difusion

YEDGAR

AND

Coeficients

Autocorrelation spectra of scattered laser light (10) were measured for all the solutions that were examined by sedimentation. All measurements were for a scattering angle close to 90”. The light source was either a He-Ne laser operating at 6328 A, or an argon ion laser operating at 4880 A. Despite the fact that the solutions were found to be polydisperse in sedimentation, the autocorrelation spectra could be fit to good accuracy to a single exponential function, which is appropriate to a monodisperse solution (10). This is due to the overwhelmingly high scattering intensity from the much heavier phase P, as is explained below. The diffusion coefficients, obtained from fitting of the exponentials and extrapolating to zero solute concentration, are given in Table I. Enzymatic

Hydrolysis

of SPM

Upon application of rat brain sphingomyelinase (6) to the SPM/TX305 mixed micellar system, practically no hydrolysis of the substrate was observed at all detergent to lipid ratios studied.

COOPER

dition, the distribution of TX305 and SPM in each phase is not identical with the overall composition of the solution, and only the average 6 can be determined, rather than 6, and 6,. As will become apparent, the experimental results do not give single values for the molecular weights and aggregation numbers of the constituents in the two species of micelles. Rather, a range of possible values is consistent with the experimental data. The determination of that range was performed by means of a computer-assisted search at each of the four fractions X,, studied. The computer procedure scanned all possible proportions of TX305 and SPM in the two phases consistent with their concentrations in solution and with the observed phase concentrations, and determined whether that particular proportion was also consistent with all observed experimental data (sedimentation, diffusion, and partial specific volume). Details of the search procedure are given in the Appendix. Micellar Properties Computer-Assisted

Derived by Search

Generally, a higher concentration of detergent in a micelle is associated with higher hydration, while a higher lipid In the TX305/SPM system, two species concentration results in greater nonsphericity. These two influences are indisof mixed micellar particles coexist in sotinguishable by the experimental procelution; one lighter and with a higher fracdures used in this work; both manifest tion of TX305, and the other much heavier and with a higher fraction of SPM. The themselves as an increase in the Stokes former is predominant in solutions of radius, rs, over the effective radius, r, (11, 12). We have introduced the approximahigh X,,. In this two-phase system, each of the phases is governed by its own tion that the combined contribution of Svedberg equation, according to which, hydration and nonsphericity is similar in the two species ol and /3, since we had no Ma = RTS, a priori grounds for assuming it greater 131 in one species or another. However, the DCJ, implications of this simplifying assumpand tion upon the calculations were tested by means of the contrary assumption: All r41 calculations were repeated assuming that the two phases had different hydration/ nonsphericity. It was found that, unless Although S, has been determined for each of the two phases, only an average the hydration/nonsphericity is drastically diffusion coefficient, DO, has been meadifferent in the two phases, the results of sured, rather than the individual coeEithe calculations presented here are correct cients, D, and D@ (see Appendix). In adto a few percent. The results that follow Computer-Assisted Determination Micellar Properties

of

TWO

PHASES

OF

SPHINGOMYELIN/TRITON

indeed suggest that the influences are in fact similar in the two phases, consistent with our assumption. The micellar properties derived from the search routine are shown in Fig. 4. This figure presents the extrema that are consistent with the experimental data, indicated by the vertical bars. Aggregation voperties. Figures 4a and b show the TX305 and SPM aggregation numbers in phases (Y and /3, respectively. The molecular weights taken in these calculations were 1290 for TX305 (5) and ‘775 for SP:M (2). The TX305 aggregation numbers for both phases are defined by the search procedure within fairly narrow limits, while those for the lipid are much broader. This is to be expected considering the great difference in the values of 6 for the detergent (0.17) and for the lipid (0.025). The density of the latter is very close to that of the solvent. Therefore, much larger variation in the amount of SPM in the micelle would be required to influence the sedimentation rate, as com-

200.

a

FIG. 4. MiceKar properties, derived from the computer-assisted search procedure, as functions of X,. Vertical bars fomr each property denote the range of values consistent with the experimental data. (See text for details.)

X-305

MICELLES

195

pared to the TX305. The range of acceptable SPM aggregation numbers in the search procedure is thus broader than for TX305 Regarding Nspm of phase cr at high X,,, the wide bars in Fig. 4a in fact reflect a small absolute uncertainty in the disposition of the SPM, since the number of SPM molecules in phase is a very small fraction of the total SPM concentration. The small uncertainty in the overall disposion of the SPM is manifested as an exaggerated uncertainty within the phase (Y micelles. From the aggregation numbers shown in Figs. 4a and b it is clear that the micelles of phase /3 are an order of magnitude heavier than those of phage LYat all X,,. Comparison also shows that phase p is by far the richer in SPM, at all ratios. For the sake of comparison, the molecular weight of the pure TX305 micelle, calculated from its measured values of S,,, Do, and G, is about 29,000, so that its aggregation number is about 22. It is thus noteworthy that the TX305 aggregation numbers in the mixed micelles (about 70 for phase cy,and 400 for phase p) are very different from that of the pure TX305 micelle, even at high X,,, where only a few SPM molecules (between 5 and 15) are present. Shape and structure of the micelles. Figure 4c shows the Stokes radius of the two phases. The computer-assisted search defines the Stokes radius of phase p to high accuracy, but that of phase (Y only within the range shown in the figure. The Stokes radius is inversely proportional to the micellar diffusion coefficient (13). Because the micelles of phase /3 are an order of magnitude heavier than those of phase LY the diffusion coefficient measured by light scattering is effectively that of phase p. Thus, the Stokes radius for phase /I is virtually a measured quantity, while for phase (Y it is characterized by the uncertainty of the search routine. Figure 4d presents the ratio of the Stokes radius to the equivalent radius-a measure of particle hydration and/or nonsphericity (11, 12). This parameter was assumed to be similar for the two phases. Its value remains roughly constant at about 2 for all composition ratios. For

196

YEDGAR

AND

comparison, this ratio is shown for the micelles of pure TX305 (single point). The aggregation numbers allow us to assess the degree of nonsphericity of the micelles by considering the packing of their hydrophobic core (14). This core contains no voids and no water of hydration, so that its volume can be calculated given the aggregation numbers of the constituents, the molecular weights of the hydrophobes, and the density of the core. It is clear that, if the core is to have no voids, at least some of the hydrophobes must have access to its center. Thus, the hydrophobic core cannot be spherical if the radius of that sphere were to be greater than the length of the longest hydrophobes that constitute it. Instead, it will approximate an ellipsoid, in which at least one of the minor axes will equal the longest hydrophobe length. In this work, the relevent hydrophobe length is the 25A length of the SPM ceramide (15). For the very light micelles of phase cr at all X,,, no significant nonsphericity is indicated by the above criterion. A typical calculation is instructive. At the highest X,, of 0.7’7, the micelle contains about 70 TX305 molecules and about 10 SPM molecules. The molecular weight of the octylphenyl hydrophobe of the TX305 is about 225, and the SPM ceramide about 480, so that the molecular weight of the hydrophobic core is about 20,550. We have taken the specific gravity of both hydrophobes at about 0.9, so that the volume of the core is about 37,250 A’. The radius of the sphere which contains this volume is about 21 A, so that no nonsphericity need be invoked in order for the SPM ceramide to have access to the center of the core. A similar calculation at low X,,, even for an SPM aggregation number as high as 100, yields a spherical radius of about 30 A. Access to the center of the core for the 25-A ceramide is provided with negligible nonsphericity. To summarize, the micelles of phase cy are spherical, presumably highly hydrated, and have a fixed number of TX305 molecules at all concentration ratios. The TX305 molecules outnumber the SPM

COOPER

molecules at most, and perhaps all, concentration ratios. Beyond these conclusions, however, no clues are provided as to the structure or organization of the micelle. The heavier micelles of phase p, unlike those of phase (Y, are found to be nonspherical at all X,, studied. Consider first the highest X,, of 0.77. At this ratio, the micelle contains about 350 TX305 molecules and about 500 SPM molecules. Proceeding as before, a molecular weight of 320,000 is found for the hydrophobic core, corresponding to a volume of 580,000 A3. The radius of the sphere which contains this volume is 52 A. To provide access to the core center, the depth of the core at some point must be no more than the 25A ceramide length. According to our earlier model (2), SPM molecules will tend to aggregate into surfaces of low curvature, except through the intervention of the detergent molecules. In the mixed micelles of phase 0, where there is a large preponderance of SPM molecules, this propensity of the SPM molecules is accommodated by their congregating preferentially on the opposite surfaces of low curvature of an oblate spheroid, thus defining its minor radius as 25 A. For the core to have the above volume the major radii must be about 75 A, resulting in a 3:l axial ratio of the core. By a similar calculation we find at the lowest X,, studied, 0.36, that the major radius of the core must be 125 A, resulting in an axial ratio of 5:l. It is obvious that the short SPM hydrophile is also to be found preferentially in the vicinity of the minor radius (the region of low curvature), and the longer TX305 hydrophile preferentially in the vicinity of the major radius (the region of high curvature). Thus, the nonsphericity of the core will be closely maintained in the micelle overall, when the hydrophilic enaround the core. Acvelope is “added” cording to this model, at the highest SPM fraction studied, X,, = 0.36, the overall micelle will be highly oblate with minor radius 40 A (the length of the SPM molecule) and major radius approaching 200 A.

TWO

PHASES

OF

SPHINGOMYELIN/TRITON

DISCUSION

The two constituents TX305 and SPM apparently can coexist in solution only as two distinct mixed micellar species; one consisting of the heavier (faster sedimenting) particles of phase /3, and the other of the slower sedimenting phase a. This two-phase behavior indicates that a continuum of micellar compositions does not exist, and that the two mixed micellar forms are distinct stable entities. This is in accord with the finding of Robson and Denis (16) who found that, when the temperature of the mixed micellar system is below the phase transition of the pure lipid bilayer, more than one population of stable mixed micelles may exist simultaneously. This was observed using either homogeneous or inhomogeneous detergents (16), suggesting that detergent inhomogeneity does not alter the two-phase behavior. In this two-phase system, changing the overall concentration ratios of the constituents has two effects: It alters the relative concentrations of the two phases, as was indicated by the Schlieren traces (cf. a,). However, as Figs. 4a and b show, changes in the overall ratio also result in changes within the micelles of each phase. Yet, Figs. 4a and b show that the number of TX305 molecules in the micelles of both phases is quite constant at all compositions (at around 70 for phase a! and around 400 for phase p). This implies that the fixed numbers of TX305 molecules provide the matrices into which SPM is taken up, as it is “added” into solution. It is likely, as we have discussed earlier regarding the TXlOO/SPM system (Z), that as the number of SPM molecules in the mixed micelle increases, the lipid molecules tend to concentrate at the low curvature regions of the oblate micelle, while the detergent is located preferentially in the regions of high curvature around the “rim” of the ellipsoid, similar to what has been described by Dennis (17) as “quasimicelles”. Extrapolating to SPM concentrations beyond those dealt with here, we would expect the .mixed micellar structure to approach that of a disk of lipid bilayer ringed by the detergent molecules, sug-

X-305

MICELLES

197

gesting the model of Small (18), or the mixed bilayered disk of Mazer et al. (19), described for anionic detergent/phospholipid mixed micelles. Although the micelles of phase ,8 become progressively heavier and more oblate at lower X,,, the Stokes radius for this phase is quite constant at all X,,, at about 150 A. Part of this insensitivity of the Stokes radius is explained by its cube root dependence on micellar volume (12, 13). However, of equal importance, it illustrates the tradeoff between nonsphericity and hydration that is characteristic of this micellar system, and which has been mentioned above. The nonsphericity at low XL, tends to increase the Stokes radius in that range, while at high X,, the high hydration of the 30 EO units in the detergent hydrophile will produce a like effect by swelling the micelle and likewise increasing the Stockes radius (12). This is confirmed in Fig. 4d, where the ratio r.J r, remains close to 2 at all mixture ratios. As confirmation of the importance of hydration of the EO chain, r,/r, for the pure TX305 micelle is little different from that of the mixed micelles (single point at X,, = 1). The behavior of the TX305/SPM system resembles that of the TXlOO/SPM system in three main features: (i) The discontinuity in the Triton aggregation number between pure detergent micelle and lipid/ detergent mixed micelle; (ii) the relatively constant number of detergent molecules in the mixed micelles; and (iii) the tendency to form an oblate or bilayer-like mixed micelle with increasing lipid concentration. On the other hand, several differences between the two systems are noteworthy. In the TXlOO/SPM system a single micellar species was observed over a wide range of ratios, and pure TX100 micelles apparently coexisted with mixed micelles at high X,,. However, in the TX305/SPM system, two mixed micellar species were observed at all ratios studied, and coexistence of pure detergent micelles with mixed micelles was not observed. Robson and Dennis (16), who analyzed the TX1001 SPM system using column chromatogra-

198

YEDGAR

AND

phy and chemical determination of the compounds, did not observe coexistence of pure TX100 micelles with mixed detergent/lipid micelles. These conflicting observations may be due to the different techniques used; using analytical ultracentrifugation and light scattering one might not distinguish between pure detergent micelles and mixed micelles containing a number of lipid molecules too small to affect the measured parameters, yet this small difference would be distinguishable by chemical analysis. The TX100 and the TX305 systems also differ markedly in the aggregation number of the pure detergent-134 for TX100 (M, 8600) vs. 22 for TX305 (MT 2900). It is interesting to note that the Stokes radius is about 50 A for both of these rather different pure detergent micelles. Here again we note that the Stokes radius is a rather insensitive indicator of micellar mass or volume, varying as its cube root. Beyond that, however, we note that r,/r, for the TX100 micelle was about 1.5, while for TX305, with its 30 EO units, r.Jre is 2.3. Thus, the relatively greater hydration of the TX305 micelle explains its disproportionately large Stokes radius. That radius is, however, still considerably less than the length of a fully extended TX305 molecule (well over 100 A). Therefore the 30-EO-unit chain is probably not fully extended, but is rather folded, as suggested by Rosch (20). If the EO chain is likewise folded in the mixed micelles, it will effectively mask an area of the mixed micellar surface which is much larger than its molecular cross section. In this regard it is noteworthy that when sphingomyelinase was applied to the SPM/TX305 system, no significant hydrolysis of the phospholipid was observed. This is unlike the SPM/ TX100 system, where the hydrolysis of the SPM was facilitated by the detergent; the enzymatic activity was maximal at an optimal SPM/TXlOO ratio which provided an optimal surface density of the substrate (7). Beyond this density the SPM molecules are organized in a too dense structure, approaching that of a liposomal bilayer, where the enzymatic utilization of

COOPER

the SPM is very poor (6, 7). As observed above, in the SPM/TX305 system the hydrolysis of the phopholipid was very poor even at elevated ratios of detergent to lipid, even though the TX305 (like the TXlOO) works to decrease the surface density of the lipid substrate. This might indicate that the 30-unit EO chain interferes sterically, preventing enzyme-substrate interaction. Notwithstanding the differences between the two systems, the behavior of the TX305 system is by and large qualitatively similar to that of the TX100 system, suggesting a general pattern for the behavior of mixed micelles of a lipid and a nonionic detergent. Of special inherent interest is the twophase behavior that is manifested. This strongly underlines what was already implicit in the earlier work, that the mixed micelle is a distinct state of the constituents that is highly ordered and highly stable. With TX305 as detergent, two such distinct states are manifest, and they apparently preserve their unique characteristics over a wide range of mixture ratios. The underlying causes of this ordering are certainly worthy of further investigation. APPENDIX I. THE DERIVATION MICELLAR PARAMETERS IN SEARCH PROCEDURE

OF THE

In addition to the measured sedimentation coefficients, S, and S,, the concentrations of the two phases, C, and C,, are known from the Schlieren trace areas, and from the fact that their sum equals the sum of the overall concentrations of the constituents, C(TX) and C(SPM). The computer-assisted search had to be carried out with the minimum number of parameters needed to express all the micellar properties, both experimental and derived. As we now show, only two parameters are required. For convenience we have chosen the ratio of the molecular weights of the two species, R = Ma/M,, and the concentration of TX305 in phase (Y, CJTX). All micellar properties, including those that provide the comparison with the experimental data, can be ex-

TWO

PHASES

OF

SPHINGOMYELIN/TRITON

pressed in terms of these two parameters and known experimental data. Consider first the diffusion coefficients. The avera:ge diffusion coefficient we have measured is weighted according to the scattering intensity from each phase (10): Do = DA. + DsIa I, + Ip *

[AlI

The scattering intensities of the two phases, I, and Ip can be replaced by C,M, and C&V,, respectively (common proportionality factors cancel) (21), giving

X-305

MICELLES

199

Thus, the compositions of the two phases are expressed in terms of experimentally determined quantities and the arbitrarily chosen parameter, CJTX). (Note that all calculations ignore the CMC. It will be much lower than any of the concentrations involved here.) The concentration ratios in each species of micelle are given by X,(TX)

= C,(TX)/C,

[A81

X,(TX)

= CB(TX)/C,.

[A91

and

From these expressions we can in turn determine the factors 6, and 6, according to Eq. [2], still in terms of experimental With the simplifying assumption of simquantities and the two chosen parameters. ilar hydration/nonsphericity in the two Fairly narrow constraints are placed phases, we may write upon the micellar properties by the trivial restriction that no concentration in any phase can be negative. Thus, for example, in the solution at X, = 0.7’7, without any additional constraints, we find that X,(TX) Substituting accordingly in Eq. [A21 yields must lie between 0.7 and 1.0. Consistency with the experimental data narrows the D = D GR2’3 + C, permissible ranges of the micellar prop0 I-441 ’ CaR+CB ’ erties further. The search procedure was carried out Thus, the diffusion coefficient, D,, and as follows: The parameter CJTX) was therefore 11, as well, are expressible in assigned a series of closely spaced values terms of the measured Do, the known in the range permitted by Eqs. [A5]-[A7]. phase concentrations, and R. Consider now the factors 6, and 6,. For each value of CJTX), the ratio R was assigned its own closely spaced series of They are determined by the respective values. This “grid” in the two-parameter compositions of the two phases (cf. Eq. [2]). If we designate the quantities of space was then searched as follows: For TX305 and SPM in phases LY and p as each parameter pair the diffusion coellicients Da and Da were found from Eqs. C.&W, C,WW, and CKW, CdSPM>, [A31 and [A4]. The factors 6, and 6, were then it is a straightforward matter to found from Eqs. [A8], [A9], and [2]. From write down
200

YEDGAR

AND

gregation number of each of the constituents in each of the phases was calculated. For example, NJTX), the number of TX305 molecules in a phase (Ymicelle, was found according to J’JaW)

=

XATWK M tx

,

[A101

where M,, is the molecular weight of a TX305 molecule. The three other aggregation numbers were found from three similar self-evident relationships. We took I&, to be 1290 (5) and the weight of the SPM molecule as 775, as in our earlier paw

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