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Langmuir 2002, 18, 612-617
Determination of Critical Micelle Concentration of Lipopolymers and Other Amphiphiles: Comparison of Sound Velocity and Fluorescent Measurements Aba Priev,† Samuel Zalipsky,‡ Rivka Cohen,† and Yechezkel Barenholz*,† Laboratory of Membrane and Liposome Research, Hebrew UniversitysHadassah Medical School, Jerusalem 91120, Israel, and ALZA Corp., Mountain View, California 94039 Received June 25, 2001. In Final Form: November 14, 2001 Critical micelle concentration (cmc) is an important parameter for preparing, solubilizing, and characterizing liposomes, surfactants, and other self-aggregating amphiphiles. We present a comparison between a direct, nondestructive method to determine cmc, in which sound velocity is measured as a function of the concentration of amphiphile, and a commonly used fluorescent method based on two fluorophores (1,6-diphenylhexa-1,3,5-triene (DPH) and 8-anilinonaphthalene-1-sulfonate (ANS)). The ultrasonic method involves accurate measurement of the sound velocity in the amphiphile dispersion and determination of the concentration corresponding to the maximum change in a gradient in the sound velocity. This method does not use a probe (like DPH or ANS), and therefore the contribution of artifacts related to impurities is minimal. Initially we used the ultrasonic method to determine the cmc’s, in several media, of three typical detergents, sodium dodecyl sulfate (SDS), Triton X-100, and Cremophor EL, for which highly reliable cmc values have been reported. The ultrasonic instrumentation, based on a cylindrical resonator method, gives precise and accurate results for the general range of cmc values for detergents (10-3-102 mM) and reflects changes in hydration and compressibility of the amphiphile. We then applied this ultrasonic method to determine the cmc’s of two series of PEGylated lipopolymers used for steric stabilization of liposomes: the neutral distearoyl glycerol and the negatively charged distearoyl phosphatidylethanolamine, both covalently attached to poly(ethylene glycol) (PEG) of Mw 750, 2000, 5000, or 12000. The cmc’s for these PEGylated lipopolymers were in the range 0.008-0.025 mM. cmc values increased 2.5-fold with increase in length of the PEG chain from 15 to 271 oxyethylene units. cmc values were the same when the linker connecting the PEG and the distearoyl moieties was negatively charged or neutral. In a comparative study, the ultrasonic method proved to be superior to commonly used methods in accuracy, speed, and applicability to both ionic and nonionic surfactants, in both aqueous and nonaqueous media.
Introduction The critical micelle concentration (cmc) is the relatively narrow concentration range over which amphiphile dispersions show an abrupt change in physical properties such as electrical conductivity, surface tension, osmotic pressure, density, light scattering, and sound velocity. At concentrations below the cmc, the amphiphile is dissociated. At the cmc, aggregation of the molecules begins to produce a micelle, and the physical properties of the dispersion show changes. Similarly, at the critical aggregation concentration (cac) the amphiphile molecules aggregate to other types of assemblies, such as vesicles. The cmc and cac values depend on intrinsic factors such as structure of the hydrophobic and hydrophilic parts of the amphiphile molecule and external factors such as medium temperature and composition (ionic strength, dielectric constant, pH). Since different experimental methods may reflect this transition to different extents, some systematic variations in operationally defined cmc or cac are expected. Methodological differences may originate from the choice of characteristic property, how the data are plotted, and, when a probe is used, its interaction with the amphiphile.1-4 Therefore, it is important to explore direct, universal methods, such as * To whom correspondence should be addressed. Phone 972 2 6758507. Fax: 972 2 6411663. E-mail:
[email protected]. † Hebrew UniversitysHadassah Medical School. ‡ ALZA Corp. (1) Gelbart, W. M.; Ben-Shaul, A.; Roux D. A. Micelles, Membranes, Microemulsions, and Monolayers; Springer-Verlag: New York, 1997.
the one based on sound velocity measurements, which do not require a probe and which are not sensitive to artifacts introduced by organic solvents. In this study we focus on the cmc determination of lipopolymers and other amphiphiles by means of sound velocity measurements. The application of ultrasonic measurements to studies of the micellization process is quite old.3 However, it has been used for only a limited number of systems because the early ultrasonic devices were not very sensitive and needed a large volume of sample.5 Measurements were time-consuming and limited to high cmc values. The cmc value was determined by the intersection of the two straight lines of sound velocity3,6 (or ultrasound absorption7) above and below the cmc region. However, the precision of such measurement depends on the width of the concentration range that shows the change in physical properties. When this change is slow, it is practically impossible to obtain a single point. In this work, we determined the cmc as the concentration (2) Moroi, A. Micelles. Theoretical and Applied Aspects; Plenum Press: New York, 1992. (3) Shinoda, K.; Nakagawa, T.; Tamamushi, B.; Isemura, T. Colloidal Surfactants; Academic Press: New York, 1963; Chapter 1. (4) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentrations of Aqueous Surfactant Systems; NSRDS-NDS36; National Bureau of Standards: Washington, DC, 1971. (5) Povey, M. J. W. Ultrasonic Techniques for Fluids Characterization; Academic Press: San Diego, CA, 1997. (6) Zielinski, R.; Ikeda S.; Nomura H.; Kato S. J. Colloid Interface Sci. 1987, 119, 398. (7) Frindi, M.; Michels, B.; Levy H.; Zana, R. Langmuir 1994, 10, 1140.
10.1021/la0110085 CCC: $22.00 © 2002 American Chemical Society Published on Web 01/11/2002
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corresponding to the maximum change in a gradient in the sound velocity. With the availability of a new ultrasonic technique based on a resonator method,8 which attains an accuracy of sound velocity of 5 × 10-4 m/s (which is about 100 times better than in previous studies), acoustics has become very attractive. It is the only technique that can provide measurements of sound velocity in sample volumes of 0.01-0.1 mL with sufficient precision. The unique simplicity of the new resonator cells used (developed by NDT Instruments, Jerusalem, Israel) enables one to make the complete measuring unit only a few millimeters in size.9 First we measured the sound velocity of three typical surfactants: the anionic sodium dodecyl sulfate (SDS) and the nonionic Triton X-100 and Cremophor EL. We have selected these surfactant systems because they have highly reliable cmc data. Cremophor EL in 2.5% ethanol and 0.1 M NaCl (as commonly used in drug formulations) was chosen as a system of greater complexity. We then applied this method to determine the cmc’s of six novel lipopolymers used for steric stabilization of liposomes,10 which consist of distearoyl glycerol (DS, neutral) or distearoyl phosphatidylethanolamine (DSPE, negatively charged), each covalently attached to poly(ethylene glycol) (PEG) of Mw 750, 2000, 5000, or 12000, and compared them with cmc’s determined using two different fluorescent probes. Experimental Methods Reagents and Procedure. SDS with a purity of >99% and Triton X-100 were obtained from Fluka; Cremophor EL with a purity of 97% was obtained from Sigma; and DSPE-PEG and DS-PEG of various PEG chain lengths were prepared by ALZA Corporation, Mountain View, CA (Zalipsky et al., to be published). Solutions were made in double-distilled, deionized, and degassed water. cmc values were determined in the following media: water (for SDS, Triton X-100, Cremophor EL, DSPEPEG, and DS-PEG), 0.1 M NaCl (for SDS), and 0.1 M NaCl containing 2.5% ethanol (for Cremophor EL). At least 15 different concentrations of amphiphile were measured to determine the cmc. All determinations were done at 25 ( 0.02 °C. Instrumentation for Acoustic Measurements. The ultrasonic device is composed of two identical acoustic resonator cells, a reference and a sample cell, each with a volume of 0.05 mL. This method employs a standing sound wave in a cavity formed by piezoceramic transducers, which is filled with the sample. The natural frequency fn of this high-quality acoustical resonator is linearly related to sound velocity U:11,12 ∆U ) U0∆fn/ fn, where fn is the frequency of the nth resonance peak of the acoustic cell measured in the sample and U0 is the sound velocity of the reference medium. The half-power width δfn of the nth resonance peak is linearly related to ultrasound absorption R:11,12 ∆Rλ ) ∆(πδfn/fn). Figure 1 is a block diagram of the ultrasonic device developed by NDT Instruments. The device consists of the acoustic cells with a temperature-control system, a computer interface, and a power supply, all installed within a single computer that runs the control and data acquisition software. The resonance frequencies of the acoustical resonator, operated at 3-3.5 MHz, were measured with the aid of a computer-controlled phasesensitive feedback circuit. (8) Sarvazyan, A. P. Annu. Rev. Biophys. Biophys. Chem. 1991, 20, 321. (9) Sarvazyan, A.; Ponomarev, V. Method and apparatus for measuring acoustic parameters in liquids using cylindrical ultrasonic standing. U.S. Patent 5,533,402, 1996. (10) Poly(ethylene glycol). Chemistry and Biological Applications; Harris, J. M., Zalipsky, S., Eds.; ACS Symposium Series 680; American Chemistry Society: Washington, DC, 1997. (11) Eggers, F.; Funck, T. Rev. Sci. Instrum. 1973, 44, 969. (12) Sarvazyan, A. P.; Chalikian, T. V. Ultrasonics 1991, 29, 119.
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Figure 1. Block diagram of acoustical device for precise sound velocity measurements. The acoustical cells are made of radially polarized piezoceramic and a temperature-control system including thermoresistor, Peltier element, and heat sink. The cylindrical tube of the acoustic cell has an inner diameter of 3 mm and a wall thickness of 0.1 mm. Temperature stability in the acoustic cells is the main limitation of precision in measurements of ultrasound velocity. Achieving the required temperature stability (of the order of 10-3 °C) has been one of the primary challenges of our research. High stability can be achieved using a differential measurement method: one acoustical cell is filled with sample and the other is filled with reference medium, and the cells are placed in the thermostated block. The difference between the ultrasound velocities in the sample and the medium is measured. Because of their small volume, these acoustic resonator cells equilibrate rapidly and have only a small temperature difference. Time for each measurement is 60 s. Fluorescent Determination of cmc. The cmc’s of PEGlipids were also measured using two different fluorescent probes, 1,6-diphenylhexa-1,3,5-triene (DPH) and 8-anilinonaphthalene1-sulfonate (ANS), using a Perkin-Elmer LS-50B luminescence spectrometer. In both cases, large increases in fluorescence intensity were observed upon micelle formation. The cmc was determined by linear least-squares fitting of the fluorescence emission at 490 nm, upon excitation at 370 nm (in the case of ANS) or the fluorescence emission at 430 nm, upon excitation at 360 nm (in the case of DPH) versus the amphiphile concentration lower and higher than the change of slope, as previously reported.13,14
Results and Discussion First we determined the cmc’s of three surfactants whose cmc values have been reported in the literature. The selection of surfactants included one anionic detergent, SDS, and one well-defined nonionic detergent, Triton X-100. Both are used extensively to solubilize membrane lipids and proteins. The third surfactant, Cremophor EL, is a complex mixture of surfactants in which the main species is polyoxyethyleneglycerol triricinoleate. Spacefilling models of these molecules are shown in Figure 2. Cremophor EL is commonly used in drug formulations (such as Taxol) for solubilization of hydrophobic or amphiphilic drugs that are poorly soluble in aqueous media. (Recently we found that Cremophor EL micelles are one of the factors that activate the complement system leading to hypersensitivity to Taxol.15) (13) Hertz, R.; Barenholz, Y. J. Colloid Interface Sci. 1977, 60, 188. (14) Esposito, C.; Colicchio, P.; Facchiano, A.; Ragone, R. J. Colloid Interface Sci. 1998, 200, 310. (15) Szebeni, J.; Alving, C. R.; Savay, S.; Barenholz, Y.; Priev, A.; Danino, D.; Talmon, Y. Int. Immunopharmacol. 2001, 1, 721.
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Figure 2. Space-filling models (after free energy minimization, using CS Chem3D software, Cambridge, MA) of SDS (A), Triton X-100 (B), the major component of Cremophor EL (C), and lipidPEG (D).
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determined accurately from the second derivative of the sound velocity curve. The dashed line in Figure 3B corresponds to the second derivative of the sound velocity/ concentration curve, and the arrow denotes the cmc. These values are compared with those obtained by other methods (Table 1). The cmc corresponds to the concentration where the second derivative of the curve in Figure 3B displays a minimum. The value obtained for Triton X-100 was 0.32 mM. Sound velocity values were also obtained for different concentrations of SDS in pure water and in 0.1 M NaCl. Figure 4 shows the first (A) and second (B) derivatives of the sound velocity/concentration curves in these media at 25 °C. Presentation of the experimental results in terms of the sound velocity derivatives or sound velocity number of a surfactant [U] ()(U - U0)/(U0C), where U0 is sound velocity of medium and C is concentration) is useful for discussing changes in hydration and in compressibility of surfactant molecules due to their aggregation state. At low concentrations of surfactant, the value of [U] is constant, corresponding to the monomer form of the surfactant. At concentrations higher than the cmc, the value of [U] decreases because of micelle formation. Sound velocity number is the sum of an instantaneous part [U]∞, which is mainly caused by the intermolecular interactions, and a relaxational part, caused by pressure-induced changes in the structure of the system and energy dissipation [U]Rel:22,23
[U] ) [U]∞ + [U]Rel
Figure 3. Changes of sound velocity data (A) for Triton X-100 and its derivatives (B). Arrow denotes cmc value.
In Figure 3A, the sound velocity values obtained for different concentrations of Triton X-100 in water at 25 °C are plotted on a log-log scale. Like many other physical properties of surfactant dispersions, the sound velocity changes with surfactant concentration at a different rate below and above the cmc, and experimental points fit two straight lines of different slopes. As shown in Figure 3A, this change of slope occurs at a Triton X-100 concentration of ∼0.3 mM. To obtain a more precise value of cmc, the second derivative of the sound velocity was calculated. Sound velocity of the dispersion in the cmc region varies in a continuous manner, as do all derivatives of it (Figure 3B). Despite the broad transition range, the cmc can be
Factors such as absorption and scattering of ultrasound waves influence the relaxational part of sound velocity measurements. But this occurs only at high concentrations and frequencies. For example, for particles with diameter 65-93 nm, there is a scattering phenomenon influence on the ultrasound attenuation only at frequencies greater than 30 MHz.24 Suspensions with concentrations close to the cmc (less than 0.3 mg/mL) and at frequencies used in our device (about 3 MHz, with wavelength 104-105 times larger than the size of micelles) have ultrasonic absorption close to that of water. In all our dilute amphiphile dispersions we did not find any significant excess ultrasound absorption that can influence sound velocity measurements. Micelle formation of surfactants in aqueous media occurs because reduction of the hydrocarbonwater interface is energetically favored. The cmc is that concentration at which the thermodynamic interaction between the hydrophobic moieties of the surfactant molecules is balanced by the hydration and/or electrostatic repulsive effects of hydrophilic headgroups. Thus, hydrophobic forces control the formation of micelles, while hydration and electrostatic forces limit the maximum size that micelles can reach under given conditions.1,3 (16) Mukerjee, P. Adv. Colloid Interface Sci. 1967, 1, 241. (17) Kalmanzon, E.; Zlotkin, E.; Barenholz, Y. In Handbook of Nonmedical Applications of Liposomes; Lasic, D. D., Barenholz, Y., Eds.; CRC Press: Boca Raton, FL, 1995; Vol. 4, p 183. (18) Cifuentes, A.; Bernal, J. L.; Diez-Masa, J. C. Anal. Chem. 1997, 69, 4271. (19) Perez-Rodriguez, M.; Prieto, G.; Rega, C.; Varela, L. M.; Sarmiento, F.; Mosquera, V. Langmuir 1998, 14, 4422. (20) Paula, S.; Sus, W.; Tuchtenhagen, J.; Blume, A. J. Phys. Chem. 1995, 99, 11742. (21) Kessel, D. Photochem. Photobiol. 1992, 56, 447. (22) Sarvazyan, A.; Hemmes, P. Biopolymers 1979, 18, 3015. (23) Tirosh, O.; Barenholz, Y.; Katzhendler, J.; Priev, A. Biophys. J. 1998, 74, 1371. (24) Stieler, T.; Scholle, F.-D.; Weiss, A.; Ballauff, M.; Kaatze, U. Langmuir 2001, 17, 1743.
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Langmuir, Vol. 18, No. 3, 2002 615 Table 1. cmc Values for SDS, Triton X-100, and Cremophor EL at 25 °C cmc, mM
surfactants
Mw
sound velocity
SDS in water SDS in 0.1 M NaCl Triton X-100 in water Cremophor EL in water Cremophor EL in 0.1 M NaCl and 2.5% ethanol
283 283 650 ≈2500 ≈2500
8.35 2.0 0.32 0.040 0.028
DPH (fluorescent) 2.0 0.12 0.039
lit. (not DPH)
source
8.0-8.4 1.9 0.30 0.039
17, 18, 19 20 16, 20 21
Table 2. cmc Values for DS-PEGs and DSPE-PEGs at 25 °C cmc, mM lipid
Mw
DSPE-PEG750 1494 DSPE-PEG2000 2774 DSPE-PEG5000 5774 DSPE-PEG12000 12774 DS-PEG750 1400 DS-PEG2000 2650 DS-PEG5000 5650 DS-PEG12000 12650
Figure 4. First (A) and second (B) derivatives of the sound velocity/concentration curve for SDS in water and in 0.1 M NaCl. Arrows denote cmc values.
According to the pseudo-phase model for micelle formation,4,25 at concentrations of surfactant in monomer form above the cmc, the concentration of monomers is constant and equal to the cmc value. The value of the sound velocity number can be given as the sum of contributions from the surfactant in the monomer and micellar states
[U]Ccmc ) Vm - Km/2β0 - 1/2F0 cmc(2β0(Vm - V1) - (Km - K1))/2β0C where Vm and Km are specific volume and compressibility, respectively, of surfactant molecules in the micelle. The large loss of bound water and changes in aggregation state of surfactants lead to a decrease in [U]. For the ionic SDS, ∆[U] of micelle formation is 0.633 mL/g (Figure 4A) or 10.1 × 10-3 mL/g per molecule. While for the nonionic Triton X-100, the acoustical effect (∆[U]) of micelle formation is about 1/5 of that (0.259 mL/g or 1.9 (25) Kudryashov, E.; Kapustina, T.; Morrissey, S.; Buckin, V.; Dawson, K. J. Colloid Interface Sci. 1998, 203, 59.
DPH ANS sound (fluorescent) (fluorescent) velocity 0.005 0.010 0.010 0.018 0.008 0.010 0.012 0.020
0.025 0.025 0.020 0.015 0.020 0.020 0.018 0.015
0.008 0.010 0.015 0.020 0.010 0.015 0.015 0.025
× 10-3 mL/g per molecule). Thus, the acoustical effect of micelle formation depends on hydration and charge of monomers. The cmc value of SDS, calculated as the minimum of the second derivative of the sound velocity, is 8.35 mM (Table 1). This value agrees well with those found in the literature, i.e., 8.0-8.4 mM.15,16 In 0.1 M NaCl, the cmc is 2.0 mM. Increasing ionic strength leads to higher aggregation numbers because of better shielding of the negatively charged headgroups. This value is lower than the cmc for SDS in water and similar to the value of 1.9 mM found in the literature for the same conditions.20 A curve of similar shape was obtained when the sound velocity was plotted versus different concentrations of Cremophor EL in water at 25 °C, and these results are given in Table 1. In this case the cmc value was 0.040 mM, which is in good agreement with the value found in the literature under the same conditions, i.e., 0.039 mM.21 The cmc’s for the DS-PEGs and DSPE-PEGs, calculated from sound velocity measurements, are presented in Table 2. They are in the range 0.008-0.020 mM for DSPE-PEGs and 0.010-0.025 mM for DS-PEGs. cmc values increase with increasing molecular weight of PEG moiety. But the effect of an 18-fold increase in the length of the polar headgroup (PEG) on the cmc is rather small (only 2.5-fold increase). This may be related to the fact that when PEGylated lipids form micelles their PEG moiety is largely in the extended brush border form;23 thus increasing PEG chain length does not greatly increase headgroup cross section. Measurement of surface potential of the micelles using 4-heptadecyl-7-hydroxycoumarin (a probe for surface potential located at the water/lipid interface) indicates that DSPE-PEG micelles are strongly negatively charged while DS-PEG micelles are not charged (Cohen R., Barenholz Y., unpublished data). Therefore the effect of PEG length on cmc is much smaller than expected from other amphiphiles having an inorganic headgroup. Comparing the two series of lipopolymers in this study shows that the only structural difference between them is in the groups which link the PEG and the distearoyl moiety (Figure 5). In the DSPE-PEG series the linker is negatively charged due to the phosphate diester, while in
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Figure 5. Structures of DSPE-PEG (top) and DS-PEG (bottom). The average number of oxyethylene units within brackets is 15, 44, 112, and 271 for derivatives of PEG750, -2000, -5000, and -12000, respectively.
the DS-PEG series there is no charge on the linker group. The fact that the cmc values in these two series are almost identical despite the large difference in surface potential and are affected by the length of the PEG chain to the same extent (Table 2) indicates that the charged phosphate group is hidden and, as was suggested by Woodle et al.,26 the inter-PEG interaction overrides the repulsion between the phosphate moieties. Finally, we compared our method of cmc determination with widely used methods based on interaction of the micelles with a fluorophore. We used two different fluorescent probes, DPH and ANS. For both fluorophores, a large increase in fluorescence intensity due to micelle formation was observed. Our measurements of cmc by these two fluorescent methods disagreed with each other. Values obtained with ANS (Table 2) were, in general, higher than those obtained with DPH, especially for the DSPE-PEG. Correlation of acoustic measurements with the results of fluorescent methods was good for the DPH probe only. This may be related to the fact that DPH is located in the hydrophobic part of the micelle,13 while ANS is adsorbed to the interface region of the micelle.12 Therefore the higher value may reflect electrostatic repulsion of the probe, which is negatively charged, from the negatively charged micelle surface. This pinpoints one of the major drawbacks of fluorescent cmc determinations, which are dependent on the mode of interaction of the surfactant with the fluorophore.3,4 In the study of the PEG-lipids we calculated cmc values as the point of intersection between two lines representing concentration-dependent fluorescence intensity, one when micelles are negligible and the other when additional amphiphile is in the form of micelles, and therefore the slope of the second line is much higher than that of the first.13,27 This is demonstrated in Figure 6. cmc measurements for DSPE-PEG2000 using turbidity measurements26 and for DSPE-PEG5000 using DPH fluorescence measurements28 found in both cases that cmc is below 20 µΜ and in a good agreement with our cmc values described in Table 2 using sound velocity. Although cmc values from sound velocity measurements are somewhat larger than those from DPH fluorescent measurements, they are similar. The lower value for (26) Woodle, M. C.; Collins, L. R.; Sponsler, E.; Kossovsky, N.; Papahadjopoulos, D.; Martin, F. J. Biophys. J. 1992, 61, 902. (27) Chattopadhyay, A.; London, E. Anal. Biochem. 1984, 139, 408. (28) Uster, P. S.; Allen, T. M.; Daniel, B. E.; Mendez, C. J.; Newman, M. S.; Zhu, G. Z. FEBS Lett. 1996, 386, 243. (29) Sou, K.; Endo, T.; Takeoka, S.; Tsuchida, E. Bioconjugate Chem. 2000, 11, 372.
Figure 6. Dependence of fluorescence intensity, using DPH probe, on concentration of DSPE-PEG750 (A) and DSPEPEG5000 (B). Only points close to cmc are plotted, although additional measurements were made up to concentrations of 10 mM.
the latter is the result of the hydrophobic DPH becoming a part of the micelle, which is a drawback of this method. Compared to detergents, PEG-lipids exhibit a narrower transition region at the cmc, which is due to the much higher aggregation number of these surfactants, attributable to their having two long acyl chains (Figure 2). Conclusions 1. Sound velocity is a useful empirical parameter that can be employed to monitor processes in which hydration and compressibility of amphiphiles are modified. Sound velocity measurements at a broad range of amphiphile concentrations have been made on SDS, Triton X-100, Cremophor EL, and lipopolymers (DS-PEG 750-12000 and DSPE-PEG 750-12000), and their cmc’s calculated. The results obtained in this study establish sound velocity measurements as the preferred technique for determination of cmc values in the range 10-3-102 mM on microliter volumes of sample. The procedure is simple, rapid, and does not require introducing an external probe. Furthermore, it is readily automated. 2. The proposed method permits determination of the cmc in ionic as well as in nonionic systems and in different mixtures of aqueous and nonaqueous media, but it is necessary to conduct very careful measurements under accurate temperature control. 3. cmc values of DSPE-PEG and DS-PEG series are similar, slightly increasing with increase in PEG moiety length, but independent of whether the PEG linker group is negatively charged or neutral, suggesting that the two series may be interchangeable in their capacity to induce steric stabilization of liposomes and other lipid assemblies or to serve as an anchor for ligand binding in order to achieve active targeting of liposomes.12
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Acknowledgment. This study was supported in part by ALZA Corp., Mountain View, CA, and by US-Israel Binational Science Foundation Grant 1999324. We thank Armen Sarvazyan (NDT Instruments, Jerusalem, Israel)
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for supplying the ultrasonic cells and Sigmund Geller for editorial assistance. LA0110085
