Langmuir 1994,10,4391-4393
Unilamellar Vesicle Diameter and Wall Thickness Determined by Zimm’s Light Scattering Technique John H. van Zanten Polymers Division, Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 Received March 1, 1994.In Final Form: July 22, 1994@
Introduction Surfactant vesicles are of current interest because of their potential application in technologies such as drug delivery and targeting,’ medical imaging,2~ a t a l y s i sand ,~ separation^.^ Unilamellar vesicles are closed-membrane capsules most often consisting of a single bilayer of noncovalently assembled surfactants encapsulating an aqueous core. The performance of vesicle preparations is strongly influenced by dispersion properties such as the surface area and encapsulated volume. These geometric properties in turn depend on the vesicle diameter, wall thickness, and vesicle concentration. The determination of these properties solely within the framework of Zimm’s light scattering technique is reported here for the first time. One should note that one of these properties, the wall thickness, has a length scale of only 30-50 A, and therefore it is quite remarkable that a light scattering technique is capable of determining this length to within several angstroms of the value determined by X-ray diffraction. Surfactant vesicle dispersions have typically been characterized by dynamic light scattering methods.6 These techniques allow for sufficiently accurate determination of the average vesicle diameter and have some success in determiningthe degree of polydispersity present in the vesicle dispersion. Prior to 1990, static light scattering investigations of vesicle dispersions appear to have been plagued by aggregate contamination and polydispersity problems.6-8 The advent of methodologiesg to produce essentially size monodisperse vesicles has facilitated their study by static light scattering methods.lOJ1 These previous investigations indicate that vesicles produced by detergent dialysis are essentially size monodisperse hollow spheres as determined within the Rayleigh-Gans-Debye (RGD)approximationof classical light scattering.12 One of these previous reports outlines a combined RGD approximation and Zimm analysis13 @
Abstract published in Advance ACS Abstracts, September 15,
1994. (1) Poste, G.; Papahadjopoulos, D. In
Uses of Liposomes in Biology and Medicine; Gregoriadis, G., Allison, A., Eds.; Wiley: London, 1979; p 101. (2) Mauk, M. R.;Gamble, R. C. Anal. Biochem. 1979,94, 302. (3) Fendler, J. H. Biomimetic Membrane Chemistry.; WileyInterscience: New York, 1982. (4) van Zanten, J. H.; Monbouquette,H. G. Biotechnol. Progr. 1992, 8, 546. ( 5 ) Ruf, H.; Georgalis, Y.; Grell, E. In Methods in Enzymology; Fleischer, S., Fleischer, B., Eds.;Academic Press: New York, 1989;Vol. 172, p 364. (6)Attwood, D.; Saunders, L. Biochim. Bwphys. Acta 1965,98,344. (7) Chong, C. S.; Kolbow, K.Biochim. Biophys. Acta 1976,436,260. (8) Herrmann, U.; Fendler, J. H. Chem. Phys. Lett. 1979, 64, 270.
(9)Milsmann, M. H.; Schwender, R. A.; Weder, H. G. Biochim. Biophys. Acta 1978, 512, 147. (10) van Zanten, J. H.; Monbouquette,H. G. J . Colloid Interface Sci.
1991, 146, 330. (11) van Zanten, J. H.; Monbouquette, H. G. J.Colloid Interface Sci. 1994,165,512. (12) Aragon, S. R.;Pecora, R.J . Colloid Interface Sci. 1982,89,2395. (13)Zimm, B. H. J . Chem. Phys. 1948, 16, 1093.
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method for determining the vesicle diameter, wall thickness, and weight-average molecular weight.” In this paper, the feasibility of determining these parameters solely within the Zimm analysis of static light scattering measurements is demonstrated.
Materials and Methods Production in Phosphatidylcholine Vesicles by Detergent Dialysis. Phosphatidylcholine vesicles, or liposomes, were prepared via detergent dialysi~.~JOJ~ The essentially size monodisperse vesicles were prepared by continuously dialyzing approximately 12 mL of a mixed micellar solution consisting of 250 mg of L-a-phosphatidylcholine (Sigma; from soybeans) and varying amounta of sodium cholate (Sigma) in 0.1% wlw NaC1. Phosphatidylcholine is a naturally occurring membrane phospholipid which forms bilayer structures. Varying the phosphatidylcholindsodium cholate ratio allows variation of the size of the vesicles produced here. The dialysis was carried out in a Liposomat apparatus (MM Developments). Static Light Scattering Measurements. Static light scattering measurements were performed with the commercially available Dawn F Laser Photometer (Wyatt Technology). The light source was vertically polarized He-Ne laser light with a wavelength in vacuo of 6328 A. The NaCl solution used in the dilutions was repeatedly filtered through 0.1p m syringe filters until the solvent background noise consisted of less than 0.1% of the total scattered intensity. Additionally, the vesicle dispersions were filtered through 0.2 pm membrane syringe filters prior to all light scattering investigations. Zimm plots were prepared with the Dawn-F,Skor-F, and Aurora soRware packages (Wyatt Technology). The dnldc value, which is required for Zimm plot analyses, was determined to be 0.160 cm3lg by static refractometry. The vesicle dispersions used in the determination of dnldc had been extensively dialyzed. Therefore, essentially all of the sodium cholate was removed prior to any measurements.
Determining the Vesicle Radius and Wall Thickness within Zimm’s Approximation for Light Scattering from Macromolecular Solutions Zimm’s analysis of static light scattering data is a wellknown method for characterizing macromolecules in solution. Zimm’s approximation for scattering from macromolecular solutions assumes that intermacromolecule interactions occur only through single contacts. Therefore, this approximation is only applicable to dilute solutions. In this approximation the light scattered by a dilute solution of scatterers can be described by the following expression.13
162R; sin2(8/2 1) 3A2
+ 2Bc
(1)
where K is an optical constant, c is the concentration, Re is the Rayleigh ratio, 8 is the scattering angle, A is the wavelength of the incident radiation in solution,RGis the radius of gyration, M, is the weight-average molecular weight, and B is the second virial coefficient. If one measures the intensity of scattered light from several dispersions of different concentrations, it is, in principle, possible to determine the radius of gyration, weightaverage molecular weight, and second virial coefficient of the scatterers. In this paper, the emphasis is on the first two quantitites, which can be interpreted in terms of the two geometric properties of surfactant vesicles, namely the vesicle radius and wall thickness. The radius of gyration of a vesicle, or hollow sphere, can be expressed in terms of the geometric radius and
0743-7463l9412410-4391$04.50l0 0 1994 American Chemical Society
Notes
4392 Langmuir, Vol. 10, No. 11, 1994 1.00
0.95
0.90
M
RG R
Msphm
0.85
0.80
0.75
R
Figure 1. Influence of the vesicle radius and wall thickness on the radius of gyration and molecular weight. Here the two dimensionless quantities,RJR (radius gyratiodradius ratio) and M/Msphe,(vesiclemolecular weightholid sphere molecular weight ratio), are calculated as a function of 6/R,the wall thicknesdradius ratio. It is apparent that while both quantities are dependent on the 6/R parameter, it is the molecular weight which is most sensitive. For phosphatidylcholine vesicles prepared by detergent dialysis, typically 6IR I0.2. 3.40 10'
I
3.20 10'
3.00 10'
i
2.80 10'
2.60 10'
i
f----d
L
2.40 10'
0
0.25
0.5
0.75
1
1.25
1.5
I
1.75
s i n 2 ( O / 2 ) + 14.30~
Figure 2. Zimm plot of light scattering by vesicles. The weight-average molecular weight for this vesicle dispersion is estimated as 39.6 x lo6 g/mol, while the radius of gyration is 38.8 nm. The symbols correspond to the following vesicle dispersion concentrations: ( 0 )4.82 x gImL, (0)5.37 x gImL,).( 6.07x lo-* g/mL, and (0) 6.98x g / d . These concentrations are typical of the concentrations considered in this study.
wall thickness in the following manner:
sensitivity of the radius of gyration and molecular weight to the vesicle radius and wall thickness is shown in Figure 1. It is apparent that when 6lR < 0.2, as is typically the case for detergent dialysis vesicles, these two quantities are very sensitive to this ratio, which makes surfactant vesicles ideal candidates for this extended Zimm analysis approach.
3 2 1 - (1 - S/R)5 R; = -R 5 1 - (1 - 6/R)3 While the molecular weight is given by
M
4 H A
= 3 - ( 3 R 2 6 - 3RS2
+ d3)
(3)
where R is the vesicle radius, 6 is the wall thickness, NA is Avogadro's number, and Y is the specific volume of a vesicle (-1 cm3/g), which can be determined by hydrodynamic methods.14 It is apparent that if one can accurately determine the radius of gyration and weightaverage molecular weight of essentially size monodisperse vesicles via light scattering measurements, then in principle one can determine the vesicle radius and wall thickness (-40 A) from these same measurements. The (14)Newman, G.C.;Huang, C. Biochemistry 1975,14, 3363.
Results and Discussion Five different vesicle preparations ranging in size from 66 to 87 nm in diameter (i.e.as determined from the RGD approximation by assuming a wall thickness of 36 A>were considered in this study. The light scattering behavior of each vesicle preparation was measured at several different concentrations. Measurements a t several different concentrations allow the extrapolation of the measured scattered intensity to zero angle and zero concentration as required by Zimm's method. A typical Zimm plot for a phosphatidylcholine vesicle dispersion is shown in Figure 2. The radius of gyration is determined from the extrapolation to zero angle for the case of zero concentra-
Langmuir, Vol. 10, No. 11, 1994 4393
Notes
1
5
3
1
9
( 2 -2(6 / R ) +16 I R)')
( 3 ( 6 / R )-3f6 /R)' + ( 6 / R ) ' )
Figure 3. Relation between vesicle radii and wall thicknesses. The observed trend of decreasing vesicle wall thickness with
increasingvesicle radii is interpretedwithin the approximation defined by eq 4. The linearity of this plot is a strongindication that it is geometric packing constraints which lead to the observed trend. Table 1. Vesicle Radii and Wall Thicknesses Calculated from Zimm Plot Paramete*
RG (A) 312 332 362 388 416
M (g/mol) 26.8 x 30.0 x 35.1 x 39.6 x 45.5 x
lo6
lo6
lo6 lo6 106
6 (A) 36.0 35.5 35.0 34.3 34.3
R (A) 329 349 379 405 433
The vesicle radii and wall thicknesses were calculated from eqs 2 and 3. These simultaneous, nonlinear equations were solved via Newton's method.ls The vesicle specific volume was taken to be 0.9848 cm3/g14J7throughout the calculations. a
-
-
tion. The molecular weight can be determined from either of two extrapolations, 8 0 when c = 0 or c 0 when 8 = 0. For all five vesicle dispersions examined, the weightaverage molecular weights determined by either extrapolation agreed exactly. This agreement is an indication of the accuracy of the molecular weight determinations considered here. Once the radius of gyration and weight-average molecular weight of the vesicles are known, eqs 2 and 3 can be solved simultaneously to determine the outer radius and wall thickness of the vesicle^.'^ This was done for all five vesicle preparations considered here, and the results of these calculations are shown in Table 1. It is the molecular weight which has the strongest influence on (15)Burden, R. L.;Faires, J. D. Numerical Methods, 3rd ed.; PWS Publishers: Boston, 1985.
the vesicle wall thickness determined by this method. The weight-average molecular weights determined here are very accurate as indicated by the fact that both of the available extrapolation procedures yield the same value for this quantity. The calculated wall thicknesses are all in the vicinity of 36 A, confirming the X-ray diffraction value found by Wilkins et a1.I6 Interestingly, however, Huang and Mason1' calculated their shell thickness, 37 A, for vesicles which were approximately 99 A in radius, which is much smaller than any of the vesicles considered here. In light of this observation, the results of Table 1 appear to indicate that the wall thickness of a phosphatidylcholine vesicle decreases with increasing vesicle size (the estimated errors in the calculated wall thicknesses are on the order of 0.1-0.3 A, a result which does not negate this observation). This phenomenon of decreasing wall thickness with increasing vesicle size may be a result of lipid packing constraints. Indeed, if one assumes that each lipid molecule, whether located in the inner or outer portion of the bilayer, occupies the same volume and has the same head group area, the following relation will hold true.
+
VI 2 - 2(6/R) ( c ~ / R > ~ R=3A1 3(6/R)- 3 ( ~ 3 / R ) ~(6/R)3
+
(4)
Here VI denotes the volume which each lipid occupies in the bilayer, and A1 is the area each lipid occupies at the vesicle surface. The linearity of the plot shown in Figure 3 demonstrates the agreement between the wall thickness trend noted here and in eq 4. If one further pursues the implications of expression 4, it is apparent that increasing the size of a vesicle which obeys this condition will lead to a vesicle wall thickness which will decrease until it reaches a limiting value. Utilizing a phosphatidylcholine lipid volume of 1253 A3 l7 allows the head group area to be estimated as 72 A2,which is in excellent agreement with other experimentally measured values. This suggests that the wall thickness trend that is observed here is due to lipid packing constraints. It may prove interesting to investigate further the validity of this trend with small-angle X-ray or neutron scattering,which would yield a direct measurement of the wall thickness, utilizing vesicles in a broader size range, such as 500-1250 A in diameter. Acknowledgment. The author acknowledges the support of the NRC-NIST Postdoctoral Research Associateship Program during the completion of this work. The author also thanks Professor Hal Monbouquette for many insightful discussions. (16) Wilkins,M. H. F.; Blaurock, A. E.; Engelman, D. M. Nature New
BWZ. 1971,230,71. (17)Huang, C . ; Mason, J. T. Proc. Natl. Acad. Sci. U S A . 1978,75, 308.
