4704
Langmuir 1996, 12, 4704-4708
Topology of Multivesicular Liposomes,
a Model Biliquid Foam
M. S. Spector and J. A. Zasadzinski*
Materials Research Laboratory and Department of Chemical Engineering,
University of California, Santa Barbara, California 93106
M. B. Sankaram
DepoTech Corporation, 10450 Science Center Drive, San Diego, California 92121
Received March 8, 1996. In Final Form: June 30, 1996X
Freeze-fracture electron microscopy was used to characterize the microstructure of a novel multivesicular
liposome (MVL) currently under investigation as a depot-type drug delivery vehicle. The interior of the
MVL includes bilayer-enclosed, water-filled compartments surrounded by an encapsulating outer membrane.
The contacts between compartments exhibit tetrahedral coordination analogous to a gas-liquid foam that
persists to the bilayer level, and the compartments take on a variety of polyhedral shapes and sizes. Close
examination of the distribution of polyhedra shows that it is nearly identical to theoretical predictions and
computer simulations of polytetrahedral random close packing. As such, the MVL structure is one of the
first experimental visualizations of the polytetrahedral random close packed molecular structure predicted
for liquids and metallic glasses.
Encapsulating drugs in conventional liposomes allows
for long-term release of drugs at therapeutic dosages, while
avoiding fluctuating or toxic levels in vivo.1 A recently
developed multivesicular liposome, or MVL, includes
hundreds of bilayer-enclosed, water-filled compartments
(see Figure 1) and is designed to be a depot to localize
drug delivery to affected areas, while avoiding uptake by
the reticuloendothelial system.2,3 MVLs are formed by
first emulsifying a mixture of an aqueous phase containing
the compounds to be encapsulated and an organic phase
containing lipids.2-4 The first emulsion is then dispersed
and emulsified in a second aqueous phase.2 After the
organic solvent is evaporated, numerous sub-micrometerto micrometer-sized water compartments are separated
by lipid bilayers and take on a close-packed polyhedral
structure (see Figure 1). The compartments in these
MVLs efficiently entrap a variety of water soluble
compounds that then slowly permeate through the
bilayers.2-5 MVLs are currently in clinical testing for
sustained intrathecal release of cytarabine for cancer
treatment, and there is great interest in how the structure
and stability of the MVL influence the rate of drug
delivery.3
In this paper, we show that the structure of MVL is
governed by simple but general topological constraints in
analogy to gas-liquid foams, simple liquids, and metallic
glasses.6-10 Freeze-fracture images of MVLs provide direct
* To whom correspondence should be addressed: Department of
Chemical Engineering, University of California, Santa Barbara,
California 93106-5080; phone, 805-893-4769; fax, 805-893-4731;
e-mail, [email protected].
X Abstract published in Advance ACS Abstracts, August 15, 1996.
(1) Lasic, D. D. Liposomes: From Physics to Applications; Elsevier:
Amsterdam, 1993.
(2) Kim, S.; Turker, M. S.; Chi, E. Y.; Sela, S.; Martin, G. M. Biochim.
Biophys. Acta 1983, 728, 339-352.
(3) Kim, S.; Howell, S. B. Cancer Treat. Rep. 1987, 71, 447-456.
Kim, S.; Chatelut, E.; Kim, J. C.; Howell, S. B.; Cates, C.; Kormanik,
P. A.; Chamberlain, M. C. J. Clin. Oncol. 1993, 11, 2186-2190. Grayson,
L. S.; Hasbrough, J. F.; Zapata-Sirvent, R.; Roehrborn, A.; Kim T.; Kim,
S. Critical Care Medicine 1995, 23, 84-90.
(4) Szoka, F.; Papahadjopoulos, D. Annu. Rev. Biophys. Bioeng. 1980,
9, 467-502. Lichtenberg, D.; Barenholz, Y. Meth. Biochem. Anal. 1988,
33, 337-343.
(5) Ostro, M. J.; Cullis, P. R. Am. J. Hosp. Pharm. 1989, 46, 15761580.
S0743-7463(96)00218-1 CCC: $12.00
visual confirmation that the compartment contacts are
tetrahedrally coordinated, as dictated by rules set down
by Plateau in the last century;9 somewhat surprisingly,
the tetrahedral coordination between bilayers persists to
the molecular scale. The compartment shapes then take
on the most dense packing consistent with the rules of
Plateau.9-14 From the measured distribution of polyhedral
facets of the MVL, we show that the distribution of
compartment shapes is in near perfect agreement with
theoretical predictions and computer simulations of
random close packing of polytetrahedra.10,13,14 Theory
predicts that the average number of edges per face of the
random close packed polytetrahedra is 5.104;10,14 our
measured value is 5.1. Hence, the observed MVL structure
takes on a predicted minimum energy configuration and
should be at least a metastable structure for a given
distribution of polyhedral cells.18 This polytetrahedral
random close packed structure of the MVL is a direct
analog of the predicted molecular structures of simple
liquids13,15 and metallic glasses,10 although the foam, being
subject to topological changes due to changes in cell size
(6) Wilson, A. J. Foams: Physics, Chemistry and Structure; SpringerVerlag: Berlin, 1989.
(7) Sebba, F. Foams and Bi-liquid FoamssAphrons; Wiley: New
York, 1987.
(8) Weaire, D. New Sci. 1994, 142, 34-42; Philos. Mag. Lett. 1994,
69, 99-102.
(9) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John
Wiley and Sons: New York, 1990; Chapter 14.
(10) Nelson, D. R.; Spaepen, F. Solid State Phys. 1989, 42, 1-90.
(11) Thomson, W. (Lord Kelvin) Philos. Mag. 1887, 24, 503-524.
(12) Weaire, D.; Phelan, R. Philos. Mag. Lett. 1994, 69, 107-110.
(13) Finney, J. L. Proc. R. Soc. London, Ser. A 1970, 319, 479-493.
(14) Coxeter, H. S. M. Ill. J. Math. 1958, 2, 746-763.
(15) Bernal, J. D. Nature 1959, 183, 141-147; note especially the
similarity between Figure 6 of this paper and Figure 1 here; Proc. R.
Soc. London, Ser. A 1964, 280, 299-322.
(16) Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. Phys. Rev.
Lett. 1984, 53.
(17) Zallen, R. The Physics of Amorphous Solids; Wiley: New York,
1983; Chapter 2. Hales, S. Vegetable Staticks; Innys and Woodward:
London, 1727.
(18) Bilayers of the same composition as the MVL will typically form
a bulk lamellar phase in excess water at true equilibrium. Simple
unilamellar and multilamellar vesicles and liposomes in water are also
quite often metastable. For a discussion see ref 19. Here, the MVL is
metastable as it takes on the minimum energy configuration given the
specific set of mechanical and chemical steps required to form the
structure.
© 1996 American Chemical Society
Topology of Multivesicular Liposomes
and number due to coarsening, rupture, or coalescence,
has an additional degree of freedom not present in the
theoretical simulations of hard or soft spheres. In addition
to being one of the first direct experimental visualizations
of the random close-packed structure, our statistical
description of MVLs is a starting point for studies of
sustained drug release and MVL stability both in vivo
and in vitro.3
Foams and emulsions have been an area of ongoing
scientific (and practical) interest for decades 6-10 because
their interfacial and rheological properties make them
ideal model systems for studying basic rules of structural
organization. A typical foam is made up of spherical gas
bubbles dispersed in a continuous, usually aqueous
medium, stabilized by a layer of surfactant at the interface.
Emulsions such as MVL are similar, except that both the
internal and external phases are liquids. As the volume
fraction of the interior phase is increased, the boundary
surfaces of the internal compartments come into contact
and flatten and take on a polyhedral shape. Plateau laid
the foundation for the theoretical studies of foam structure
in 1873 by devising a set of rules governing the topological
features of the polyhedra.8,9 In order to be stable against
spontaneous rearrangement, only three faces of the foam
can meet to form an edge and only four such edges can
meet at a vertex. These rules imply that every vertex in
a foam has tetrahedral coordination, with the edges
meeting at an angle of 109° 28′ and the faces meet at an
angle of 120°. The problem is then finding the most dense
packing consistent with these rules.9,10 The solution is
simple in two-dimensions, where Plateau’s rules dictate
that three edges meet at a vertex, giving triangular
coordination. The resulting hexagonal lattice forms the
most dense periodic structure in a plane; hence, a twodimensional foam prefers hexagonal facets.9,10
The situation in three-dimensions is more complicated.
The regular polyhedron that most closely meets Plateau’s
rules is the pentagonal dodecahedron.9,10 However, due
to its 5-fold symmetry, the pentagonal dodecahedron
cannot form a periodic structure that fills space.16 The
incompatibility of the preferred short range order with a
simple global packing is known in condensed matter
physics as “frustration”.10,15,16 Similar packing frustration
due to the incompatibility of local tetrahedral coordination
with global packing order arises in a number of physical
systems including glasses9,15 and quasicrystals.16
The most dense way to regularly pack three-dimensional
space is with rhombic dodecahedra, giving the familiar
face-centered cubic lattice; however, each vertex is connected to six edges, violating the local tetrahedral packing
rules of Plateau.10 In 1887, Lord Kelvin proposed as a
solution the truncated octahedron or tetrakaidecahedron,
whose faces consist of six squares and eight hexagons.11
This polyhedron forms the unit cell of the body-centered
cubic lattice. Recently, a lattice structure with two
different cell shapes dominated by pentagonal faces that
fills space with 0.4% less surface area than the Kelvin
structure was found by Weaire and Phelan.12 Although
the Kelvin and Phelan structures fill three-dimensional
space in a regular manner, both require large distortions
of the preferred tetrahedral angle, violating the local
packing rules of Plateau.
As an alternative, Bernal considered the structure of a
foam in terms of an irregular packing of tetrahedrally
coordinated polyhedra.15 Such a model, called random
close packing (or dense random packing), fills space with
a random arrangement of slightly distorted tetrahedra
(19) Kaler, E. W.; Murthy, A. K.; Rodriguez, B.; Zasadzinski, J. A.
Science 1989, 245, 1371-1374.
Langmuir, Vol. 12, No. 20, 1996 4705
and leads to a distribution of polyhedral shapes.10 Bernal
proposed that such a packing necessarily gives polyhedra
with a predominance of pentagonal faces, which has also
been found in computer simulations.13 Coxeter derived
a statistical model in which he divided space into a regular
honeycomb and showed that, in the simplest model, this
could fill space if each polyhedral face had qideal edges
such that
qideal ) 2π/cos-1(1/3) ) 5.104
(1)
Since the dihedral angle of a tetrahedron is cos-1(1/3),
one needs 2π/cos-1(1/3) of them to fill the 2π radians of
angle around a vertex, or a 5.104 sided polygon.10,13 The
fractional part, or qideal - 5 ) 0.104 represents the closure
failure when packing tetrahedra. While a non-integersided polyhedra is hard to imagine in Euclidean space, it
is interesting to note that qideal is very close to the average
number of edges per face of 5.143 for Kelvin’s tetrakaidecahedron and 5.107 for the Phelan structure and can be
matched physically by a distribution of polytetrahedra.
While theoreticians have debated the best way to
randomly pack space, direct experimental observations
on real foams and emulsions have primarily been limited
to macroscopic model systems.6-10 One of the earliest
recorded experimental measurements of the structural
effects of close packing was performed in 1727 by Hales.17
He allowed fresh peas to swell in a closed pot and observed
the predominance of dodecahedra with pentagonal faces.
More recently, Bernal obtained similar results using
plasticene balls and ball bearings to model the structure
of simple liquids.15 In the classic work by Matzke, an
ideal foam was assembled by individually compressing
thousands of equally sized soap bubbles in a spherical
beaker. By observing the 600 central bubbles, Matzke
was able to establish a catalog of bubble shapes.20 While
67% of the facets were pentagonal, most polyhedra had
a distribution of four- to seven-sided faces.
While the rules of Plateau and the concepts of random
close packing have been verified at the macroscopic level,
theoretical models based on these principles are used to
describe a variety of systems down to the molecular
level.10,15-17 Little experimental work has been done to
verify these packing rules at the microscopic level, even
less at the molecular scale. As foams are usually opaque,
optical microscopy is usually limited to bubbles near the
periphery of the sample and to resolution at the micrometer scale. On the other hand, electron microscopy has
been used to visualize the interior structure of aqueous
microstructures using rapid freezing methods, but freezing
gases have proven difficult.15 MVLs, being a biliquid foam,
are nearly ideal specimens for freeze-fracture replication
techniques, and we can examine the structure at length
scales from about 2 nm to 100 µm.22
MVLs were prepared using a double emulsification
process.2,3 A mixture of dipalmitoyl phosphatidylglycerol,
dioleoyl phosphatidylcholine, cholesterol, and triolein was
dissolved in chloroform. A 0.1 N HCl solution containing
20 mg/mL of cytarabine was added to the chloroform
solution at equal volume (5 mL each). This mixture was
stirred in a high-speed mixer (9000 rpm) to form a waterin-oil emulsion. Twenty milliliters of a solution containing
glucose (32 mg/mL) and lysine (40 mM) was added to the
(20) Matzke, E. B. Am. J. Bot. 1950, 33, 58-92.
(21) Zasadzinski, J. A.; Bailey, S. M. J. Electron. Microsc. Tech. 1989,
13, 309-334.
(22) Chiruvlou, S.; Naranjo, E.; Zasadzinski, J. A. In Structure and
Flow in Surfactant Solutions; ACS Symposium Series 578; Herb, C. A.,
Prud’homme, R. K., Eds.; American Chemical Society: Washington,
DC, 1994; Chapter 5.
4706 Langmuir, Vol. 12, No. 20, 1996
Spector et al.
Figure 1. Electron micrograph of freeze-fracture replica showing a cross section through two multivesicular liposomes. The MVLs
are, on average, about 10 µm in diameter. The polyhedral interior compartments range from about 100 nm to several micrometers.
The bar represents 2 µm.
emulsion and stirred again (4000 rpm) to form a waterin-oil-in-water double emulsion. The chloroform was
evaporated by flushing nitrogen gas over the solution.
The MVLs were isolated by centrifugation at 600g and
washed with 0.9% NaCl solution. Samples for TEM were
prepared using standard freeze-fracture techniques.21,22
A small droplet (0.5 µL) of solution was sandwiched
between two copper planchettes (Baltech, Hudson, NH),
equilibrated in an environmental chamber at 25 °C and
>95% relative humidity,23 and then plunged into liquid
propane cooled by liquid nitrogen.21,22 The samples were
transferred under liquid nitrogen to a Balzers 400 freeze
etch device, where they were fractured at 10-7 Torr and
-140 °C. The exposed sample surfaces were shadowed
with a 1.5 nm layer of platinum at a 45° angle with respect
to the fracture surface, followed by a 15 nm layer of carbon
deposited normal to the surface. The copper planchettes
were dissolved in chromic acid, leaving the platinumcarbon replicas behind. The replicas were cleaned in
doubly-distilled water and collected on Formvar-coated
electron microscope grids. The replicas were imaged using
a JEOL 100 CX II TEM operating in conventional
transmission mode at 100 kV.
Figure 1 shows typical fractures through two MVLs
revealing the bilayer walls of the multiple interior
compartments, tightly packed into a roughly 10 µm sphere.
The inner compartments are polydisperse, ranging from
less than 100 nm to more than a micrometer in diameter
(Figure 2). However, the MVLs themselves are more
monodisperse, with an average diameter of about 10 µm.
Occasionally, the fracture surface goes around the entire
MVL and exposes its outer layer. An example of this type
of fracture is shown in Figure 3, where we see a dimpled
spherical structure, similar to a golf ball in appearance.
The packing of the inner compartments does not cause
the outer bilayer to compress, so the outermost compartments remain spherical.
(23) Bailey, S. M.; Chiruvolu, S.; Longo, M. L.; Zasadzinski, J. A. J.
Elect. Microsc. Tech. 1991, 19, 118-126.
The most striking feature of the fracture surfaces in
Figure 1 is the high degree of faceting of the compartment
walls. This is even more evident at higher magnifications
as seen in Figure 2. It is well established that the fracture
surface in bilayers propagates along the interface between
the hydrocarbon tails of opposing monolayers.24 Hence,
the surfaces of the MVL in Figure 2 are the bilayer walls
of the interior compartments. Most often, the fracture
takes a random path through the MVL but tends to stay
near the equatorial plane. This is seen in the MVLs shown
in Figures 1 and 2. A quick examination of Figure 2 shows
the preponderance of three edges terminating at a single
vertex, indicative of the local tetrahedral coordination
predicted by Plateau (the fourth edge is out of the plane
of fracture, roughly normal to the fracture surface). It is
clear from Figure 2 that the tetrahedral coordination of
vertices and faces in the MVL are maintained to bilayer
length scales. There is also a striking uniformity of the
angles between the edges terminating at the vertex. This
is somewhat surprising in that at these length scales there
are a number of additional forces that influence bilayer
curvature and interactions;25,26 Plateau’s rules for packing
were derived from a macroscopic force balance without
regard for the details of the specific materials making up
the contacts.9
In order to compare the topology of our lipid foam to the
predictions from the random packing model, we determined the facet distribution by counting the number of
edges of the exposed MVL faces. We restricted the
counting to polyhedra at least four compartments away
from the outer bilayer of the MVL to eliminate the effects
of the boundary. We also ignored facets partially obscured
by imperfections in the replica and those nearly normal
to the fracture plane where the shape could not be
(24) Branton, D. In Freeze-etching, Techniques and Applications;
Benedetti, E. L., Favard, P., Eds.; Societé Française de Microscope
E
Ä lectronique: Paris, 1973; Chapter 10.
(25) Helfrich, W. J. Phys. (Paris) 1985, 46, 1263-1280.
(26) Israleachvili, J. N. Intermolecular and Surface Forces, 2nd ed.;
Academic Press: London, 1992; Chapter 18.
Topology of Multivesicular Liposomes
Langmuir, Vol. 12, No. 20, 1996 4707
Figure 3. Electron micrograph of a replica showing the outer
surface of a multivesicular liposome. The abrupt change in the
gray scale near the center of the MVL is due to the shadowing
effect of the freeze-fracture replica. The white region near the
bottom is a crack in the replica. The pebbled exterior of the
MVL is reminiscent of a golf ball. The bar represents 2 µm.
Figure 2. Electron micrograph of replicas showing enlarged
sections of multivesicular liposomes. The complete faceting of
the interior compartments is evident. Note the tetrahedral
coordinationsalmost every vertex has three edges, and each
face is connected to three others. The fourth edge and third face
are normal to the fracture surface and not visible in the images.
The tetrahedral coordination and angles persist to bilayer
resolution. From images such as these it is simple to determine
the distribution of edges per face (see Figure 4) and to show
that the average number of edges per face is 5.107, in close
agreement with Coxeter’s prediction of 5.104. The average
number of faces per polyhedra can be calculated from the
average number of faces and is 13.4, roughly midway between
the dodecahedron that makes up the fcc lattice and Kelvin’s
tetrakaidecahedron.10 The bar represents 0.5 µm.
unambiguously determined. Some edges having a small
curvature were included. The results from counting 1024
facets give the statistical distribution of edges per face
shown as dark bars in Figure 4. We find that the most
prevalent polyhedral faces are pentagons, in qualitative
agreement with the experimental results of Matzke.20
However, we find about 39% pentagons compared to his
67%, which is likely due to the polydispersity of the
compartments in the MVL compared to Matzke’s idealized
foam.
Computer simulations of the random close packing of
hard spheres have been performed by Finney.11 After
finding the close-packed structure, he performed a Voronoi
construction to find unit cells for each sphere. The
resulting structures confirm the basic tetrahedral character of the random close packing model and that fivesided facets predominate the Voronoi polyhedra. The
distribution of edges per face of the polyhedra found in
the computer simulation are shown in Figure 4 as the
lighter bars. This simulation gives remarkably close
agreement in the percentage of pentagonal facets. However, we find almost equal numbers of four- and six-sided
facets, while the simulation gives approximately 50% more
six-sided faces than four-sided faces. This is likely due
to the large polydispersity in the size of our compartments,
Figure 4. Distribution of the number of edges per facet
measured from the freeze-fracture images. The results from
counting 1024 facets in MVL foams give 19 triangles, 266
quadrilaterals, 401 pentagons, 273 hexagons, 54 heptagons,
and 11 octagons and are shown as the dark bars. The
experimental results are compared to the results from computer
simulations of random close packing (light bars). 13
compared to the simulation, which assumed a monodisperse distribution of spheres. On average, the facets have
q ) 5.107 edges per face, in remarkable agreement with
the predictions of the statistical model of Coxeter, who
predicted a unit cell with qideal ) 5.104.10,14 It is also
possible to calculate the average number of faces, F, per
polyhedra from q using the Euler relation in three
dimensions10
V-E+F)2
(2)
in which V is the number of vertices, E the number of
edges, and F the number of faces of a generic polyhedra.
If tetrahedral coordination is imposed on the polyhedra,
the following relations hold10
3V ) 2E ) qF
(3)
4708 Langmuir, Vol. 12, No. 20, 1996
Spector et al.
Inserting eq 3 into eq 2 and solving for F gives
F ) 12/(6 - q)
(4)
Hence, the MVLs are made up, on average, of 13.4-sided
polygons, roughly midway between the 12-sided dodecahedron that forms the basis of the face-centered cubic
lattice and Kelvin’s 14-sided tetrakaidecahedron.10
Our results show that the apparently complex structure
of a multivesicular liposome can be completely understood
using the classical rules of Plateauswho predicted
tetrahedral coordination of foam bubblessin combination
with the concept of random close packing of polyhedra.
Freeze-fracture electron microscopy images show that
these topological constraints are valid down to the bilayer
level. As the local tetrahedral coordination is incompatible
with any regular global packing, nature relies an a
distribution of polyhedral shapes and sizes to allow for
close packing. We have shown that a statistical analysis
of the shapes of the compartments of the MVLs agrees
very closely with theoretical predictions and computer
simulations of random close packing. In addition to
extending these structural concepts to a real biliquid foam,
we have shown that the MVL structure is at least a
metastable minimum energy configuration for a given
distribution of polyhedral cells, which is an important
starting point for our ongoing studies of in vitro and in
vivo drug delivery from MVLs.
Acknowledgment. We thank David Nelson and David
Morse for valuable discussions and Rosa Solis for assistance in sample preparation. This research was
supported by the DepoTech Corporation, NSF Grant CTS9305868, NIH Grant GM47334, and the MRL Program of
the NSF under Grant DMR-9123048.
LA960218S