Association of hydrophobically-modified poly(ethylene glycol) with fusogenic liposomes.

Abstract

We present results on using cooperative interactions to shield liposomes by incorporating multiple hydrophobic anchoring sites on polyethylene glycol (PEG) polymers. The hydrophobically-modified PEGs (HMPEGs) are comb-graft polymers with strictly alternating monodisperse PEG blocks (M(w)=6, 12, or 35 kDa) bonded to C18 stearylamide hydrophobes. Cooperativity is varied by changing the degree of oligomerization at a constant ratio of PEG to stearylamide. Fusogenic liposomes prepared from N-C12-DOPE:DOPC 7:3 (mol:mol) were equilibrated with HMPEGs. Affinity for polymer association to liposomes increases with the degree of oligomerization; equilibrium constants (given as surface coverage per equilibrium concentration of free polymer) for 6 kDa PEG increased from 6.1+/-0.8 (mg/m(2))/(mg/ml) for 2.5 loops to 78.1+/-12.2 (mg/m(2))/(mg/ml) for 13 loops. In contrast, the equilibrium constant for distearoylphosphatidylethanolamine-poly(ethylene glycol) (DSPE-PEG5k) was 0.4+/-0.1 (mg/m(2))/(mg/ml). The multi-loop HMPEGs demonstrate higher levels of protection from complement binding than DSPE-PEG5k. Greater protection does not correlate with binding strength alone. The best shielding was by HMPEG6k-DP3 (with three 6 kDa PEG loops), suggesting that PEG chains with adequate surface mobility provide optimal protection from complement opsonization. Complement binding at 30 min and 12 h demonstrates that protection by multi-looped PEGs is constant whereas DSPE-PEG5k initially protects but presumably partitions off of the surface at longer times.

Full text

Page 1

Association of hydrophobically-modified poly(ethylene glycol) with
fusogenic liposomes
Debra T. Augustea, Robert K. Prud’hommea,*, Patrick L. Ahlb,1, Paul Meersb,2, Joachim Kohnc
aDepartment of Chemical Engineering, Princeton University, Engineering Quadrangle, Princeton, NJ 08544, USA
bDrug Delivery, Elan Pharmaceuticals, One Research Way, Princeton, NJ 08540, USA
cDepartment of Chemistry, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854, USA
Received 20 March 2003; received in revised form 12 August 2003; accepted 28 August 2003
Abstract
We present results on using cooperative interactions to shield liposomes by incorporating multiple hydrophobic anchoring sites on
polyethylene glycol (PEG) polymers. The hydrophobically-modified PEGs (HMPEGs) are comb-graft polymers with strictly alternating
monodisperse PEG blocks (Mw=6, 12, or 35 kDa) bonded to C18 stearylamide hydrophobes. Cooperativity is varied by changing the degree
of oligomerization at a constant ratio of PEG to stearylamide. Fusogenic liposomes prepared from N-C12-DOPE:DOPC 7:3 (mol:mol) were
equilibrated with HMPEGs. Affinity for polymer association to liposomes increases with the degree of oligomerization; equilibrium constants
(given as surface coverage per equilibrium concentration of free polymer) for 6 kDa PEG increased from 6.1F0.8 (mg/m2)/(mg/ml) for 2.5
loops to 78.1F12.2 (mg/m2)/(mg/ml) for 13 loops. In contrast, the equilibrium constant for distearoylphosphatidylethanolamine-
poly(ethylene glycol) (DSPE-PEG5k) was 0.4F0.1 (mg/m2)/(mg/ml).
The multi-loop HMPEGs demonstrate higher levels of protection from complement binding than DSPE-PEG5k. Greater protection does
not correlate with binding strength alone. The best shielding was by HMPEG6k-DP3 (with three 6 kDa PEG loops), suggesting that PEG
chains with adequate surface mobility provide optimal protection from complement opsonization. Complement binding at 30 min and 12 h
demonstrates that protection by multi-looped PEGs is constant whereas DSPE-PEG5k initially protects but presumably partitions off of the
surface at longer times.
D 2003 Published by Elsevier B.V.
Keywords: Fusogenic liposome; Hydrophobically modified PEG; Liposome protection; Complement assay; Comb-graft; Protein shielding
1. Introduction
Liposomes are spheres made up of lipid bilayers, enclos-
ing aqueous volumes [1]. They act as models for biological
membranes and show great potential as drug delivery
vehicles, especially in cancer and gene therapy [2–10].
Certain fusogenic liposomes, such as those incorporating
N-acyl phosphatidylethanolamines (NAPEs), have the abil-
ity to deliver dextran to erythrocyte ghosts [11] and transfect
ovarian cancer cells with DNA encoding a GFP protein
[12]. Nonetheless, the use of fusogenic liposomes and other
liposomal formulations is often limited by their rapid uptake
by the mononuclear phagocytic system (MPS) [9,13–18].
The concept of sterically stabilized or long circulating
liposomes was first realized in 1987 when lipids modified
with different polymers and polysaccharides were incorpo-
rated into the bilayer to increase the circulation half-life of
liposomes [3,4,7–10,15,17,19–30]. The most effective
coating was formed by integrating distearoylphosphatidyle-
thanolamine-poly(ethylene glycol) (DSPE-PEG5k) with a 5
kDa molecular weight PEG chain [6,7,10, 17,22,26,29,31].
Addition of 2.5 to 10 mol% DSPE-PEG5k into liposomes
made up of distearoylphosphatidylcholine (DSPC) increases
the circulation half-life of liposomes from 0.47 to 8.4 h [17].
It is postulated that increased circulation is a result of
PEG producing a steric barrier to protein binding. The
structure of DSPE-PEG5k, as described by Woodle and
Lasic [3], has the lipid embedded within the hydrophobic
bilayer and the hydrophilic PEG chain protruding into the
0005-2736/$ - see front matter D 2003 Published by Elsevier B.V.
doi:10.1016/j.bbamem.2003.08.007
* Corresponding author. Tel.: +1-609-258-4577; fax: +1-609-258-0211.
E-mail address: prudhomm@princeton.edu (R.K. Prud’homme).
1Present address: BioDelivery Systems International, Inc., 4 Bruce
Street, Newark, NJ 07103, USA.
2Present address: Transave, Inc., 11 Deer Park Drive, Suite 117,
Monmouth Junction, NJ 08852, USA.
www.bba-direct.com
Biochimica et Biophysica Acta 1616 (2003) 184–195

Page 2

aqueous medium. The preference of PEG for water allows
PEG to extend even at low grafting densities [32] and thus
creates a repulsive, steric barrier. Senior [14] observed a
decrease in the rate of protein adsorption onto liposomes
incorporating DSPE-PEGs. These results were confirmed by
Chonn et al. [33] who showed that greater protein binding,
which occurred on bare liposomes, correlated with shorter
circulation half-lives [33]. Liu et al. [16] also concluded that
recognition and uptake of liposomes was determined by
adsorption of specific proteins associated with opsonization,
namely the complement proteins. Therefore, we developed
an automated in vitro assay to measure liposome comple-
ment depletion.
In vitro binding of complement to liposomes has been
shown to correlate inversely with circulation lifetime [20].
The complement system consists of a collection of serum
proteinsthatactasacascadeforrecognitionofforeignagents.
The most important of these proteins is C3, which is present
inthebloodstreamatlevelssimilartosomeimmunoglobulins
(1–2 mg/ml). Two consequences of complement activation
are opsonization and lysis of target cells [16].
In this paper, we present the concept of multiply attached
polymer chains as a mechanism for preparing protected
liposomes. The approach exploits recent interest in cooper-
ative binding [34] where multiple relatively weak binding
interactions can lead to strong overall association. The
concept is demonstrated by a series of new PEG-based
comb copolymers with concatenated PEG chains having
hydrophobic anchoring groups between the linked PEG
chains. These polymers allow the comparison of binding
vis a ` vis protection with polymers having exactly the same
ratio of PEG to hydrophobe, but with varied cooperativity
by varying the concatenation or degree of polymerization.
These constructs overcome several limitations with the
previous method of stabilizing liposomes with PEG-lipids:
(1) the PEG-lipids must be incorporated during the liposome
formation process rather than adding them to preformed
liposomes [7,9], and (2) the single lipid anchoring limits the
size and amount of PEG polymer that can be attached [22].
The multiply attached PEGs allow the addition of soluble
polymer to the preformed liposomes, which permits greater
flexibility in processing and tailoring liposome formula-
tions. The second limitation arises because the singly
attached PEG will partition off of the liposome surface if
the PEG is too soluble. Experimentally, loss of protection is
observed for PEG molecular weights above 5 kDa [22].
With multiple attachments, higher molecular weight PEGs
can be attached to the liposome with high binding affinities.
The hydrophobically modified PEG polymers (HMPEGs)
used in this study are comb-graft polymers with strictly
alternating monodisperse PEG blocks (Mw6, 12 or 35 kDa)
bonded to C18 stearylamide hydrophobes, with 2 to 13
hydrophobe anchors per polymer chain [35,36]. We report
the ability of these polymers to associate with fusogenic
liposomes at equilibrium and the ability of the polymers to
shield liposomes from complement binding. We compare
our results to DSPE-PEG5k, which has been studied previ-
ously [15,17,21,26,33].
2. Materials and methods
2.1. Materials
1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-
distearoyl-sn-glycero-3-phosphoethanolamine-N-methoxy
polyethylene glycol (DSPE-PEG5k), and 1,2-dioleoyl-sn-
glycero-3-phosphoethanolamine-N-dodecanoyl (N-C12-
DOPE) were purchased from Avanti Polar Lipids (Alabaster,
AL, USA). 1,1V -Dioctadecyl-3,3,3V ,3V -tetramethylindodicar-
bocyanine perchlorate (DiD) was acquired from Molecular
Probes (Eugene, OR, USA). The 0.2-Am polycarbonate
membrane filters, semi-micro disposable cuvettes, and 96-
wellplates were obtained from VWR (Bridgeport,NJ, USA).
The HMPEG polymers were synthesized at Rutgers Univer-
sity (Piscataway, NJ, USA) as described by Heitz et al. [35].
Slide-A-Lyzer cassettes with a 10000 MWCO membrane
were procured from Pierce Biotechnology (Rocksford, IL,
USA). Sheep erythrocytes and hemolysin rabbit anti-sheep
erythrocyte stromata serum were purchased from Biowhit-
taker (Walkersville, MD, USA). Lyophilized rat sera, gelatin
veronal buffer (GVB2 +: 0.15 M CaCl2, 0.5 mM MgCl2,
0.1% gelatin, 1.8 mM sodium barbital, 3.1 mM barbituric
acid, 141 mM NaCl, pH 7.4) and gelatin veronal buffer with
EDTA (GVB-EDTA: in addition to the ingredients in
GVB2 +it contains 10 mM EDTA, pH 7.4) were acquired
from Sigma (St. Louis, MO, USA).
2.2. Preparation of liposomes
N-C12-DOPE:DOPC (7:3, mol:mol) large unilamellar
vesicles (LUVs) were prepared as described by Shangguan
et al. [11] with some modifications. The lipids were mixed
in chloroform, dried under reduced pressure using a Bu ¨chi
RE 111 Rotovapor and 461 water bath (Bu ¨chi Labortechnik
AG, Flawil, Switzerland), then left under vacuum overnight
to remove any residual solvent. The lipid film was hydrated
with a TES buffer solution (10 mM TES, 150 mM NaCl, 0.1
mM EDTA, pH 7.4). After vortexing, the lipid solution
underwent five cycles of freezing in liquid nitrogen and
thawing in a room temperature water bath. The sample was
then extruded 10 times through a 0.2-Am polycarbonate
membrane filter at 250 psi using a 10-ml Lipex extruder
(Northern Lipids, Inc. Vancouver, BC, Canada). The lip-
osomes were stored at 4 jC under nitrogen.
To aid in separation from unbound HMPEG polymer, the
liposome density was increased by encapsulating a sucrose
solution and a fluorescent marker (DiD) was added for
visibility. Sucrose-encapsulating liposomes (N-C12-DOPE:
DOPC:DiD 7:2.9:0.1 mol:mol:mol) were prepared as de-
scribed above except in a sucrose buffer solution (10 mM
TES, 250 mM sucrose, pH 7.4). After the liposomes were
D.T. Auguste et al. / Biochimica et Biophysica Acta 1616 (2003) 184–195
185

Page 3

made, non-encapsulated sucrose was removed by dialysis
against the TES buffer (as described above) using a Slide-A-
Lyzer cassette with a 10000 MWCO. Dialysis occurred at 4
jC overnight. Sucrose-encapsulating liposomes incorporat-
ing DSPE-PEG5k were made using the same method
described. The amount of DSPE-PEG5k (x) added was
subtracted from the moles of DOPC (2.9?x), keeping the
amount of DiD and N-C12-DOPE constant. Thus, the
composition of the liposomes containing DSPE-PEG5k is
written as N-C12-DOPE:DOPC:DSPE-PEG5k:DiD
(7:(2.9?x):x:0.1, mol:mol:mol:mol).
The concentration of liposomes in solution was deter-
mined by the phosphate assay as described by Chen et al.
[37]. Sizes of the liposomes were determined by quasi-
elastic light scattering using a NICOMP 270 submicron
particle sizer (NICOMP Instruments, Goleta, CA). Sucrose
encapsulating and buffer encapsulating liposomes had num-
ber-averaged diameters of 62.1F16.4 and 112.8F28.5 nm,
respectively.
2.3. Adsorption
Liposomes were equilibrated with polymer at a final
concentration of 1.4 mM lipid in TES buffer. Hydrophobi-
cally modified polymer was added, either solubilized in
TES buffer or as dry mass, to achieve the desired
concentration. For DSPE-PEG5k-containing liposomes,
four liposome compositions were prepared with increasing
amounts of polymer coverage (0.14, 0.28, 0.70, and 2.40
times C*, i.e. full surface coverage as calculated from the
dimensions of the PEG loops [38]). The DSPE-PEG5k-
containing liposomes were diluted as described above. All
samples were vortexed and allowed to equilibrate over-
night at room temperature in an Eppendorf 5436 Thermo-
mixer (Brinkman Instruments, Westbury, NY, USA). After
a 24-h equilibration, an initial fraction of 200 Al was
removed. The remaining fraction was then centrifuged at
21000?g in the Eppendorf 5417r Centrifuge (Brinkmann
Instruments, Westbury, NY, USA) at 4 jC. The superna-
tant was removed. Phosphate and PEG assays were
performed on the supernatant and initial fractions to detect
the amount of PEG per lipid in each sample. The
association constant, K, was calculated by determining
the initial slope (first four data points) of each adsorption
profile, such that
K ¼
dC
d½CpðfreeÞ?uðmg=m2Þ
ðmg=mlÞ:
ð1Þ
2.4. PEG Assay
The amount of PEG was quantified by an assay described
by Baleux [39], wherein 25 Al of an iodine-potassium iodide
solution (0.04 M I2, 0.12 M KI) was added to 1 ml of a
diluted sample. Samples were diluted to an optimal adsorp-
tion range (0.1<AU<1.0). The diluted sample and color
reagent were mixed in a disposable semi-micro cuvette with
a 1.0-cm path-length. After 5 min, the optical density (OD)
of the solution was determined at ambient temperature by a
UV-2101PC adsorption spectrophotometer (Shimadzu Sci-
entific Instruments, Princeton, NJ, USA) in the visible
region, k=500 nm. Because the lipid in the assay could
affect the OD, multiple calibration curves were required.
Table 1 describes the correlation between the HMPEG
concentration and OD for 0, 10, 30, and 50 AM lipid.
Calibration curves were completed for DSPE-PEG5k with
varying lipid concentrations; however, there was negligible
dependence in lipid concentration. The slope given is an
average of all of the calibration data taken at different lipid
concentrations. The variation in the assay with different
polymer architectures is due to the differences in hindrance
to helix formation, which is the origin of the colored
complex.
2.5. In vitro complement depletion assay
The complement assay is an in vitro assay that measures
the depletion of complement protein from serum by the
ability of the treated serum to achieve complement-mediated
lysis of activated sheep red blood cells (RBCs). The
complement assay was performed as described by Ahl et
al. [20]. Activation of the sheep erythrocytes was performed
Table 1
HMPEG correlation values for quantification of PEG (mg/l) as a function of the optical density at increasing concentrations of lipid in AM
0 AM lipid10 AM lipid
R2
d[OD]/d[Cp]
Polymer 30 AM lipid50 AM lipid
d[OD]/d[Cp]
R2
d[OD]/d[Cp]
R2
d[OD]/d[Cp]
R2
HMPEG6k-DP3
HMPEG6k-DP13
HMPEG12k-DP2.5
HMPEG12k-DP5
HMPEG35k-DP2.5
DSPE-PEG5k
0.038
0.022
0.054
0.046
0.049
0.046
0.987
0.971
0.996
0.973
0.976
0.931
0.041
0.023
0.053
0.050
0.048
–
0.980
0.980
0.982
0.982
0.978
–
0.043
0.022
0.056
0.048
0.052
–
0.980
0.998
0.982
0.997
0.979
–
0.046
0.023
0.057
0.053
0.053
–
0.973
0.989
0.988
0.992
0.992
–
The square of the Pearson product moment correlation coefficient, R2, interprets the proportion of the variation in Yattributable to the variation in X. It is given
as follows, where a value of one indicates that the estimated value is equal to the actual value [53]:
nðRXYÞ ? ðRXÞðRYÞ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
½nRX2? ðRXÞ2?½nRY2? ðRYÞ2?
R2¼
q
:
D.T. Auguste et al. / Biochimica et Biophysica Acta 1616 (2003) 184–195
186

Page 4

by first washing the RBCs three times by adding GVB2 +,
centrifuging at 8000?g for 4 min, and removing the
supernatant. The RBCs were resuspended at 108cells/ml,
determined by hemacytometry. Next, the RBCs were incu-
bated at 37 jC for 30 min with hemolysin rabbit anti-sheep
erythrocyte stromata serum at 1:500 (v/v). The activated
RBCs were washed three times and resuspended at 108
cells/ml. Activated RBCs were stored at 4 jC and were used
within 1 week.
Each individual complement assay consisted of the
following six samples that were prepared in 200-
Al volumes: TES buffer (the negative control, without
liposomes), 8 mM unmodified liposomes in TES buffer
(the positive control), and four test samples containing
8 mM liposomes in TES buffer with increasing amounts
of polymer. The samples were equilibrated overnight at 4
jC in the thermomixer. Each sample was then incubated
with 100-Al reconstituted rat sera, diluted 1:1 (v/v) with
GVB2 +, at 37 jC for 30 min with gentle shaking.
Addition of 300 Al of GVB2 +was followed by vortexing
and centrifugation at 8000?g for 4 min. We employed a
BiomekR 2000 Laboratory Automation Workstation
(Beckman Coulter, Brea, CA, USA) to perform the
pipetting for the rest of the assay. A 100-Al volume of
supernatant was diluted 1:1 (v/v) followed by eight
successive serial dilutions in GVB2 +. Next, 100 Al of
activated sheep RBCs was added to each dilution and
allowed to incubate for 30 min at 37 jC with gentle
shaking. Hemolysis was quenched by addition of 300 Al of
GVB2 +-EDTA. RBCs that were not lysed were sedi-
mented by centrifuging the samples at 8000?g for 4
min. A 200-Al aliquot from the supernatant of each
sample was transferred to a 96-well plate. Hemolysis
was determined by measuring the optical density of 200
Al of each sample well at 415 nm using a 3550-UV
spectrophotometer plate reader (Bio-Rad Laboratories,
Hercules, CA, USA). Buffer encapsulating N-C12-DOPE:
DOPC:DiD (7:2.9:0.1, mol:mol:mol) liposomes and su-
crose encapsulating N-C12-DOPE:DOPC:DSPE-PEG5k:
DiD (7:(2.9?x):x:0.1, mol:mol:mol:mol) were used in
the complement assays. Sucrose encapsulation enables
pelleting of the liposomes but does not interfere with
the complement assay.
The complement assay results are plotted as the
percent hemolysis versus the log of the inverse of the
serum dilution. The CH50, utilized in related literature
[40–42], is the serum dilution required to achieve 50%
hemolysis and is directly proportional to the amount of
active complement in the serum. The CH50 value for
each hemolysis curve was obtained by a linear fit to a
log–log version of the von Krough equation [43]. The
inhibition of liposome complement binding or surface
‘‘protection’’ mediated by HMPEG or DSPE-PEG5k ad-
dition can be quantitatively described as the percentage of
the maximum expected CH50 shift from the CH50 of the
bare liposome to the CH50 of the buffer, i.e. no liposome
sample. This can be calculated using the following
equation, where B is buffer, BL is bare liposomes, and
PL is polymer coated liposomes:
% Protection¼CH50PL? CH50BL
CH50B? CH50BL
? 100
ð2Þ
3. Theory and models
3.1. Defining coverage, C*
The HMPEGs consist of PEG backbones with C18H37
hydrophobes that are described by the size of the PEG
spacer (molecular weight of PEG between hydrophobes)
and by the number of loops (or degree of polymerization,
denoted DP) [35,36]. The polymers are designated:
HMPEGUXU-DPUYU, where X is the molecular weight of the
PEG spacers in Daltons and Yis the average number of PEG
spacers.
The conformation of the entire PEG polymer chain
tethered to the lipid membrane is shown schematically in
Fig. 1. Our previous studies have shown [38] that the
chain can be treated as a series of subchains, having one-
half the molecular weight of the PEG unit between hydro-
phobes. These subchains obey random-walk statistics and
occupy an area at the interface given by a sphere of
diameter [44]
nmb¼ 0:76m1=2
b
½˚A?;
ð3Þ
where mbis the molecular weight of the subchain. The
terminal PEG segments of the chain are treated differently
because they are free and not bound at each end; therefore,
they occupy a size corresponding to a sphere of diameter
twice the molecular weight of the internal subchains (see
Fig. 1). The number of spheres, Nb, is equal to two times
the degree of polymerization minus the two ends
(Nb=2Dp?2). The number-averaged diameter for spheres
of a polymer chain is given as follows [38]:
¯n ¼
2
Nbðn2mbÞ þNb? 2
Nb
ðnmbÞ:
ð4Þ
From the mean diameter, we determine the area
occupied at the surface from Nbp(n¯/2)2. The total area
of one polymer is then the number of subchains times the
average area occupied by a subchain. Thus, HMPEG6k-
DP3 has four subchains, a mean diameter of 50 A˚, and
requires an area of 7900 A˚2per polymer. The amount of
polymer to cover 1-m2lipid, C*, is 21 nmol, or 0.88 mg,
of HMPEG6k-DP3. Assuming that each lipid head area is
approximately 70 A˚2[45] and that one half of the lipid is
on the exterior, there are 4.7 Amol of lipid per square
meter. Alternately, we can base the coverage on the
number of hydrophobes required to cover 1-m2of lipid
D.T. Auguste et al. / Biochimica et Biophysica Acta 1616 (2003) 184–195
187

Page 5

bilayer or 4.7 Amol of lipid. See Table 2 for polymer
details.
The idea of coverage is based on the amount of
polymer needed to cover the exterior surface area of
liposomes. From the random walk approximation described
above, which we have verified by neutron scattering for
the HMPEG chains [38], we are able to approximate the
area occupied by the HMPEG polymers and the DSPE-
PEG5k polymer. Because the polymers differ greatly in
molecular weight and number of subchains, we find this
the best means for comparison.
3.2. Partitioning model
A partitioning model can describe the association of a
hydrophobe to a phospholipid bilayer. Consider the
bilayer and aqueous solution as two phases. It is
assumed that there is a partition coefficient which relates
the amount of bound polymer per lipid area, [PL]/[L]
(in mg/m2), with the concentration of free polymer, [P]
(in mg/ml) such that
½PL?
½L?
where C is the partition coefficient determined by the
difference in free energy of the polymer between the two
phases and c is the activity coefficient, representing the
deviation from ideality [46]. The plot of [PL]/[L] vs. [P]
yields an association isotherm that is linear at low polymer
concentrations and has a decreasing slope due to non-ideal
interactions (c>1) which depends on the polymer type. A
strict thermodynamic analysis will define c as the ratio of
the polymer activity coefficients in both the aqueous and
bilayer phases, c=cP
ing model relates to a simple binding model where
[P]+[L]f[PL]. The slope, C/c, is equivalent to the associ-
ation constant divided by the number of available sites, K/N
[46].
¼C
c½P?;
ð5Þ
L/cP
A. Porcar shows how this partition-
3.3. Cooperativity
We define cooperativity as the increased probability of
the polymer to remain adsorbed due to its multiple
attachment sites. It is our hypothesis that increasing the
number of hydrophobic anchors on a PEG polymer
increases the cooperativity of the polymer binding to the
liposome membrane while still maintaining the ability to
add the protective polymer after the formation of the
vesicles. The cooperativity of a set of polymers can be
evaluated by comparing the equilibrium constants, which
assesses the ability of a polymer to leave the liposome
surface. Thus, a polymer’s cooperativity relies on its
architecture. For a single hydrophobic anchor attached to
Table 2
Description of hydrophobically modified PEG polymers
n¯, A˚
Polymer
Nb
MW,
kDa
Polymer
area,
?1017m2
7.9
35.0
13.3
26.5
38.8
2.3
C*,
mg/m2
Chm*,
hydrophobe
mol%
HMPEG6k-DP3
HMPEG6k-DP13
HMPEG12k-DP2.5
HMPEG12k-DP5
HMPEG35k-DP2.5
DSPE-PEG5k
450
43
75
65
128
54
42
112
48
106
138
5781
0.88
0.53
0.60
0.66
0.59
0.42
0.89
1.21
0.40
0.53
0.14
1.55
24
3
8
3
1
To convert C* (mg/m2) to Chm*, determine the moles polymer per
4.7?10? 6mol of lipid then multiply by the number of hydrophobes (DP-1)
and 100 to obtain the mol% hydrophobes per lipid, or Chm*.
Fig. 1. Diagram of (a) a covalently bound PEG to a lipid and (b) a hydrophobically modified PEG associating with a lipid membrane.
D.T. Auguste et al. / Biochimica et Biophysica Acta 1616 (2003) 184–195
188