Molecular Dynamics Simulation of PEGylated Membranes with

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Molecular dynamics simulation of PEGylated membranes with cholesterol:building towards the DOXIL formulation Aniket Magarkar, Tomasz Róg, and Alex Bunker J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp504962m • Publication Date (Web): 26 Jun 2014 Downloaded from http://pubs.acs.org on July 1, 2014

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The Journal of Physical Chemistry

Molecular Dynamics Simulation of PEGylated Membranes with Cholesterol: Building Towards R the DOXIL Formulation Aniket Magarkar,† Tomasz Róg,‡ and Alex Bunker∗,† Centre for Drug Research, Faculty of Pharmacy, University of Helsinki, Helsinki, Finland, and Department of Physics, Tampere University of Technology, Tampere, Finland E-mail: [email protected]

∗

To whom correspondence should be addressed Centre for Drug Research, Faculty of Pharmacy, University of Helsinki ‡ Department of Physics, Tampere University of Technology †

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Abstract PEGylation has been used successfully to increase the circulation time of drug delivery liposomes by providing an external steric sheath. In all FDA approved PEGylated drug delivery liposomes, cholesterol is a key component. In a continuation of our previous work we have simulated a PEGylated membrane with cholesterol added to the membrane formulation to determine the effect on membrane structure of the cholesterol-PEG interaction. We show that, like the case for the liquid crystalline membrane, PEG enters into the lipid bilayer, however in a specific fashion: the PEG winds along the β face of the cholesterol. Additionally PEG interferes with the role cholesterol plays in structuring and compacting the membrane; when the membrane is PEGylated the area per lipid increases, rather than decreases, with increasing cholesterol. Our studies provide mechanistic explanations for existing experimental results concerning the effect of adding cholesterol to the PEGylated liposome, including alteration to the liposome compressibility and permeability, and the possible PEG induced release of cholesterol from the membrane.

Keywords molecular dynamics simulation, PEGylation, cholesterol, drug delivery, nanomedicine

Introduction Since the 1970’s liposome based systems have been used in drug delivery. 1 A protective layer on the outside of the drug delivery liposome can be formed through the inclusion of phospholipids functionalized with polymer chains. The current gold standard for this polymer is poly(ethylene) glycol (PEG), and liposomes that have incorporated a protective polymer coating this way are known as ”PEGylated”. PEGylation increases blood circulation lifetime through steric shielding. 2–7 The first, and so far one of the most successful, clinically

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approved example of the use of PEGylated liposome based drug delivery systems is the drug R 8 , which has been extensively studied experimentally. 8 Although current experiDOXIL

mental techniques provide us with insight into the effect of PEGylation on liposomes, these do not provide the mechanism for these changes. All atom molecular dynamics simulation can provide structural insights into these interactions and thus can look at conformational dynamics and behavior of the PEG polymer in PEGylated liposomes. While PEGylation has proved successful there is currently an active effort to find alternative polymers to PEG. 9 In order to take a rational design approach it is necessary to first know all details of how PEG is functioning. So far there are a number of studies detailing molecular dynamics simulations of PEG, 10–12 PEG with lipid bilayers without cholesterol both with coarse grained Martini models 13–15 and all atom models. 16–18 Cholesterol is an important component in drug delivery liposome formulations, as it is expected to play a role in lipid packing and stability, thus affecting the drug release rate. 19 The specific interactions of between PEG and cholesterol in PEGylated drug delivery liposomes has so far not been studied with all atom resolution. Recently, the molecular dynamics simulation of PEGylated liposome with cholesterol has been reported using a coarse grained Martini model. 20 As many interaction details are lost in Martini models as a result of the coarse graining, 21 the more detailed picture presented by atomistic simulations has the opportunity to gain further understanding into drug delivery liposome structure and interactions. In previous work we have studied the PEGylated liposome membrane structure, 18 effect of PEG grafting density 22 and effect of cholesterol on the liposome membrane without PEG on the interaction with salt ions in the bloodstream. 23 In this study, in a continuation of our effort to understand the structure and properties of PEGylated liposomes, we have incorporated both PEG and cholesterol into the simulated membrane, studying several levels of cholesterol concentration. We show that with the introduction of cholesterol into the liposome, PEG enters the membrane, in a very specific fashion disrupting the membrane

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structure. This will in turn affect several properties of the liposome membrane including the surface area, 24 the permeability of the liposome, 25,25,26 and position of cholesterol in the membrane. 27 We have also simulated the specific formulation of the FDA approved R . We also continued our studies on the incorporation of drug delivery liposome DOXIL

two biochemically different targeting peptides, 28 the AETP moiety and the RGD peptide, described in further detail below, including cholesterol into the membrane and studying the lower density of PEG found in the experimental formulation.

Methods Systems Simulated A total of eight membrane bilayers composed of mixtures of DSPC, DSPE-PEG2000 and cholesterol have been simulated. The content of cholesterol and PEG2000 were systematically varied. The first five membrane bilayers have a ratio of DSPC:cholesterol of 6:0, 5:1, 4:1, 3:1, 2:1, 1:1 respectively, with 10% of DSPE-PEG2000 molecules. The sixth simulated system consists of a DSPC bilayer with 33% of cholesterol and 5% of DSPE-PEG2000 to R 8 , doxorubicin encapsulated model the composition of the liposome membrane of DOXIL R contains α-tocopherol at low concentration in a PEGylated liposome. (Note: DOXIL

which is ignored in our simulation studies). For the last two simulated systems, each had the same composition as the fifth system, DSPC membrane containing 33% cholesterol and 5% DSPE-PEG2000, but with targeting moieties, the RGD peptide (ACDCRGDCFCG) and the AETP moiety (WTPVWR), attached to the end of the PEG2000 molecule at 1% molar concentration in the membrane formulation, for a total of two peptides in the simulation, R 8 , is also a model for one on each leaf of the membrane. This formulation, that of DOXIL

the formulations that have been studied in vitro and in vivo in our previous study, 28 the only difference being their use of hydrogenated soy phosphatidylcholine(HSPC) instead of pure DSPC. Explicit solvent molecules and NaCl at physiological concentration (125mM) was 4


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added to all systems. Apart from these, Na+ counter ions were used to obtain charge neutrality for all systems. The exact number of molecules in each system is shown in Supporting Information as table S1.

Construction of the Simulated Systems For all of the simulations, membrane bilayers containing DSPC and cholesterol were obtained from previous studies. 23 To these, DSPE-PEG2000 molecules were added in the required proportion. This was achieved through altering the headgroups of a subset of the DSPC lipids and attaching the PEG polymer. The conformation of PEG2000 is obtained from the equilibrated trajectories from previous studies. 22 Salt ions were added to the system by replacing water molecules. The DSPE-PEG2000 with AETP and RGD targeting moieties were attached to the end of PEG2000 terminal oxygen through a maleimide linker, as performed in our previous studies. 28

Molecular Model Parametrization We have used the OPLS-AA force field 29 for PEG, cholesterol, and ions and for the lipids we used a recently developed OPLS-AA compatable force field for lipids. 30 The TIP3P water model, 31 which is compatible with the OPLS-AA force field, is used in this study.

Molecular Dynamics Simulation Parameters In the MD simulations, periodic boundary conditions were used with the minimum image convention in all three directions. The linear constraint solver (LINCS) algorithm 32 was used to preserve the covalent bond lengths. The temperature of the systems simulated was controlled using the Nosé-Hoover 33,34 thermostat. The temperature for solute and solvent were controlled independently. The pressure was controlled using the Parrinello-Rahman barostat 35 with semi-isotropic control. The Lennard-Jones interactions cut off was set to

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1.0 nm. For the electrostatic interactions particle mesh Ewald method 36 was used. All simulations were carried out at a constant pressure of 1 bar and physiological temperature (310 K).

System Size and Equilibration Time All simulated systems consist of a square section of membrane bilayer with 288 lipid molecules (144 per leaflet), with a width of approximately 8-10 nm. Simulations were carried out for 200 ns with a 2 fs timestep. The system was found to take 100 ns to equilibrate and this time was not considered in the analysis of the simulation. This was determined from the time needed for the number of ions bound to the PEG oxygens and membrane headgroups, 18 and the area per lipid of the membrane, to stabilise (Figure S3. In Supporting Information).

Simulations and Analysis Protocol The Gromacs 37 software package, version 4.6, was used to carry out and analyse the MD simulations. Visualisation of the trajectories was performed using Visual Molecular Dynamics (VMD). 38 All the analysis was performed using the last 100 ns of the trajectory, once equilibration has been established. Visualisation of the membrane bilayers was performed using VMD to observe the behaviour and interactions in the simulated system over time. Specific interactions of cations as a function of time were investigated. The mass density profile perpendicular to the membrane normal was calculated to study the average behaviour of each component of the membrane bilayers. To study the interactions of the RGD peptide and AETP targeting moieties we calculated the surface area of the targeting moieties in contact with various components of the simulated system, as performed in previous studies. 28 While the calculation of the surface area per lipid for a single component bilayer is simply the total area divided by the number of lipids in a single leaf, the definition of this quantity is no longer trivial for a mixed system. This issue has already been discussed in depth by others. 39,40 In this study we have used a simple method in which we assume an area of 0.39 6


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nm2 for each cholesterol, the area per cholesterol molecule measured in monolayer experiments. 41,42 The deuterium order parameter, SCD , 43 is a property of the bilayer that provides information concerning the level of lipid chain ordering. It can be obtained accurately from NMR experiments, and is defined as:

SCD =

3 2

cos2 θi −

1 2

(1)

where θi is the angle between the C-D bond (C-H in simulations) of the i-th carbon atom and the bilayer normal. The angular brackets denote averaging over time and over relevant C-D bonds in the bilayer.

Results Visualisation of the trajectories We visualised the trajectories of the simulations of membranes containing cholesterol at increasing concentration from 16% to 50%. As shown in 1, PEG enters the membrane bilayer in all cases, irrespective of cholesterol concentration, as long as cholesterol is present. In previous work, 18 we have observed PEG entry into the membrane interior for the case of the PEGylated membrane bilayer in the liquid crystalline state, however, PEG is excluded from the bilayer core for the case of the pure DSPC membrane in the gel state. Unlike the case of the liquid crystalline membrane, in the membranes containing cholesterol, the PEG appears to enter in a specific conformation, looping vertically into the membrane core. We examine the significance of this below. We have also investigated the behaviour of salt ions in the simulated systems. In all cases, with the exception of the DSPC membrane with 5% PEG and 33% cholesterol, we could see that the Cl− ions are expelled from the PEG layer. The Na+ ions interact with both membrane head groups and the PEG polymer, as we have seen in our previous studies. 18,22 Closer examination of the system with 50% cholesterol shows

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that the boundary between the membrane head group area and the PEG layer becomes blurred, indicating a decrease in the ordering of the membrane as shown in 2. The figure (Fig. 2) with standard deviation shown as error bars, indicating this to be a significant effect is included in the supplementary material as figure S3.

Effect of cholesterol on the surface area of the lipid bilayer and order of acyl chains In previous work 23 we have studied the effect of cholesterol with DSPC bilayers (without PEGylation) with increasing content of cholesterol. We observed that in this system the area per lipid is relatively constant, in the range of 0.42-0.43 nm2 . As shown in 3, when we added PEG at 10% formulation density, the area per lipid is not affected by the presence of PEG when the concentration is raised from 16% to 20%, but then with further increase in the cholesterol concentration, the area per lipid rises significantly. This indicates that PEG disrupts the lipid bilayer structure. This may have implications concerning the lipid packing effects resulting from interactions between the lipid and cholesterol molecules. In 2 the value of the of the deuterium order parameter (see methods section) along the acyl chain is shown. The deuterium order parameter has a direct inverse relationship to the surface area per lipid; in fact, since it can be measured experimentally through NMR, it is used as a measurement of the area per lipid in experimental systems. 44 In 2 we see that the deuterium order parameter, and thus the degree of lipid chain ordering, is significantly lower for the PEGylated bilayer than for its non-PEGylated counterpart, in agreement with our observation of an increase in the area per lipid.

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Effect of Cholesterol and PEG on the membrane structure and liposome-cation interactions We have analysed the effect of varying the levels of both cholesterol and PEG in the lipid membrane on the binding of cations to the membrane surface. As shown in 4A, we observe that, in the absence of cholesterol and PEG, and presence of NaCl at physiological concentration, the Na+ ions collocate with the phosphate group as shown from their respective mass density peaks, as seen in our previous studies. 45 In the presence of cholesterol at a level of 33%, however, the mass density peak for Na+ ions is reduced. Maintaining this level of cholesterol, in the presence of PEG at 5% formulation density, this peak once again increases, showing an approximately equal tendency for the Na+ ions to be located at the membrane head groups, or in the PEG region. When the PEG formulation density is increased to 10%, the Na+ ions show a much higher preference to be in the PEG layer and the interactions of the Na+ ions with the membrane head groups is, once again, decreased. The Cl− ions, however, do not interact with the membrane head groups in all of the above cases and are expelled out of the PEG layer with an increase in the PEG formulation density. Next we studied the effect of systematically increasing the cholesterol level in the membrane and observing its effect in membranes with 10% PEGylated lipid content. As shown in 4B, in the absence of cholesterol PEG is completely expelled from the membrane bilayer, as seen in our previous studies. 18 This is expected as the DSPC membrane is in the tightly packed gel state. We see that once cholesterol is added to the membrane the mass density peak for cholesterol outside the membrane shifts closer towards the membrane. This peak remains more or less constant in the range of cholesterol concentrations between 16% and 33%, though we see a small rise in the tail of the mass density peak extending into the membrane interior with increasing cholesterol content, indicating increased penetration into the membrane interior by PEG. We, however, see a qualitative change in the result for 50% cholesterol in the membrane, where the peak is still closer to the membrane head groups, and the shoulder representing PEG that has penetrated into the membrane interior, is notably 9



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enhanced. This is in agreement with the results of the visualisation and also area per lipid calculations of a qualitative change in the membrane structure at 50% cholesterol content. For the case of 5% PEG formulation density, PEG penetration into the membrane is also observed. Penetration of PEG into the lipid bilayer may affect the overall lipid packing and structure of the membrane. In 4C we observed the behaviour of the Na+ ions with increase in the level of cholesterol. We observe that, as a result of the introduction of cholesterol, the mass density peak for Na+ ions at the membrane head group is shifted towards the membrane. The Na+ peak at the membrane head groups for various levels of cholesterol, qualitatively remains about the same in the concentration range 16% to 33%, however, at the 50% cholesterol level, the mass density peak for the Na+ ions at the membrane interface, and in the PEG region, both decrease. This is once again in agreement with previous results showing the 50% cholesterol system to be qualitatively different from the others. At 5% PEGylated lipid concentration, the mass density peaks for the Na+ ions at the membrane head groups and in the PEG layer are of similar height. The figure (Fig. 4) with standard deviation shown as error bars is included in the supplementary material as figure S4.

Analysis of interactions of Cations From the mass density results shown in 4A and 4C, we could see that cations have a preference to collocate with membrane head groups and PEG depending on the cholesterol and PEG concentration. In order to understand this change in detail, we calculated the number of interactions of cations with both membrane head group and PEG oxygens with the same protocol we have followed in previous studies, 18,22 and this is shown in 5. The number of Na+ ions interacting with the head group increases at 16% cholesterol content and then follows the same correlation with the area per lipid plot, that is as the area per lipid increases, the number of cations bound to head groups increases. The number of Na+ ions interacting with PEG though, remains 62-66%, except for the case of 50% cholesterol. As we have 10


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already seen, in 3B, at 50% cholesterol concentration, the maximum amount of PEG enters the membrane, thus limiting the availability of sites that interact with the Na+ ions as shown in Supporting Information, Figure S2.

Effect of PEG on the Cholesterol location As shown in 1, it can be observed that PEG interferes with the membrane lipid packing through interacting with the cholesterol, and in 3 it becomes evident that PEG penetrates the lipid bilayer, as cholesterol concentration rises. To study the effect of PEG on the positioning of the cholesterol in the DSPC membrane, we compared the mass density profiles of the 10 DSPC cholesterol membranes with and without PEG (6). It can be seen that in the presence of PEG the cholesterol peak is shifted away from the membrane center, in the direction of the water phase. The figure (Fig. 6) with standard deviation shown as error bars is included in the supplementary material as figure S5.

Entrance of PEG into the membrane core It is evident from the mass density analysis that PEG enters the lipid bilayer in the presence of cholesterol, however, in its absence PEG is entirely excluded from the membrane. We visualised 14 cases where PEG entered the membrane, from the 5 simulations of PEGylated membranes with cholesterol present. In all cases we see that the PEG polymer has completely entered the membrane, in a specific way, as shown in 7A. The PEG has entered the membrane at the site where cholesterol is present such that it aligns itself to it. We could not see penetration of PEG surrounded by DSPC only, in any of our simulations. Thus PEG shows specificity to enter the lipid bilayer at the cholesterol site. The cholesterol ring is asymmetric with two methyl groups protruding from one face known as the beta-face or rough face and the other flat face known as the alpha face. This asymmetry and presence of the methyl group has an important role in the packing of acyl chains in the membrane and on the strength of the ordering effect of cholesterol. 19,46 On a closer look at these interactions as 11



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shown in 7B, it can be seen that PEG interacts with only the rough side, i. e. the beta side of the cholesterol in all cases. This is in agreement with our previous observation that, for the case of saturated chains, the interactions between the beta face and chains are weaker than the corresponding interaction with the alpha face. 47,48

Analysis of PEGylated liposome model with targeting moieties In order to achieve targeted drug delivery, the surface of drug delivery liposomes can be functionalized with targeting moieties. In a previous study, 28 we found that a new targeting moiety, AETP, did not improve the efficacy of drug delivery liposomes, in spite of it showing promise in phage display screening results in mouse tumour models. Through simulations of liquid crystalline and gel PEGylated membranes functionalized with the AETP moiety, and the RGD peptide, that has already been shown to be efficacious, we were able to show that the issue was that the AETP moiety was masked by the PEG. We have now repeated these R formulation, similar to that used in the original experiment simulations with the DOXIL

that our original simulation was combined with. This can thus be seen as a continuation of our previous work, adding cholesterol to the simulation, increasing the match to the experimental system. The 100 ns of equilibrated simulation revealed that with this formulation ∼40% of the surface area of AETP is covered by PEG, as compared to ∼25% for the RGD peptide, as shown in 8. Also, once again, for both AETP and the RGD peptide contact with the membrane headgroups is limited, thus not a dominant mechanism. The total surface area available to the solvent, thus available to its receptor, is less than 50% for the AETP. We once again, using a model closer to the experimental system, see the same result that the issue with the AETP moiety is coverage by the protective PEG layer and not interaction with other elements of the lipid membrane.

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Discussion We continue our study of the biophysical properties of PEGylated liposomes using molecular dynamics simulation. Previously we have reported the membrane structure of gel and liquid crystalline bilayers and the effect of PEG polymer density. 18,22 In this study, we incorporate an important component of the liposome formulation, cholesterol, in our membrane model. As seen from the area per lipid vs. cholesterol content in the lipid bilayer plot (3), the liposome surface area is unchanged with the addition of cholesterol at a level of 16.66 molar %. Any further increase in the cholesterol content, however, increases the surface area. This confirms that PEG plays a role in the overall membrane bilayer structure. The visualization of the simulation trajectories (1), showed that the PEG not only interacts with the lipid head groups, but also enters the membrane bilayers in all cases where cholesterol is present. As shown in the mass density profile result (4B), the PEG layer outside the membrane is compacted to be closer to the membrane, and unlike the case of the pure gel state DSPC bilayer, some PEG enters into the membrane core. Garbuzenko et. al. 24 performed experimental studies of HSPC liposomes with 40% cholesterol, varying DSPE-PEG content from 0 to 9%. They observed a peak in the bilayer compressibility at 7 mol % DSPE-PEG. The increasing compressibility from 0 to 7 mol % was seen to reflect dehydration of the lipid bilayer resulting from the presence of the PEG corona. The decreasing compressibility, when DSPE-PEG concentration is increased further reflects the destabilisation of the lipid bilayer leading to micellization. They postulated that the cause of this reversal in the effect of PEGylation resulted from the transition of the PEG corona from the mushroom to the brush density regime. Our simulation hints at the existence of another factor giving rise to this result: the PEG polymer enters the membrane pushing the lipids apart to insert itself, thus beyond a certain density disrupting the membrane structure. The effect of the PEGylation with PEG2000 on the permeability of the vesicle for the neutral molecule D-glucose was studied in vitro by Nikolova and Jones. 26 They observed that 13



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at physiological temperature the permeability initially drops with the inclusion of PEG, but then rises sharply in at approximately 5-7 molar % DSPE-PEG and once again decreases when the molar % of DSPE-PEG is increased to 8-9 %. Once again, this observation is attributed to the change in the structure of the PEG layer from the mushroom to brush regime with increasing PEG density, and our results suggest another factor is possibly involved: the presence of PEG can be seen to be inducing two competing effects, on one hand disrupting the membrane structure through insertion into the membrane core, and on the other creating an additional steric barrier coating the membrane, thus in different concentrations it could be lowering or raising the membrane permeability. The entry of the PEG polymer into the lipid bilayer is very specific in the membrane with cholesterol, unlike the case of the liquid crystalline membrane. 18 When observed in detail, we could see that PEG not only enters at the interface of DSPC and cholesterol normal to the membrane, but also interacts specifically with the β side of cholesterol. Since we are below the melting temperature of pure DSPC the membrane will have a very tight structure, and admittedly dynamics is slow. Possibly our simulation has not captured the full picture of the interaction between PEG and cholesterol; the result is, however, very striking in the degree to which it is pronounced: we do not see a single instance of PEG polymers within the membrane orienting in any other fashion in any of our simulations. We thus feel that we are justified in drawing our conclusions. In a recent paper by Janout et al. 27 results from the transport of fluorescent markers is interpreted to indicate the possible existence of a mechanism whereby PEGylated lipids stimulate the release of cholesterol from phospholipid membranes. While we do not see any instance of the cholesterol molecule leaving the membrane, our results can support their mechanism. The PEG polymer inserting into the membrane, in the fashion we have seen could, at sufficient concentration, and given sufficient time, ease the cholesterol molecule out of the membrane. As shown in 6, in the presence of PEG, the cholesterol peak is shifted away from the membrane centre indicating the possibility that the PEG is starting to lift the cholesterol molecule out of the membrane.

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It is known that that Na+ ions present in the blood plasma bind to to the carbonyl and phosphate groups in the headgroups of lipid membranes. 45,49 In previous work 23 we have also shown that when cholesterol is present in the membrane this binding is substantially reduced, and we proposed a mechanism for this phenomenon. We now see that when PEG is added at 5% of formulation density, the Na+ ions show an almost equal tendency to bind to the membrane head groups and to the PEG oxygens. Furthermore, if the PEG density is increased to 10%, then the Na+ ions show a preference to bind to the PEG oxygens rather than to the phosphate groups of the lipids. The effect of the Cl− ions is consistent with our previous results. 18,22 Targeting moieties are often attached on the outside of liposomes to achieve targeted drug delivery. We here presented, in a continuation of previous work, 28 one such case. We showed that the same phenomenon we previously observed still occurs with the membrane formulation that was experimentally studied: the more hydrophobic AETP targeting moiety interacts with the PEG polymer and thus is covered with it to a greater extent than the RGD peptide, as shown in 8.

Supporting information Supporting tables and figures are included in file ‘Supplementary Material.pdf”. Final configurations for all systems simulated, and topologies of all systems simulate can be found at https://github.com/aniketsh/DSPE-PEG.

Acknowledgements We wish to thank the Academy of Finland (T. R. Center of Excellence in Biomembrane Research), the European Research Council (Advanced Grant project CROWDED-PROLIPIDS), and the Finnish Cultural foundation (A. M.) for financial support. We also thank the CSC - IT Centre for Science Ltd. (CSC) (Espoo, Finland) for computational resources. 15



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0.5 16.66% Cholesterol 20% Cholestrerol 25% Cholesterol 33.33% Cholesterol 50% Cholesterol

Scd

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0.45

0.4 4

6

8 10 12 Segment number

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Figure 2: Profiles of the order parameter -Scd for the SN2 chain of DSPC in DSPC with PEG (solid line) and without PEG (dashed line) in the DSPC bilayers.

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Mass density (Kg m )

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10 -1

Chol. 16% Chol. 20% Chol. 25% Chol. 33% Chol. 50%

Distance from phosphate group peak (nm)

0

Figure 6: Mass density profile of the cholesterol oxygen peaks as function of level of cholesterol, dashed lines are systems with PEG at 10 %.

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'(!)& Figure 7: Penetration of PEG into the lipid bilayer. The PEG enters the lipid bilayer when cholesterol is present in it. However the position of PEG is always adjacent to the cholesterol in all lipid bilayers. In all the cases of PEG - cholesterol interactions, PEG interacted with the β side of cholesterol

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References (1) Lasic, D. D. Novel applications of liposomes. Trends Biotechnol. 1998, 16, 307 – 321. (2) Harris, J. M.; ; Martin, N. E.; Modi, M. PEGylation: A novel process for modifying pharmacokinetics. Clin. Pharmacokinet. 2001, 40, 539 – 551. (3) Harris, J. M.; Chess, R. B. Effect of PEGylation on pharmaceuticals. Nat. Rev. Drug. Discov. 2003, 2, 214 – 221. (4) Allen, T. M.; Hansen, C.; Martin, F.; Redemann, C.; Yau-young, A. Liposomes containing synthetic lipid derivatives of pole(ethylene glycol) show prolonged circulation half lives in vivo. Biochim. Biophys. Acta 1991, 1066, 29 – 36. (5) Allen, T. M.; Hansen, C. Pharmacokinetics of stealth versus conventional liposomes: effect of dose. Biochim. Biophys. Acta 1991, 1068, 133 – 141. (6) Papahadjopoulos, D.; Allen, T. M.; Gabizon, A.; Mayhew, E.; Matthay, K.; Huang, S. K.; Lee, K. D.; Woodle, M. C.; Lasic, D. D.; Redemann, C. Sterically stabilized liposomes: improvements in pharmacokinetics and antitumir therapeutic efficacy. Proc. Natl. Acad. Sci. 1991, 88, 11460 – 11464. (7) Klibanov, A. L.; Maruyama, K.; Torchilin, V. P.; Huang, L. Amphipathic polyethelyneglycols effectively prolong the circulation time of liposomes. FEBS Lett. 1990, 268, 235 – 237. (8) Gabizon, A.; Catane, R.; Uziely, B.; Kaufman, B.; Safra, T.; Cohen, R.; Martin, F.; Huang, A.; Barenholz, Y. Prolonged circulation time and enhanced accumulation in malignant exudates of doxorubicin encapsulated in polyethylene-glycol coated liposomes. Cancer Res. 1994, 54, 987 – 992. (9) Knop, K.; Hoogenboom, R.; Fischer, D.; Schubert, U. Poly(ethylene glycol) in drug

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he Journal of Physical Page 30Chemist of 30 PEG2000% Cholesterol%

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Molecular Dynamics Simulation of PEGylated Membranes with

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