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All-Atom Molecular Dynamics-Based Analysis of Membrane Stabilizing Copolymer Interactions with Lipid Bilayers Probed under Constant Surface Tensions Evelyne M. Houang, Frank S. Bates, Yuk Yin Sham, and Joseph M. Metzger J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08938 • Publication Date (Web): 19 Oct 2017 Downloaded from http://pubs.acs.org on October 20, 2017

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The Journal of Physical Chemistry

All-Atom Molecular Dynamics-Based Analysis of Membrane Stabilizing Copolymer Interactions with Lipid Bilayers Probed under Constant Surface Tensions

by Evelyne M Houang1, Frank S Bates2, Yuk Y Sham*1,3,4, and Joseph M Metzger*1.

1

Integrative Biology and Physiology, University of Minnesota, United States

2

Department of Chemical Engineering and Materials Science, University of Minnesota

3

University of Minnesota Informatics Institute

4

Bioinformatics and Computational Biology Program, University of Minnesota, United

States

Correspondence directed to:

Joseph M. Metzger Ph.D. email: [email protected]

Phone: 612-625-8296

Yuk Y. Sham, Ph.D. email: [email protected] Phone: 612-625-6255

1 ACS Paragon Plus Environment


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Abstract

An all-atom phospholipid bilayer and triblock copolymer model was developed for Molecular Dynamics (MD) studies. These were performed to investigate the mechanism of interaction between membrane stabilizing triblock copolymer P188 and 1-palmitoyl-2oleoyl-sn- glycero-3-phosphatidylcholine (POPC) lipid bilayers under applied lateral surface tension (γ) to model membrane mechanical stress. Results showed that P188 insertion is driven by the hydrophobic polypropylene oxide (PPO) core and dependent on bilayer area per lipid. Moreover, insertion of P188 increased the bilayer’s resistance to mechanical rupture, as observed by a significant increase in the absolute lateral pressure required to disrupt the bilayer. To further investigate the specific chemical features of P188 underlying membrane stabilizer function, a series of MD simulations with triblock copolymers of the same class as P188 but of varying chemical composition and sizes were performed. Results showed that triblock copolymer insertion into the lipid bilayer is dependent on overall copolymer hydrophobicity with higher copolymer hydrophobicity requiring a reduced bilayer area per lipid ratio for insertion. Further analysis revealed that the effect of copolymer insertion on membrane mechanical integrity was also dependent on hydrophobicity. Here, P188 insertion significantly increased the absolute apparent lateral pressure required to rupture the POPC bilayer thereby protecting the membrane against mechanical stress. In marked contrast, hydrophobic copolymers decreased the lateral pressure necessary for membrane rupture and thus rendering the membrane significantly more susceptible to mechanical stress. These new in silico findings align with recent experimental findings using synthetic lipid bilayers and in muscle cells in vitro and mouse models in vivo. 2 ACS Paragon Plus Environment

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Collectively, these data underscore the importance of PEO-PPO-PEO copolymer chemical composition in copolymer-based muscle membrane stabilization in vitro and in vivo. All-atom modeling with MD simulations holds promise for investigating novel copolymers with enhanced membrane interacting properties.



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Introduction

Biological phospholipid membranes are composed of assemblies of amphiphilic lipid molecules. Membranes feature a specific lipid density via hydrophobic interactions between their acyl chains1 and serve as a functional barrier between the intracellular and the extracellular environments. The investigation of the triblock copolymer class of Poloxamers as membrane interacting molecules has generated significant attention as they have demonstrated usefulness in a broad range of industrial2 and biomedical applications3–5. Of particular interest is their function as lipid membrane stabilizing agents3,6,7. Poloxamers are a class of amphiphilic triblock copolymers composed of a polyethylene oxide (PPO) core flanked on both sides by linear chains of polyethylene oxide (PEO) that have been designed with specific modifications in overall molecular weight and in relative PPO/PEO ratio. These two parameters are hypothesized to be critical elements underlying how copolymers modulate membrane interactions8,9. Triblock copolymer archetype Poloxamer 188 (P188, PEO75-PPO30-PEO75 , PPO/PEO = 0.20 and MW=8400 Da) has been well established as a lipid membrane stabilizing copolymer and has been found protective in an extensive range of clinical conditions of membrane injury, including electrical shock10, irradiation11,12, thermal burns4, and other diseases that affect cell membrane integrity13–18. Of particular interest, P188 has shown muscle membrane stabilizing efficacy against mechanical stress in vitro and in vivo. Specifically, P188 confers protection to muscle membranes in animal models of Duchenne Muscular Dystrophy(DMD) 19–22. DMD is a disease of striated muscle deterioration that results from the lack of dystrophin, a cytoskeletal protein essential for 4 ACS Paragon Plus Environment

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maintaining the structural integrity of the muscle cell membrane during muscle contraction23. For this study’s purpose, we define membrane stabilization as prevention of membrane injury ranging from pore formation to complete membrane rupture. It remains unclear what is the mechanism and driving force underlying the P188lipid bilayer interaction and what specific chemical and structural characteristics of P188 make it an effective membrane stabilizer. Previous experimental studies on lipid monolayers, as well as on giant unilamellar vesicles, have suggested that copolymer stabilization of lipid membranes under mechanical stress is highly dependent on the copolymer PPO/PEO ratio7,8. PEO180, a homopolymer of comparable size as P188, but which consists entirely of hydrophilic PEO units lacks significant membrane stabilization efficacy relative to P18822. In comparison, hydrophobic poloxamers, such as PEO7PPO54-PEO7 (PPO/PEO = 3.86), have been shown to disrupt and permeabilize normal healthy cell membranes22. Understanding the driving forces underlying the interactions of block copolymers with lipid bilayer membranes, particularly under physiologically relevant mechanical stress, is critically important in designing and optimizing membrane stabilizing copolymers for biomedical applications. Molecular dynamics (MD) simulations have been well established as a principal method to probe both interactions and dynamics of membrane interacting molecules that cannot readily be observed with experimental techniques24,25. Recent efforts directed to the computational study of copolymer-lipid interactions have mostly been applied based on coarse-grained8,26,27 and united atom28–30 models. These simplified models allow for larger timescale simulation, however, they yield only a partial view of the membrane structural properties and limited atomic resolution information31.



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Importantly, these previous studies have focused on copolymer-bilayer interactions under constant pressure and temperature (NPT) and constant area and temperature conditions (NPAT), which model membranes under normal non-stretched (unstressed) conditions. No study to date, to the best of our knowledge, has applied all-atom MD simulations to investigate the interaction of copolymers with membranes undergoing lateral mechanical stress, a more relevant physiological state in the context of membrane stress in muscle membrane diseases such as DMD. Steered MD simulation utilizing artificial forces to mimic mechanical forces has been employed to explore protein unfolding in atomic force microscopic studies32. In an analogous approach to track and mimic the dynamic behavior of copolymers interacting with a mechanically stressed membrane, we carried out all-atomistic MD simulations of copolymer-bilayer systems under constant pressure, surface tension and temperature (NPγT) ensemble conditions. Here, an increase in surface tension (γ) is used to induce expansion in its conjugate thermodynamic variable, the bilayer area per lipid molecule (A0), which is defined as the surface area in the x-y plane divided by the number of lipid molecules in each leaflet. This expansion in A0 leads to a decrease in bilayer density and this relationship can be used as a computational variable to evaluate how copolymer chemical features influence their interaction with bilayer membranes under lateral mechanical stress. The rationale for using increases in surface tension γ to induce bilayer mechanical stress is grounded on multiple computational studies using MD to simulate the effects of surface tension on the structure of phospholipid bilayers by evaluating A0, lipid-order parameters, membrane thickness, and lipid molecule planar diffusion33–36. In


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these studies, an increase in the applied surface tension of the bilayer resulted in a significant increase in the A0 as well as increased lipid lateral diffusion and decreased lipid-tail order, all representative of reduced bilayer structural integrity35,37. As P188 is hypothesized to only insert into damaged membranes6,38,39, we tested whether increasing A0 via increased surface tension would lead to increased P188bilayer interaction. We demonstrate that P188 interaction with lipid bilayers is dependent on A0 with the copolymer remaining outside the membrane and insertion occurring at an ~15-20% increase in A0. Additionally, we show that P188 insertion into the membrane significantly increases the lateral pressure required for membrane rupture and thereby membrane strength under mechanical stress. To further evaluate the effects of varying molecular weight and PPO/PEO ratios on bilayer interactions, we also assessed PEO180 , PEO140-PPO44- PEO140 , PEO13-PPO30- PEO13 and PEO7PPO54-PEO7. Here, evidence is provided that membrane insertion and stabilization efficacy is dependent on the PPO/PEO ratio, with more hydrophobic copolymers inserting at significantly lower A 0 as well as decreasing the lateral pressure required to rupture the membrane. In this study, we developed an in silico MD model to evaluate triblock copolymerPOPC bilayer interactions at the molecular level with the overarching goal of using this model to further design and optimize potential membrane stabilizing copolymers. We use a POPC bilayer as a representative, artificial and simple model of the more complex and heterogeneously composed biological cell membrane and found comparable conclusions between our computational and previously published experimental results in cell and animals22,55,56 6,8,38,578,28.



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Methods

Initial structures All-atom systems of copolymers with POPC (1-palmitoyl-2-oleoyl-sn- glycero-3phosphatidylcholine (C16:0–18:1PC)) bilayers were generated via molecular modeling using Schrödinger Maestro40. POPC lipid bilayers containing 280 lipids (140 per leaflet) lipid molecules were simulated using Desmond40–42 with the OPLS 2005 force field43 and TIP3P explicit solvation model44 which has been commonly used as the solvent model in all-atom MD systems of various lipid bilayers under different force fields44–46 (Figure 1A). The final unit cell size for the system was ~96 x ~92 x 70 angstroms with counter ions of Na+ and Cl- (150 mM) added to charge neutralize the system to allow the simulations to be carried out under periodic boundary condition using particle mesh Ewald47. POPC systems were simulated at physiological temperature (310K) and atmospheric pressure (1 atm). Due to the standard OPLS 2005 force field not accurately reproducing copolymer physical behavior in water, custom partial charges on the copolymer PEO and PPO blocks were assigned based on previously published quantum chemical calculations of charges of small molecules representing either the PEO or PPO monomer28. These parameters were further validated in our system by reproducing experimentally obtained values of the copolymer radius of gyration in water48. To create the initial starting configuration to evaluate the interaction of copolymer with the bilayer under increasing constant surface tension γ, the copolymers were placed in the solvent near the lipid head group region at random position. To


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create the initial starting configuration for the membrane rupture simulations, the copolymer was initially inserted into the lipid bilayer before constant surface tension γ was applied.

Molecular Dynamics Each simulation was initialized by a 5000 steps conjugate gradient energy minimization with heavy atoms restrained at 50 kcal/(mol*Å2). The restraint system was gradually heated to 310 K for 100 ps followed by a 100 ps equilibration with gradual removal of the heavy atoms restraint at 10 ps interval under a NVT condition. The final unrestrained equilibration was carried out for 100 ps followed by 100 ns of production simulation (or until membrane rupture) at 1 atm and 310 K at NPT or at NPγT conditions, where γ was set constant at 0 up to 70 mN/m. The simulations were carried out under a periodic boundary condition using particle mesh Ewald47. The SHAKE49 method was employed to restrain all hydrogen bonds. A 2 fs time step was used with coordinates saved at 1 ps time intervals and three to four 80-100 ns simulations were carried out for each of the system runs. While this timescale of simulation does not necessarily lead to thermodynamic equilibrium, it was enough to observe copolymer insertion at high surface tension. All membrane analysis, including area per lipid A0, membrane thickness Lz and mass density profiles, was performed using VMD50 and MEMBPLUGIN51. The computational resources used in this study were provided by the University of Minnesota Supercomputing Institute.



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Membrane lateral pressure calculations The mean lateral pressure of the membrane at rupture was determined to estimate membrane strength and was calculated from the equation: γ = Lz (PN - PL) where γ is the surface tension applied on the system, Lz is the box normal size (membrane thickness), PN is the normal pressure and PL is the lateral pressure34. A surface tension of γ = 70 mN/m was used to induce membrane rupture52,53 which was defined in this study by irreversible pore formation within the bilayer. The mean lateral pressure at membrane rupture was averaged over 3-4 individual simulations for each membrane ± copolymer systems.

Results Interaction of copolymers with POPC bilayers at increased A0 Using all-atom MD, the behavior of POPC lipid bilayers under applied mechanical lateral stress was evaluated. Increasing γ applied on the POPC bilayer from 0 mN/m (or NPT condition) to 40, 50, 60 and 70 mN/m lead to increased bilayer average A0, with a rupture surface tension threshold observed at γ = 70 mN/m for the pure POPC bilayer (Figure 1A,B, Table 1). To evaluate the dependence of copolymer composition (Figure 1C) on membrane interaction under mechanical stress, copolymer + POPC bilayer systems at increasing constant surface tensions were simulated for 100 ns. Under NPT conditions, P188 (PEO75-PPO30- PEO75, PPO/PEO = 0.2) remained completely outside of the bilayer over the course of the 100 ns simulation (Figure 2A, Figure 3). However, spontaneous insertion into the bilayer was observed at increased 10 ACS Paragon Plus Environment

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surface tension γ = 50 mN/m and above at an average A0 of ~85 Å2 (Figure 2B). Mass density profiles of block components revealed that once inserted, the hydrophobic PPO block preferentially occupied the hydrophobic acyl chain region of the bilayer while the PEO hydrophilic chain remained in the solvent region outside the bilayer (Figure 3). Further, within the timeframe of the MD simulations, the copolymer did not completely penetrate across the bilayer. To evaluate the role of the PPO core in driving copolymer-bilayer interactions, the completely hydrophilic homopolymer PEO180 was simulated. We observed that PEO180 never inserted into the bilayer within the timeframe of the MD simulations at either γ = 50 mN/m (average area per lipid of ~86 Å2) or γ = 60 mN/m (average area per lipid of ~96 Å2). Further, the PEO chain remained largely outside of the bilayer with sporadic interaction with the bilayer phosphate headgroups (Figure 4). These results are evidence that the hydrophobic PPO core is a primary driver of copolymer insertion into lipid bilayers. In stark contrast, the highly hydrophobic PEO7-PPO54- PEO7 (PPO/PEO = 0.8) quickly and spontaneously inserted into the POPC bilayer even under non-stressed NPT conditions at A0 ~62.5 Å2 (Figure 4). Insertion was again driven by the PPO block, which dwelled well within the hydrophobic tail region, while the relatively small flanking PEO chains were constrained to the lipid head group region (Figure 4B). Comparison of the electron mass density for the PPO block showed that PEO7-PPO54PEO7 is more integrated within the alkyl tail region and center of the bilayer relative to the more hydrophilic copolymers that exhibit shallower insertions. We further evaluated how copolymer overall hydrophobicity influences average A0 of insertion. Here we analyzed copolymer PEO13-PPO30- PEO13 (PPO/PEO = 0.5),



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which has the same PPO core size as PEO75-PPO30- PEO75 but with decreased PEO flanking chain lengths. Insertion was observed at surface tension γ = 40 mN/m and above at average A0 of ~73 Å2 (Figure 5A, B) further supporting that the more hydrophobic the copolymer, the lower the A0 threshold for insertion. We also tested whether the PPO size and/or overall copolymer size affects insertion. As such, we evaluated whether PEO140-PPO44- PEO140 (PPO/PEO = 0.2), a copolymer of equivalent PPO/PEO ratio as PEO75-PPO30- PEO75 but of higher molecular weight, would interact differently with the bilayer under varied surface tension. Interestingly, we observed that PEO140-PPO44- PEO140 inserted at surface tensions γ = 50 mN/m and above and at an average A0 of ~85 Å2, indicating that the overall copolymer size of equivalent PPO/PEO does not affect the average A0 of insertion.

Influence of copolymer insertion on membrane rupture pressure

To further mechanistic understanding of how PEO75-PPO30- PEO75 stabilizes membranes under mechanical stress we evaluated the effect of copolymer insertion on membrane strength as defined by the lateral pressure required for membrane rupture (Figure 6). An applied surface tension of γ=70 mN/m on the POPC bilayer leads to irreversible membrane rupture within ~5.5 ns of simulation (Figure 1B) at a lateral pressure threshold of -262 bar ±2.0 (Figure 6A) and an A0 of 103 ± 1.0 (Figure 6B).This surface tension value was thus used to induce irreversible membrane mechanical stress to evaluate how copolymer insertion affects the lateral pressure threshold for rupture. The presence of PEO75-PPO30- PEO75 inserted into the POPC


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bilayer significantly increased resistance to rupture (*P < 0.0001) with rupture occurring at a lateral pressure of -298 bar ± 1.0 and at an increased A0 of 125 ± 0.4 at time of rupture, indicating that the membrane can withstand higher mechanical stress in the presence of the copolymer. Similarly, PEO140-PPO44- PEO140 reinforced membrane resistance against lateral stress by significantly increasing the pressure required to rupture the membrane to -304 bar±10 (*P < 0.0001) (Figure 6A) and an A0 of 135± 10. Interestingly, insertion of PEO13-PPO30- PEO13 did not significantly affect rupture pressure or A0, as compared to the pure POPC bilayer, indicating that the PPO/PEO ratio has a role in stabilization of the membrane. In marked contrast, the presence of the highly hydrophobic PEO7-PPO54- PEO7 (PPO/PEO = 0.8) within the bilayer led to significantly decreased resistance to mechanical stress, with membrane rupture occurring at -243 bar ± 3.0, a much lower pressure than required to rupture the pure POPC bilayer. Moreover, rupture occurred at a lower A0 of 95 ± 2.0 indicating that the presence of PEO7-PPO54- PEO7 further destabilized the POPC membrane and rendering it more susceptible to mechanical rupture. Taken together, these results indicate that there is an optimal PPO/PEO ratio in combination with mass, at which presence of the copolymer within the membrane during mechanical stress leads to stabilization of the membrane against rupture, and that there is a threshold hydrophobicity at which the presence of the copolymer leads to membrane destabilization.



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Discussion

We developed and implemented the first all-atomistic computational study of PEO-PPO-PEO triblock copolymer interaction with lipid bilayers under physiologically relevant lateral mechanical stress. Our results show that copolymer interaction with lipid bilayers under mechanical stress is dependent on bilayer area per lipid and PPO/PEO composition. More specifically, evidence is provided that insertion of a PEOPPO-PPO copolymer is driven by the hydrophobic PPO core with evidence that there is an optimal PPO/PEO ratio and mass at which insertion and membrane stabilization occurs. We sought here to establish an in silico MD model system to provide molecular level insight into copolymer-bilayer interactions under mechanical stress. The goal is to help further mechanistic understanding of what makes P188 a membrane stabilizer to further guide the design and development of PEO-PPO-PEO based copolymers for optimal biological membrane stabilization. Biological cell membranes are structurally and heterogeneously complex and difficult to study experimentally. As such, studies of membranes are mostly performed on simplified artificial homogenous lipid model monolayers and bilayers and liposomes. While these simplified models provide very useful information about the physical properties of lipid bilayers, results from these models cannot be completely extended to intact biological cell membranes. Another note of importance is that lipid bilayers studied experimentally are probed under macroscopic sizes compared to the microscopic bilayers generated for MD simulations, with the latter tending to support higher absolute values of applied surface tension and induced A0 before rupture54. Thus, caution should be taken when directly comparing 14 ACS Paragon Plus Environment

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absolute area, pressure and tension values obtained from biophysical experiments to those obtained from in silico simulations. Nonetheless, we find good correlation between our computational results and previously published biological and biophysical experimental results from our group22,55,56 and others6,8,38,578,28. A recent study from our group demonstrated the physiological efficacy of membrane stabilizing copolymers in dystrophic muscle cell membranes under conditions of mechanical stress22. Here, membrane stress included hypo-osmotic membrane swelling in vitro and lengthening contraction injury in vivo22. Together with other studies 6,38,578,28, it has been proposed that the lipophilic portion of the molecule (PPO) adsorbs to the membrane surface with some penetration into the hydrocarbon core and the hydrophilic tails (PEO) remaining in the water layer acting as a steric constraint against complete solubilization of the bilayer by the PPO core58. The strength of this interaction is thought to be delicately balanced by the PPO/PEO balance and molecular weight22. Most previous biophysical and computational studies of PEO-PPOPEO copolymer interactions with phospholipid bilayers have been performed under nonmechanical stress conditions28–30,57,59,60. However, a few experimental studies have used monolayers spread on an air-water interface in a Langmuir trough system as a simplified model of the membrane outer leaflet. These studies monitored copolymer interactions with the monolayer at varying surface pressures and surface areas. Here, lateral compression or expansion of the monolayer via surface-pressure-area isotherms was thus used as a comparable model of lateral mechanical membrane expansion6,8,39. While direct quantitative comparisons between our MD results and the experimental surface-pressure area isotherms values obtained in these studies is not possible due to



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the difference in area-surface tension relationship between monolayers and bilayers, and between phospholipid types at physiological temperature61,62, our data are consistent with direct experimental observation that P188 inserts into areas of low lipid density at low surface pressures6,39. Insights from our MD simulations include that P188 (PPO/PEO = 0.20 and Mn = 8400 g/mol) inserts only at average A0 of ~85 Å2, which is equivalent to ~30% above unstressed bilayer A0. These results support the hypothesis that P188 only inserts into areas of the membrane that are low density or damaged. Additionally, our results are consistent with the experimental observations of PPO/PEO ratio and molecular size and bilayer interaction are governed by overall hydrophobicity having a critical role in copolymer insertion into bilayer membranes58,63. Moreover, in general, the PEO configuration remained extended across the phospholipid surface suggesting a role for the PEO block in membrane stability. We further show that copolymer PEO140-PPO44- PEO140 also inserts at an average A0 of ~85 Å2 despite this copolymer being significantly larger molecular weight than P188, suggesting that PPO/PEO ratio has a significant role in insertion while size plays a larger role in membrane stabilization against mechanical stress. We also demonstrate that the completely lipophilic PEO180 homopolymer, at comparable mass to P188, does not insert at any area-per-lipid value studied underlining the need of the PPO core for insertion into the bilayer. Increasing the PPO/PEO to ~0.50, such as is the case for PEO13-PPO30-PEO13, facilitated insertion at lower A0 than P188, but this is still above the non-stressed A0. In marked contrast, the highly hydrophobic copolymer


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PEO7-PPO54- PEO7 with PPO/PEO ~0.80 immediately inserts into a non-stressed bilayer underscoring the critical role of PPO/PEO ratio. In conclusion, bilayer mechanical strength is critical to proper membrane function. This is well understood to be influenced by membrane composition such as presence of cholesterol which significantly increases membrane rupture tension64. In addition, studies have shown that certain nanoparticles can also embed in and affect the mechanical properties of membranes65. In this context, we provide computational insights of copolymer-bilayer interactions that corroborate experimental findings in synthetic monolayers6,39 and bilayers7,59, as well as cellular membranes22,55. These reports lend further validity and confidence to using constant surface tension MD simulations of POPC bilayers as a valuable tool to further our understanding of PEOPPO-PEO triblock copolymer-bilayer interactions. This approach is valuable as it affords the unique opportunity to computationally control and fine tune copolymer chemistry and architecture to evaluate interactions using more complex and more biological-like lipid bilayers.



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Acknowledgements This work was supported by grants from National Institutes of Health, the Lillehei Heart Institute, the Muscular Dystrophy Association (J.M.M.) and American Heart Association Pre-doctoral fellowship (E.M.H.). The University of Minnesota Supercomputing Institute provided all the necessary computational resources for the MD simulations.

Disclosure J.M.M. is on the scientific advisory board of and holds shares in Phrixus Pharmaceuticals Inc., a company developing novel therapeutics for heart failure.


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Figure 1. Schematics of applied surface tension on all-atom in silico POPC bilayer and chemical structures of block copolymers (A) POPC bilayer system undergoing applied surface tension (in mN/m). Water molecules and counter ions are not displayed for clarity (B) Area per lipid of the POPC bilayer under increasing surface tension γ as a function of time. NPT (Normal Pressure and Temperature) represents the bilayer under 0 mN/m tension, *denotes bilayer rupture (C) Chemical structures and nomenclatures of block copolymers. The blue and red bars denote the PEO and PPO blocks, respectively. 25 ACS Paragon Plus Environment


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Figure 2. MD snapshots of PEO75-PPO30-PEO75 –POPC bilayer interaction under (A) 0 mN/m applied surface tension (NPT ensemble), (B) 50 mN/m applied surface tension The blue and red bars denote the PEO and PPO blocks respectively. Water molecules and counter ions are not displayed for clarity


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Figure 3. Molecular Dynamics simulations of PEO75-PPO30-PEO75 (A) MD snapshots of PEO75-PPO30-PEO75 depicting membrane insertion and interaction of PPO (red) with a POPC lipid bilayer at γ = 50 mN/m but not under NPT conditions. (B) Mass density profiles of PEO (blue), PPO (red) and of the phosphate groups of the POPC bilayer obtained from the 100 ns simulation trajectories at NPT (left) and increased surface tension (right) .



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Figure 4. Molecular Dynamics simulations of PEO180 and PEO7-PPO54-PEO7 (A) MD snapshots depicting lack of of PEO180 insertion at γ = 60 mN/m (left) and insertion of PEO7-PPO54-PEO7 under NPT conditions (right) (B) Mass density profiles of PEO (blue), PPO (red) and of the phosphate groups of the POPC bilayer obtained from the 100 ns simulation trajectories o PEO180 at γ = 60 mN/m (left) and PEO7-PPO54-PEO7 under NPT conditions (right) .


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Figure 5. Molecular Dynamics simulations of PEO13-PPO30-PEO13 and PEO140-PPO44PEO140 (A) MD snapshots insertion of PEO13-PPO30-PEO13 at γ = 40 mN/m (left) and insertion of PEO140-PPO44-PEO140 at γ = 50 mN/m (right) (B) Mass density profiles of PEO (blue), PPO (red) and of the phosphate groups of the POPC bilayer obtained from the 100 ns simulation trajectories of PEO13-PPO30-PEO13 (left) and PEO140-PPO44PEO140 (right) .



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Figure 6. Effect of copolymer insertion on rupture pressure (A) and area per lipid A0 at rupture (B). (*P < 0.0001, via one-way ANOVA compared to membrane group, +P < 0.0001 compared to PEO75-PPO30- PEO75 group, &P < 0.0001 compared to PEO140PPO44- PEO140 group, and #P < 0.0001 compared to PEO7-PPO54- PEO7 group). Mean values are derived from 3-4 independent simulations. Error bars shown as mean ± S.E.M.


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Surface tension γ (mN/m)

Area per Lipid (Å2)

Bilayer Thickness (Å)

NPT (0)

62.5

39.0

40

77.2

33.9

50

86.2

33.6

60

95.7

30.1

70

103.3*

26.65*

Table 1: Structural measurements of POPC bilayers under increasing constant surface tension γ. *at time of rupture

Triblock copolymer

Homopolymer

Polymers

Poloxam er

Pluronic

PEO unitsa

PPO unitsa

Total Mnb

PEO wt%c

PEO75-PPO30-PEO75

P188

F68

150

30

8400

79

PEO140-PPO44-PEO140

P338

F108

PEO7-PPO54-PEO7

P331

L101

14

54

3800

20.6

PEO13-PPO30-PEO13

P184

L64

13

30

2900

46.4

-

180

-

8000

100

PEO180

Table 2: Summary of triblock copolymers. Pluronic®: BASF trademark designation; PEO: Polyethylene oxide; PPO: Polypropylene oxide; HLB: hydrophile-lipophile balance where a high HLB value indicates a relatively more hydrophilic polymer. a

Total number of EO or PO monomer units in a polymer chain.

b

Number average molecular weight in g/mol determined by 1H NMR end-group

analysis. c

PEO weight percent to total molecular weight



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