Characterization of Conformation and Interaction of Gene DeliveryVector Polyethylenimine with Phospholipid Bilayer at DifferentProtonation StateChandan Kumar Choudhury,*,† Abhinaw Kumar,‡,§ and Sudip Roy†
†Physical Chemistry Division, National Chemical Laboratory, Pune 411008, India‡Department of Chemistry, Indian Institute of Science Education and Research, Pune 411008, India
*S Supporting Information
ABSTRACT: Polyethylenimine (PEI) is a pH sensitive polymer possessing stretchedand coiled conformation at low and high pH, respectively. It is an efficient genedelivery agent. Thus, the interaction of PEI with the biomembrane is very crucial tounderstand the gene delivery mechanism. In this report, we have investigated thestructural properties of PEI and bilayer due to the interaction of PEI with lipidmolecules. PEI has coil structure at high pH while at low pH it is elongated. Theneutral PEI chain predominately settles itself at the bilayer water interface. We do notfind any disruption or pore formation on the bilayer due to interaction of neutral PEIchain. PEI at low pH gets elongated due to electrostatic interaction between charges ofthe protonated sites. This protonated PEI chain interacts with bilayer membrane, which leads to formation of water/ion channelthrough the membrane. We have analyzed the structure of the channel and water dynamics along the channel.
■ INTRODUCTION
Polycationic polymers are used to disrupt cell membranes,which facilitates the transport of materials from the externalenvironment to the cell.1−6 These membranes act as a selectivebarrier that regulates the flow or transport of materials from theexternal to the internal environment of the cell, thus protectingagainst foreign substances.7 In addition to many vital functionsof membranes, one of the most indispensable functions is itsstability against external perturbations. In the past it has beenshown that the membranes get ruptured upon the induction ofexternal forces like stress and the electroporation techni-que.8−11 The membrane rupture occurs due to the formation ofpores. It is assumed that initially short-lived small hydrophobicpores are formed and then lipid molecules reorient to formhydrophilic (head groups) pore walls.10 Under mechanicalstress, hydrophilic pores are formed in peptide-free lipidbilayers.9 It is also well-known that the proteins and peptidescan create channels and regulate the permeability of ions andprotons through them. A number of studies has revealed thatcytolytic and antimicrobial agents and some polyelectrolyteoligomers are able to disrupt the lipid bilayers by formingstabilized pores.12−17 The study of stabilized pores isbiologically very important because they can assist the transportof polar molecules and ions across the membranes and couldalso lead to the initiation of cell lysis or fusion.18,19 In additionto small molecules, pores formed by the electroporationtechnique can also facilitate DNA uptake by the cells.20 Smallpores formed by antimicrobial peptides destroy transmembraneion gradients and electrical potential, which can lead to celldeath.15 Most of these peptides are either cationic oramphipathic.
Polycations have been used for the delivery of geneticmaterials to the cells.5,21,22 They are also used as biocidalagents.23−25 Thus the study of the impact of synthetic andnatural polycations on the bilayer membranes is very crucial.Polycations are internalized in the cell in three steps: (a)binding of polycations with the phospholipids or glycolipids inthe membrane, (b) internalization into the cells, and (c) exitfrom the endosomes.26−28 This whole process is termedpolycation-meditated endocytosis. In the recent past, research-ers have widely used polycationic polymers to disrupt the cellmembranes and transport materials to the cell.1−6 Helander etal.1 studied the microbicidal activity of polyethylenimine (PEI),a polycationic polymer, and its interaction with Gram-negativebacteria. They concluded that Gram-negative bacteria arepermeable to hydrophobic probes such as antibiotics and 1-N-phenylnaphthylamine because of the presence of PEI. Mecke etal.2 investigated the dimyristoylphosphatidylcholine (DMPC)supported lipid bilayers using atomic force microscopy withdifferent sizes of poly(amidoamine) (PAMAM) dendrimers, apolycationic polymer. They observed that the higher generationdendrimers (e.g., G7) caused the formation and growth ofholes in membranes whereas the ability to remove lipids frombilayers was reduced for G5 and completely lost for G3. Sikoret al.5 in their study showed that the nonspecific interactionsbetween the polyplexes and the unilamellar DMPC vesicle inthe presence of PEI result in the transport of molecules to thecell nucleus. Genetic materials were transfected by the opening
Received: August 1, 2013Revised: September 6, 2013
of small pores in the nuclear membrane. Dynamic lightscattering and ζ potential study showed that the interaction ofmodified polycation (by introduction of hydrophobic group)with 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine(POPC) membrane enhances the hydrodynamic radius and ζpotential.4 This has been associated with the penetration ofpolycation into the lipid bilayer. The hydrophilic poreformation in the lipid bilayer because of the incorporation ofpolycation facilitates the flow of water and ions through it.4
PEI based gene vectors are considered to be versatile genedelivery agents.28,29 The polyplexes are formed with linear(LPEI) or branched (BPEI) PEI. PEI complexes with nucleicacids through electrostatic interactions form polyplexes. Thesepolyplexes enter the cell through endocytosis. The comparativetransfection efficiency of LPEI or BPEI is quite controversial.Dai et al.30 reported that both the LPEI and BPEI have similartransfection efficiency when N/P ratio is higher where N is thenumber of polymer nitrogen atoms and P the number of DNAphosphorus atoms. In this scenario, not all the PEI interactionsites are bound with the polyplex; some free PEI fraction exists.These free PEIs, apart from enhancing the transfectionefficiency, also give rise to toxicity.31 The mechanism of theescape of polyplex after the internalization is debatable. Themost generally accepted mechanism is the “proton sponge”hypothesis.32 However, alternative mechanisms are alsosuggested.33 A recent study has shown that the proton spongeeffect of PEI does not include the change in lysosomal pH, andthis led them to believe that this effect is not the dominantmechanism of polyplex release.34 Thus the study of interactionof PEI with bilayer and the mechanism of transfection of PEIinto cells are of immense interest for the gene therapycommunity. Although the interactions of PEI with lipid bilayershave been investigated experimentally,1,2 no simulations havebeen performed. Molecular simulations can provide detailedinsight about the interaction of lipids and PEI and its effect onthe bilayer membrane. Therefore, the scope of this work spansfrom understanding conformation of PEI in differentprotonation states, which mimic the low and high pH in thelipid bilayer, to the transfection mechanism of PEI, along withpore formation.In this study, we report results based on simulation of linear
PEI (LPEI) in different protonation states with 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) molecules. We have usedclassical molecular dynamics (MD) simulations to determinehow LPEI interacts and changes conformation with the lipid-bilayer membrane. We mimic LPEI in two different pHconditions, high and low, that is, basic and acidic, respectively.A low pH (acidic conditions) leads to the protonation ofnitrogen atoms of the LPEI chain, and here we term it asprotonated PEI, while at high pH (basic conditions), we call itunprotonated PEI. We have allowed PEI to sampleconformations with the lipid bilayer by placing it in differentprobable sites in the bilayer. The protonated PEI chain indeeddamages the structural integrity of the lipid bilayer forminghydrophilic pores. Helander et al. have experimentally reportedthis.1 We observe the change in the orientation of the lipidmolecules alongside the pore. We also addressed the waterdynamics along the pore.
■ METHODSComputational Details. We had performed all atom molecular
dynamics (MD) simulations of lipid bilayer along with onepolyethylenimine (PEI) chain. The equilibrated structure of 72
DOPC molecules was obtained from Siu et al.35 To increase thelength scale, this system was replicated along the Y-axis, forming abilayer with 144 DOPC lipid molecules (see Figure S1 of SupportingInformation). This pure lipid bilayer system was then simulated for250 ns for characterizing the bilayer properties. The last 100 ns oftrajectory was used for the analysis, and bilayer properties werecomputed and tabulated in Table 1. The area per lipid of the pure
system was 0.76 ± 0.02 nm2, which is very close to that reported bySiu et al.35 (0.74 ± 0.03 nm2). The difference in area per headgroupcan be attributed to the size of the system. The mean square lateraldisplacement was computed for the phosphorus atoms present in eachleaflet of the bilayer. It was calculated by averaging the last 100 ns ofthe trajectory in steps of 10 ns. The lateral diffusion coefficientobtained was 1.84 × 10−7 cm2/s while the experimentally reported onefrom a pulsed field gradient NMR experiment was 1.37 × 10−7 cm2/s.36 Thus good agreement of these values validates the bilayer structureand properties. In addition to these properties, we had also calculatedthe bilayer width (calculated as the distance between the intersectionline of the density profiles of the lipid and water molecules), which was3.83 nm.
PEI in both forms (unprotonated and protonated) were taken fromour earlier work,37 where we have characterized the PEI conformationand dynamics in pure water. The radius of gyration (Rg) gives a senseof the size of the polymer coil. The end-to-end distance is the distancethat connects the two terminal atoms of the polymer chain, while thesquare radius of gyration (Rg
2) is the average squared distance of anypoint in the polymer coil from its center of mass. The average end-to-end distance and radius of gyration of unprotonated PEI in water were2.37 ± 0.82 nm and 0.97 ± 0.16 nm, while for protonated PEI, thesevalues were 5.38 ± 0.56 nm and 1.79 ± 0.74 nm, respectively (seeTable 1).37
PEI, being an efficient gene delivery agent, its atomic levelinteraction with biological membranes and its fall out are very crucialto understand. Because the all atomistic MD simulation limits itself tothe short time scale (in the range of nanoseconds), it is almostimpossible to predict the probable insertion mechanism of polymer inthe lipid bilayer from the solution. Coarse graining of the PEI andbilayer molecules could enhance the time scale to an order ofmagnitude higher; however one would miss some important localatomistic level interactions. Thus it is reasonable to consider the initialposition of PEI by placing it at different favorable positions of thebilayer. So, to study the PEI−bilayer interaction, different sets ofsimulations were performed where unprotonated or protonated linearPEI chain was separately placed in different regions of the lipid bilayersystem. The unprotonated PEI is a coiled polymer while theprotonated PEI is elongated.37,38 The initial coordinates wereconstructed by placing PEI at the water or the bilayer region.Unprotonated PEI with different radii of gyration were preparedseparately by placing it in the bilayer hydrophobic region (systemUn_b, see Figure S2a and S9a,c,e of Supporting Information) and inthe water region (system Un_w, see Figure S3a and S8a,c,e ofSupporting Information). For protonated PEI, being elongated, threedifferent positions in the bilayer−water system were probable where itcould be placed. It was placed in the middle of the two bilayer leaflets
Table 1. The Properties of Lipid (DOPC)−Water Systemand PEI (Unprotonated and Protonated)−Water System.
(i.e., in the hydrophobic region), perpendicular to the Z-axis (systemPr_b⊥, see Figure S4a of Supporting Information), that is, the bilayerplane. In the second simulation, it was placed parallel to the Z-axis,spanning across the water and bilayer regions (system Pr||, see FigureS5a of Supporting Information), and in the third set, it was placed inthe water region, perpendicular to the interfacial axis (Z-axis) (systemPr_w⊥, see Figure S6a of Supporting Information). These figures weregenerated using PyMOL.39
For each of these systems, the simulation conditions were adoptedfrom Siu et al.’s article.35 Amber force field40,41 was used for DOPC35
and PEI.38 TIP3P water model42 was used to solvate each system suchthat no water molecules were present inside the bilayer. The hydrogenbonds were constraint with the LINCS algorithm.43 The time step ofintegration was 2 fs. Periodic boundary conditions were applied in alldirections. The nonbonded potential energy cutoff was 1.0 nm. Theparticle-mesh Ewald algorithm44 was used for long-range electrostaticinteractions. The simulations were performed using Gromacs-4.5.545
with NPγT ensemble. All the simulations were performed at 310 K(well above the transition temperature of 253 K). Berendsenthermostat and barostat46 were used for the temperature and pressurecoupling with time constant of 10 fs and 1 ps, respectively. The DOPCbilayers were subjected to a surface tension, γ, of 220 bar/nm persurface with reference z-pressure of 1 bar and volume compressibilityof 4.5 × 10−5 bar−1.Initially, systems Un_b and Un_w were equilibrated for 4 ns by
restraining the position of the PEI molecule at its mean position suchthat the neighboring molecules get equilibrated with the PEI molecule.Water and PEI molecules of system Pr|| and Pr_b⊥ were positionrestrained for 0.5 ns. For system Pr_w⊥, only the PEI chain wasposition restrained for 0.5 ns. For each of these systems, the positionwas restrained with force constant, kpr, of 1000 kcal mol−1 nm−2 usingthe following equation:
= | − |V r k r R( )i i ipr pr2
(1)
The position restraining of PEI molecules allows us to obtainequilibrated water or lipid molecules around it. The coordinate files atthe end of these simulations were used as initial structures for furthersimulations of 250 ns. The trajectories were recorded at an interval of1 ps. The last 100 ns of the production runs was analyzed. A framenear 250 ns was extracted from the Pr|| system such that the whole ofthe PEI was inside the simulation box. This frame served as the initialstructure for another 100 ns simulation where the trajectory wasrecorded every 100 fs. This extracted structure was also used forgenerating a condensed trajectory of 4 ns, recording the trajectoryevery 10 fs. This condensed trajectory was used for analyzing thedynamical properties of water molecules in the bilayer pore.In this work, PEI was placed in the bilayer and the water region in
different simulated systems. We have compared the end-to-enddistance and the radius of gyration of PEI in different protonationstates when placed in lipid bilayer system. These values were animportant benchmark to understand the structural properties of PEI ininteraction with bilayer system.
■ RESULTS AND DISCUSSIONS
The properties for the lipids with embedded unprotonated andprotonated PEI had been computed and discussed. Theseproperties were compared with the pure lipid−water system.Also the structural properties of PEI for each of the systemswere evaluated. These properties were compared with the purePEI−water system. For the Pr|| system, disruption of the bilayerwas observed due to the formation of a pore. Theconformations of lipids and the dynamics of water in thevicinity of pore were also studied.Structural and Dynamical Properties of Bilayer. The
partial density along the interfacial axis (Z-axis) for DOPC,water, and PEI molecules was computed and plotted in Figure1 for every system. The bilayer width calculated as the distance
between the intersection points of the density plot of lipid andwater was smaller for system Un_w (3.70 nm) compared withthe pure lipid bilayer (3.83 nm) and Un_b (3.85 nm) systems(Figure 1, Tables 1 and 2). The bilayer width for the Pr|| systemwas ca. 3.50 nm; for systems Pr_b⊥ and Pr_w⊥, it was ca. 3.86nm, Table 2. The bilayer widths for the Pr_b⊥ system andPr_w⊥ systems were close to that of the pure lipid bilayersystem (Table 1), but the Pr|| system had a much smaller bilayerwidth. From the partial density plot (Figure 1b), we couldnotice that the partial density of the lipid molecules for the Pr||system was less than the other two systems. We also observed(from the density profile of water molecules) that there wasfinite density of water molecules along the hydrophobic regionfor system Pr|| (also see Figure 2b). In this system (Pr||), aprotonated PEI chain was placed parallel to the Z-axis spanningacross the lipid molecules with ends in the water region (referto Figure 2a). The finite density of water molecules in theinterior of the bilayer suggests the presence of water moleculesthat were in connection with the bulk water. The existence ofwater molecules can be attributed to the presence of thepartially hydrophilic protonated PEI chain, which passesthrough the bilayer region. The polymer chain being chargedattracts water molecules, which find a path to cross the bilayerregion. Disruption in the bilayer due to this decreases theoverall average partial density of the lipid molecules. However,decrease in the bilayer width for this system was subject tofurther investigation, which is discussed later in this paper. Thisdisruption resulted in pore or channel formation as thesnapshot after 250 ns of simulation (see Figure 2b) alsosuggests.
Figure 1. Partial density profile for (a) unprotonated and (b)protonated PEI−bilayer−water system. The density plots (of waterand lipids) for each of the systems were shifted such that theintersection points coincide. The density for PEI is placed on the rightside.
The position of PEI after equilibration for systems Un_b andUn_w, in Figure 1a, was almost the same. The PEI moleculesdiffused to the interface (see Figures S2b and S3b ofSupporting Information) from their respective startingpositions, that is, from water (Un_w) and from middle of thebilayer (Un_b). This indicates whether one simulates PEI byplacing it in the bilayer region (as in system Un_b) or in thewater region (system Un_w), it ends up at the interfacialposition because of favorable interactions. Thus the startingposition of unprotonated PEI was immaterial. However, thequestion remains whether the initial position (initialinteractions with the regions) could favor some specificconformation of PEI. Therefore, the conformational analysisof PEI is also an important aspect of this paper.Area per lipid is one of the important structural character-
istics of the bilayer, and it also serves as a quantity to confirmequilibration of such self-assembled systems. Area per lipid forall the systems is plotted in Figure 3 and tabulated in Table 2.
From the plots, it was apparent that the systems were well-equilibrated. For system Un_b, average area per lipid moleculewas 0.76 ± 0.14 nm2, and for system Un_w⊥, it was 0.76 ± 0.02nm2. The average areas per lipid for systems Pr_b⊥ and Pr_w⊥were 0.76 ± 0.02 and 0.75 ± 0.02 nm2, respectively (Table 2).These values were same as that of the pure lipid bilayer system(refer to Table 1). So, the presence of unprotonated (Un_b,Un_w) and protonated (systems Pr_b⊥ and Pr_w⊥) PEI didnot change the lateral area. A visual inspection of the Pr|| systemshowed that the conformation of lipid molecules in the vicinityof PEI had changed. This had resulted in increase of the areaper lipid of this system. Further in the article, we have analyzedthe orientation of lipid molecules around the polymer chain forthe Pr|| system.Similar to the structural properties, dynamical properties of
lipid molecules could get altered due to perturbation. Thepresence of PEI in the vicinity of the head groups of lipidmolecules and the interaction between them might slow thelateral motion of lipid molecules. Therefore, we calculated thelateral mean square displacement (in the XY plane; MSD) of Patoms of the leaflets. The last 100 ns of the production runtrajectory was split into 10 equal intervals comprising 10 nseach. For each of these trajectories, the lateral MSD in the XYplane was calculated. These plots were averaged and plotted inFigure 4. Lateral diffusion coefficient of lipids were computedfrom the slope of these plots and are tabulated in Table 2. Forsystems Un_b and Un_w, lateral diffusion coefficients weresame. Although the diffusion coefficients for these two systemswere smaller than that for the pure bilayer system, they werewithin the error bar with the pure lipid bilayer system. Thus,the presence of unprotonated PEI had no effect or negligibleeffect on the lateral diffusion of lipid molecules. The diffusioncoefficients for systems Pr||, Pr_b⊥, and Pr_w⊥ were smaller(Table 2) than the pure and unprotonated systems. The PEI
Table 2. The Properties of the Lipid (DOPC)−Water−PEI Systema
aThe unprotonated PEI was placed in the bilayer (system Un_b) and water (system Un_w) region of the water−bilayer system. Protonated PEI wasplaced parallel to the interfacial (Z) axis (system Pr||), perpendicular to the Z-axis in bilayer (system Un_b⊥), and perpendicular to the Z-axis in water(system Pr_w⊥).
Figure 2. Snapshots at 0 ns (a) and 250 ns (b) of system Pr||. Here PEIwas placed parallel to the Z-axis, spanning across the water and bilayerregions. Water molecules are shown as gray spheres. To obtain theclear position of PEI, DOPC and water molecules have been madetransparent by 30%. H-atoms are not shown for clarity.
Figure 3. Area per lipid of the (a) unprotonated and (b) protonated PEI−bilayer−water system.
chain being protonated interacted with the lipid molecules andslowed the lateral movement of the molecules.Thus, the presence of unprotonated PEI shows negligible
effect on the structural and dynamical properties of bilayer,while the protonated PEI slows the motion of the lipidmolecules, and in particular, Pr|| deforms the bilayer forming apore. PEI in both forms (unprotonated and protonated) settlesnear the interface of the lipid bilayer system. However,protonated PEI was more bound to the bilayer headgroupbecause of the higher electrostatic interactions between thecharged PEI atoms with the hydrophilic headgroup and watermolecules present at the interface.Structural Properties of PEI in the Bilayer. Properties of
the polymer also change due to its interaction with the bilayer.
PEI may also take conformations that are biased due to theneighboring atoms, as well as the initial conformation and initialenvironment. To understand this, we calculated end-to-enddistance and radius of gyration (Rg) of PEI as a function of timefrom the last 100 ns of the production run trajectory andplotted them in Figure S7 of Supporting Information. Theaverage end-to-end distances for systems Un_b and Un_wwere 2.82 and 0.84 nm, respectively. Their respective averageRg were 1.13 and 0.76 nm (see Table 2). Thus when PEI wasplaced in the water region (at the beginning of simulation,system Un_w), it attained a highly coiled structure. In fact, thisstructure was slightly more coiled compared with the purePEI−water system (see Tables 1 and 2). From the distributionplots (see Figure 5a,b) of end-to-end distance and Rg, it was
Figure 4. Lateral mean square displacement of the P atoms present in the single leaflet of the bilayer for (a) unprotonated and (b) protonated PEI−bilayer−water system.
Figure 5. The distribution of end-to-end distances and radius of gyration of PEI for (a, b) unprotonated and (c, d) protonated systems. Its variationwith time are shown in the Figure S7 of Supporting Information.
evident that unprotonated PEI in the Un_b system scans amuch wider region than that in the Un_w system. Interestinglythere were small overlaps of end-to-end distance and Rgdistributions of Un_b and Un_w systems. In the case of theUn_w system, PEI was confined to a certain compactconformation. A similar end-to-end distance and Rg of PEI asa function of time (see Figure S7 of Supporting Information)and its distributions (see Figure 5c,d) for the protonated PEIshowed that PEI was confined to an extended conformation inevery system, as in pure water. The average values are tabulatedin Table 2. The elongation of the structure could be due to theelectrostatic repulsion between the monomers of PEI, whichrestricts the conformational flexibility.However, the question remains open whether different
starting (initial) conformations of unprotonated PEI can resultin different conformations of the chain and therefore can residein a different location of the bilayer. To investigate it furtherand statistically prove the result, we had performed six moresimulations starting from different conformations of unproto-nated PEI initially positioned in the hydrophilic (threesimulations, see Figure S8 of Supporting Information) andhydrophobic (three simulations, Figure S9 of SupportingInformation) region of the bilayer. These unprotonated chainsof different conformation with Rg 0.80, 1.10, and 1.25 nm wereextracted from trajectories generated from a system where thePEI chain was simulated only in water.37 These conformationswhen placed in the water region (above the interface) of lipidbilayer system, they settled in the interface by attainingequilibrium Rg of 0.85, 0.80, and 0.87 nm, respectively (seeFigures S8b,d,f, S10a, and S11a of Supporting Information).These PEI chains on positioning in the bilayer region getexpanded, and in all three cases, terminal groups of the PEIchains touched the bilayer−water interface on both sides (seeFigures S9b,d,f and S10b of Supporting Information). For 0.80and 1.10 systems, the Rg were approximately 1.2 nm and for the1.25 system, the Rg was 1.4 nm (see Figure S11b of SupportingInformation). So it is evident that the unprotonated PEI gainsconformational flexibility in the bilayer and expands itself.However, PEI chains with the same conformation in waterpreferred the coiled conformation and sampled the interfaceregion.Pore Formation and Water Dynamics in the Pore. The
PEI chain of the Pr|| system passes through the lipid region withits terminal groups touching the bulk water molecules on both
sides of the bilayer (see snapshot Figure 2a and density profileof PEI molecule (Figure 1b, green dashed lines)). The densityprofile plot of the water confirmed the presence of watermolecules in the bilayer region (from 2.5 to 5.5 nm, see Figure1b and Figure 2b). Also the unprotonated PEI system whenplaced initially in the hydrophobic region of the bilayerexpands, and the end touches the bulk water on both sides.Here, we did not see any transport phenomena of water or ionsalong the polymer backbone. However, in the case ofprotonated PEI, we did observe the transport of water andions across the membrane. The increase in hydrophilicity of thePEI chain because of the charged amine groups had effectivelyhelped in forming a pore. Similar pore formation was alsoobserved by Groot et al.47 in case of nanoscopic hydrophilicchannels. Visualization of the trajectory also revealed thepresence of water molecules and ions across the bilayer regionalong the PEI chain. The pore radius we had calculated was0.73 ± 0.13 nm, which is relatively small in size.19 The variationof pore radius with simulation time is shown in Figure S13 ofSupporting Information. Transport of water molecules alongthis bilayer−PEI channel and the dynamics of water weresubjects of our investigation. The presence of multiple cationicmoieties along the polymer chain provides a polar environmentinside the lipid bilayer, which was favorable for water moleculesto penetrate deep in the hydrophobic region of the bilayer. Inour earlier studies, we have shown that water can penetrate onlyto some certain extent of the hydrophilic headgroup regionwithout any external perturbation.48
We have calculated the flux of the water molecules passingthrough the pore formed in the Pr|| system. The 100 nstrajectory (saved every 100 fs) was used for the calculation offlux. We had divided the bilayer in two regions. Region I wasthe interior of the bilayer whose Z-coordinate ranges from 3.60to 4.50 nm, while region II spaned from 2.10 to 3.60 nm and4.50 to 5.90 nm (Figure S12 of Supporting Information). Theboundaries for region I and region II had been chosen from thedensity profiles of water and the PEI molecule (Figure 1b).Figure 6a shows the schematic diagram of the boundaries of theregions (also see Figure S12 of Supporting Information.). Theboundaries (extreme) of the region II were approximatelymerging with the bulk water. Water molecules present in regionI were tagged and stored every frame. They were counted ifthey crossed region II in the subsequent frames and weresimultaneously untagged. Such counts were recorded for every
Figure 6. (a) Schematic representation for the different regions in the interior of bilayer. Region I is the interior of the bilayer defined as the regionbetween 3.6 and 4.5 nm of the Z-axis. Region II is the interfacial region ranging from 2.1 to 3.6 nm and 4.5 to 5.9 nm of Z-axis. These boundarieshave been taken from the partial density profile of the Pr|| system. (b) Flux defined as the number of water molecules passing through the pore to thebulk water region for the Pr|| system.
frame. It was also possible that none of the tagged watermolecules (present in region I) crossed region II for some ofthe frames. Then the count for these frames was set to 0. It wasalso possible that a water molecule, once in region I, crossedregion II and re-entered region I. All such incidences wereconsidered as distinct, and the water molecules were taggedagain. The counts were averaged for every nanosecond andplotted in Figure 6b. An average of around 150 watermolecules/ns passes through the channel. Ions can also flowthrough this channel. However, only a few ions were added toneutralize the system. So because of poor statistics, we did notanalyze and report the flow of ions.The electrostatic interaction between water and protonated
PEI favors the water molecules residing in the pore for sometime. But we had observed that these water molecules also flowin and out from the channel. Therefore, residence time for thewater molecules along the polymeric chain, that is, in theinterior of the bilayer, for system Pr|| was computed. Only thosewater molecules were considered that were within the distanceof 1.5 nm from the polymer backbone and present in theinterior of bilayer (by defining the Z-coordinate boundariesbetween 2.70 and 5.40 nm, Figure 1b). The number of watermolecules in the bilayer region that satisfied the aboveconditions as function of time is shown in Figure 7a. Thesame has also been calculated from the condensed trajectory(see Computational Details) and depicted in Figure S14 ofSupporting Information. From these two figures, we observethat an average of around 250 water molecules are present inthe hydrophobic region in every frame. The methodology forcalculating the residence time was same as that reported in thearticle by Choudhury et al.37 The condensed trajectory was splitinto four intervals, 0−1 ns, 1−2 ns, 2−3 ns, and 3−4 ns (0−1ns was not considered for calculation of residence time). Ineach of the frames, unique water molecules (which satisfied thecriteria of lying within the distance of 1.5 nm from the polymerbackbone and present in the interior of bilayer) were recorded.They were tracked for subsequent time (frames). If the watermolecules were continuously not found for 2 ps, the time wasrecorded as the residence time. The residence time plots fromthese split trajectories were averaged and plotted in Figure 7b.The plot was normalized with the residence time at 0 ps. Sincethe nature of the plot was biexponential, it was fitted with abiexponential function, eq 2, with relaxation times τf and τs, andaf and as are the, respective, amplitudes of the fast and slowrelaxation components. The values of the fast and slowrelaxation with their respective components are tabulated in
Table 3. There exists heterogeneity in the system because of thepresence of two distinct molecular species, one with slow and
the other one with fast relaxation,49 in the water moleculesalong the polymer chain in the bilayer region.
= + +τ τ− −y a a ae et tf
/s
/0
f s (2)
The relaxation of these water molecules was slowercompared with the unprotonated PEI in water system (1stsolvation shell).37 This slow relaxation may be attributed to thestronger H-bond network of the protonated groups of PEI inwater (lipid−PEI system). These relaxations were similar to theprotonated PEI in water system.37 The higher τf, that is, slowermotion than that of the protonated (1st solvation) system, wasdue to the restricted motion of the water molecules in thebilayer region. This motion was along the polymer chain.The mean square displacement (MSD) of water molecules
present along the polymer chain was also computed and plottedin Figure 8. From the residence time plot (Figure 7b, onlythose water molecules were considered that reside for aminimum of 20 ps. The detailed computations have been
Figure 7. (a) Total number of water molecules present as a function of simulation time in the hydrophilic pore formed of the Pr|| system. (b)Residence time probability of the water molecules present in the pore.
Table 3. The Relaxation Coefficients (af, as) for the Fast andSlow Relaxation Times (τf, τs, respectively) for the Pr||System
af τf (ps) as τs (ps)
Pr|| system 0.78 0.25 0.24 4.31
Figure 8. The mean square displacement of water molecules presentin the pore. Inset shows the semilog plot for the mean squaredisplacement at the sub-picosecond scale.
described elsewhere.37 MSD was calculated by using thecondensed split trajectories. The individual MSD plots fromthese split trajectories were averaged and plotted in Figure 8.The diffusion coefficient obtained from the slope was 1.63 ×10−5 cm2/s. The inset shows the semilog plot of the MSD ofwater molecules present in the interior of bilayer in the sub-picosecond region. This plot was fitted to eq 3, where the valueα1 indicated the type of diffusion followed by the watermolecules.50
α= αdr t20
1 (3)
A system follows a ballistic or Fickian diffusion if α1 is 2 or 1,respectively. For this system, α1 was 1.8. In this case, thediffusive motion is much more like the ballistic, that is, theconfined water moves in coordination.Orientation of Lipid Molecules around the Pore. The
incorporation of PEI in the lipid bilayer system for Pr|| systemcreated a channel, which leads to a change in the orientation ofthe lipid molecules. This change was visually observed in thetrajectory. It is schematically shown in Figure 6a. Theorientations were such that the lipid molecules tilt or orientthemselves along the PEI chain. To quantify the change inorientation, we calculated the orientation of lipids along the Z-axis. We defined three groups, head, middle and tail, for lipidmolecules as represented in Figure S15 of SupportingInformation. Middle and head groups comprise the atoms ofthe phosphate and choline moieties, respectively, and the tailgroup consisted of all the remaining atoms up to the start ofunsaturation (see Figure S15 of Supporting Information). Theremaining atoms were not considered since they were spreadout because of unsaturation in hydrocarbon moieties. Thecenter of mass (COM) for each of these groups were computedfor every frame. An angle between the line formed by the COMof middle and tail groups with the XZ-plane (perpendicular tothe bilayer plane) was computed for every lipid molecule ineach frame. These angles were classified as vicinity or far angleon the basis of the position of the phosphorus (P) atom withrespect to PEI chain. If the P atom of a lipid molecule fallswithin a distance of 5 Å (see Figure S16 of SupportingInformation, radial distribution function between P atoms andbackbone atoms of PEI had minima of the largest peak at 5 Å)from the PEI backbone, then the angles computed were termedas vicinity angle. If the separation of the P atom of a lipid fromthe PEI backbone was greater than 5 Å, then the angle wastermed as far angle. These angles were computed for the last100 ns of the trajectory, and their distributions are plotted in
Figure 9a. Similar distributions were computed for the angleformed between the COM of head, middle, and tail groups (asdefined above) for each of the lipid molecules and are plottedin Figure 9b. These plots were normalized by the total numberof lipids in each sections (i.e., vicinity and far). From Figure 9a,it is noticeable that the lipids that are away from PEI prefer tostay around 0° and have a lower probability for higher angles,while for the lipids staying in the vicinity of PEI, in addition tostaying around 0°, they also prefer to stay around 42° and 75°.The conformations of lipids within the vicinity of PEI aredifferent because phosphate moiety is tilted and it makes thepore hydrophilic. Figure 9b shows the distribution of the angleformed by head, middle and tail groups for each of the lipidmolecules. We see that the angles of the lipids that are at adistance >5 Å from the PEI backbone mostly stay around 109°while those in the vicinity prefers to stay around 90°. Thepresence of PEI also had an effect on the tilting of theheadgroup, which eventually provides a hydrophilic channeland water can flow through it.
■ CONCLUSIONS
Lipid bilayer with embedded polycationic polymer, PEI, at twodifferent protonation states was simulated by all atomistic MD.We studied the effect of PEI on the lipid bilayer system. Inaddition to the pure lipid bilayer system, bilayer systems withunprotonated and protonated PEI were separately studied.Unprotonated PEI always settled at the interface when it wasplaced in the hydrophilic region (in water) at the start of thesimulation. When it was positioned in the hydrophobic region,the PEI chain gains conformational flexibility and expands whilesampling across the membrane. In the hydrophilic region, PEIis more coiled compared with when it is placed in thehydrophobic region. In the case of protonated PEI, it settles atthe interface, irrespective of whether it was placed in the bilayeror water region at the start of simulation. An exception wasobserved for the Pr|| system where PEI was parallel to the Z-axis. The presence of unprotonated PEI does not significantlyperturb the bilayer properties; whereas protonated, beingcharged, interacts to a greater extent with the interfacialmolecules. This interaction resulted in reduction of lateraldiffusion of the lipid molecules.Though the unprotonated PEI spans across the membrane in
most cases when it was placed in the bilayer, no disruption inthe bilayer has been observed in the simulation time scale. Theprotonated PEI in the Pr|| system disrupts the structuralintegrity of lipid bilayers. The presence of multiple cationic
Figure 9. Orientation of lipid molecules in the vicinity of pore and away from it. (a) shows the distribution of the angle formed between the center ofmass of the middle and tail group and the XZ-plane. (b) shows the distribution of angles formed with the head, middle, and tail moieties.
moieties along the polymer chains provides a favorable polarenvironment inside the lipid bilayer for the water molecules topenetrate across the bilayer. This eventually leads to theformation of a hydrophilic pore where water molecules andions can flow through it. These observations are also supportedby the experimental studies by Helander et al. on Gram-negative bacteria.1 These water molecules are homogeneous,and they ballistically diffuse along the pore with the diffusioncoefficient of 1.63 × 10−5 cm2/s. We have also observed theinclination of the lipid molecules toward the pore. This newinsight of the distortion of lipid bilayers can be valuable tounderstand the effect of concentration of PEI on the bilayer,which eventually may help in designing PEI as better genedelivery vector.
■ ASSOCIATED CONTENT
*S Supporting InformationSnapshots of the pure system and snapshots at 0 and 250 ns forUn_b, Un_w, Pr_b⊥, Pr||, and Pr_w⊥ systems, the variation ofend-to-end distance and the radius of gyration with thesimulation time, snapshots for the Un_b and Un_w fordifferent Rg of PEI, their partial densities, and Rg, pore radiusfor the Pr|| system as a function of simulation time, the radialdistribution function of PEI atoms with the P atoms of the lipidmolecules, and the structure of DOPC molecule showing thegrouping for head, middle, and tail moieties. This material isavailable free of charge via the Internet at http://pubs.acs.org.
Present Address§A.K.: Department of Chemistry, University of Utah, Salt LakeCity, Utah.
NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
C.K.C. thanks University Grants Commission, New Delhi, forthe fellowship. S.R. acknowledges Center of Excellence (COE)for Scientific Computing and CSC0129 of National ChemicalLaboratory for providing the computational time and funding,respectively. S.R. gratefully acknowledges financial supportreceived from the Center of Excellence in Polymers, COE-P(SPIRIT), established from funding received from the Depart-ment of Chemicals and Petrochemicals, India. A.K. wassupported by Inspire grant from Department of Science andTechnology, Government of India.
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