A detailed investigation of the formation kinetics and layerstructure of poly(ethylene glycol) tether supported lipid

bilayers

Stefan Kaufmann

Department for Materials Science,ETH Zurich, Zurich, Switzerland

Georg Papastavrou

Department of Inorganic, Analytical and Applied Chemistry,University of Geneva, Geneva, Switzerland

Karthik KumarDepartment for Materials Science,

ETH Zurich, Zurich, Switzerland

Marcus TextorDepartment for Materials Science,

ETH Zurich, Zurich, Switzerland

Erik Reimhult ∗

Department for Materials Science,

ETH Zurich, Zurich, Switzerland

Received XXXXth Month, 200X

Accepted XXXXth Month, 200XDOI: 10.1039/

Supported lipid bilayers formed from liposomescontaining phospholipids with covalently at-tached poly(ethylene glycol) (PEG-SLBs) po-tentially circumvent two current limitationsof membrane sensor platforms, namely air-stability and limited aqueous space betweenthe sensor substrate and the membrane. How-ever, questions regarding the formation kinet-ics through self assembly and the presence ofa PEG cushion underneath the lipid bilayerare still unanswered. Quartz crystal microbal-ance with dissipation monitoring and fluores-cence recovery after photobleaching (FRAP)measurements show that PEG-SLB formation

∗Corresponding author. Address: Department forMaterial Science, ETH Zurich, Wolfgang-Pauli-Str. 10,Zurich, Switzerland, Tel.: +41 44 633 75 47, Fax: +4144 633 10 27

through self-assembly is possible in the mush-room regime while it is hindered in the brushregime. The observed dependence of the kinet-ics on grafting density and molecular weight ofthe PEG-lipids is attributed to the electrostaticand steric shielding effect of the enveloping PEGlayer. In the mushroom phase, non-denselypacked PEG does not completely screen lipid-surface interactions while in the brush phase,densely packed non-interacting PEG chains sta-bilise liposomes and prevent overall attractiveinteractions. Force-distance measurements areused to directly measure the thickness of thePEG-SLB structure and demonstrate the pres-ence of PEG chains on both sides of the lipid bi-layer. FRAP measurements support this findingby showing increased lipid mobility for increasedPEG layer thickness through decoupling of the

1

membrane from the substrate. Force-distanceand FRAP measurements further reveal the mo-bility of the PEG-lipids and the novel detailedbehavior of laterally mobile PEG mushroomsunder mechanical compression.

1 Introduction

Membrane proteins require incorporation intoa suitable lipid bilayer environment to retaintheir tertiary structure and thereby their ac-tivity. Supported lipid bilayers (SLBs), whichare extended planar lipid bilayers assembled atthe liquid-solid interface, have been proposed assurface modifications for biosensors and otherplatforms for the study of membrane proper-ties and, in particular, transmembrane proteinfunction.[1, 2, 3] However, it has been reportedthat the close proximity of the SLB to the sub-strate causes pinning and partial denaturationof transmembrane proteins with hydrophilicdomains.[4, 5, 6, 7] In response, several groupshave developed platforms where the lipid mem-brane is reconstituted using a poly(ethylene gly-col) (PEG) spacer.[8, 9, 10, 11, 12] All theseplatforms essentially create a dense layer ofcovalently-linked short ethylene glycol spacers,which are functionalised with a lipid or choles-terol derivative that creates an amphiphilic sub-monolayer onto which an SLB can be formed.These tethered lipid membranes, however, havetoo short PEG spacers and too dense packing ofimmobilised PEG-lipids in the proximal leafletto provide the ideal environment for large mem-brane proteins. They are also challenging toform, requiring ultraflat substrates and opti-mum conditions.[10]

Cremer and coworkers demonstrated that SLBscan also be assembled from so-called PEG-liposomes or stealth liposomes.[7, 13] PEG-liposomes comprise a percentage of lipids witha linear PEG chain attached to their head-group and are commonly used in drug de-livery research, as the stealth properties ofthe PEG shell result in increased long cir-culation times in vivo compared to the non-PEGylated liposomes.[14] Formation of SLBswith low concentrations of PEG-lipids of much

higher molecular weight than typically used fortethered SLBs was shown to be possible viaself-assembly.[13] Enhanced stability upon airexposure was also demonstrated.[13] Further-more, it was shown that size-discriminatorybinding of proteins through the PEG shell couldoccur, meaning that proteins in a PEG-SLBwould be accessible for ligand binding to studyfunctionality.[13] The interaction of polymerswith lipid bilayers in various configurations hasbeen summarised by Tribet and Vial.[15]

Yet several questions remain regarding the for-mation and structure of PEG-SLBs that areof great importance for their application. Themost important questions are how they form,how their formation by self-assembly proceedsand whether a PEG layer is present betweenthe lipid bilayer and the substrate to providethe desired additional spacer. Kuhl et al.[16]showed by SFA measurements that the inter-bilayer interactions are greatly modified by theinsertion of polymers. They found that PEGbilayers do not adhere because of steric re-pulsion of the polymer chains.[16] PEG itselfshows no interaction with SiO2 or glass sup-ports. Given the previously observed highermechanical stability and the repulsion of PEG-lipid membranes, it is therefore remarkable thatPEG-SLBs seem to form although the drivingforce for rupture depends on liposome-surfaceattraction and liposome-liposome interaction,observable as a critical liposome coverage forSLB formation.[17, 18, 19] Furthermore, giventhat lipids are expected to show a higher affin-ity for the substrate than PEG and that fluo-rescence recovery after photobleaching measure-ments (FRAP) did not indicate decoupling ofthe membrane from the substrate [13], one hasreason to expect that PEG-lipids are expelledfrom the interface.

This work presents a study of SLB formation ki-netics using PEG-liposomes on SiO2 and glassas well as a detailed investigation of their me-chanical properties and structure. PEG molec-ular weights (MW) of 2000 Da and 5000 Da at-tached to phosphotidylethanolamine (PE) lipids(PEG(2)-PE and PEG(5)-PE respectively) in-corporated at different concentrations in phos-phatidylcholine (PC) liposomes were studied us-

2

ing quartz crystal microbalance with dissipa-tion monitoring (QCM-D) and FRAP to deter-mine the liposome adsorption and rupture ki-netics, and the formation of PEG-SLBs. Thestructure of self-assembled PEG-SLBs was in-vestigated by force-distance measurements andthe thicknesses of the respective layers of themulti-layer structure were analysed. We demon-strate that the PEG-SLB formation is onlypossible in the mushroom regime of the poly-mer, slowed down towards the transition be-tween mushroom and brush and completely pre-vented in the brush regime. FRAP experimentsshowed an increased mobility of the lipids indi-cating that the bilayer was lifted and decoupledfrom the support. These findings are confirmedby force-distance measurements, which directlydemonstrated that PEG chains are present onboth sides of the lipid bilayer. Force-distancemeasurements furthermore allow probing of theunique behaviour of PEG mushrooms that arelaterally mobile during mechanical compression.Figure 1 presents the identified self-assemblyroute and the molecular structure of the usedPEG-SLBs (with PEG(5)-PE).

2 Theory

2.1 Polymer mushroom-to-brush

transition

Linear polymer chains grafted on a surfaceare divided into the mushroom and brushregimes.[20, 21] Whether a grafted polymer filmis in the mushroom or brush state is depen-dent on the molecular weight of the polymerand its surface concentration of grafting sites.The mushroom regime is defined as s > RF andthe brush regime as s < RF , where RF is theFlory radius.

RF = a ⋅N3/5, (1)

where a is the size of one monomer, N the de-gree of polymerisation and s the distance of twografting sites, where

s = (A/m)1/2 (2)

and A is the average area per lipid molecule andm the mole fraction of PEG-lipids. Figure 2

presents the transition curve (solid line) fromthe mushroom to the brush regime as a func-tion of the mole fraction of PEG-lipids in a sup-ported lipid bilayer comprised of POPC. Alsoshown are two additional curves, a dotted anda dashed curve which represent error ranges re-lated to the uncertainty in the average area perlipid molecule from 50 A2 to 70 A2 and varia-tions in a of 3.5 A to 3.9 A .[20, 22, 23, 24] Thearrows in figure 2 indicate the concentrationsused in this investigation and chosen to result inlipid bilayers with the PEG chains in either themushroom regime (1, 2, 3 mol% PEG(2), 0.25,0.5, 1 mol% PEG(5)), in the transition regime (5mol% and 2 mol%, respectively) or in the brushregime (7 mol% and 3 mol%, respectively) as-suming a symmetric distribution of PEG chainsbetween the two leaflets. The de Gennes theorypredicts a maximum extension length Lmushroom

max

equal to RF in the mushroom regime which is in-dependent of the grafting density. In the brushregime the maximum extension length is givenby equation 3.[20]

Lbrushmax = N ⋅ a5/3

s2/3 . (3)

2.2 Fitting of force-distance

curves

The root mean square radius of a polymer insolution is given by the unperturbed radius ofgyration Rg.[25]

Rg = a√

N√6

(4)

In real solvents, forces between the segmentsof the polymer can lead to a larger or smallersize of the radius Rg than given in equation 4.Rg in a non-ideal solvent is then described asRF = αRg, where the intramolecular expansionfactor α describes the influence of the solventon the unperturbed radius of gyration, now de-noted the Flory radius RF given by equation 1.Dolan and Edwards[26] derived the repulsive en-ergy per unit area, W (D), for surfaces con-taining an end-grafted polymer layer as givenin equation 5.

W (D) = 361

s2kBT ⋅ e−D/Rg (5)

3

Applying the Derjaguin approximation,F (D) = 2πRW (D), with R the radius of theAFM tip, the force-distance relation is given byequation 6.[27]

F (D)R

= 72π1

s2kBT ⋅ e−D/Rg (6)

Equation 6 is valid for low coverage (s > Rg,mushroom regime). The force-distance relationin equation 6 was used to fit force curves per-formed on PEG-SLBs with PEG densities in themushroom regime. Li and Pincet introduced amodified force-distance relation for dense poly-mer mushroom layers based on the Dolan andEdwards theory as given in equation 7.[28]

F (D)R

= 144π1

s2kBT ⋅ e−√3D/2Rg (7)

Force-distance relations describing the interac-tions between two surfaces each containing apolymer layer (symmetric case) are appropriateto describe the situation of a single, symmet-ric PEG-supported lipid bilayer structure. Forthe above mentioned PEG molecular weights(MW), the unperturbed radius of gyration Rg

(equation 4), the maximum extension length ofone polymer layer LPEG (equation 1 and 3) andthe grafting distance s (equation 2) are sum-marised in the theory section of table 1 (a=3.7A, N=MW/(44 Da), with 44 Da being themolecular weight of the monomer CH2-CH2-O).The intramolecular expansion factor α for thesevalues is 3.6 for 2 mol% PEG(2)-PE and 3.9 for1 mol% PEG(5)-PE respectively, and was cal-culated by α = RF

Rg.

3 Experimental

3.1 Buffer solution

10 mM 4-(2-Hydroxyethyl)piperazine-1-ethane-sulfonic acid (HEPES) (Fluka, Switzerland) and150 mM NaCl was dissolved in ultrapure water(Millipore, USA) and 150 mM NaCl was added.The pH was adjusted to 7.4 with 6 M NaOH(Fluka, Switzerland) and it will be referred toas HEPES buffer.

3.2 Substrate preparation and

cleaning

Silicon wafer diced to pieces of 10 mm x 10 mmwere cleaned in an ultrasonic bath (Bandelin,Germany) in toluene and isopropyl alcohol for10 min and stored in ethanol. The substrateswere rinsed with ultrapure water (Millipore,USA) and cleaned in a pre-heated UV-Ozonecleaner for 30 min (UV-clean, Boekel Instru-ments, USA) before use. QCM-D (Q-Sense,Sweden) crystals were cleaned with 2% SDSand ethanol in an ultrasonic bath for 10 minand treated in a pre-heated UVO cleaner for30 min. Microscopy glass cover slips (MenzelGmbH, Braunschweig, Germany) were stored inethanol and rinsed before use with ultrapure wa-ter and treated in a pre-heated UVO cleanerfor 30 min. AFM tips (2.8 N/m, Nanosensors,Switzerland; 0.01 - 0.08 N/m, NT-MDT, Rus-sia) were cleaned with Cobas cleaner (Roche,Switzerland) and ethanol, and treated in a pre-heated UVO cleaner for 30 min. AFM tipswere surface modified by immersing the cleanedcantilevers in a 1 mg/ml filtered solutionof PLL(20 kDa)-g [3.5]-PEG(2 kDa) (Poly(L-Lysine)-graft-Poly(Ethylene Glycol), SuSoSAG, Switzerland) in 10 mM Hepes (pH 7.4) for30 min, followed by rinsing with ultrapure wa-ter and subsequent drying with a gentle streamof nitrogen as reported by Pasche et al..[29]

3.3 Vesicle preparation

Unilamellar vesicles were prepared by mix-ing the desired mole fraction of POPC(1-Palmitoyl-2-Oleoyl-sn-Glycerol-3-Phospho-choline), PEG(2)-PE (1,2-Dioleoyl-sn-Gly-cero-3-Phosphoethanolamine-N-[Methoxy-(Polyethylene glycol)-2000]), PEG(5)-PE(1,2-Dioleoyl-sn-Glycero-3-Phosphoethanola-mine-N-[Methoxy(Polyethylene glycol)-5000])and NBD-PC (1-Palmiotyl-2-[12[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl]-sn-Gly-cerol-3-Phosphocholine) purchased from AvantiPolar lipids (Alabaster, AL, USA). 1 mol%NBD-PC was used as label for microscopy mea-surements and was present in all used vesicles.PEG(2)-PE/CF (1,2-Distearoyl-sn-Glycero-

4

3-Phosphoethanolamine-N-[poly(ethyleneglycol)2000-N’-carboxyfluorescein]) was usedas a PEG chain label for microscopy measure-ments. The lipids were dissolved in chloroform.After mixing, the solutions were dried under astream of nitrogen for at least 1 hour followedby resuspending the lipids in HEPES buffer.Unilamellar vesicles were obtained by extrud-ing the solution 31 times through two stackedpolycarbonate membranes (Avestin, Ottawa,Canada) with a pore size of 100 nm using a Li-posofast extruder (Avestin, Ottawa, Canada).Vesicle size and distribution was determinedby dynamic light scattering (Malvern 3000 HS,Malvern Instruments, UK) yielding an averagesize of 103 ± 7 nm for all vesicles.

3.4 QCM-D

Quartz crystal microbalance with dissipationmonitoring (QCM-D) measurements were per-formed on a Q-Sense E4 (Q-Sense, Sweden).[30]The technique is based on the change in res-onance frequency and energy dissipation uponadsorption of material on an oscillating piezo-electric quartz crystal resonator. It is frequentlyused to measure kinetics of the vesicle adsorp-tion and to monitor the formation process ofsupported lipid bilayers.[31, 32, 33] The reso-nance frequency shift, Δf , of the freely oscil-lating crystal depends on the adsorbed masswhich includes coupled water while the dissi-pation shift, ΔD, measures the damping of thecrystal oscillations by energy losses in viscousoverlayers. The crystals were immediately in-serted into the flow chambers after the clean-ing procedure and after a baseline had beenestablished in pure HEPES buffer. The sam-ple solutions were pumped into the cells usinga high-precision multichannel dispenser (IPCIsmatec SA, Switzerland). All measurementswere done in batch exchange to keep consump-tion of lipid solutions low and using maximumpumping speed to insert the solutions (> 1ml/min, exchanging 1 ml). During the measure-ments the 3rd, 5th, 7th, 9th and 11th overtoneswere recorded. Only Δf and ΔD recorded atthe 3rd overtone normalised to the fundamentalresonance Δf = Δf3

3 are presented in the figures

for simplicity and consistency.

3.5 FRAP

NBD-PC was used as the fluorescently labelledlipid for FRAP measurements. Measurementswere performed on a Zeiss LSM510 confocallaser scanning microscope (Carl Zeiss AG, Ger-many) equipped with a 25-mW Argon laser (lineused: 488 nm) and a 63x 1.4NA oil DIC plan-apochromat objective. Cleaned glass slides weremounted in a home-built liquid cell and lipidsolutions were added and left for up to sev-eral hours (depending on the timescale for SLBformation that was measured by QCM-D) be-fore exchanging the solution several times withbuffer to remove liposomes from the bulk so-lution. The size of the images was 70.9 μm x70.9 μm and bleaching experiments were donewith a bleach spot diameter of 20 μm. The timedelays used during the measurements were 0 s,10 s and 1 min and were set manually depend-ing on the recovery rate. For the evaluation ofthe diffusion coefficients the model published bySoumpasis[34] was used while the mean inten-sity of the region of interest was divided by themean intensity of an unbleached region withinthe image to correct for bleaching effects.

3.6 Atomic force microscopy

Force-distance measurements were performedwith an Asylum MFP-3D (Asylum Research,USA). Silicon wafer pieces (Si(100) SSP, Siliconmaterials, Germany) fixed with UV adhesive(NO63, Norland products, USA) to plastic Petridishes (TPP, Switzerland) were incubated in thedesired liposome solution for a time exceedingthe SLB formation time as determined by QCM-D. Measurements were performed with cleaned,uncoated tips as well as tips modified with PLL-g-PEG coating. For measurements with un-modified AFM tips the vesicle solution was notexchanged whereas in the case of modified tipsthe vesicle solution was exchanged by buffer.The spring constants of the used silicon tipswas specified by the manufacturer as 0.01 - 0.08N/m (NT-MDT) and 2.8 N/m (Nanosensors),respectively. The spring constant was measured

5

for each tip using the thermal noise method ofthe Asylum MFP-3D according to the proce-dure proposed by Hutter and Bechhoefer.[35]The raw data is transformed into force separa-tion graphs using the linear increase of the de-flection vs. the linear variable differential trans-former signal when the AFM tip is in hard con-tact with the substrate.[36] The approach ve-locity of the tip was varied between 2 ⋅ 10−7 m/sand 6 ⋅ 10−7 m/s. Changes in approach velocitydid not lead to different force curves within theerrors of our measurements.

4 Results and discussion

4.1 Self assembly of polymer sup-ported lipid bilayers

Figures 3 a) and b) show QCM-D curves forpure POPC liposomes and liposomes containingPEG(2)-PE and PEG(5)-PE lipids respectively.SLB formation for POPC shown in figures 3 a)and b) proceeds by initial adsorption of lipo-somes illustrated by a reduced frequency andincreased dissipation value until a critical sur-face coverage is reached. In the next step theadsorbed liposomes open up, release the waterand trigger the phase transition from liposomesto SLB, which is identified by a reversal of thefrequency and dissipation slopes.[18] The finalfrequency and the low dissipation shift indicatethe formation of an SLB on the surface.

Figure 3 a) reveals the trend for liposomes withincreasing PEG(2)-PE concentration. TypicalSLB formation kinetics are observed for lowconcentrations of PEG(2)-PE while this is notthe case for high concentrations. 1 and 2mol% PEG(2)-PE show similar kinetics to purePOPC. SLB formation for 3 mol% PEG(2)-PEis, however, slowed down considerably. For thisreason only the start of the liposome rupture isvisible in figure 3 a) as extrema in Δf and ΔD.5 mol% and 7 mol% PEG(2)-PE do not form anSLB. They remain in the liposome adsorptionphase and level off at a low surface coverage.Figure 3 b) shows the same trend for PEG(5)-PE as observed for PEG(2)-PE. 0.25 mol% and0.5 mol% show similar kinetics as pure POPC

whereas 1 mol % results in slow SLB formation.For 2 mol% and 3 mol% liposomes adsorb to thesurface without rupturing. The final absolutefrequency and dissipation shifts show increasingvalues for liposomes with increasing PEG-lipidconcentrations and are summarised in table 2.

FRAP measurements confirmed the formationof fluid SLBs in the mushroom regime. Diffusioncoefficients and recovered fractions are listed intable 3. FRAP measurements on layers formedwith concentrations of 5 and 7 mol% PEG(2)-PE, and 2 and 3 mol% PEG(5)-PE showed aninhomogeneous intensity distribution caused bylow levels of liposome adsorption and no fluores-cence recovery was observed for these samples(see figure S2 in supplementing information).

4.2 Discussion of the formationprocess of PEG-supported

lipid bilayers

The QCM-D curves in figures 3 a) and b)show that for 1,2 and 3 mol% PEG(2)-PEand for 0.25, 0.5 and 1 mol% PEG(5)-PESLB formation is analogous to the SLB forma-tion from pure POPC.[31, 32, 33] The homo-geneity of PEG-SLB in the mushroom regimewas also confirmed by fluorescence microscopyshowing homogeneous fluorescence for labeledPOPC lipids (NBD-PC) and labeled PEG-lipids(PEG(2)-PE/CF) on the microscopic scale andwith AFM in the sub-micron range (see fig-ures S1 and S2 in supplementing information).No multilayer formation or aggregation of PEG-lipids were observed for PEG-SLBs.

Concentrations of 3 mol% PEG(2)-PE and 1mol% PEG(5)-PE however show a significantlyincreased SLB formation time. The formationkinetics indicate that addition of PEG-PE lipidsleads to shielding of the interactions with thesubstrate. As the SLB formation still proceedsfor concentrations in the mushroom regime, itis suggested that the POPC-substrate interac-tion is still strong enough to trigger the fusionprocess. A higher PEG-PE lipid concentrationin the brush regime leads to shielding of the in-teraction to an extent that results in significantprevention of liposome adsorption and SLB for-

6

mation as seen in the QCM-D measurements infigures 3 a) and b). The measured adsorbedmass values are low for high concentrations ofPEG-PE lipids (5 and 7 mol% PEG(2)-PE and2 and 3 mol% PEG(5)-PE).In agreement with these findings, Holland etal.[37] reported enhanced stability for liposomesincluding PEG-lipids by studying liposomal fu-sion. They showed that the incorporation of2 mol% PEG(2)-PE and 1 mol% PEG(5)-PEin PE:PS liposomes blocks Ca2+ induced fusionand that only an addition of acceptor liposomes(POPC) can restore the fusogenic activity bylowering the overall concentration of PEG-lipidsdue to PEG-lipid exchange between the vesi-cles. This agrees with the screening seen by in-creasing PEG-PE lipid concentrations to 5 and7 mol% for PEG(2)-PE and 2 and 3 mol% forPEG(5)-PE, respectively, in our measurements.These concentrations prevent substantial ad-sorption of liposomes to the surface. In addi-tion, the screening also explains the slowing-down of the SLB formation process for 2 mol%PEG(2)-PE and 1 mol% PEG(5)-PE. As thePEG concentration decreases, the SLB forma-tion process approaches that of pure POPC.The stability of PEG-liposomes against ruptureand formation of planar SLBs at high concen-trations of PEG-PE lipids (3, 5 and 7 mol%PEG(2)-PE and 1, 2 and 3 mol% PEG(5)-PE)can also be understood in terms of the mini-mum energy geometry for the PEG-lipid mem-brane. A single chain mean field approach waschosen by Szleifer et al.[38] to determine therange of stability for spontaneous liposome for-mation in terms of mol% and molecular weightof PEG-lipids. This approach gives informationabout the energetic contributions of the PEG-PE lipids and the energetically most favourablestructure. As stated by Szleifer et al.[38] thefree energy of curvature, f(c), per unit bilayerarea expanded around a planar film is given bythe quadratic expression

f(c)A= f(0)

A+ 1

2Kc2 (8)

with c = 1/R and R is the radius of curva-ture of the bilayer surface, A the area and Kthe elastic constant. If K > 0 a planar film is

thermodynamically stable and for K < 0 lipo-somes will be spontaneously formed. Szleifer etal.[38] demonstrated that for a fixed molecularweight of PEG, the initial positive K decreasesfor increasing PEG-lipid concentrations, result-ing in a negative value for relatively low molarratios of PEG (≈ 12 mol% for PEG(2)-PE and≈ 5 mol% for PEG(5)-PE in DMPC). Sponta-neous liposome formation becomes thermody-namically favourable by an asymmetric distri-bution of PEG-lipids at finite curvature in theinner and outer monolayer. The asymmetryreduces the stress associated with symmetricpacking of the PEG chains in the planar lipid bi-layer. This agrees with our results, as the ther-modynamic stabilisation by forming an asym-metric PEG-lipid distribution can be associatedwith the decreased propensity of SLB formationfor increased PEG-PE lipid concentrations. Inaddition, the stress associated with a symmetricpacking of the PEG-PE lipids in a planar lipidbilayer is assumed to become significant at themushroom-to-brush transition when the PEGchains start to feel repulsive forces. The ob-served retardation of SLB formation kinetics to-wards and its prevention above the mushroom-to-brush transition are likely due to an increasedactivation energy and reduced thermodynamicdriving force.

Differences are also evident in the final values forfrequency and dissipation shifts for PEG-SLBscompared to pure POPC SLBs. IncreasingPEG-PE lipid concentrations lead to increas-ing absolute frequency and dissipation shifts asseen in figures 3 a) and b) and are summarisedin table 2. The increase in absolute frequencyshift is caused by the additional mass of thePEG chains and the coupled water.[39, 40] Flex-ible polymer chains attached to the lipid bi-layer also increase the energy loss of the oscil-lation as evident from the observed increaseddissipation. It can be excluded that the highermass and dissipation is due to intact, unrup-tured vesicles as FRAP measurement clearly in-dicate a fluid, complete lipid bilayer with over-all fluorescence recovery values that are closeto 100%. Diffusion coefficients show increasedmobility of the POPC lipids within the PEG-SLB compared to a 100% POPC SLB under

7

the same conditions, which demonstrates thatthe interaction of the lipids with the substrateis reduced. Analogous increase in the fluidity ofa membrane as a function of the tether lengthfor substrate bound polymer spacers has previ-ously been reported.[41, 42, 43] An increase inthe diffusion coefficient with effective PEG layerthickness up to close to the brush transition isobserved. Therefore, this is an indication thatPEG chains are indeed present underneath theself-assembled lipid bilayer forming a cushion todecouple the lipids and the substrate. It is in-teresting to note that PEG-PE remains as fluidas POPC in a pure POPC SLB, but has a sig-nificantly lower diffusion coefficient than POPCin the same membrane.

4.3 Structure of PEG-supportedlipid bilayers

QCM-D measurements showed that PEG doesnot adsorb to an SiO2 surface and the QCM-D investigation of the PEG-SLB formation ki-netics demonstrated that an increasing mol%of PEG-PE lipids acts as a barrier to rup-ture. On the other hand the increase in lipiddiffusion coefficient for PEG-SLBs over purePOPC SLBs suggests the presence of a PEGspacer layer also between the substrate and thePOPC lipids. It is therefore interesting to di-rectly measure the structure of the PEG-SLBthat is being formed. There are two main sce-narios for how the PEG-lipids could partitionduring the formation process: a) Vesicles ad-sorb to the surface and the interactions be-tween POPC and the surface displace the PEG-lipids. The PEG-lipids are pushed aside and af-ter rupture of the vesicles the PEG-lipids settlein the upper leaflet of the bilayer at twice theconcentration per surface area. b) Despite thesurface-POPC interaction driving the SLB for-mation the equilibrium state of the adsorbedplanar membrane includes PEG-lipids also inthe lower leaflet. As discussed in the previ-ous section for low PEG-lipid concentrations,energetic considerations favour the symmetricdistribution of the PEG-lipids within the twomonolayers to avoid stress between neighbour-ing PEG chains for a planar bilayer.[38] Fu-

sion of liposomes with incorporated PEG-PElipids at low concentrations was reported to takeplace[37], which suggests strong interactions inspite of the PEG-lipids. The two different ar-chitectures are schematically shown in figure 4.These two layer structures would be distinguish-able by their height. The theory by de Gennespredicts that the thickness of polymer coils isindependent of the grafting density in the mush-room regime and is given by the Flory dimen-sion RF [21]. Values are listed for these two layerstructures ((a) and (b)) in table 1 where LPEG

is the thickness of one PEG layer and LSLB thethickness of the whole structure (see figure 4).Table 1 lists estimations for thickness values ofthe structures assuming a POPC SLB thicknessof 5 nm, an area per lipid molecule of 60 A2 anda monomer size of 3.5 A.Direct force-distance measurements allow mea-surements of the force response and the thick-ness of the respective layers. The followingAFM tip configurations were used in order tohave a well defined tip-sample interaction:

i) clean tips where SLB formation on the tipis possible

ii) modified tips coated with PLL-g-PEG,where adsorption of vesicles and SLB for-mation is prevented

Figure 5 illustrates the different situations forthe choice of AFM tips.Force curves on SLBs show characteristic fea-tures, so called jump-in events.[44, 45, 46] Thejump-in events are visible as abrupt changes inthe distance of the AFM tip at constant (oreven reduced force) and describe the penetra-tion of the AFM tip through the lipid bilayer.This makes the beginning and end of the SLBpenetration easily identifiable. The self-healingproperty of SLBs renders it possible to conductrepeated force measurements on the same sam-ple.Physiological conditions were used for the forcemeasurements. The ionic strength of 150mM NaCl ensured that the Debye length of< 1 nm[25] was sufficiently small to measure thethickness of a lipid bilayer.The PEG chains incorporated in the supportedlipid bilayer increase the total thickness of the

8

structure by many nanometres and completelyscreen charges in the lipid bilayer for which rea-son only steric interactions are measured thatcan directly be associated with the thickness ofthe structure.[29]

4.3.1 i) Force spectroscopy with unmod-ified tips

Measurements with unmodified tips were car-ried out in 0.1 mg/ml vesicle solution withoutexchanging the solution. The excess of vesiclesin solution is expected to lead to the forma-tion of an SLB also on the silicon tip.[44, 46]Transfer of lipid material can also occur fromthe substrate to the tip to form an SLB on theAFM tip. Two different types of curves wererecorded. In approximately 95 % of more than600 curves on different positions only one jump-in event was recorded (△ in figure 6) and in theremaining 5 % a second jump-in event appeared(○ in figure 6). After rinsing with HEPES buffer,second jump-ins could also be observed but insmaller number. The occurrence of these secondjump-in events was infrequent and depended onthe AFM tip, suggesting that it only occurredfor AFM tips with a comparatively big tip ra-dius mostly by picking up lipid material fromthe surface. Figure 6 shows two typical forcecurves, one of which shows one jump-event (△)and the second one two jump-in events (○) for 1mol% PEG(5)-PE. In figure 7, eight force curveswith one jump-in event are superimposed (un-filled symbols) and the solid line presents anaverage of 37 force curves. Two force curveshaving two jump-in events are added to figure 7(filled symbols). Figure 8 shows eight super-imposed force curves with two jump-in events(unfilled symbols) and the solid line presents anaverage of 58 force curves.

The force curves showing only a single jump-in were fitted using equation 6 and equation 7.For the derivation of these equations the Der-jaguin approximation is used. It assumes thatthe characteristic radius of the tip is much largerthan the characteristic length scale of the in-teraction. In our case the tip radius (supplierinformation) and the length scale of interactionis of the same order of magnitude. Todd and

Eppell[47] showed that the violation of the Der-jaguin approximation results in overestimationof the forces. For the fitting procedure the tipradius was set to 30 nm. With respect to fit-ting the PEG compression the thickness of thePOPC lipid bilayer has to be taken into account.The compression of the PEG polymers hap-pens before the rupture of the POPC lipid bi-layer since the hard wall contact is reached afterthe jump-in. The jump-in distance for 1 mol%PEG(5)-PE was evaluated to be 4.3 ± 0.6 nm(114 jump-ins), corresponding to the expectedthickness of the SLB.[48] Thus, the origin wasshifted by 4.3 nm to exclude the separation dis-tance from pure POPC. For the fitting proce-dure, the only two fitted parameters were the ra-dius of gyration Rg and the grafting distance s.The average separation from the hard-wall con-tact to the onset of the compression of the PEGchains yields, if properly calibrated, the totalmembrane thickness. For force curves with a 1mol% PEG(5)-PE SLB on the substrate the av-erage separation from hard-wall contact to theonset of compression of PEG chains was deter-mined to be (16.1 ± 1.9) nm. The onset of thecompression is defined here as the separationwhere the exponential fit (equation 6 and 7) tothe data exceeds 3 mN/m, which is approxi-mately the standard deviation of the baselinenoise (cantilever not in contact with the sam-ple) of these force curves. Values of the fits tothe experimental data obtained from 95 curveswere averaged after fitting and are summarisedin table 1.

As the measurements were done in vesicle solu-tion with an excess of vesicles, the appearance ofa vesicle under the tip with a subsequent com-pression and rupture of the vesicle cannot beexcluded completely. For that reason furthermeasurements with PLL-g-PEG modified tipswere done.

4.3.2 ii) Force spectroscopy with PLL-g-PEG modified tips

PLL-g-PEG coatings are known to prevent non-specific biological interactions on surfaces andtherefore prevent adsorption of a POPC SLB orliposomes on the AFM tip.[49] Measurements

9

with PLL-g-PEG coated tips were done on SLBscontaining 1 mol% PEG(5)-PE and 2 mol%PEG(2)-PE rinsed several times after SLB for-mation before measuring. More than 1000 forcecurves did not show an event with a secondjump-in which confirms that no SLB was formedon the tip nor a liposome captured betweentip and substrate. These findings also supportthe interpretation of double jump-in events ofuncoated tips as being due to compression oftwo opposing PEG-SLBs. Figure 9 shows forcecurves for 2 mol% PEG(2)-PE (dot-dashed line,◇) and 1 mol% PEG(5)-PE (dashed line, +) andas a direct comparison POPC without PEG-lipids (solid line, ○).These curves were fitted with equation 6 andequation 7. The solid curves shown in figure 9show the fits to the data.

The average separation from hard-wall contactto the onset of the compression of the PEGchains for 2 mol% PEG(2)-PE was determinedto be (11.4 ± 1.1) nm and (19.1 ± 1.5) nm for 1mol% PEG(5)-PE.

The radius of gyration Rg obtained from thefits are summarised in table 1. The valueswere obtained by fitting 98 and 82 force curvesfor 2 mol% PEG(2)-PE and 1 mol% PEG(5)-PE respectively. Averaging was done after thefitting procedure and the only two fitted pa-rameters were the radius of gyration Rg andthe grafting distance s. The thickness of thePOPC lipid bilayer is taken into account byevaluating the jump-in distances. For PEG(2)-PE and PEG(5)-PE the jump-in distance wasevaluated to be 3.4 ± 0.2 nm (98 jump-ins) and4.8 ± 0.3 nm (82 jump-ins), respectively. Thejump-in distance for pure POPC was evaluatedto be 4.1 ± 0.2 nm. For all measurements thesame tip was used with subsequent cleaning andrefreshing of the PLL-g-PEG coating.

The origin of the force curves was shifted by3.4 nm and 4.8 nm respectively to exclude theseparation distance from pure POPC. Table 1summarises the averaged results of the fits toall curves.

Figure 10 shows force curves for 2 mol%PEG(2)-PE (dot-dashed line, ◇) and 1 mol%PEG(5)-PE (dashed line, +) and POPC with-out PEG-lipids (solid line, ○). All structures

were measured with the same tip and the curvesdisplayed in figure 10 are a representation of thePEG compression regimes before the disruptionof the lipid bilayer of more than 50 averagedcurves. For clarity the curves are displayed withan offset where the steep increase in the force-distance curve is taken as the new origin of thecurves. In this representation the compressionof the PEG chains can be inspected directly.

To determine the influence of the PLL-g-PEGmodification of the AFM tips on the forcecurves, measurements on a bare silicon surfacewere conducted. The force curves showed ashort-range repulsion and no adhesion. Equa-tions 6 and 7 were also used to fit these forcecurves, although the PLL-g-PEG polymer layeris known to be in the brush regime for this graft-ing ratio.[29] The force curves were fitted in aforce range up to 30 mN/m assuming a tip ra-dius of 30 nm. The value of 30 mN/m is ex-ceeding the force range that was considered inthe fitting procedure for PEG compression inPEG-SLBs. The values obtained from these fitsgive an estimation of the steric repulsion, whichis hidden in the fit values in table 1 and is dueto the PLL-g-PEG coating of the tip. Table 1summarises the averaged results of the fits to49 curves. The values attributed to the com-pression of the PLL-g-PEG coating are signif-icantly lower than the ones obtained from thefits shown in table 1 and they confirm that theforces needed to compress the PLL-g-PEG coat-ing are far higher than the ones needed to com-press the PEG layer in the PEG-SLB.

4.4 Discussion of the structure ofPEG-supported lipid bilayer

4.4.1 i) Force spectroscopy with unmod-ified tips

The two different types of force curves seen infigure 6 for measurements with unmodified tipsdescribe the situation with only a PEG-SLB onthe substrate (one jump-in event) and an addi-tional PEG-SLB adsorbed on the AFM tip (twojump-in events), respectively. This behaviouris schematically illustrated in figure 5 i). Thelower loading force for the first jump-in in fig-

10

ure 6 indicates that the higher curvature of thetip results in a less stable SLB (b, ≈ 6 nN). Thesecond jump-in is found at comparable separa-tions for all types of force curves and originatesmost likely from the SLB on the flat substrate(a, ≈ 20 − 30 nN). In addition to the two jump-in events (a and b in figure 6) there is an eventhappening before the rupture of the first SLBon the tip denoted as c in figure 6. We call thisevent a maximum as it has a different behaviourfrom a jump-in event. The increase before themaximum is slow and extended for a long dis-tance. Two interpretations are possible:

i) Compression of a vesicle adsorbed on thesurface or tip

ii) Compression of the PEG-PE lipids incor-porated in the SLB

PEG-liposomes have an average size of 103 ±7 nm in diameter as described in the Experimen-tal section. Vesicles are deformed upon adhe-sion on the surface and show a decreased heightcompared to the nominal bulk diameter.[32, 19]Liang et al.[50] reported force measurements onEggPC liposomes with diameters of 37±7.9 nm.The measured onset of compression in their casewas 32.2 ± 4.2 nm, which corresponds to thesolution diameter as obtained by light scatter-ing. Brochu and Vermette[51] published mea-surements of Young’s moduli for surface-boundliposomes, extruded through 100 nm pore mem-branes, using force-distance measurements. Forone layer of liposomes they reported an onset ofcompression at 110 ± 20 nm (zero-force separa-tion to hard wall). According to these studiesone would expect to find instead the onset ofcompression on the order of the liposome di-ameter in solution if these are present on thesurface. The measured onset of compression asseen in figure 6 in the range of 40 nm in our caseis however much smaller than the liposome-sizemeasured in solution, which is 103 ± 7 nm.The second interpretation (ii) is that in a firststep the polymers are compressed which gives aslow and smooth increase in force. As the PEG-lipids are mobile in the lipid bilayer they willprefer to leave the area of high pressure whichis finite due to the relatively small tip area andconcentration of polymer.

As described in the theory section, s = √A/mgives the distance between two grafting sites andA/m is the area where only a single PEG-chainis present. The projected area of the tip is Atip =π ⋅r2 with r = 30 nm. In a rough estimation, thenumber of PEG-lipids under the tip would beapproximately n = m ⋅ Atip/A, which is 93 and48 for 2 mol% PEG(2)-PE and 1 mol% PEG(5)-PE respectively.

Subramanian et al.[52] calculated escape tran-sitions upon compression for polymers inthe mushroom regime which are permanentlygrafted to a surface but are mobile on that sur-face, i.e. the chains are allowed to move lat-erally, but the total number of chains is fixed.They calculated that the force first increasesfor weak compressions, reaches a maximum andthen decreases to zero, similar to what is ob-served here. Not all force curves with two jump-in events however showed such a maximum. Inapproximately half of the force curves the max-imum (c in figure 6) and the first jump-in eventat low force (b in figure 6) could not explicitly bedifferentiated or are combined in one jump-in.But it is likely that this is a first experimentalobservation of an escape transition for a later-ally mobile tethered polymer layer, which is tobe investigated further.

Figure 7 superimposes eight force curves (un-filled symbols) that only have one jump-inevent. From these superimposed curves it is ev-ident that the onset of the compression of thepolymers starts between a separation of approx-imately 18 - 20 nm. The solid line shows anaverage of 37 force curves. Averaging leads toa smearing out of the sharp jump-in event dueto variations in the break through force. How-ever, the compression of the polymer is retained.The onset of compression of the average forcecurve occurs at approximately 20 nm of separa-tion. If the compression is described accordingto equation 6 one finds an onset of the compres-sion of the PEG chains at 16.1 ± 1.9 nm of sep-aration. Therefore, the behaviour of the forcecurves favours structure b.

Figure 8 shows the superposition of eight forcecurves (unfilled symbols) for the case of twojump-in events. The onset of the compressionof the structure starts between a separation of

11

approximately 35 - 40 nm. The superimposedforce curves show a good correlation in the twojump-ins whereas in the polymer compression,a variation in the interaction length is notice-able. The situation is interpreted as sketchedin figure 5 i) on the right, where a PEG-SLBis present on the tip as well as on the sub-strate. The curvature of the AFM tip presentsan energetically unfavourable situation for thePEG-SLB and variation in its stability or breakthrough force is expected. The solid line in fig-ure 8 is an average of 58 force curves all showingtwo jump-in events. Again, the jump-in eventsare smeared out due to variations in the breakthrough force. The onset of compression for theaveraged force curve is found at approximately40 nm. A PEG-SLB system comprising two op-posing bilayers would have a thickness of 24 nmfor structure a and 35.2 nm for structure b in fig-ure 4 according to table 1. Thus, the measure-ments again predict a thickness of the structurein good agreement with structure b.

4.4.2 ii) Force spectroscopy with PLL-g-PEG modified tips

Situation ii) in figure 5 with PLL-g-PEG mod-ified tips allows only a PEG-SLB on the sub-strate. The interaction distance with the AFMtip can therefore be directly correlated to thePEG-SLB thickness. From figure 9 showing sin-gle force curves it is evident that the onset ofthe compression starts at approximately 12 - 15nm for 2 mol% PEG(2)-PE and at 17 - 20 nmfor 1 mol% PEG(5)-PE. The onset of the com-pression for 2 mol% PEG(2)-PE using the ex-ponential fit function in equation 6 results in aseparation of 11.4 ± 1.1 nm and 19.1 ± 1.5 nmfor 1 mol% PEG(5)-PE. Again, according to ta-ble 1, these values agree with structure b in fig-ure 4. Figure 10 shows the averaged force curvesfrom direct force measurements with PLL-g-PEG modified tips. This regime describes thepolymer compression and from table 1 for 2mol% PEG(2)-PE, 2 × LPEG =7.4 nm, and for1 mol% PEG(5)-PE, 2 ×LPEG = 12.6 nm, is ex-pected for structure b. These values agree wellwith the onset of the averaged force curves seenin figure 10 and agree with structure b.

All curves showing a single jump-in event in sit-uation i) and all force curves in situation ii) werefitted with equation 6 and equation 7. The re-sults are shown in table 1. To ensure that thePLL-g-PEG coating of the AFM tip in situationii) does not distort the result a modified tip wasmeasured against a bare silicon wafer (depictedin situation ii) figure 5 on the right hand side).The fit values are shown in table 1. The radiiof gyration obtained from the fits overestimatethe radius of gyration that was calculated intable 1.∗ However, the results from the fits as-suming the compression of a symmetric polymerlayer, as given for an SLB with PEG on bothsides, give the correct dimension for structureb.

The results from the two different situationsi), unmodified and ii), PLL-g-PEG modifiedAFM tips, both agree with the structure wherePEG chains are present on both sides of thelipid bilayer. Consequently, the AFM measure-ments quantitatively confirm the presence ofPEG chains underneath the lipid bilayer, whichwas indirectly indicated by the FRAP results.

4.5 Concluding remarks

We showed that PEG-SLB formation by self-assembly is possible for low concentrationsof PEG-PE lipids (mushroom regime) and isprevented for higher PEG-PE concentrations(brush regime). QCM-D measurements demon-strated that the SLB formation-preventing ef-fect of PEG-PE lipids is due to increased shield-ing of liposome-surface and liposome-liposomeattraction. The PEG-SLB structure on the sub-strate has PEG-PE lipids in both the lowerand upper leaflet as confirmed by AFM force-distance measurements. The supporting PEGcushion for high molecular weight PEG-PEleads to a large separation of the membranefrom the substrate, which increases lipid mobil-ity as demonstrated by FRAP and would pro-vide ample room for incorporation of membrane

∗The fit results are between Rg and the LPEG valuesfrom the De Gennes theory (based on the Flory radiusRF ). If α, the intramolecular expansion factor, approx-imates 1, then Rg ≈ RF . α=1 for an ideal solvent andwater can be approximated as a good solvent for PEG.

12

proteins. An interesting behaviour of the self-healing polymer membrane under mechanicalcompression was also observed, demonstratingthat this platform also could fill a need in exper-imental investigations of finite compression ofliquid crystalline two-dimensional polymer lay-ers. Given that most natural biological mem-branes contain high percentages of carbohy-drate polymers linked to mobile lipids, we pro-pose that the controlled structure of the PEG-SLB can serve as a model to be further devel-oped for e.g. glycolipid eukaryote and bacterialmembranes. The described methodology can beused to probe the mostly unknown detailed me-chanical and structural characteristics of thesemembranes.

5 Acknowledgement

The authors thank the FIRST Center for Micro-and Nanoscience, the Light Microscopy Centreand the Biologically Oriented Materials Group(Prof. Viola Vogel) at ETH Zurich, Switzerlandfor the use of their equipment. The authors alsothank the Laboratory of Colloid and SurfaceChemistry at the University of Geneva, Switzer-land for their invaluable advice and helpful dis-cussions. This work was supported by the SwissCompetence Center for Materials Research andTechnology of the ETH Domain, Switzerland.

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Table 1: Experimental values obtained from fitting the force curves and theoretic values based onthe De Gennes theory. Fit values obtained using equation 6 (1) and equation 7 (2) respectively.L∗SLB: values from the onset of compression of PEG chains in force-distance curves.

Experimental TheoryL∗SLB Rg s LPEG LSLB Rg s

System (nm) (nm) (nm) (nm) (nm) (nm) (nm)1 mol% PEG(5)-PE, (16.1 ± 1.9) (3.9 ± 0.8)1 (3.9 ± 1.4)1 (a) 7.0 12.0 1.6 5.5unmodified tip (3.4 ± 0.7)2 (5.5 ± 2.0)2 (b) 6.3 17.6 1.6 7.7

2 mol% PEG(2)-PE, (11.4 ± 1.1) (2.1 ± 0.3)1 (6.5 ± 1.4)1 (a) 3.7 8.7 1.0 3.9modified tip (1.8 ± 0.2)2 (9.1 ± 1.9)2 (b) 3.7 12.4 1.0 5.5

1 mol% PEG(5)-PE, (19.1 ± 1.5) (4.3 ± 0.5)1 (8.1 ± 2.1)1 (a) 7.0 12.0 1.6 5.5modified tip (3.7 ± 0.4)2 (11.4 ± 2.9)2 (b) 6.3 17.6 1.6 7.7

Bare Si surface, (0.7 ± 0.1)1modified tip (0.7 ± 0.1)2

Table 2: Results from QCM-D measurements.System Frequency shift Dissipation shiftPOPC −25.7 ± 0.6 Hz 0.19 ± 0.07 ⋅ 10−6

1 mol% PEG(2)-PE −34.9 ± 0.6 Hz 2.0 ± 0.2 ⋅ 10−6

2 mol% PEG(2)-PE −37.6 ± 2.4 Hz 2.2 ± 0.3 ⋅ 10−6

3 mol% PEG(2)-PE −41.4 ± 2.3 Hz 2.5 ± 0.2 ⋅ 10−6

0.25 mol% PEG(5)-PE −29.6 ± 0.1 Hz 1.6 ± 0.1 ⋅ 10−6

0.5 mol% PEG(5)-PE −34.0 ± 0.6 Hz 2.7 ± 0.1 ⋅ 10−6

1 mol% PEG(5)-PE −39.1 ± 3.0 Hz 3.3 ± 0.4 ⋅ 10−6

16

Table 3: Results from FRAP measurements.System Diffusion coefficient Recovered fractions1 mol% PEG(2)-PE 1.5 ± 0.1 μm2/s 97 ± 0.4 %2 mol% PEG(2)-PE 2.2 ± 0.4 μm2/s 97 ± 2 %3 mol% PEG(2)-PE 1.9 ± 0.2 μm2/s 98 ± 0.3 %0.25 mol% PEG(5)-PE 1.9 ± 0.2 μm2/s 98 ± 0.2 %0.5 mol% PEG(5)-PE 2.6 ± 0.5 μm2/s 97 ± 0.8 %1 mol% PEG(5)-PE 2.2 ± 0.4 μm2/s 94 ± 6 %POPC 1.2 ± 0.4 μm2/s 95 ± 2 %2 mol% PEG(2)-PE/CF 1.1 ± 0.4 μm2/s 99 ± 1%

17

Fig. 1 Schematic of the envisioned process for PEG-SLB self-assembly. Liposomes incor-porating a low percentage of lipids with PEG chains attached to their headgroupself-assemble on the SiO2 surface and fuse into a PEG-SLB. The final structure fea-tures PEG chains on both sides of the lipid bilayer in which the chemical structure ofa PEG(5)-PE lipid is emphasised.

Fig. 2 Transition between mushroom and brush regime as function of the molecular weightof the polymer and the mole fraction of the PEG-lipids. The solid line shows thetransition for an area per lipid molecule of 60 A2 and a monomer size of 3.7 A. Thedotted line represents a lower transition using an area per lipid molecule of 50 A2 anda monomer size of 3.9 A, whereas the dashed line assumes an area per lipid moleculeof 70 A2 and a monomer size of 3.5 A. The arrows indicate the concentrations used inthis paper. Two PEG molecular weights were used, 2000 and 5000 Da (dashed verticallines) and their concentrations were 1, 2, 3, 5, 7 mol% (MW 2000) and 0.25, 0.5, 1, 2,3 mol% (MW5000) respectively.

Fig. 3 QCM-D measurements of SLB formation for pure POPC and liposomes containingPEG-PE for 0.1 mg/ml liposome solution in batch exchange. Solid lines present fre-quency shifts and dashed lines are dissipation values. All mixtures contained 1 mol%NBD-PC.a) Pure POPC and liposomes containing PEG(2)-PE+: pure POPC; ×: 1 mol% PEG(2)-PE; �: 2 mol% PEG(2)-PE; ○: 3 mol% PEG(2)-PE; ◆: 5 mol% PEG(2)-PE; ▴: 7 mol% PEG(2)-PE.b) Pure POPC and liposomes containing PEG(5)-PE+: pure POPC; ×: 0.25 mol% PEG(5)-PE; �: 0.5 mol% PEG(5)-PE; ○: 1 mol%PEG(5)-PE; ◆: 2 mol% PEG(5)-PE; ▴: 3 mol% PEG(5)-PE.

Fig. 4 Possible structures for the PEG-SLB in the mushroom regime. a: shows a repre-sentation of a possible structure where the PEG-lipids are present only in the upperleaflet of the lipid bilayer, while b: shows a possible structure where the PEG-lipidsare present in both leaflets of the lipid bilayer. Structure b has an increased thicknesscompared to structure a. This difference is the basis of the height measurements byAFM.

Fig. 5 Illustration of the experimental settings. Situation i) describes the two possibilitiesof unmodified AFM tips: PEG-SLB on the substrate only (left image) and PEG-SLB on the AFM tip (right image). Situation ii) describes the situation of PLL-g-PEG modified tips with a PEG-SLB on the substrate (left image) and the controlmeasurement to determine the influence of the PLL-g-PEG coating of the tip withouta PEG-SLB on the substrate (right image).

Fig. 6 Force-distance curves with unmodified tips on 1 mol% PEG(5)-PE SLB. Solid linewith unfilled circles (○) shows a curve displaying two jump-in events and a maximumand the dashed line with unfilled triangles (△) shows a one jump-in event.

Fig. 7 Force curves with unmodified tips on 1 mol% PEG(5)-PE SLB having one jump-inevent were superimposed (8 force curves, unfilled symbols), and 37 force curves wereaveraged represented in one force curve (solid line). In addition two force curvesshowing two jump-in events are added in the figure (filled symbols). For clarity thenumber of datapoints was reduced. Arrows indicate jump-in events (discontinuities inthe force curve).

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Fig. 8 Force curves with unmodified tips on 1 mol% PEG(5)-PE SLB having two jump-inevents were superimposed (8 force curves, unfilled symbols), and the solid line presentsan average of 58 force curves. For clarity, the number of datapoints was reduced.Arrows indicate jump-in events (discontinuities in the force curve).

Fig. 9 Force curves with a PLL-g-PEG modified tip. POPC SLB (unfilled circles, ○), 2 mol%PEG(2)-PE SLB (unfilled diamonds, ◇ and 1 mol% PEG(5)-PE SLB (plus signs, +)are shown. The solid lines show the Dolan and Edwards fit (equation 5) for 2 mol%PEG(2)-PE SLB and 1 mol% PEG(5)-PE SLB. Results of the fit are Rg = 2.2 nm ands =5.2 nm for 2 mol% PEG(2)-PE SLB and Rg =4.0 nm and s =6.9 nm for 1 mol%PEG(5)-PE SLB. For clarity, the number of datapoints was reduced.

Fig. 10 Enlarged section of the compression at low forces for averaged curves (>50 curves) witha PLL-g-PEG modified tip. POPC (solid line with unfilled circles, ○), 2 mol% PEG(2)-PE (dot dashed line with unfilled diamonds, ◇) and 1 mol% PEG(5)-PE (dashed linewith plus sign +) are shown. The curves were shifted to consider only the compressionof the PEG chains.

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21

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Figure 10:

24