Nanoroughness Strongly Impacts Lipid Mobility in SupportedMembranesFlorence Blachon,† Frederic Harb,‡ Bogdan Munteanu,§ Agnes Piednoir,† Remy Fulcrand,†

Thierry Charitat,∥ Giovanna Fragneto,⊥ Olivier Pierre-Louis,† Bernard Tinland,# and Jean-Paul Rieu*,†

†Universite Lyon, Universite Claude Bernard Lyon 1, CNRS, Institut Lumiere Matiere, F-69622 Villeurbanne, France‡Doctoral School for Science and Technology, Platform for Research in NanoSciences and Nanotechnology, Campus Pierre Gemayel,Lebanese University, Fanar-Metn BP 90239 Beirut, Lebanon§CNRS, INSA de Lyon, LaMCoS, UMR5259, Universite de Lyon, 69621 Lyon, France∥Universite de Strasbourg, Institut Charles Sadron, UPR22, CNRS, 67034 Strasbourg Cedex 2, France⊥Institut Laue-Langevin, 71 Avenue des Martyrs, F-38042 Grenoble, France#CINaM-CNRS, Aix-Marseille Universite, UMR7325, 13288 Marseille, France

*S Supporting Information

ABSTRACT: In vivo lipid membranes interact with roughsupramolecular structures such as protein clusters and fibrils.How these features whose size ranges from a few nanometers to afew tens of nanometers impact lipid and protein mobility is stillbeing investigated. Here, we study supported phospholipid bilayers,a unique biomimetic model, deposited on etched surfaces bearingnanometric corrugations. The surface roughness and meancurvature are carefully characterized by AFM imaging usingultrasharp tips. Neutron specular reflectivity supplements thissurface characterization and indicates that the bilayers follow thelarge-scale corrugations of the substrate. We measure the lateralmobility of lipids in both the fluid and gel phases by fluorescencerecovery after patterned photobleaching. Although the mobility isindependent of the roughness in the gel phase, it exhibits a 5-fold decrease in the fluid phase when the roughness increases from0.2 to 10 nm. These results are interpreted with a two-phase model allowing for a strong decrease in the lipid mobility in highlycurved or defect-induced gel-like nanoscale regions. This suggests a strong link between membrane curvature and fluidity, whichis a key property for various cell functions such as signaling and adhesion.

■ INTRODUCTIONFor more than three decades, supported phospholipid bilayers(SPBs) on various substrates have attracted considerableinterest as in vitro cell membrane models but also for theirpotential biotechnological applications.1−4 One of the greatadvantages of using planar solid SPBs as opposed to free lipidbilayer vesicles is the ability to apply surface-sensitive analyticalor structural techniques such as atomic force microscopy(AFM),5 Forster resonance energy transfer (FRET),6 fluo-rescence correlation spectroscopy (FCS),7 fluorescence recov-ery after photobleaching (FRAP),8 or X-rays and neutronscattering techniques.4 Furthermore, different strategies enablethe reconstitution of receptor proteins or transporter channelsin SPBs in order to probe or to simulate various cell functions.9

The thin water layer between the bilayer and the surfacepreserves the fluidity of the phospholipids, which isfundamental for many cellular functions. However, recentstudies have reported decoupled phase transitions andasymmetric molecular distributions between the upper andlower leaflets of SPBs that do not occur in the free-standing

membranes, (See ref 10 for a review.) For the same lipid at thesame temperature, lateral mobility, as characterized in this studyby the diffusion coefficient of fluorescent analogs ofphospholipids, is different on mica than on glass.11−14 Theelectrostatic interactions between surfaces and bilayers arepossible candidates for these mobility changes. Changes in thethickness of the interstitial water layer between the substrateand the bilayer or in the thickness of the bilayer have beenreported when the surface charge density is varied.15 Anothercandidate is the surface nanoscale roughness, which was shownto theoretically increase the mean substrate/bilayer distanceand decrease the adhesion energy using a low roughnessapproximation (i.e., when the mean amplitude of corrugationsis lower than the bilayer thickness).16,17

SPBs are generally deposited on flat, hydrophilic surfaces(e.g., mica, glass, and SiO2). However, in vivo, surfaces with

Received: September 17, 2016Revised: February 16, 2017Published: February 20, 2017

Article

pubs.acs.org/Langmuir

© 2017 American Chemical Society 2444 DOI: 10.1021/acs.langmuir.6b03276Langmuir 2017, 33, 2444−2453

lipid layers interacting are not flat. Cell membranes interactwith protein clusters (e.g., adhesion clusters) or with thefibrillar structure of the extracellular matrix, which has a typicalsize of about 10 nm.18 Phospholipid multibilayers are alsofound on many tissue surfaces and especially articularsurfaces.19 It is remarkable that these rough surfaces with a100 nm typical roughness value20 exhibit very low frictioncoefficients (μ ≃ 0.001) when sliding over their counterfaces.19

Moreover, recent patterning technologies in the field ofbiosensors or cell and tissue engineering combine fluid SPBsand functionalized topographical features.21 Understanding theformation and structure of SPBs on rough surfaces such asporous solids and nanoparticle carpets is very important tobuild lipid-based sensors on nanoporous surfaces22 and tounderstaning how inhaled nanoparticles interact with thepulmonary surfactant layers.23

In the past decade, the influence of nanotopographicalfeatures and roughness on the structure of SPBs has beeninvestigated both theoretically and experimentally. Bilayers areable to span over pores from a few tens of nanometers24,25 tothe micrometer diameter26 in both the fluid and gel phases. Inthe fluid phase, they may lose their integrity when deposited onsurfaces covered with nanoparticles with radii in between 0.6and 11 nm.27 The 11 nm threshold is close to the equilibriumradius of curvature estimate that might occur for an unbindingtransition with the membrane floating above the roughsubstrate28 as discussed in the Supporting Information. SPBson SiO2 nanobeads display larger melting temperatures andlarger local lipid order parameters than lipid vesicles of thesame radius in the 5−40 nm range.29,30 Nanocorrugations31 orhighly curved membrane tubes32 trigger lipid sorting and phasetransitions.The question of lipid mobility vs nanotopography has been

addressed in only a few studies. Mobility seems not to besignificantly affected by the presence of nanodots,21 nano-corrugations,31 or nanoporous surfaces33 as compared to plainsurfaces of the same material (glass or silicon). Typical scales ofthe topographical features in these studies were the following: 7nm diameter for adsorbed nanodots, nanocorrugated surfaceswith a few hundred nanometers and a few tenths of ananometer for lateral and vertical scales, respectively, andnanoporous surfaces with a pore size of about 2.5 nm. A slightdecrease in the diffusion coefficient D was observed when SPBswere deposited on etched surfaces with increasing root-mean-squared roughness (Rq) in a narrow range between 0.15 and0.25 nm, and a much larger variation was observed by changingthe glass treatment.34 Variations of 2- to 3-fold were observedon a variety of nanoporous oxide and organic xerogel films.35

However, the surface chemistry and topographic effects wereintermingled in these two studies. At least two studies reportedchanges in the lipid diffusion coefficient with changes in the real3D area induced by the roughness.22,36 Most of these studieswere performed with spot-based FRAP. SPBs were investigatedat only one temperature, and the roughness was notcharacterized up to the nanoscale using, for instance, ultrasharpAFM tips.As compared to the free-standing fully hydrated phospholipid

bilayers, there are fewer molecular dynamics (MD) simulationsof supported lipid bilayers.37 Only a few of them have started toaddress the issue of surface topography.38,39 In this work, weinvestigate the relationship between the surface topography andthe diffusion coefficient of lipids in SPBs on two different typesof rough surfaces with a typical amplitude and wavelength of

respectively 20 and 50 nm: etched glass presenting holes andetched silicon presenting spikes or dots.Solid surfaces are characterized by atomic force microscopy

(AFM) using ultrasharp tips and neutron reflectivity (NR).Diffusion coefficient D is measured by the FRAPP method(fluorescence recovery after patterned photobleaching) allow-ing us to probe the diffusion law efficiently over several ordersof magnitude with the same experimental setup.11 We observethat D decreases by a factor of 5 in the fluid phase when Rqincreases from 0.1 to 3 nm, whereas in the gel phase D isroughness-independent. A simple two-phase model with aslower diffusion coefficient in regions with high curvature (R ≤40 nm) captures very satisfactorily the experimental observa-tions in the fluid phase if the slow D value is comparable to thatof the gel phase.

■ EXPERIMENTAL SECTIONSPB Deposition. Phospholipids were purchased from Avanti Polar

Lipids: 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1-palmitoyl-2-oleo-yl-sn-glycero-3-phosphocholine (POPC), and 1-palmitoyl-2,6-[(7-nitro-2,1,3-benzoxadiazol-4-yl)amino]hexanoyl-sn-glycero-3-phospho-choline (NBD-PC). One wt % fluorescent lipid NBD-PC wasincorporated into DMPC and POPC bilayers for FRAPP measure-ments. Lipid molecules, solubilized in 9:1 chloroform/ethanol, weredeposited on an ultrapure water subphase (18 MΩ·cm, Milli-Q) of aLangmuir trough. After solvent evaporation (about 20−30 min), lipidswere compressed up to 40 mN/m for DPPC and up to 30 mN/m forPOPC and DMPC to form an interfacial monolayer on the subphasesurface. The first monolayer of lipids was transferred to the substrateby pulling up the substrate from the subphase at a speed of 5 mm/min(Langmuir−Blodgett method). The second monolayer was transferredaccording to the out-of-equilibrium Langmuir−Schaefer method.40

Substrate Preparation. For FRAPP experiments, SPBs weredeposited on pieces of a one-side-polished (100) Si wafer or oncircular windows of BK7 glass (Melles Griot), which is a borosilicatecrown glass. For NR experiments, we used 8 × 5 × 1.5 cm3 (111)single crystals of silicon. Silicon substrates were etched repeatedly byreactive-ion etching (Oxford, RIE 80) at 60 mTorr pressure and 250W power with 6.7 and 25.6 sccm gas flow rates for oxygen and SF6,respectively. The surface roughness of BK7 were prepared by achemical etching process with a 1:1 sodium hydroxide/ethanolsolution in a ultasonic bath at room temperature. Substrates wereconserved in air under a clean atmosphere for several weeks. Prior tolipid transfer, BK7 was cleaned in an ultrasonic bath with soap(Microson, Fisher Scientific) for 20 min, and Si substrates were treatedfor 3 min at 120 °C with a plasma cleaner (30 sccm oxygen and 10sccm argon, high rf level). Samples were then rinsed thoroughly inpure water. These cleaning procedures ensure hydrophilic surfaces butdo not increase the roughness significantly.

FRAPP Measurements. The light beam of an etalon-stabilizedmonomode Ar laser (0.5W at 488 nm) is split, and the two resultingbeams are crossing on the sample at an angle θ, providing aninterference fringe pattern for FRAPP measurements. The fringespacing i = 2π/q, where q = 4π/λ sin(θ/2), is the wave vector rangingfrom 1 to 80 μm and defines the diffusion distance. A bleach pulse setto 1 s with a 0.5 W laser intensity wrote a fringe patterned into thesample that, because of diffusion, disappeared with time. After thebleach pulse, the beam intensity is reduced to a few milliwatts: underthese circumstances, we observed no further bleaching of the NBD-labeled lipids. Data (Supporting Information Figures S7 and S8) werefitted to a single exponential exp(−t/τq), and D was calculated from τq= 1/Dq2. Error bars in figures refer to the standard deviation obtainedfrom measurements at five different locations on the same sample. Thefollowing two special features of the setup are worthy of note. (i) Theuse of the same periodic sinusoidal pattern for bleaching and readingallows a single mode of the diffusion equation to be probed. (ii)

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Because of the very low contrast signal, we estimate that the immobilefraction is always lower than 20%.AFM Imaging and Image Analysis. AFM imaging was

performed in tapping mode in air using an MFP-3D AFM (AsylumResearch). The set point was adjusted to have minimal forces, the scanrate was set at 1 Hz, and the gain was optimized to reduce noise. Initialroughness characterization was obtained from 5 × 5 μm2 and 1 × 1μm2 scans for glass BK7 and Si surfaces, respectively, at 256 × 256pixels2 with standard aluminum reflex-coated silicon cantilevers(Nanoworld ARROWTM - NCR, hereafter referred as NCR tips, 42N/m nominal spring constant, 10 nm tip radius). The root-mean-squared (rms) roughness Rq was calculated with public softwareGwyddion. Sharper tips, hereafter referred to as SSS tips (Nano-sensorsTM SSS - NCHR, 42 N/m nominal spring constant, 2 nm tipradius) and scan sizes of 1× 1 μm2 at 512 × 512 pixels2 were used tomeasure mean curvature C. We calculated C with Matlab (MathWorks,Natick, MA) using the formula C = ((1 + hx

2)hxx − 2hxhyhxy + (1 +

hy2)hyy)/((1 + hx

2 + hy2)3/2) where = ∂

∂h zuu and = ∂

∂ ∂h zu vuv

2are first and

second derivatives (u = x or y) of the surface height z(x, y).NR Measurements and Analysis. The NR experiments at the

solid−liquid interface were carried out at time-of-flight reflectometerFIGARO (fluid interfaces grazing angles reflectometer) at the ILL,Grenoble, France. Data were collected with neutron wavelengths λ inthe range of 0.2−2 nm at two different incident angles (θ = 0.8 and3.2°) and Δλ/λ = 7% for a total average measuring time of 1.5 h/curve. Slits were set up so that the sample was always underilluminated(70% illumination). Details of the experimental setup are given in ref41. The ratio between the specularly reflected and the incomingintensities, i.e., the specular reflectivity R(Q), is measured as a function

of the wave vector transfer Q. In specular geometry, Q is perpendicularto the reflecting surface and R(Q) is related to the scattering lengthdensity (SLD) profile across the interface by the square modulus of itsFourier transform. For SPBs, the profiles were modeled as a series offive thin layers located in between Si(111) and the buffer: twoheadgroup layers, an inner membrane layer for the hydrophobic part, aSiO2 oxide layer (Ox) on the silicon block (Si), and a thin water layerbetween the bilayer and the oxide layer. They were fitted with Auroresoftware.42 Each layer y was characterized by its thickness (ty),scattering length density (SLDy), roughness (σy), and percentage ofwater in each layer (Nwy). The SLDs of Si and Ox were taken as 2.07× 10−6 and 3.47 × 10−6 Å−2, respectively. Sample holders were laminarflow cells that allowed solvent exchange in order to apply fivecontrasts, namely, D2O (SLD = 6.35 × 10−6 Å−2), H2O (SLD = −0.56× 10−6 Å−2), OMW (oxide match water: 60% D2O, 40% H2O, SLD =3.41 × 10−6 Å−2), SMW (silicon match water: 38% D2O, 62% H2O,SLD = 2.07 × 10−6 Å−2), and 4MW (four match water: 66% D2O, 34%H2O, SLD = 4.00 × 10−6 Å−2). The sample temperature wascontrolled by a water bath at T = 20 and 50 °C to investigate the geland fluid phases of SPBs, respectively. The bare substrate (Si/Ox/solvent interface) was characterized first by the set of four parameters,σSi, tOx, σOx, and NwOx, kept fixed in the subsequent analysis with SPBs.

■ RESULTS AND DISCUSSIONBare Substrate Characterization. Silicon wafers (here-

after denoted as Si) were etched by dry reactive ion etching(RIE). Circular plane windows of borosilicate BK7 glass(hereafter denoted as BK7) were submitted to wet etching in a1:1 sodium hydroxide/ethanol solution. Both substrates were

Figure 1. AFM images in air (tapping mode) of etched surfaces. (A) Reference bare silicon wafer surface (Rq = 0.11 nm). (B, C) 2D and 3D views ofa roughened silicon wafer surface etched by RIE for 20 min (Rq = 1.7 nm). (D) Reference borosilicate crown glass BK7 sonicated for 20 min in a 1:1sodium hydroxide/ethanol solution (Rq = 0.8 nm). (E, F) 2D and 3D views of a roughened BK7 surface after prolonged sonication in a 1:1 sodiumhydroxide/ethanol solution (Rq = 6.2 nm).

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used for FRAPP experiments. The roughness Rq is controlledby the etching duration as evidenced by tapping mode AFMimages. For reference Si surfaces, Rq is less than 0.2 nm over 1μm2 regions (Figure 1A). Prolonged RIE treatment induces aforest of peaks on the Si surface. Figure 1B,C shows 2D and 3Dviews of a surface etched for 20 min with peaks ∼10−15 nm

high and a resulting rms roughness of Rq = 1.7 nm. Rq increasesroughly exponentially with etching time until a plateau isreached at about Rq = 3 nm after 30 min (not shown). BareBK7 surfaces are not as homogeneous as silicon surfaces if theyare not etched during some minimum time because of thepresence of residues of industrial polishing. At least 20 min of

Table 1. Main Parameters Extracted by Fitting NR Experiments of DPPC Bilayers on Three Si Substrates of IncreasingRoughnessa

reference Si intermediate Rq large Rq

bare substrate Rq AFM (nm) 0.7 ± 0.1 1.7 ± 0.3 3.4 ± 0.5σSi (nm) 0.3 ± 0.1 0.8 ± 0.4 2.1 ± 0.3tOx (nm) 1.3 ± 0.1 1.2 ± 0.2 2.0 ± 0.4σOx (nm) 0.4 ± 0.1 1.1 ± 0.2 2.5 ± 0.2

bilayer T (°C) 20 ± 0.1 20 ± 0.1 50 ± 0.1 20 ± 0.1tw (nm) 0.4 ± 0.2 0.3 ± 0.2 0.4 ± 0.2 0.5 ± 0.2tbi (nm) 4.8 ± 0.4 5.5 ± 0.2 5.6 ± 0.2 5.1 ± 0.1σbi (nm) 0.7 ± 0.2 1.2 ± 0.2 1.3 ± 0.3 2.5 ± 0.5% water 10 ± 10 10 ± 10 15 ± 10 10 ± 10

aσSi, σOx, and σbi are the layer interfacial width (roughness) of the silicon/oxide, oxide/water, and bilayer/water interfaces, respectively; tOx, tw, and tbiare the thickness of the oxide layer, interstitial water layer, and lipid bilayer, respectively; the water percentage is the one detected in the DPPC headlayers (we do not detect a significant amount of water in the hydrophobic tail layer). For intermediate Rq, the bilayer was probed at twotemperatures.

Figure 2. Mean curvature of etched surfaces. (A, C) 3D rendering views taken with supersharp SSS tips and (B, D) associated calculated meancurvature maps of rough Si (Rq = 1.7 nm) (A, B) and BK7 (Rq = 6.9 nm) (C, D) surfaces. (E) Variation of the relative hidden area ((A3D − A2D)/A2D) as a function of the measured rms roughness Rq for Si and BK7 surfaces imaged with conventional (NCR) or supersharp (SSS) tips. (F)Proportion Φ(40 nm) of the surface with an absolute value of the local curvature radius |RC| that is lower than 40 nm.

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wet etching is necessary to remove these residues in order toget the low roughness reference for BK7 at about Rq = 0.8 nm(Figure 1D). Several holes and lines are visible on this referenceimage. Long wet etching treatments induce an rms roughnessincrease of up to more than 10 nm with craters of up to 50 nmin depth (e.g., 2D and 3D views of a Rq ≃ 6 nm etched BK7sample in Figure 1E,F, respectively). Qualitatively, the surfacetopography of the etched BK7 is almost the mirror-symmetricimage of the etched Si surface as it presents large holes ofvarious depths (Figure 1F) instead of peaks (Figure 1C). Forthe whole substrate examined in this work, we measured byAFM a low variability in roughness of ΔRq/Rq ≤ 10% whenimaging different regions of the same sample.We performed NR experiments on (111) single crystals of

silicon in order to supplement the surface characterization ofthe bare substrate (in particular, the roughness and thickness oftheir oxide layer) and to measure the vertical density profile ofSPBs. A reference crystal was used after polishing, and twoothers were submitted to prolonged RIE treatments. Topo-graphical AFM images (on a 10 × 10 μm2 scale) and theanalysis of NR measurements (see below) on these baresubstrates gave similar hierarchies of roughness values (Rq = 0.7nm for the reference, 1.7 nm for the rough surface, and 3.4 nmfor the very rough surface, see Table 1 and SupportingInformation Figure S1). Note that the values obtained by AFMare always about 35% higher than those obtained by NR.To evaluate tip convolution effects, we changed the tip size.

Nanocorrugation peaks of rough Si are narrower with sharpertips (ultrasharp SSS tips with a typical tip radius of r = 2 nm)than with conventional tips (NCR tips with r = 10 nm) asshown in Supporting Information Figure S2A,C. Calculatingmean curvature maps (Experimental Section) enables us tohighlight differences in peak diameter and local curvature valuesof Si surfaces for different tips (Supporting Information FigureS2C,D). When probed with SSS tips, the local mean curvatureof Si frequently approaches |C| = 108 m−1 (i.e., |R| = 2/|C| ≃ 20nm) for both positive and negative curvatures (Figure 2A).However, whatever the tip, the image presents roughly thesame peak density because the mean distance between nearestneighbors (i.e., 50−100 nm) is larger than the tip size. Thecurvature map of BK7 surfaces presents features that are notimmediately visible in 3D views (Figures 2C): holes and cratersare connected by narrow valleys (in red on Figure 2D) withhigh positive curvature values (C = 108 m−1). On the otherhand, the tops of the corrugations with negative curvature (inblue) are less sharp.We further characterize the surface topography by computing

the relative hidden area [(A3D − A2D)/A2D, where A3D is thearea of the real 3D surface and A2D is the 2D projected area],the histograms of mean curvature (Supporting InformationFigure S3B,D), and the fraction Φ(40 nm) of the surface withan absolute value of the local radius of curvature that is smallerthan |RC| = 40 nm (we discuss this value later). For eachsurface, the roughness Rq and the relative hidden area are wellcorrelated quantities, but the two curves exhibit different slopes,indicating that Si and BK7 are not exactly mirror surfaces(Figure 2E). The use of ultrasharp tips does not significantlychange these two quantities, indicating that Rq is well measuredby AFM even with conventional tips. Interestingly, anapproximate linear relation holds between the local Φ(40nm) and global Rq quantities.

βΦ = − > Φ = ≤R R R R R R(40 nm) ( ) if and (40 nm) 0 ifq q0 q q0 q q0

(1)

Rq0 is a roughness threshold, below which the mean surfacecurvature almost never exceeds |1/RC|. As seen in Figure 2F,fitting parameters β and Rq0 are larger for Si surfaces (β = 0.050nm−1, Rq0 = 0.80 nm) than for BK7 surfaces (β = 0.0028 nm−1,Rq0 = 0 nm). Here, tip convolution has a strong impact on themeasurement (Figure 2F): the sharper the tip, the larger the Φ(40 nm). Of course, choosing a different critical thresholdradius, RC, gives different statistics of the curvature fractionϕ(RC) (Supporting Information Figure S3A,C).

Structure of Supported Bilayers on Rough Surfaces.SPBs were deposited by the Langmuir−Blodgett (LB)deposition method for the first leaflet and the Langmuir−Schaefer (LS) method for the second leaflet. DMPC waschosen for FRAPP experiments because its melting transition isclose to room temperature. POPC SPBs, fluid over the entiretemperature range of the study, were also explored with thistechnique for comparison. DPPC was chosen for NRexperiments because it has a longer chain, which enables easierdecoupling between roughness and bilayer thickness effectswhen fitting the specular reflectivity data.After bilayer deposition on a given rough substrate, SPBs

were imaged by AFM in water. For a given substratum, wecould not observe any significant difference between theseimages and those of the same bare rough substratum imagedeither before the LB−LS deposition or after removing the SPBs(Supporting Information Figure S4). This suggests that thebilayer follows the substrate corrugations. Because a membranefloating far from the substrate is probably very easily deformedby the AFM tip during scanning, especially in the fluid phase,24

we also probed the vertical scattering length density profileSLD(z) along the vertical coordinate z of SPBs by NR, which isa noninvasive technique. This SLD(z) is related to the numberof nuclei per unit volume Vi(z) and to the neutron scatteringlength bi of species i as SLD(z) = ∑i Vi(z)bi. We apply thecontrast variation method,43 which increases the effectivespatial resolution of NR (Experimental Section).Typical reflectivity curves R(Q), defined as the intensity ratio

of neutrons in the specular direction to those in the incidentbeam and measured with respect to the momentum transfer Qnormal to the surface, are displayed together with the fittedSLD(z) curves in Supporting Information Figures S5 and S6for the smoother and the rougher substrates, respectively. Theraw data are very different in the presence of an SPB ascompared to the bare substrate case, and one also observeslarge differences between the two substrates. The fitting modelconsists of a stack of thin layers located in between the two bulkphases (the silicon bulk material and the buffer, see theExperimental Section). The main parameter values from thefitting procedure are reported in Table 1. The thickness of theoxide layer and interstitial water layer between the oxide andthe bilayer are not changing with the roughness. The lowpercentage of water in bilayers (only a small amount wasdetected in the chain region) indicates that they perfectly coverthe surfaces, even the rougher ones, confirming the very highquality of Langmuir−Blodgett−Schaefer depositions.11 What-ever the roughness or the temperature, the top bilayerroughness (σbi) approaches that of the SiO2 oxide layer (σOx)which is close to that of the Si−SiO2 interface (σSi). Differencesbetween the bilayer roughness in the gel phase are significant:σbi = 0.7 ± 0.2 nm for the smoother substrate, and σbi = 1.2 ±

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0.2 nm and 2.5 ± 0.5 nm for the intermediate and roughersubstrates, respectively. These results indicate that the SPBs arefollowing the roughness of the substrate at large scales, and wedo not observe an unbinding transition characterized by adecoupling of substrate and bilayer roughnesses. Becausespecular reflectivity provides an averaged measurement over alarge area, this does not exclude very slight unbinding ofmembranes at small scales. This is further discussed in theSupporting Information.FRAPP Measurements of the Diffusion Coefficient.

Typical FRAPP signals and monoexponential fits with thecharacteristic time τq related to the diffusion constant D areshown in Supporting Information Figures S7 and S8. Thediffusion coefficient D of DMPC in the fluid phase (28 °C)strongly depends on the roughness Rq (Figure 3A). For a givenroughness value, D is slightly affected by the substrate type orby the lipid type. For Si surfaces, D decreases from nearly 10 ×10−8 cm2/s on the smooth substrate to 2.2 × 10−8 cm2/s on theroughest substrate (Rq = 2.2 nm). On BK7 surfaces, a similar 4-to 5-fold decrease in D is observed between 6.7 × 10−8 cm2/s atRq = 0.7 nm (smoothest one) to about 1.6 × 10−8 cm2/s at Rq =4.7 nm. At larger Rq on BK7, D seems to reach a plateau.Plotting the inverse of D as a function of Rq shows a strikinglinear dependence (except for the point of BK7 with the largestroughness, Figure 3B):

η= +D D

R1 1

0q

(2)

Interestingly, we find almost the same intercept 1/D0 for thetwo surfaces: D0 = 13.5 × 10−8 cm2/s for Si and D0 = 10.4 ×10−8 cm2/s for BK7. These values are close to the fluid phasevalues reported for free membranes44 of SPBs on glass.11,12,34

The slope η describing the roughness dependence of D is

slightly larger on Si than on BK7 (η = 1.7 × 107 and 1.3 × 108

s/cm2/nm, respectively).In the gel phase, the FRAPP measurements (DMPC SPB at

12 °C) exhibit strikingly different behavior: D does not dependon Rq for either Si or BK7 (Figure 3C). Furthermore, weobserve a nearly 10 times larger D on Si than on BK7 at about1.6 × 10−9 cm2/s.

Origin of the 5-Fold Decrease in D in the Fluid Phase.The strong roughness dependence of D in the fluid phase wasnever reported to the best of our knowledge.Hidden area AH is a natural candidate for explaining this

observation. Indeed, the rough surface is three-dimensional(3D), and the lipids have to diffuse up and down, leading tolonger trajectories of diffusion to reach the same mean-squareddisplacement as for a flat surface. Detailed experimental andnumerical investigations of this effect36,45 have shown that theratio of the diffusion coefficient between flat and 3D surfaces(i.e., D2D/D3D) is proportional to the ratio A3D/A2D betweenthe area of the real 3D surface and the projected area. Thehidden area measured in this work (i.e., A3D/A2D ≤ 1.25 inFigure 2F) is too low to be the source of the 5-fold mobilitydecrease in the fluid phase.We have evidence that surface interactions are not

significantly affected by the etching process. First, we measuredby NR an oxide layer thickness in the range of 1.2−2 nm for allsamples investigated (Table 1). Second, the thickness of theinterstitial water layer, which is sensitive to the interactionbetween substrate and bilayer, is not significantly correlatedwith the sample roughness. Finally, it is known that when thesubstrate type or salt concentration is changed, diffusioncoefficient values D present larger relative variations in the gelphase than in the fluid phase.11,12 Here, D is nearly roughness-independent in the gel phase but is 10 times larger on silicon

Figure 3. Diffusion coefficient D of DMPC (black) and POPC (purple) supported bilayers on BK7 (closed symbols) and Si (open symbols)surfaces. (A) Plot of D vs rms roughness Rq in the fluid phase (28 °C for DMPC and 22 °C for POPC). D decreases with Rq and seems weaklydependent on the substrate (Si or glass BK7) and lipid type. (B) Same data plotted for inverse diffusion coefficient 1/D. (C) In the gel phase forDMPC (12 °C), D is independent of Rq on both surfaces but almost 10 times faster on Si than on BK7. (D) 1/D in the fluid phase plotted as afunction of the proportion of highly curved regions Φ(RC) with RC = 40 nm. Lines correspond to eq 3.

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than on glass (Figure 3C). One explanation of this strikingfinding is that the surface/bilayer interactions depend on agiven substrate type but are not modified by the etchingprocess.Another reported mechanism influencing lipid mobility is

membrane confinement. The Saffman Delbruck (SD) model46

is a hydrodynamic model that describes the lipid membrane asa thin layer of viscous fluid of viscosity μ and thickness hsurrounded by a less viscous bulk liquid. When the membraneis confined in an area of radius RSD, this model predicts alogarithmic dependence of the diffusion constant, D = kBTln(RSD/r)/(4πμh), where kB is the Boltzmann constant, T is theabsolute temperature, and r is the radius of the diffusingmolecule (here, the lipid molecule). By measuring the diffusionconstant of lipids and proteins on membrane tubes with theradius varying between 8 and 250 nm, Domanov et al.concluded that this equation applies by replacing RSD with themembrane tube RT.

47 Even if the SD model does not accountfor the dissipation due to the thin water layer under thesupported membrane, it is interesting to ask whether such amechanism may hold with our bilayers supported on roughsurfaces. However, the mobility is much less reduced in tubes(2- to 3-fold when RT ≈ 10 nm as compared to flat and freemembranes) than in our supported case. In addition, thefraction of the surface with a highly curved region is very small.In conclusion, although they can influence the diffusion

coefficient to some extent (typically up to 25% changes for thehidden area effect), the hidden area, chemistry, and confine-ment are not sufficient to explain the 5-fold decrease in D in thefluid phase.Our measurements show that 1/D is linear with roughness

Rq, which is a global quantity. The structure and physicalproperties of SPBs such as the diffusion coefficient shouldrather depend on a local quantity such as the local meancurvature C = 2/R than on Rq. We propose that the localdiffusion coefficient Dloc is influenced by the local curvature ona scale of about 10 nm. Because FRAPP measurements have aspatial resolution equal to the interfringe spacing (i.e., at least afew micrometers), we do not measure Dloc but instead a meandiffusion coefficient D over a heterogeneous landscape. Thereare several possible types of curvature-induced mobility defects(Figure 4A): holes free of lipids (type 1) and regions withincreased lipid order in the border of holes (type 2) or in highlycurved regions covered with a membrane (type 3).Holes in LB SPBs have been reported in many AFM

studies.48 A more recent AFM-based analysis showed that fluidSPBs do not cover silica beads with radii of curvature lowerthan a critical radius RC(F) = 11 nm27 because it costs toomuch bending energy. Our substrates present a few spots ofultrahigh curvature that could probably not be covered bybilayers. They could act as obstacles for lipid diffusion.Assuming that the bilayer/substrate adhesion is not changedbetween the fluid and gel phases and using a rescaling for the

critical radius in the gel phase, κ κ=R G R F G F( ) ( ) ( )/ ( )C C ,we obtain RC(G) = 35 nm in the gel phase (with a 10-foldlarger bending stiffness in that phase, see the first section of theSupporting Information). An ordering of the lipids might occuraround the edges of these defects as shown schematically byblue bilayer regions in Figure 4A. This scenario is supported bythe results of Heath et al.,49 who managed to produce quasi-1DSPBs with variable widths. They measured above the meltingtransition (fluid phase) a 3-fold decrease in the lipid diffusion

coefficient when the width decreases from about 50 to 25 nm,suggesting lipid ordering in the vicinity of the SPB edge. Adecrease in mobility in highly curved regions (i.e., type 3defects represented as blue regions in Figure 4A) could beassociated with increased packing. In the framework of the freearea model, D can vary by orders of magnitude with packing.50

Both experimental29,30 and theoretical studies51,52 have shownthat an asymmetry in lipid packing between the two lipidleaflets may induce an increase in the local order parameters,diffusion coefficient, or bending rigidity of highly curvedmembranes for a curvature radius between 10 and 40 nm.Gathering all of these possible scenarios and typical length

scales, we chose in this study |RC| = 40 nm for the thresholddefining highly curved defect regions, and we plot in Figure 3Dthe inverse of D as a function of the fraction of a highly curvedsurface Φ(40 nm). The data are described by the followinglinear relation with parameters already fitted from Figures 2Fand 3B thanks to eqs 1 and 2:

η ηβ

= + + ΦD D

R1 1

(40 nm)0

q0(3)

Two-Phase Model for the Diffusion of Lipids in aRough Landscape. To investigate further the hypothesis ofthe presence of regions where the diffusion is altered, wedescribe now a simple two-phase model. A 2D random walk issimulated on a binary surface made of flat portions and defectswith surface fractions ϕ1 and ϕ2 and diffusion coefficients D1and D2, respectively (Figure 5B). To illustrate the model, anAFM-based binary surface is chosen with a threshold on theabsolute value of the mean curvature |C| that controls ϕ2(Figure 5C). We also run so-called obstacle simulations withimpenetrable defects (i.e., type 1, Figure 5A). We computedmean-squared displacements (MSD) and calculated theapparent diffusion coefficient D from a linear fit of MSDversus time for values larger than the mean flight time betweendefects.Simulations with obstacles (Figure 5C) are noisy because

simulated walkers may be locally trapped in small pocketsdepending on the threshold value. Similarly, the results do notdepend only on ϕ2 but also on the defect topology; the results

Figure 4. Possible scenarios for the conformation of supportedbilayers on rough surfaces. (A) In the fluid phase, the fluid bilayer(inner red bilayer) mostly follows the surface, but sharp peaks maypierce the membrane and create holes (a type 1 defect). Around theedges of these defects, an ordering of the lipids (inner blue bilayer)may occur, resulting in a lower mobility (a type 2 defect). In highlycurved regions, lipids are also more ordered and their mobility isdecreased (a type 3 defect). (B) In the gel phase, the whole bilayer isin a homogeneous state (inner blue bilayer everywhere). The morerigid bilayer may partially unbind in highly curved regions (mark 4).

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are different if we use a random distribution of defects insteadof the AFM-based map (not shown). A large decrease in Dcompatible with our FRAPP measurements in the fluid phaseoccurs only for ϕ2 ≥ 50%. This large value is already reportedin the literature53 and corresponds to the obstacle percolationtransition. In our NR measurements or in our AFM images, weare far from detecting 50% holes in the bilayer. In conclusion,we believe that impenetrable obstacles cannot explain ourobservations.The diffusion constant D does not depend on the defect

topology for the two-phase simulations (type 2 and 3 defects)but only on ϕ2, as a random distribution of defects givesessentially the same results as the AFM-based map for a givenϕ2 (not shown). The simulated data can be fitted satisfactorilywith a very simple formula that is exact in 1D (solid line inFigure 5C):

ϕ ϕ=

−+

D D D1 1 2

1

2

2 (4)

This equation is similar to eq 3. Taking Φ(40 nm) = ϕ2, wecan identify D1 and D2 with experimentally measuredquantities, namely, 1/D1 = ηRq0 + 1/D0 and D2 = (α + 1/D1)

−1. D1 is close to the value for free membranes [i.e., about(5−10) × 10−8 cm2/s)], and we also obtain D2 = 2.2× 10−9

cm2/s for Si and D2 = 2.3× 10−10 cm2/s for BK7. These valuesare close to those measured in the gel phase: Dgel(Si) = 1.62 ×10−9 cm2/s and Dgel(BK7) = 1.64 × 10−10 cm2/s. Of course, D2and α depend on the threshold RC chosen to calculate ϕ(RC).Alternately, one may fix D2 at Dgel and estimate this threshold.In conclusion, it is interesting that almost the same diffusion

coefficient was measured on silicon and glass for a givenroughness Rq ,but this similarity may be fortuitous. Indeed, onglass both the slow-phase diffusion coefficient D2, whichprobably depends on chemistry (see the next section), and theproportion of defects ϕ2 that depends only on the topographyare much smaller than on silicon.Gel Phase: Possible Unbinding Transition and Role of

Surface Chemistry. In the framework of our two-phasemodel, the origin of the slow mobility of liquid membranes onrough surfaces is lipid ordering in or around defect regionsabove the main transition temperature Tm. Once the temper-ature is reduced below Tm, the full SPB becomes ordered and

homogeneous (Figure 4B). The diffusion coefficient Dgel shouldbe almost independent of the roughness as observed (Figure3C). In principle, we should detect the slight hidden area effectdiscussed above (up to a 25% change in the diffusion coefficientdue to area changes, Figure 2E). Because error bars on Dgel aregenerally slightly lower than 20% for glass surfaces, we cannotexclude a partial unbinding transition in highly curved regionsas depicted in Figure 4C and discussed in the SupportingInformation.Finally, our measurements indicate that the mobility is much

more sensitive to the surface chemistry in the gel phase than inthe fluid phase. Extrapolated at zero Rq, D0 is only 23% loweron BK7 than on Si above Tm, whereas below Tm, Dgel is 10times lower on BK7 than on Si. This is not fully surprisingbecause it is known that Dgel is, for instance, much moresensitive to changes in the ionic strength than Dfluid.

12 Inaddition, differences between the mobility of bilayers supportedon mica or glass have been reported to be larger in the gel thanin the fluid phase.11

■ SUMMARY AND CONCLUSIONS

We have investigated the effect of nanoroughness on thediffusion of supported phospholipids on etched surfaces. Theroughness has a strong influence in the fluid phase but not inthe gel phase. This difference cannot be explained by the effectof chemistry, hidden area, or obstacles in the bilayer. However,it can be explained by a strong dependence of the mobility onlocal curvature. We show that a simple two-phase model withfast and slow regions allows one to explain FRAPP measure-ments quantitatively in the fluid phase. In that framework, onlya small percentage of slow nanoscale regions (i.e., typically 7%)with a diffusion coefficient similar to that of the gel phase(which could be triggered by high local curvature) is sufficientto reproduce a 5-fold decrease in D with respect to the smoothdefect-free surface. In the gel phase, as the bilayer fullycongeals, D is independent of the roughness. The use of aprobe sensitive to the ordering of the lipids (such as Laurdan54)should enable the quantification of the fraction of ordereddomains in order to demonstrate the proposed two-phasemodel. We hope that this model will stimulate theoreticalinvestigations or experimental measurements at the single-molecule level, such as fast AFM, to provide more physical

Figure 5. Random walk simulations on heterogeneous surfaces. (A) Enlarged area of the simulated trajectory randomly moving around impenetrableobstacles in black. (B) Enlarged area of a simulated trajectory moving more slowly on black than on white regions (two-phase model). (C) Simulateddiffusion coefficient as a function of the defect ratio (two-phase and obstacle models in blue and red, respectively). The two-phase simulation wasperformed with D1 = 25 D2 and fitted with eq 4.

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insight into the microscopic mechanisms involved in the strongdecrease in lipid mobility on rough surfaces. The control ofmobility by nanoscale roughness paves the way for practicalapplications such as sorting and partitioning of lipids andproteins on surfaces and could have a major impact on variousbiological processes such as raft formation and proteinclustering.

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.lang-muir.6b03276.

Local unbinding of lipid membranes on rough substrates:models and discussion. Bare surface characterization andcomparison of images with or without SPBs: comple-mentary AFM analysis. Neutron reflectivity: specularreflectivity curves and fitted SLD. Fluorescence recoveryafter patterned photobleaching: typical curves. (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: jean-paul.rieu@univ-lyon1.fr.

ORCIDJean-Paul Rieu: 0000-0003-0528-8819NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work is supported by French Research Program ANR-12-BS04-0008-01, BIOLUB project. We thank M. El Mamouhdi,A. Petit, and B. Chami for preliminary work and A.-M. Trunfio-Sfarghiu, Y. Hayakawa, C. Loison, and F. Dekkiche for helpfuldiscussions. Furthermore, we thank the ILL for beam time andthe use of the PSCM facilities. We are grateful for the help andsupport of P. Gutfreund and Y. Gerelli during the neutronexperiments on FIGARO at the ILL, Grenoble.

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