Nanoroughness Strongly Impacts Lipid Mobility in Supported

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Nanoroughness Strongly Impacts Lipid Mobility in Supported Membranes Florence Blachon,† Frédéric Harb,‡ Bogdan Munteanu,§ Agnès Piednoir,† Rémy Fulcrand,† Thierry Charitat,∥ Giovanna Fragneto,⊥ Olivier Pierre-Louis,† Bernard Tinland,# and Jean-Paul Rieu*,† †

Université Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, 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, Université de Lyon, 69621 Lyon, France ∥ Université 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 Université, UMR7325, 13288 Marseille, France ‡

S Supporting Information *

ABSTRACT: In vivo lipid membranes interact with rough supramolecular structures such as protein clusters and fibrils. How these features whose size ranges from a few nanometers to a few tens of nanometers impact lipid and protein mobility is still being investigated. Here, we study supported phospholipid bilayers, a unique biomimetic model, deposited on etched surfaces bearing nanometric corrugations. The surface roughness and mean curvature are carefully characterized by AFM imaging using ultrasharp tips. Neutron specular reflectivity supplements this surface characterization and indicates that the bilayers follow the large-scale corrugations of the substrate. We measure the lateral mobility of lipids in both the fluid and gel phases by fluorescence recovery after patterned photobleaching. Although the mobility is independent of the roughness in the gel phase, it exhibits a 5-fold decrease in the fluid phase when the roughness increases from 0.2 to 10 nm. These results are interpreted with a two-phase model allowing for a strong decrease in the lipid mobility in highly curved or defect-induced gel-like nanoscale regions. This suggests a strong link between membrane curvature and fluidity, which is a key property for various cell functions such as signaling and adhesion.

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INTRODUCTION For more than three decades, supported phospholipid bilayers (SPBs) on various substrates have attracted considerable interest as in vitro cell membrane models but also for their potential biotechnological applications.1−4 One of the great advantages of using planar solid SPBs as opposed to free lipid bilayer vesicles is the ability to apply surface-sensitive analytical or structural techniques such as atomic force microscopy (AFM),5 Förster resonance energy transfer (FRET),6 fluorescence correlation spectroscopy (FCS),7 fluorescence recovery after photobleaching (FRAP),8 or X-rays and neutron scattering techniques.4 Furthermore, different strategies enable the reconstitution of receptor proteins or transporter channels in SPBs in order to probe or to simulate various cell functions.9 The thin water layer between the bilayer and the surface preserves the fluidity of the phospholipids, which is fundamental for many cellular functions. However, recent studies have reported decoupled phase transitions and asymmetric molecular distributions between the upper and lower leaflets of SPBs that do not occur in the free-standing © XXXX American Chemical Society

membranes, (See ref 10 for a review.) For the same lipid at the same temperature, lateral mobility, as characterized in this study by the diffusion coefficient of fluorescent analogs of phospholipids, is different on mica than on glass.11−14 The electrostatic interactions between surfaces and bilayers are possible candidates for these mobility changes. Changes in the thickness of the interstitial water layer between the substrate and the bilayer or in the thickness of the bilayer have been reported when the surface charge density is varied.15 Another candidate is the surface nanoscale roughness, which was shown to theoretically increase the mean substrate/bilayer distance and decrease the adhesion energy using a low roughness approximation (i.e., when the mean amplitude of corrugations is 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, 2016 Revised: February 16, 2017 Published: February 20, 2017 A

DOI: 10.1021/acs.langmuir.6b03276 Langmuir XXXX, XXX, XXX−XXX

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Langmuir lipid layers interacting are not flat. Cell membranes interact with protein clusters (e.g., adhesion clusters) or with the fibrillar structure of the extracellular matrix, which has a typical size of about 10 nm.18 Phospholipid multibilayers are also found on many tissue surfaces and especially articular surfaces.19 It is remarkable that these rough surfaces with a 100 nm typical roughness value20 exhibit very low friction coefficients (μ ≃ 0.001) when sliding over their counterfaces.19 Moreover, recent patterning technologies in the field of biosensors or cell and tissue engineering combine fluid SPBs and functionalized topographical features.21 Understanding the formation and structure of SPBs on rough surfaces such as porous solids and nanoparticle carpets is very important to build lipid-based sensors on nanoporous surfaces22 and to understaning how inhaled nanoparticles interact with the pulmonary surfactant layers.23 In the past decade, the influence of nanotopographical features and roughness on the structure of SPBs has been investigated both theoretically and experimentally. Bilayers are able to span over pores from a few tens of nanometers24,25 to the micrometer diameter26 in both the fluid and gel phases. In the fluid phase, they may lose their integrity when deposited on surfaces covered with nanoparticles with radii in between 0.6 and 11 nm.27 The 11 nm threshold is close to the equilibrium radius of curvature estimate that might occur for an unbinding transition with the membrane floating above the rough substrate28 as discussed in the Supporting Information. SPBs on SiO2 nanobeads display larger melting temperatures and larger local lipid order parameters than lipid vesicles of the same radius in the 5−40 nm range.29,30 Nanocorrugations31 or highly curved membrane tubes32 trigger lipid sorting and phase transitions. The question of lipid mobility vs nanotopography has been addressed in only a few studies. Mobility seems not to be significantly affected by the presence of nanodots,21 nanocorrugations,31 or nanoporous surfaces33 as compared to plain surfaces of the same material (glass or silicon). Typical scales of the topographical features in these studies were the following: 7 nm diameter for adsorbed nanodots, nanocorrugated surfaces with a few hundred nanometers and a few tenths of a nanometer for lateral and vertical scales, respectively, and nanoporous surfaces with a pore size of about 2.5 nm. A slight decrease in the diffusion coefficient D was observed when SPBs were deposited on etched surfaces with increasing root-meansquared roughness (Rq) in a narrow range between 0.15 and 0.25 nm, and a much larger variation was observed by changing the glass treatment.34 Variations of 2- to 3-fold were observed on a variety of nanoporous oxide and organic xerogel films.35 However, the surface chemistry and topographic effects were intermingled in these two studies. At least two studies reported changes in the lipid diffusion coefficient with changes in the real 3D area induced by the roughness.22,36 Most of these studies were performed with spot-based FRAP. SPBs were investigated at only one temperature, and the roughness was not characterized up to the nanoscale using, for instance, ultrasharp AFM tips. As compared to the free-standing fully hydrated phospholipid bilayers, there are fewer molecular dynamics (MD) simulations of supported lipid bilayers.37 Only a few of them have started to address the issue of surface topography.38,39 In this work, we investigate the relationship between the surface topography and the diffusion coefficient of lipids in SPBs on two different types of rough surfaces with a typical amplitude and wavelength of

respectively 20 and 50 nm: etched glass presenting holes and etched 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) allowing us to probe the diffusion law efficiently over several orders of magnitude with the same experimental setup.11 We observe that D decreases by a factor of 5 in the fluid phase when Rq increases from 0.1 to 3 nm, whereas in the gel phase D is roughness-independent. A simple two-phase model with a slower diffusion coefficient in regions with high curvature (R ≤ 40 nm) captures very satisfactorily the experimental observations in the fluid phase if the slow D value is comparable to that of the gel phase.

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EXPERIMENTAL SECTION

SPB Deposition. Phospholipids were purchased from Avanti Polar Lipids: 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), 1,2dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), and 1-palmitoyl-2,6-[(7nitro-2,1,3-benzoxadiazol-4-yl)amino]hexanoyl-sn-glycero-3-phosphocholine (NBD-PC). One wt % fluorescent lipid NBD-PC was incorporated into DMPC and POPC bilayers for FRAPP measurements. Lipid molecules, solubilized in 9:1 chloroform/ethanol, were deposited on an ultrapure water subphase (18 MΩ·cm, Milli-Q) of a Langmuir trough. After solvent evaporation (about 20−30 min), lipids were compressed up to 40 mN/m for DPPC and up to 30 mN/m for POPC and DMPC to form an interfacial monolayer on the subphase surface. The first monolayer of lipids was transferred to the substrate by pulling up the substrate from the subphase at a speed of 5 mm/min (Langmuir−Blodgett method). The second monolayer was transferred according to the out-of-equilibrium Langmuir−Schaefer method.40 Substrate Preparation. For FRAPP experiments, SPBs were deposited on pieces of a one-side-polished (100) Si wafer or on circular windows of BK7 glass (Melles Griot), which is a borosilicate crown glass. For NR experiments, we used 8 × 5 × 1.5 cm3 (111) single crystals of silicon. Silicon substrates were etched repeatedly by reactive-ion etching (Oxford, RIE 80) at 60 mTorr pressure and 250 W power with 6.7 and 25.6 sccm gas flow rates for oxygen and SF6, respectively. The surface roughness of BK7 were prepared by a chemical etching process with a 1:1 sodium hydroxide/ethanol solution in a ultasonic bath at room temperature. Substrates were conserved in air under a clean atmosphere for several weeks. Prior to lipid transfer, BK7 was cleaned in an ultrasonic bath with soap (Microson, Fisher Scientific) for 20 min, and Si substrates were treated for 3 min at 120 °C with a plasma cleaner (30 sccm oxygen and 10 sccm argon, high rf level). Samples were then rinsed thoroughly in pure water. These cleaning procedures ensure hydrophilic surfaces but do not increase the roughness significantly. FRAPP Measurements. The light beam of an etalon-stabilized monomode Ar laser (0.5W at 488 nm) is split, and the two resulting beams are crossing on the sample at an angle θ, providing an interference fringe pattern for FRAPP measurements. The fringe spacing i = 2π/q, where q = 4π/λ sin(θ/2), is the wave vector ranging from 1 to 80 μm and defines the diffusion distance. A bleach pulse set to 1 s with a 0.5 W laser intensity wrote a fringe patterned into the sample that, because of diffusion, disappeared with time. After the bleach pulse, the beam intensity is reduced to a few milliwatts: under these circumstances, we observed no further bleaching of the NBDlabeled lipids. Data (Supporting Information Figures S7 and S8) were fitted to a single exponential exp(−t/τq), and D was calculated from τq = 1/Dq2. Error bars in figures refer to the standard deviation obtained from measurements at five different locations on the same sample. The following two special features of the setup are worthy of note. (i) The use of the same periodic sinusoidal pattern for bleaching and reading allows a single mode of the diffusion equation to be probed. (ii) B


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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 of a 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 1:1 sodium 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 sodium hydroxide/ethanol solution (Rq = 6.2 nm). of the wave vector transfer Q. In specular geometry, Q is perpendicular to the reflecting surface and R(Q) is related to the scattering length density (SLD) profile across the interface by the square modulus of its Fourier transform. For SPBs, the profiles were modeled as a series of five thin layers located in between Si(111) and the buffer: two headgroup layers, an inner membrane layer for the hydrophobic part, a SiO2 oxide layer (Ox) on the silicon block (Si), and a thin water layer between the bilayer and the oxide layer. They were fitted with Aurore software.42 Each layer y was characterized by its thickness (ty), scattering length density (SLDy), roughness (σy), and percentage of water 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 laminar flow cells that allowed solvent exchange in order to apply five contrasts, 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 was controlled by a water bath at T = 20 and 50 °C to investigate the gel and 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.

Because of the very low contrast signal, we estimate that the immobile fraction is always lower than 20%. AFM Imaging and Image Analysis. AFM imaging was performed in tapping mode in air using an MFP-3D AFM (Asylum Research). The set point was adjusted to have minimal forces, the scan rate was set at 1 Hz, and the gain was optimized to reduce noise. Initial roughness characterization was obtained from 5 × 5 μm2 and 1 × 1 μm2 scans for glass BK7 and Si surfaces, respectively, at 256 × 256 pixels2 with standard aluminum reflex-coated silicon cantilevers (Nanoworld ARROWTM - NCR, hereafter referred as NCR tips, 42 N/m nominal spring constant, 10 nm tip radius). The root-meansquared (rms) roughness Rq was calculated with public software Gwyddion. Sharper tips, hereafter referred to as SSS tips (NanosensorsTM SSS - NCHR, 42 N/m nominal spring constant, 2 nm tip radius) and scan sizes of 1× 1 μm2 at 512 × 512 pixels2 were used to measure mean curvature C. We calculated C with Matlab (MathWorks, Natick, MA) using the formula C = ((1 + hx2)hxx − 2hxhyhxy + (1 + ∂z

∂ 2z

hy2)hyy)/((1 + hx2 + hy2)3/2) where hu = ∂u and huv = ∂u∂v are 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 reflectometer FIGARO (fluid interfaces grazing angles reflectometer) at the ILL, Grenoble, France. Data were collected with neutron wavelengths λ in the range of 0.2−2 nm at two different incident angles (θ = 0.8 and 3.2°) 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 ref 41. The ratio between the specularly reflected and the incoming intensities, i.e., the specular reflectivity R(Q), is measured as a function

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RESULTS AND DISCUSSION Bare Substrate Characterization. Silicon wafers (hereafter 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 a 1:1 sodium hydroxide/ethanol solution. Both substrates were

C


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Table 1. Main Parameters Extracted by Fitting NR Experiments of DPPC Bilayers on Three Si Substrates of Increasing Roughnessa intermediate Rq

reference Si bare substrate

bilayer

Rq AFM (nm) σSi (nm) tOx (nm) σOx (nm) T (°C) tw (nm) tbi (nm) σbi (nm) % water

0.7 0.3 1.3 0.4 20 0.4 4.8 0.7 10

± ± ± ± ± ± ± ± ±

0.1 0.1 0.1 0.1 0.1 0.2 0.4 0.2 10

1.7 0.8 1.2 1.1 20 0.3 5.5 1.2 10

± ± ± ± ±

0.1 0.2 0.2 0.2 10

± ± ± ±

large Rq

0.3 0.4 0.2 0.2 50 0.4 5.6 1.3 15

± ± ± ± ±

0.1 0.2 0.2 0.3 10

3.4 2.1 2.0 2.5 20 0.5 5.1 2.5 10

± ± ± ± ± ± ± ± ±

0.5 0.3 0.4 0.2 0.1 0.2 0.1 0.5 10

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

Figure 2. Mean curvature of etched surfaces. (A, C) 3D rendering views taken with supersharp SSS tips and (B, D) associated calculated mean curvature 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.

high and a resulting rms roughness of Rq = 1.7 nm. Rq increases roughly exponentially with etching time until a plateau is reached at about Rq = 3 nm after 30 min (not shown). Bare BK7 surfaces are not as homogeneous as silicon surfaces if they are not etched during some minimum time because of the presence of residues of industrial polishing. At least 20 min of

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


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

wet etching is necessary to remove these residues in order to get the low roughness reference for BK7 at about Rq = 0.8 nm (Figure 1D). Several holes and lines are visible on this reference image. Long wet etching treatments induce an rms roughness increase of up to more than 10 nm with craters of up to 50 nm in depth (e.g., 2D and 3D views of a Rq ≃ 6 nm etched BK7 sample in Figure 1E,F, respectively). Qualitatively, the surface topography of the etched BK7 is almost the mirror-symmetric image of the etched Si surface as it presents large holes of various depths (Figure 1F) instead of peaks (Figure 1C). For the whole substrate examined in this work, we measured by AFM a low variability in roughness of ΔRq/Rq ≤ 10% when imaging different regions of the same sample. We performed NR experiments on (111) single crystals of silicon in order to supplement the surface characterization of the bare substrate (in particular, the roughness and thickness of their oxide layer) and to measure the vertical density profile of SPBs. A reference crystal was used after polishing, and two others were submitted to prolonged RIE treatments. Topographical AFM images (on a 10 × 10 μm2 scale) and the analysis of NR measurements (see below) on these bare substrates gave similar hierarchies of roughness values (Rq = 0.7 nm for the reference, 1.7 nm for the rough surface, and 3.4 nm for the very rough surface, see Table 1 and Supporting Information Figure S1). Note that the values obtained by AFM are 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 sharper tips (ultrasharp SSS tips with a typical tip radius of r = 2 nm) than with conventional tips (NCR tips with r = 10 nm) as shown in Supporting Information Figure S2A,C. Calculating mean curvature maps (Experimental Section) enables us to highlight differences in peak diameter and local curvature values of Si surfaces for different tips (Supporting Information Figure S2C,D). When probed with SSS tips, the local mean curvature of Si frequently approaches |C| = 108 m−1 (i.e., |R| = 2/|C| ≃ 20 nm) for both positive and negative curvatures (Figure 2A). However, whatever the tip, the image presents roughly the same peak density because the mean distance between nearest neighbors (i.e., 50−100 nm) is larger than the tip size. The curvature map of BK7 surfaces presents features that are not immediately visible in 3D views (Figures 2C): holes and craters are connected by narrow valleys (in red on Figure 2D) with high positive curvature values (C = 108 m−1). On the other hand, the tops of the corrugations with negative curvature (in blue) are less sharp. We further characterize the surface topography by computing the relative hidden area [(A3D − A2D)/A2D, where A3D is the area of the real 3D surface and A2D is the 2D projected area], the histograms of mean curvature (Supporting Information Figure S3B,D), and the fraction Φ(40 nm) of the surface with an absolute value of the local radius of curvature that is smaller than |RC| = 40 nm (we discuss this value later). For each surface, the roughness Rq and the relative hidden area are well correlated 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 significantly change these two quantities, indicating that Rq is well measured by AFM even with conventional tips. Interestingly, an approximate linear relation holds between the local Φ(40 nm) and global Rq quantities.

(1)

Rq0 is a roughness threshold, below which the mean surface curvature almost never exceeds |1/RC|. As seen in Figure 2F, fitting parameters β and Rq0 are larger for Si surfaces (β = 0.050 nm−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 the measurement (Figure 2F): the sharper the tip, the larger the Φ (40 nm). Of course, choosing a different critical threshold radius, RC, gives different statistics of the curvature fraction ϕ(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 was chosen for FRAPP experiments because its melting transition is close to room temperature. POPC SPBs, fluid over the entire temperature range of the study, were also explored with this technique for comparison. DPPC was chosen for NR experiments because it has a longer chain, which enables easier decoupling between roughness and bilayer thickness effects when fitting the specular reflectivity data. After bilayer deposition on a given rough substrate, SPBs were imaged by AFM in water. For a given substratum, we could not observe any significant difference between these images and those of the same bare rough substratum imaged either before the LB−LS deposition or after removing the SPBs (Supporting Information Figure S4). This suggests that the bilayer follows the substrate corrugations. Because a membrane floating far from the substrate is probably very easily deformed by the AFM tip during scanning, especially in the fluid phase,24 we also probed the vertical scattering length density profile SLD(z) along the vertical coordinate z of SPBs by NR, which is a noninvasive technique. This SLD(z) is related to the number of nuclei per unit volume Vi(z) and to the neutron scattering length bi of species i as SLD(z) = ∑i Vi(z)bi. We apply the contrast variation method,43 which increases the effective spatial 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 incident beam and measured with respect to the momentum transfer Q normal to the surface, are displayed together with the fitted SLD(z) curves in Supporting Information Figures S5 and S6 for the smoother and the rougher substrates, respectively. The raw data are very different in the presence of an SPB as compared to the bare substrate case, and one also observes large differences between the two substrates. The fitting model consists of a stack of thin layers located in between the two bulk phases (the silicon bulk material and the buffer, see the Experimental Section). The main parameter values from the fitting procedure are reported in Table 1. The thickness of the oxide layer and interstitial water layer between the oxide and the bilayer are not changing with the roughness. The low percentage of water in bilayers (only a small amount was detected in the chain region) indicates that they perfectly cover the surfaces, even the rougher ones, confirming the very high quality of Langmuir−Blodgett−Schaefer depositions.11 Whatever the roughness or the temperature, the top bilayer roughness (σbi) approaches that of the SiO2 oxide layer (σOx) which is close to that of the Si−SiO2 interface (σSi). Differences between the bilayer roughness in the gel phase are significant: σbi = 0.7 ± 0.2 nm for the smoother substrate, and σbi = 1.2 ± E


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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 weakly dependent 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 for DMPC (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 a function of the proportion of highly curved regions Φ(RC) with RC = 40 nm. Lines correspond to eq 3.

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 depend on Rq for either Si or BK7 (Figure 3C). Furthermore, we observe a nearly 10 times larger D on Si than on BK7 at about 1.6 × 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 was never 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 to longer trajectories of diffusion to reach the same mean-squared displacement as for a flat surface. Detailed experimental and numerical investigations of this effect36,45 have shown that the ratio of the diffusion coefficient between flat and 3D surfaces (i.e., D2D/D3D) is proportional to the ratio A3D/A2D between the area of the real 3D surface and the projected area. The hidden area measured in this work (i.e., A3D/A2D ≤ 1.25 in Figure 2F) is too low to be the source of the 5-fold mobility decrease in the fluid phase. We have evidence that surface interactions are not significantly affected by the etching process. First, we measured by NR an oxide layer thickness in the range of 1.2−2 nm for all samples investigated (Table 1). Second, the thickness of the interstitial water layer, which is sensitive to the interaction between substrate and bilayer, is not significantly correlated with the sample roughness. Finally, it is known that when the substrate type or salt concentration is changed, diffusion coefficient values D present larger relative variations in the gel phase than in the fluid phase.11,12 Here, D is nearly roughnessindependent in the gel phase but is 10 times larger on silicon

0.2 nm and 2.5 ± 0.5 nm for the intermediate and rougher substrates, respectively. These results indicate that the SPBs are following the roughness of the substrate at large scales, and we do not observe an unbinding transition characterized by a decoupling of substrate and bilayer roughnesses. Because specular reflectivity provides an averaged measurement over a large area, this does not exclude very slight unbinding of membranes at small scales. This is further discussed in the Supporting Information. FRAPP Measurements of the Diffusion Coefficient. Typical FRAPP signals and monoexponential fits with the characteristic time τq related to the diffusion constant D are shown in Supporting Information Figures S7 and S8. The diffusion coefficient D of DMPC in the fluid phase (28 °C) strongly depends on the roughness Rq (Figure 3A). For a given roughness value, D is slightly affected by the substrate type or by 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 the roughest substrate (Rq = 2.2 nm). On BK7 surfaces, a similar 4to 5-fold decrease in D is observed between 6.7 × 10−8 cm2/s at Rq = 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 striking linear dependence (except for the point of BK7 with the largest roughness, Figure 3B): 1 1 = + ηR q D D0

(2)

Interestingly, we find almost the same intercept 1/D0 for the two 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 phase values reported for free membranes44 of SPBs on glass.11,12,34 The slope η describing the roughness dependence of D is F


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Langmuir than on glass (Figure 3C). One explanation of this striking finding is that the surface/bilayer interactions depend on a given substrate type but are not modified by the etching process. Another reported mechanism influencing lipid mobility is membrane confinement. The Saffman Delbruck (SD) model46 is a hydrodynamic model that describes the lipid membrane as a thin layer of viscous fluid of viscosity μ and thickness h surrounded by a less viscous bulk liquid. When the membrane is confined in an area of radius RSD, this model predicts a logarithmic dependence of the diffusion constant, D = kBT ln(RSD/r)/(4πμh), where kB is the Boltzmann constant, T is the absolute temperature, and r is the radius of the diffusing molecule (here, the lipid molecule). By measuring the diffusion constant of lipids and proteins on membrane tubes with the radius varying between 8 and 250 nm, Domanov et al. concluded that this equation applies by replacing RSD with the membrane tube RT.47 Even if the SD model does not account for the dissipation due to the thin water layer under the supported membrane, it is interesting to ask whether such a mechanism may hold with our bilayers supported on rough surfaces. However, the mobility is much less reduced in tubes (2- to 3-fold when RT ≈ 10 nm as compared to flat and free membranes) than in our supported case. In addition, the fraction 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 the hidden area effect), the hidden area, chemistry, and confinement are not sufficient to explain the 5-fold decrease in D in the fluid phase. Our measurements show that 1/D is linear with roughness Rq, which is a global quantity. The structure and physical properties of SPBs such as the diffusion coefficient should rather depend on a local quantity such as the local mean curvature C = 2/R than on Rq. We propose that the local diffusion coefficient Dloc is influenced by the local curvature on a scale of about 10 nm. Because FRAPP measurements have a spatial resolution equal to the interfringe spacing (i.e., at least a few micrometers), we do not measure Dloc but instead a mean diffusion coefficient D over a heterogeneous landscape. There are several possible types of curvature-induced mobility defects (Figure 4A): holes free of lipids (type 1) and regions with increased lipid order in the border of holes (type 2) or in highly curved 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 fluid SPBs do not cover silica beads with radii of curvature lower than a critical radius RC(F) = 11 nm27 because it costs too much bending energy. Our substrates present a few spots of ultrahigh curvature that could probably not be covered by bilayers. They could act as obstacles for lipid diffusion. Assuming that the bilayer/substrate adhesion is not changed between the fluid and gel phases and using a rescaling for the critical radius in the gel phase, R C(G) = R C(F ) κ(G)/κ(F ) , we obtain RC(G) = 35 nm in the gel phase (with a 10-fold larger bending stiffness in that phase, see the first section of the Supporting Information). An ordering of the lipids might occur around the edges of these defects as shown schematically by blue bilayer regions in Figure 4A. This scenario is supported by the results of Heath et al.,49 who managed to produce quasi-1D SPBs with variable widths. They measured above the melting transition (fluid phase) a 3-fold decrease in the lipid diffusion

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

coefficient when the width decreases from about 50 to 25 nm, suggesting lipid ordering in the vicinity of the SPB edge. A decrease in mobility in highly curved regions (i.e., type 3 defects represented as blue regions in Figure 4A) could be associated with increased packing. In the framework of the free area model, D can vary by orders of magnitude with packing.50 Both experimental29,30 and theoretical studies51,52 have shown that an asymmetry in lipid packing between the two lipid leaflets may induce an increase in the local order parameters, diffusion coefficient, or bending rigidity of highly curved membranes 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 threshold defining highly curved defect regions, and we plot in Figure 3D the inverse of D as a function of the fraction of a highly curved surface Φ(40 nm). The data are described by the following linear relation with parameters already fitted from Figures 2F and 3B thanks to eqs 1 and 2: η 1 1 = + ηR q0 + Φ(40 nm) D D0 β (3) Two-Phase Model for the Diffusion of Lipids in a Rough Landscape. To investigate further the hypothesis of the presence of regions where the diffusion is altered, we describe now a simple two-phase model. A 2D random walk is simulated on a binary surface made of flat portions and defects with surface fractions ϕ1 and ϕ2 and diffusion coefficients D1 and D2, respectively (Figure 5B). To illustrate the model, an AFM-based binary surface is chosen with a threshold on the absolute value of the mean curvature |C| that controls ϕ2 (Figure 5C). We also run so-called obstacle simulations with impenetrable defects (i.e., type 1, Figure 5A). We computed mean-squared displacements (MSD) and calculated the apparent diffusion coefficient D from a linear fit of MSD versus time for values larger than the mean flight time between defects. Simulations with obstacles (Figure 5C) are noisy because simulated walkers may be locally trapped in small pockets depending on the threshold value. Similarly, the results do not depend only on ϕ2 but also on the defect topology; the results G


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

(4)

homogeneous (Figure 4B). The diffusion coefficient Dgel should be almost independent of the roughness as observed (Figure 3C). In principle, we should detect the slight hidden area effect discussed above (up to a 25% change in the diffusion coefficient due to area changes, Figure 2E). Because error bars on Dgel are generally slightly lower than 20% for glass surfaces, we cannot exclude a partial unbinding transition in highly curved regions as depicted in Figure 4C and discussed in the Supporting Information. Finally, our measurements indicate that the mobility is much more sensitive to the surface chemistry in the gel phase than in the fluid phase. Extrapolated at zero Rq, D0 is only 23% lower on BK7 than on Si above Tm, whereas below Tm, Dgel is 10 times lower on BK7 than on Si. This is not fully surprising because it is known that Dgel is, for instance, much more sensitive to changes in the ionic strength than Dfluid.12 In addition, differences between the mobility of bilayers supported on mica or glass have been reported to be larger in the gel than in the fluid phase.11

This equation is similar to eq 3. Taking Φ(40 nm) = ϕ2, we can identify D1 and D2 with experimentally measured quantities, 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 values are 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, D2 and 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 given roughness Rq ,but this similarity may be fortuitous. Indeed, on glass both the slow-phase diffusion coefficient D2, which probably depends on chemistry (see the next section), and the proportion of defects ϕ2 that depends only on the topography are much smaller than on silicon. Gel Phase: Possible Unbinding Transition and Role of Surface Chemistry. In the framework of our two-phase model, the origin of the slow mobility of liquid membranes on rough surfaces is lipid ordering in or around defect regions above the main transition temperature Tm. Once the temperature is reduced below Tm, the full SPB becomes ordered and

SUMMARY AND CONCLUSIONS We have investigated the effect of nanoroughness on the diffusion of supported phospholipids on etched surfaces. The roughness has a strong influence in the fluid phase but not in the gel phase. This difference cannot be explained by the effect of chemistry, hidden area, or obstacles in the bilayer. However, it can be explained by a strong dependence of the mobility on local curvature. We show that a simple two-phase model with fast and slow regions allows one to explain FRAPP measurements quantitatively in the fluid phase. In that framework, only a 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 sufficient to reproduce a 5-fold decrease in D with respect to the smooth defect-free surface. In the gel phase, as the bilayer fully congeals, D is independent of the roughness. The use of a probe sensitive to the ordering of the lipids (such as Laurdan54) should enable the quantification of the fraction of ordered domains in order to demonstrate the proposed two-phase model. We hope that this model will stimulate theoretical investigations or experimental measurements at the singlemolecule level, such as fast AFM, to provide more physical

are different if we use a random distribution of defects instead of the AFM-based map (not shown). A large decrease in D compatible with our FRAPP measurements in the fluid phase occurs only for ϕ2 ≥ 50%. This large value is already reported in the literature53 and corresponds to the obstacle percolation transition. In our NR measurements or in our AFM images, we are far from detecting 50% holes in the bilayer. In conclusion, we believe that impenetrable obstacles cannot explain our observations. 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 gives essentially the same results as the AFM-based map for a given ϕ2 (not shown). The simulated data can be fitted satisfactorily with a very simple formula that is exact in 1D (solid line in Figure 5C): 1 − ϕ2 ϕ 1 = + 2 D D1 D2

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insight into the microscopic mechanisms involved in the strong decrease in lipid mobility on rough surfaces. The control of mobility by nanoscale roughness paves the way for practical applications such as sorting and partitioning of lipids and proteins on surfaces and could have a major impact on various biological processes such as raft formation and protein clustering.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b03276. Local unbinding of lipid membranes on rough substrates: models and discussion. Bare surface characterization and comparison of images with or without SPBs: complementary AFM analysis. Neutron reflectivity: specular reflectivity curves and fitted SLD. Fluorescence recovery after patterned photobleaching: typical curves. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jean-Paul Rieu: 0000-0003-0528-8819 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by French Research Program ANR-12BS04-0008-01, BIOLUB project. We thank M. El Mamouhdi, A. Petit, and B. Chami for preliminary work and A.-M. TrunfioSfarghiu, Y. Hayakawa, C. Loison, and F. Dekkiche for helpful discussions. Furthermore, we thank the ILL for beam time and the use of the PSCM facilities. We are grateful for the help and support of P. Gutfreund and Y. Gerelli during the neutron experiments on FIGARO at the ILL, Grenoble.

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Nanoroughness Strongly Impacts Lipid Mobility in Supported

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