Shear and Compression Rheology of Langmuir Monolayers of Natural

Article pubs.acs.org/Langmuir

Shear and Compression Rheology of Langmuir Monolayers of Natural Ceramides: Solid Character and Plasticity Iván López-Montero,† Elisa R. Catapano,† Gabriel Espinosa,‡,§ Laura R. Arriaga,‡,∥ Dominique Langevin,‡ and Francisco Monroy*,†,‡ †

Departamento de Química Física I, Universidad Complutense, 28040 Madrid, Spain Laboratoire de Physique des Solides, Université Paris Sud XI, 91405 Orsay, France § Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, 58060 Morelia, Michoacán, Mexico ‡

S Supporting Information *

ABSTRACT: The present work addresses the fundamental question of membrane elasticity of ceramide layers with a special focus on the plastic regime. The compression and shear viscoelasticity of egg-ceramide Langmuir monolayers were investigated using oscillatory surface rheology in the linear regime and beyond. High compression and shear moduli were measured at room temperaturea clear signature for a solid behavior. At deformations larger than one per mill, eggceramide monolayers display plastic features characterized by a decrease of the storage modulus followed by a viscous regime typical of fluid lipids. This behavior is accompanied by a marked decrease of the loss modulus with increasing stress above a yield point. The results permit to univocally classify ceramide monolayers as 2D solids able to undergo plastic deformations, at the difference of typical fluid lipid monolayers. These unusual features are likely to have consequences in the mechanical behavior of ceramide-rich emplacements in biological membranes.

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study membrane mechanics.10,11 Indeed, monolayers studies have crucially contributed to the creation of the modern picture of biological membranes as heterogeneous systems with a complex functional dynamics.12−15 Whereas the bare water surface can be described only by a surface tension, when an adsorbed layer is present the surface tension is lowered, the difference between this tension and the bare water tension being the surface pressure. In addition, a viscoelastic behavior is observed upon application of surface stresses.11,16,17 The measurement of viscoelastic parameters can be made with two types of devices: those measuring shear parameters that operate at constant surface area and those measuring compression parameters from changes in surface tension caused by lateral compression or expansion (see refs 11 and 18 and references therein). Fluidity is one of the main characteristics of biological membranes and is quantified by the inverse surface shear viscosity.32 An early method for the measurement of shear viscosity makes use of shear flow through surface canals. Many data were early collected for monolayers of fatty acids.19 Since then, much information has been accumulated on the structure,20−23 dynamics,24,25 and rheo-

INTRODUCTION Ceramides are a family of sphingolipids with a small-head sphingosine unit linked to a fatty acid.1 For years, it was assumed that the role of ceramides in biological membranes was to promote strong intermolecular interactions due to their ability to form head-to-head hydrogen bonds.2 Today, more specific functions are envisaged for ceramides,3,4 mainly in cell processes involving membrane reorganization such as cell differentiation, proliferation, and death. In vivo, plasma membrane ceramides are synthesized within the plasma membrane by enzymatic conversion from sphingomyelin.5 There, ceramides frequently segregate into ordered membrane domains with gel- or solid-like character.5,6 Although the precise biological function of those ceramide domains formed in the plasma membrane has not been elucidated yet, their possible role in the immobilization of certain signaling proteins has been suggested.7,8 The mechanical properties of ceramide monolayers are different from those of the other membrane componentsa fact likely related to their biological function. Ceramide molecules pack as wedges;9 thus, they are prone to assemble as inverted micelles in aqueous media. Despite their unfavorable molecular shape to form bilayers, they can be easily spread on the water surface to form Langmuir monolayers, which have been proved as adequate models to © XXXX American Chemical Society

Received: February 4, 2013 Revised: April 24, 2013

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dx.doi.org/10.1021/la400448x | Langmuir XXXX, XXX, XXX−XXX

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cm2 (R0 being the initial radius) to the actual area A(h) = π(R0 − h tan θ)2 (here, h is the cup elevation with respect to the initial position measured with a micrometric screw). In the classical uniaxial method, we used a Langmuir balance (702BAM, NIMA, UK) equipped with two symmetrically moving barriers. The maximum surface area was 700 cm2. In this method, a unique aliquot of 50 μL of lipid solution was spread onto the free surface of the subphase contained in the Langmuir trough or in the circular cup. After chloroform evaporation and monolayer equilibration in the diluted state (1 h after spreading), the compression isotherm was recorded at a constant compression rate of 5 cm2/min, unless stated otherwise. In these conditions, the strain rates are slow enough (du/dt ≈ 10−4 s−1) to ensure quasi-static compression and near-equilibrium conditions. We also performed a series of experiments adding successive aliquots of lipid solution without compressing with the barriers; this method will be referred to as “successive deposition”. Given the fact that the pressure isotherms are very sharp close to an area of 50 Å2, the reproducibility is relatively poor in this regiontypically a few percent standard deviation in the lipid surface areas. 3. Oscillatory Compression Rheology. The simplest method for studying the compression viscoelasticity of a monolayer is to perform sinusoidal compressions of the layer with the barriers of the Langmuir trough, measuring the change in surface pressure and the phase shift between this signal and the unilateral deformation.34 Such a uniaxial deformation produces uniaxial strain; thus, the compression response actually contains isotropic compression and shear components.35 When the Wilhelmy plate is parallel to the barriers, prior to any relaxation, the compression modulus is the sum of the compression and the shear moduli, E = K + G.35 A given lipid packing state (π0, A0) was reached by compressing a dilute monolayer at a very low rate (5 cm2/min) after which the monolayer was subjected to a sinusoidal compression deformation. The available area varies as

logical properties of monolayers.26−28 It has also been shown that the rheological properties of mono- and bilayers of lipids were frequently similar.29 This is because the two monolayers composing the bilayer can slide freely one upon the other, provided no molecular species (such as cholesterol, when present in large amounts) bridge the two monolayers. The response of bilayers to stresses is then simply equal to the sum of the monolayer responses.29,30 In a recent paper, the solid character of membrane domains enriched in ceramides was clearly demonstrated.31 Experiments were performed with mixed ceramide−sphingomyelin monolayers at pressures comparable to those existing in biological membranes. The viscoelastic parameters were measured and a soft-solid behavior characterized by a finite shear modulus and a relatively high viscosity was revealed in the linear regime.31 In another recent work, strong differences between the shear properties of ceramides and typical membrane lipid monolayers were evidenced.10 While typical lipid monolayers behave as Newtonian liquids, ceramide-containing monolayers could exhibit nonlinear features, particularly stress softening and shear melting.10 Consequently, the membrane regions containing ceramides might behave as pastes with a very limited molecular mobility31 as compared to more common fluid membrane environments where lipids reorganize more rapidly by lateral diffusion.32 In this paper, building upon the previous results,31 we address an extensive study of the nonlinear rheology of ceramide monolayers, a question of special relevance for understanding the mechanics of ceramidecontaining membranes. Now, we take advantage of surface rheology studies beyond the linear regime to explore the plasticity of natural egg-ceramide Langmuir monolayers, under both compression and shear deformations.

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A(t ) = A 0[1 + u0 sin(ωt + ϕu)]

(1)

where ω is the excitation frequency, u0 is the deformation amplitude (u0 = (Amax − A0)/A0, Amax being the maximum area), and ϕu accounts for a possible initial phase. The surface pressure was simultaneously monitored as a function of time. In the linear regime, the stress σ is proportional to the deformation u:

MATERIALS AND METHODS

1. Lipids and Chemicals. Egg ceramide was supplied by Avanti Polar Lipids as a powder. Just before use, the lipids are dissolved in chloroform (Sigma-Aldrich) to achieve a final concentration of 1 mg/ mL. The stock solutions were kept at −20 °C. Experiments on Langmuir monolayers were performed by spreading the lipid on a water subphase. High-purity water was produced by a Milli-Q source system (Millipore, resistivity higher than 18 MΩ cm; γ = 72.6 mN/m at 20 °C). 2. Compression Isotherms. Surface Pressure π vs Molecular Area A. The monolayers were spread from the lipid chloroform solution (1 mg/mL) and the solvent was left to evaporate. The surface pressure was measured with paper Wilhemy plates. The surface area available to the monolayer can be changed following two different methods: (a) isotropic and (b) uniaxial compression. In both methods, the surface pressure is measured at the center of the trough using a paper Wilhelmy plate attached to a force sensor (PS4, NIMA). In some experiments, two sensors were used, with plates parallel and perpendicular to the direction of the barriers. The subphase temperature was controlled by recirculating water from a thermostatic bath (Polyscience) through a fluid circuit placed at the bottom of the trough and measured by a Pt-100 sensor. The experimental setups were placed in a transparent plexiglass box in order to avoid undesirable air streams and/or dust deposition on the surface during experiments. In the isotropic compression method, a monolayer is spread in a diluted state in a homemade conical cup based on the design proposed in ref 33. This device allows the measurement of the surface pressure under an isotropic compression produced by a radial contraction of the surface area available to the monolayer. The cup was carved in a monolithic Teflon rod with an axisymmetric conic profile (25 cm top diameter, 10 cm depth, θ = 30° inclination). As the cup is raised, while maintaining the water elevation fixed, the film is uniformly compressed from an initial maximal area, A0 = πR02 = 160

σ(t ) = E*u(t )

(2)

where E* = E′ + iE″ is a complex viscoelastic modulus with a real part E′ accounting for the pure elastic response and the imaginary part E″ for the viscous losses, the stress being

σ(t ) = π(t ) − π0 = σ0 sin(ωt + ϕπ )

(3)

where π0 is the average pressure of the unstressed state, σ0 the stress amplitude, and ϕπ a phase factor accounting for the delay imposed by viscous friction within the response. The compression elasticity E′ and the compression loss modulus E″ are then calculated as

E′ = (σ0/u0) cos ϕ

(4)

and E″ = (σ0/u0) sin ϕ

(5)

where ϕ is the stress-to-strain phase difference ϕ = ϕu − ϕπ and tan ϕ = E″/ E′. If the stress response is nonlinear, a strain-dependent modulus is defined as the series expansion34,36 E*(u) = E0* + E1*u + E2*u 2 + ...

(6)

where E*k = E′k + iE″k. Consequently, in the nonlinear regime, a Fourier-series expansion should be used to accurately fit the experimental data:

π(t ) = π0 +

∑ σ0(k) sin(kωt + ϕπ(k)) k

B

(7)


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Figure 1. (A) Surface pressure π−A isotherms of egg-ceramide monolayers measured upon uniaxial (black line) and isotropic (red line) compression, both at a rate of 5 cm2/min (see Materials and Methods for details). Inset: isotherm measured with successive depositions of lipids. The continuous black line represents the compression isotherm obtained by the uniaxial method. (B) BAM micrographs representative of different monolayer states reached by different methods (the symbol indicate the average surface area; scale bar 100 μm). The bright ruffles observed upon uniaxial compression at 45 Å2 correspond to thick line defects caused near collapse (these lines are oriented parallel to the barriers, thus perpendicular to the direction of the compression stress). (C) Elastic compression moduli, K isotropic (red line) and E uniaxial (black line), of the eggCer monolayers calculated from the compression isotherms in (A) using eqs 12 and 13, respectively. where σ(k) 0 stands for the amplitude of each harmonics (ωk = kω; k = 1, 2, 3, ...) in the nonlinear response function (eq 6); the generalized viscoelastic modulus reads as

E′k − 1 = (σ0(k)/u0) cos ϕ(k)

(8)

E″k − 1 = (σ0(k)/u0) sin ϕ(k)

(9)

σ(t ) = G*γ(t )

where G* is the shear viscoelastic modulus G* = G′ + iG″, G′ being the storage modulus and G″ the loss modulus, accounting for the dissipation. In this instrument, a given packing state is reached by subsequent dropwise addition of lipid chloroform solution (0.01 mg/mL). The monolayer is left to equilibrate for 1 h and then presheared at a fixed frequency (1 Hz, 0.1% shear amplitude, 1 h, typically) prior to measurements. Again, despite the high resolution in torque measurements, the experimental reproducibility is limited by the capacity to reproduce identical monolayer states in different experiments and is around ±10% for G. 5. Brewster Angle Microscopy. BAM measurements were performed in a Langmuir balance (702BAM, NIMA, UK) installed on a Nanofilm EP3 ellipsometer (Germany) with a polarized incident laser of λ = 532.0 nm. An incidence angle θ = 55.2 ± 0.1° was chosen in order to maximize the reflected intensity and the polarization sensibility. BAM images are taken simultaneously to the surface pressure monitorization.

− ϕu accounts for the k-order viscous where the phase shift ϕ = delay imposed by nonlinear frictional losses. The frequency spectrum and the amplitudes of the harmonics can be obtained from the Fourier transform of σ(t). Within the linear regime only the fundamental peak is present in the response spectrum, while other less intense peaks, corresponding to higher harmonics, can be observed in the nonlinear regime.34 All experiments were performed at room temperature (T = 25.0 ± 0.5 °C). Although the method is quite sensitive (stresses are measured within ±0.01 mN/m), the main experimental error arises from the difficulty to reproduce identical surface states in independent experiments. The resulting uncertainty on the moduli is up to ±10%, the largest errors corresponding to surface areas close to 50 Å2 where the surface pressures vary sharply. 4. Oscillatory Shear Rheology.37−39 We used a shear rheometer (Physica MCR301, Anton Paar) equipped with a biconical bob tool (68.3 mm diameter, 5° cone angle). Temperature control (±0.1 °C) is performed with a Peltier element assisted by an external water thermostat. A detailed description of the flow analysis in this device can be found in the article of Erni et al.37 The bicone can be positioned very accurately at the interface position by a normal force assisted surface detection of the liquid/air interface. A sinusoidal strain of amplitude γ0 is applied to the monolayer at a frequency ω; this is (k)

γ(t ) = γ0 sin(ωt )

(11)

ϕ(k) π

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RESULTS 1. Compression Isotherms. Figure 1A shows the pressure−area (π−A) isotherms of eggCer measured at room temperature (25 ± 1 °C) in the two compression geometries: uniaxial and radial (isotropic). The inset also shows a curve obtained after spreading different amounts of lipids without compressing the layers (successive deposition). All isotherms share several features. The compression isotherm obtained in the uniaxial geometry is qualitatively similar to that recently obtained by Busto et al.40 for synthetic C16-ceramide. For molecular areas above 75 Å2, the pressures are near zero, compatible with a gaseous-like state. Upon uniaxial compression below 75 Å2, the pressure increased up to a pseudo-plateau at a pressure ca. 5 mN/m, whereas upon isotropic compression the pressure remains close to zero. A similar behavior is found for the uncompressed layers as shown in the inset in Figure 1A.

(10)

The torque response in the normal axis (σ) is then measured with an accuracy of ±20 μN/m. If the stress response is below this value, it is discarded by the software. The analysis includes corrections for tool inertia and bulk flow39 (see Supporting Information in ref 31 for details). In the linear regime, the shear stress is C


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maximum value (Kmax ≈ 220 mN/m, Emax ≈ 340 mN/m; see Figure 1C). The maximum moduli, equivalent to a minimal compressibility, corresponds to pressures close to the biologically relevant pressure in the bilayer (πbil ≈ 30 mN/m).43 Above this maximum, the compression moduli decrease, signaling the onset of the collapse (saturation of pressure). At A ≈ 50 Å2, the values of the uniaxial compression modulus are systematically larger than those of the isotropic compression modulus (E > K), a fact that could be related to the existence of a finite shear modulus: E = K + G (see Supporting Information for a detailed description of the 2D elasticity of solid Langmuir monolayers). The relation between G, E, and K, however, is only valid for solids, in the absence of relaxation.35 In order to check for the influence of possible relaxations, we have measured the surface pressures at different compression rates (Figure 2). One sees that a difference

At smaller surface areas, close to 50 Å2, the three isotherms rise suddenly and enter a collapse regime at A ≈ 40 Å2. The collapse observed upon uniaxial compression is characterized by a higher pressure (π(col) ≈ 45 mN/m) than the one observed upon isotropic compression (π(col) ≈ 35 mN/m) or successive deposition (π(col) ≈ 16 mN/m). This suggests that the layers are trapped into different metastable configurationsa frequent situation in the collapse region.41 Another explanation of the difference between surface pressures measured in the Langmuir trough and in the conical cup is the following: upon lowering the level of the liquid, the monolayer could be partially deposited on the cup’s wall, as observed by van Hunsel and Joos.42 In ceramides monolayers, the consequences of such potential losses are however limited. The surface pressure is equal to zero or to πcol, except close to 50 Å2 where it changes sharply: losing ceramides by deposition onto the cup surface will merely shift the pressure curve along the area axis. Since as quoted in the Materials and Methods section, the reproducibility is poor in this region (a few percent in area), the loss of material in the cup does not have significant consequences. To obtain more information about the structure of eggCer monolayers, BAM images were taken during the uniaxial compression (see Figure 1B, left panel). In the very diluted state (π < 1 mN/m), the monolayer is heterogeneous: gaseouslike regions (dark) coexist with solid-like regions (bright). Upon further compression, the gaseous regions progressively disappear; their irregular shapes evolve into smaller circular defects whereas the solid regions merge into large platforms. Above 2 mN/m, the monolayer is homogeneous and very dense. Near the collapse, the monolayer thickens into a ruffled structure, which indicates multiple folding across the trough (see Figure 1B, left panel), a behavior compatible with the usual collapse mechanisms described in ref 41. Images taken under successive depositions are similar, the ruffles however not being observed in the collapse region (Figure 1B, right panel). The compression modulus, K, is related to the increase in monolayer pressure caused by an isotropic compression (see Supporting Information for details). For insoluble monolayers, the isotropic compression modulus K is obtained from the numerical derivative of the π−A isotherm measured in the circular cup, where the area is isotropically varied by decreasing the radius R of the cup: ⎛ ∂π ⎞(iso) R ⎛ ∂π ⎞ =− ⎜ ⎟ K = −A⎜ ⎟ ⎝ ∂A ⎠T 2 ⎝ ∂R ⎠T

Figure 2. Anisotropy in the compression isotherms recorded at different compression rates. The full line curves were obtained using a Wilhelmy plate parallel to the trough’s barriers and the dotted lines with a plate perpendicular to the barriers.

between the surface tension measured with plates respectively parallel and perpendicular to the barriers become visible at large compression rates, i.e., when the relaxation has not enough time to be completed. The data in Figure 2 assign the crossover between the fluid-like to the solid-like regime at strain rates of the order of u̇c ≈ 50 cm2/min ≈ 10−3 s−1. Solid-like features emerge only at du/dt > u̇c; the mechanical response now becomes anisotropic, i.e. π∥ > π⊥, and then G > 0 (see Figure 2). However, in compressing more slowly, du/dt < u̇c, the system relaxes and becomes fluid-like; thus G = 0, the same pressure being measured by the two sensors. In the case of the data shown in Figure 1, enough time has been allowed for the relaxation to be complete. In the collapse region, the differences between K and E are likely due to the nonequilibrium effects mentioned earlier, in particular differences in texture evidenced in Figure 1B. The data of Figure 2 also suggest that the characteristic time of the viscoelastic relaxation is of the order of minutes. 2. Compression Rheology. The dynamic response to an uniaxial compression of variable amplitude was measured in oscillatory experiments performed at a constant frequency (ω = 2π/T = 0.21 s−1; period T = 30 s). The explored amplitudes ranged from 0.3% up to 10% of the initial equilibrium area. Because large compression deformations give rise to morphology changes at low pressures (π < 1 mN/m, solid−gas equilibrium) and at high-pressures (π > 40 mN/m, monolayer

(12)

The uniaxial compression modulus, E, is related to the change in monolayer pressure caused by uniaxial compression (see Supporting Information for details). It can be calculated from the numerical derivative of the π−A isotherms measured by lateral compression of the monolayer in the Langmuir trough with a plate in parallel with the compression barriers: ⎛ ∂π ⎞(uniax) ⎛ ∂π ⎞ = −A⎜ ⎟ E = −A⎜ ⎟ ⎝ ∂A ⎠T ⎝ ∂A ⎠T

(13)

Figure 1B shows the values of the two moduli (K and E), calculated from the respective compression isotherms in Figure 1A, using eqs 12 and 13, respectively. In the diluted regime (A > 50 Å2), the monolayers are highly compressible (K ≈ 0 mN/ m, E < 50 mN/m). However, below 50 Å2, both moduli were observed to increase suddenly with decreasing surface area. When compressing below 50 Å2, the moduli increased up to a D


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collapse), the rheological study was restricted to the regions where the monolayer is homogeneous and solid. Figure 3A

Figure 4. (A) Oscillatory compression stress−strain plots of eggCer monolayers at different pressures (π = 8 mN/m (□); 20 mN/m (○); 27 mN/m (△)). The frequency of the oscillations is 0.033 Hz; the amplitude u = 0.01. The straight lines represent the asymptotic linear behavior σ0 = Eu0, defining the equilibrium modulus E in Figure 1B. (B) Compression−expansion cycles for egg ceramide (at π = 27 mN/ m). A reversible hysteresis loop is clearly visible (compression rate 5 cm2/min).

Figure 3. (A) Experimental strain u = (A − A0)/A0 and (B) stress time-traces recorded upon oscillatory compression at a frequency of 0.033 Hz (30s period) for eggCer monolayers at π = 25 mN/m in the linear (0.005 strain amplitude; left panels) and nonlinear regime (0.08 amplitude; right panels). (C) Fourier-transform stress spectra.

experiments, in order to maintain a linear response, the strain amplitude was set to 0.5% (u = 0.005 ≪ uC). Figure 5A shows the frequency dependence of the linear compression elastic modulus (E′) measured at different pressures. At low pressures (π < 20 mN/m), the compression modulus was found to be frequency independent, with values compatible with the compression modulus E∥fast measured with a Wilhelmy plate parallel to the barriers at high compression velocity (100 cm2/ min), as shown in Figure 6. This suggests that the relaxation time is longer than (du/dt)−1 for this velocity, i.e., longer than about 10 min. The oscillatory compression is indeed fast (the period being 100 s for a frequency of 0.01 Hz). A weak, but systematic, decrease of the compression modulus with frequency is observed at the highest pressure studied, π > 30 mN/m, even for the low values of u used (≪uC). Figure 5B shows the experimental values of the loss modulus obtained for the same monolayer states as in Figure 5A. The values of the elastic modulus were found significantly higher than those of the loss modulus (E′ ≫ E″)a behavior typical of elastic solids characterized by small frictional losses. Similarly to E′, no frequency dependence was observed for E″ at low pressures. As expected, the absolute values of E″ increased with surface pressure, reaching a relatively high value at the highest pressure explored (E″ ≈ 75 mN/m at π ≈ 30 mN/m). However, at this high pressure, the loss modulus was observed to decrease with increasing deformation frequencya fluidization effect concomitant with the dynamic softening observed in E′ (see Figure 5A). The decrease of E′ when ω increases is anomalous, since linear causality implies that E′ should increase instead, while E″ decreases. However, and although at low frequencies the layer responds linearly, it is possible that it enters a nonlinear regime when ω increases (u small, but du/dt large); in such a case causality would no longer imply an increase of E′ with ω.

shows the typical area variation (strain) imposed at the linear (ΔA/A < 0.02; left panel) and nonlinear (ΔA/A > 0.02; right panel) regime. The stress responses are shown in Figure 3B and the corresponding Fourier spectra in Figure 3C. At small deformations, the pressure response can be accurately fitted with a single sinusoid (eq 3) with a frequency ω identical to the excitation frequency (Figure 3B, left panel). This is confirmed by the Fourier transform of the stress versus time function (see Figure 3C, left). The right panels in Figure 3 show the typical nonlinear stress response observed for a large amplitude deformation (Figure 3A,B). In that case, the Fourier spectrum shows a number of harmonics of the fundamental response (Figure 3C, right panel). Figure 4A shows the strain−stress plots measured at different surface pressures and the same frequency (0.033 Hz, 30 s period). A linear Hookean regime is observed at low pressure (π ≈ 8 mN/m). At higher surface pressures (π ≥ 20 mN/m), above a critical deformation threshold uC ≈ 0.02, the stress− strain curves clearly deviate from the linear asymptotic behavior: σ < σlin = E′u. This results in a smaller effective modulus, suggesting stress softening behavior. In this regime, the FT revealed the presence of higher harmonics, confirming the presence of nonlinear effects.34 Beyond uC, a plastic plateau is observed for π = 27 mN/m. Figure 4B shows the existence of hysteresis at this surface pressure during different compression−expansion cycles performed at a compression rate as slow as 5 cm2/min. The oscillatory barrier experiments also allow the study of the frequency dependence of the viscoelastic modulus. In these E


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this nonlinear regime is observed above low values of du/dt (≈ 10−3 s−1), consistent with the behavior of the compression isotherms at increasing compression velocity (see section 1 in Results). 3. Shear Rheology. The solid character of ceramide monolayers is better demonstrated in mechanical experiments probing the shear response: a fluid has a finite compression modulus but a zero shear modulus.10,31 Because the surface pressures cannot be measured in the shear cell, and since we have found that they depend on the monolayer preparation procedure, in the following the monolayers will be characterized by the area per molecule. Figure 7A shows the stress−strain curves obtained upon oscillatory shear at constant frequency (1 Hz) in ceramide

Figure 5. (A) Frequency dependence of the compression modulus E′ as obtained from oscillatory barrier experiments (u = 0.01) at different pressures (molecular area between parentheses): π = 5 mN/m (55 Å2) (□); 10 mN/m (50 Å2) (○); 15 mN/m (48 Å2) (△); 20 mN/m (48 Å2) (▽); 30 mN/m (46 Å2) (◇)). (B) Frequency dependence of the loss modulus E″ measured at the same pressures as in (A). (C) Stress Fourier spectra for a dense monolayers (π = 30 mN/m) at low (ω0 = 3.5 mHz; left panel) and high frequency (ω0 = 42 mHz; right panel).

Figure 7. (A) Shear stress−strain plots of egg-ceramide Langmuir monolayers in different packing states and at a frequency of 1 Hz; molecular areas: (□) 90, (○) 75, (△) 65, (▽) 63, (◇) 60, (◁) 54.5, (▷) 52, (⬡) 49.5 (∗) 49, and (⬠) 45 Å2. (B, C) Area dependence of the yielding parameters characterizing the plastic plateau: (B) yield strain; (C) yield stress.

monolayers for different surface concentrations. At low concentrations (A > 65 Å2), the stress−strain plots are linear, the monolayer behaving fluid-like: σ = G″γ and G′ = 0. At somewhat larger concentrations (A < 65 Å2), the stress response evidence a finite shear modulus characteristic of the solid phase (G′ > 0).11,33,39 Then, the stress response is characterized by an initial linear regime beginning at a critical (or yield) strain γC (Figure 7A), which is followed by a plastic plateau, characterized by a relatively low yield stress, σY. The yield strain (Figure 7B) and the yield stress (Figure 7C) progressively increase when the surface concentration decreases: the denser the monolayer, the higher the yield strain and stress, a behavior typical of 3D solid materials. The yield strains for shear deformations are found comparable to those for compression deformations (uC) at comparable surface concentrations. Nonlinear effects are seen already at

Figure 6. Surface area dependence of the compression modulus. The lines represent the values of E∥ obtained in continuous compression experiments performed at high (1 cm2/min: continuous line) and low (100 cm2/min: dashed line) compression rate. The symbols corresponds to data measured at discrete states reached by successive deposition: (○) isotropic modulus, K; (△) compression modulus measured in oscillatory barrier experiments, E′ (0.033 Hz, u = 0.01).

Indeed, this is exactly what we observe in the Fourier transform of the stress responses (see Figure 5C): nonlinear harmonics are present at high strain rates (right panel), whereas they are absent at low strain rates (left panel of Figure 5C). Note that F


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deformations as low as γC ≈ 0.1%; consequently, the measurements were made with a strain amplitude as low as γ = 0.05% (= 5 × 10−4 < γC) for the study of the linear regime. Figure 8 shows the frequency dependence of the shear viscoelastic moduli. The values of the shear modulus in Figure

Figure 8. Frequency dependence of the shear moduli as obtained from oscillatory shear experiments with γ = 5 × 10−4 (0.05%) at different states (A = 70 (□), 60 (○), and 50 Å2 (△)). (A) Storage modulus, G′; (B) loss modulus, G″. The line represents weak power-law behavior typical of solid materials, ∼ω0.2.

Figure 9. Nonlinear strain-dependence of the (A) shear modulus G′ and (B) loss modulus G″ of eggCer monolayers at different packing states (symbols as in Figure 6; the frequency was fixed at 1 Hz).

8A reach very large values, G′ ranging from 1 up to 100 mN/m, as expected for solid monolayers.10 Ceramide monolayers behave thus as relatively hard solids, with equivalent bulk moduli G′/d comparable to usual 3D solids (d being the monolayer thickness: with d ≈ 1 nm, G′3D is up to 0.1 GPa, of the order of the values found for soft solids). Data in Figure 8A display a power-law dependence characterized by a weak exponent, G′ ∼ ω0.2, also typical of soft solids.44 Figure 8B shows the frequency dependence of the shear loss modulus in the same conditions as in Figure 8A. The frictional losses were found essentially constant, independently of the frequency of the shear deformation, a behavior also typical of solids.44 In order to study nonlinear effects, the shear viscoelasticity was determined as a function of the applied strain at the constant frequency of 1 Hz. Figure 9A shows the values measured for the shear storage modulus, which systematically decrease with increasing strain rates, a clear signature of stress softening: the denser the monolayer, the more significant the softening. At large strains, G′ reaches a near zero value compatible with a fluid-like behavior, thus revealing shear melting features. Figure 9B shows that G″ reaches values near zero as well at these large strain amplitudes. These results could have important biological implications in the context of real biomembranes, as will be discussed in the following.

perpendicular to the direction of stress appear, indicating the onset of collapse,46 which is reached when the surface pressure does not evolve further. 2. Mechanical Properties. The mechanical parameters of the Langmuir monolayers of single ceramides should provide useful information to understand their structural properties and eventually the reasons for segregation from complex lipid mixtures. Mechanical studies on pure-ceramide monolayers are relatively scarce and mainly focused on the equilibrium properties obtained from the compression isotherms.40,45 From those studies, ceramide monolayers are known to possess a very low compressibility compared to more common lipids.47 In addition to the structural characterization, the present surface rheology study unequivocally demonstrates the mechanically solid character of Tegg ceramide monolayers. This solid-like behavior is radically different to that of most lipids composing biological membranes. Particularly, important differences are found in the compression and shear elasticity as further described below. a. Compression Elasticity. In the diluted regime (A > 50 Å2), the monolayers are relatively compressible (E < 50 mN/m, K ≈ 0 mN/m). However, below 50 Å2, both moduli increase sharply with decreasing the surface area accessible to the eggCer molecules, a fact likely related to the attractive hydrogen-bonding interactions between ceramide heads.2 In the biologically relevant state (πbil ≈ 30 mN/m),43 the uniaxial modulus is high (E > 300 mN/m) compared to that of typical fluid lipid monolayers, such as POPC or E. coli lipids (representative of eukaryote and prokaryote membranes, respectively), for which much lower values (ca. 100 mN/m) are found at this pressure.57 Even for saturated sphingolipids in the gel state, such as C16-sphingomyelin at room temperature

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DISCUSSION 1. Equilibrium Properties. The compression isotherm of eggCer was found similar to previous literature data on similar ceramide monolayers.40,45 At very low surface pressures (π ≈ 0, A > 50 Å2), BAM revealed the coexistence of solid and gas-like phases. At π ≈ 5 mN/m (A < 50 Å2), the monolayer becomes homogeneous and fully solid (G′ > G″). Similar phase behavior was previously reported by Fanani and Maggio for synthetic ceramides. 45 Upon further compression, buckling lines G


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compression and shear moduli in Figures 1C and 9A (at γ → 0), respectively. As expected, a monotonous decrease between a value compatible with an incompressible fluid (G = 0; ν = 1) and a solid with increasing shear modulus (0 < G < K; 1 > ν > 0) is observed with increasing monolayer pressure. At low pressure, the shear modulus vanishes (G ≈ 0); thus, the system behaves as an incompressible fluid (ν = 1). The limit ν = 0 corresponds to a rigid solid with G ≈ K → ∞. Petkov et al.56 showed that G can also be determined using the compression isotherms measured with Wilhelmy plates respectively parallel and perpendicular to the compression barriers:

(Tm ≈ 40 °C), the uniaxial modulus is also lower (E ≈ 100 mN/m) than that of eggCer monolayers and similar to that of fluid monolayers. The moduli for ceramide monolayers are similar to those for gel-like DPPC monolayers (E ≈ 300 mN/ m)48 or for liquid monolayers containing large cholesterol contents, such as the mixtures of sphingomyelin and cholesterol (SM/Chol 1:1 molar; K ≈ 400 mN/m).49 Values of the compression modulus as high as 300 mN/m have been reported for bovine brain ceramide,50,51 400 mN/m for C24:1 ceramide, and 600 mN/m for C16:ceramide.52 A study of C16:ceramide monolayers has revealed that their compression modulus significantly decreases when crossing the transition temperature from the solid to the liquid-condensed state (from 700 mN/m for the solid down to 200 mN/m for the liquidcondensed (LC) monolayer phase).40 In addition, small amounts of ceramides (10 mol %) increased the elastic modulus of fluid membranes by a factor of 4 and 2 respectively for bilayers in the liquid-disordered (ld) and liquid ordered (lo) phases.53 Regarding the frequency dependence of the dynamic elasticity, ceramide monolayers differ also significantly from fluid systems. The storage modulus is much higher than the loss modulus, E′ ≫ E″ (see Figure 5), as expected for elastic solids. At the biologically relevant state (πbil ≈ 30 mN/m), E′ is very large (E′ > 400 mN/m) compared to typical fluid lipid monolayers. The dynamical softening observed in the denser states (see Figures 4A and 5A) is also characteristic of soft solids, which can locally yield when compressed faster than the microscopic time corresponding to the slippage of the lattice planes.54 Yielding effects are shown in the stress−strain curves (see Figure 4A), after which nonlinear plastic features are observed. At moderate pressures below the collapse, the quasireversible character of the hysteresis cycles (see Figure 4B) suggests that plastic softening may be related to an anharmonic interaction potential rather than to irreversible diffusive transport.47,55 However, when entering the collapse, a strong irreversibility characterizes the compression−expansion cycles (data not shown), as expected, for instance, if fractures take place.54 b. Shear Elasticity. In the biologically relevant state, ceramide monolayers are characterized by a limit value of the shear modulus as high as G′ ≈ 80 mN/m, a value 3 orders of magnitude higher than that measured for lipid monolayers in the gel state, like DPPC.10 In Figure 10 we show the values of the Poisson ratio, ν = (K − G)/(K + G), calculated from eq A7 in the Supporting Information, using the experimental values of

E =K+G E⊥ = K − G

(14)

Figure 11 shows that these relations are fulfilled here provided the isotherms measured at the fastest compression velocity are

Figure 11. Dependence of the shear modulus on the lipid area: (filled symbols; ●) G′ obtained from the low γ limit in Figure 9; (hollow symbols) obtained using eqs 14 with the anisotropy measurements in Figure 2 at different compression rates: 100 (□), 50 (○), and 1 cm2/ min (△).

used (100 cm2/min). This confirms that the relaxation has no time to proceed at this velocity, in agreement with the fact that E∥ is equal to E′ in the frequency range investigated (excluding data at high frequencies for the largest surface pressures, see section 2). For A < 55 Å2, E∥ and E⊥ drop due to the onset of collapse; hence the agreement with eq 14 is lost. 3. Viscous Losses. The viscous losses are found much larger for ceramide monolayers than for fluid layers made of molten lipids like POPC and E. coli lipids.10 In the biologically relevant state (πbil = 30 mN/m), the compression loss modulus of monolayers of eggCer is as high as E″ ≈ 50 mN/m, a value larger than that of the gel-like DPPC phase (E″ ≈ 10 mN/m)48 or for fluid monolayers (E″ ≈ 5 mN/m for E. coli lipids and for POPC).57 Similar conclusions are obtained from the shear experiments: the shear viscous losses are significantly higher for ceramides (G″ ≈ 10 mN/m) than for fluid monolayers (G″< 0.1 mN/m, typically)10 and saturated sphingomyelin and other condensed phospholipid mixtures containing cholesterol.31 In general, the viscous moduli were found lower than those of the storage moduli (E″/E′ < 1, Figure 5; G″/G′ < 1, Figure 9), which points out the predominantly solid character of ceramide monolayers. This is emphasized by the plots in Figure 12, which also evidence the correlation existing among the frictional losses and the elastic storage moduli with increasing molecular packing (increasing E′ and G′, respectively). 4. Mechanical Plasticity. Plasticity describes the nonreversible deformation of an elastic material beyond the linear

Figure 10. Dependence of the Poisson ratio on the shear modulus calculated using the compression and shear moduli in Figures 1C and 9A (at γ → 0), respectively. The fluid-like value is reached only at vanishing shear rigidity (ν = 1 at G = 0). H


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phenomenon becomes more pronounced with decreasing molecular area, a behavior compatible with the progressive dominance of the plasticity mechanism with increasing packing: see Figure 7B,C showing that the shear yield strain γC and yield stress σY progressively increase with decreasing molecular area. Plastic deformations are likely related to changes in monolayer structure. At the yield point, the energy (per unit area) necessary for a plastic distortion, Eplas = σYuC, increases with surface pressure, as shown in Figure 14. At low surface

Figure 14. Yielding energy involved in plastic deformation (plastic energy (Fplast) vs total elastic energy (FT)). The line corresponds to FT = Fplas.

Figure 12. Correlation between the loss moduli and the corresponding storage moduli in eggCer monolayers. (A) compression (3.5 mHz; u = 0.01) and (B) shear (1 Hz; u = 5 × 10−4). The lines correspond in both cases to loss moduli equal to storage moduli.

pressure this energy is comparable to the elastic energy, Eplas ≈ FT = 1/2G′u2. However, at higher pressure (π > 10 mN/m), the plastic energy becomes progressively independent of the pressure, its fractional contribution to the whole elastic energy becoming smaller. Plastic deformations are observed in most solid materials; however, its physical mechanism can vary widely depending on the microscopic structure. 54 For crystalline solids, plasticity is a consequence of long-range order.54,59 When stressed parallel to a crystallographic axis, a dislocation line may slip a large distance past each other along their crystallographic directions, resulting in a plastic deformation. Such a slip is favored by the presence of other dislocations, which allow the material to undergo large deformations without a significant change in molecular distribution.54 Consequently, the energy involved in the plastic deformation of an ordered solid is relatively smaller than the cohesion energy of the crystalline lattice. In lower density or amorphous materials, however, the entire material lacks longrange order, so the above mechanism no longer exist. These materials can still undergo a plastic deformation through the large amount of free volume present in these systems, which can be easily redistributed upon sufficient stress. In that case, however, the plastic energy usually represents a high fraction of the whole mechanical energy. This mechanism could be relevant in the plastic deformations observed in the low pressure states. However, at higher pressures, the dislocation mechanism could become dominant. In the present system, the existence of dislocation bands appearing upon lateral deformation was previously revealed by Brewster angle microscopy (see Figure 1).31 Upon uniaxial compression, dislocations defects appear at pressures as low as π ≈ 15 mN/m (G0 ≈ 20 mN/m), becoming increasingly dominant at higher pressures approaching the collapse (see BAM images in Figure 1). Consequently, an increasingly higher plasticization could be explained as a progressive influence of the slipping mechanism due to an increasing number of dislocations.

hookean regime. The plastic deformation occurs in response to an applied stress exceeding the yield point. In the studied solid monolayers deformed at very low strain, the stress response is linear, independently of the nature of the deformation (shear or compression) and/or the packing state (see Figures 4A and 7A, respectively). Beyond a critical strain, upon both compression (uC, Figure 4A) and shear (γC, Figure 7A), yielding is observed, the stress increasing less rapidly with strain. As a consequence, the effective moduli E′ and G′ are smaller than their Hookean limits. Similar nonlinear features were observed in the loss moduli (Figure 8B), which exhibit shear melting. At low strain, G′′ is independent of the strain (or strain rate), whereas at higher strain it decreases and falls to zero (shear melting), similarly to other dense monolayer systems.33,58 Figure 13 shows the dependencies of the loss moduli on the molecular area for low (0.1 s−1) and high shear rate (900 s−1). At low packing density, G″ is independent of shear rate (G″ ≈ 3 × 10−2 mN/m at A > 70 Å2). The nonlinear shear-melting

Figure 13. Dependence of the loss modulus on the lipid area at two different shear rates and a constant frequency (1 Hz): low-rate (○) at γ̇ = 0.1 s−1; high rate (●) at γ̇ = 900 s−1. I


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“Nanociencia Molecular” (CSD2007-0010), and S2009MAT1507T (NOBIMAT) from CAM. I.L.M. thanks support from “Juan de la Cierva” program (MICINN) and NOBIMAT (CAM). E.R.C. was supported by the FPU program (MEC) and G.E. by CONACYT. F.M. thanks Universidad Complutense and Triangle de la Physique for financial support during a sabbatical stay at LPS. We acknowledge CAI Infrarrojo-RamanCorrelador (UCM) for BAM time.

5. Biological Implications. Recently, Cremesti et al.7 have suggested an immobilization role for ceramide-rich domains formed in the plasma membrane during apoptosis, leading to an accretion of immobilized proteins triggering the signaling events previous to apoptosis. Our results throw light onto the origin of the immobilization capacity of the solid ceramide domains, the ceramide-rich domains sequestrating elements for signaling proteins. It has been recently reported that, generally, some membrane proteins partition into ceramides domains,60 the studied proteins being involved in other signaling processes. Note that protein mobility will be largely reduced in a ceramide-rich environment. At higher temperatures, the ceramide layer could melt into a liquid condensed phase, which is essentially fluid (G′ ≈ 0), but with a high viscosity. Furthermore, the stress softening behavior in ceramide layers could be relevant for protein motion, particularly during protein folding: ceramides could provide a pasty environment at rest, protecting proteins against conformational denaturation arising from thermal fluctuations. However, protein function requires large conformational changes, which could be allowed by the plasticity of the surrounding ceramide environment. Therefore, we conjecture about the possible mechanical role of ceramides in membrane physiology.

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CONCLUSIONS We have performed rheological experiments on Langmuir monolayers of egg ceramide, both upon compression and shear. At high enough surface pressure, the monolayers are solid, characterized by high values of the compression and shear moduli. These 2-dimensional solids have a small Poisson ratio typical of solids (ν < 1) but softer than rigid crystals (ν = 0). At high strains, the highly packed monolayer undergoes plastic deformations possibly in a way similar to dislocation slipping in solids. These results illustrate the mechanical behavior of a molecular solid in two dimensions. To our knowledge, they provide the first direct determination of a Poisson coefficient in a Langmuir solid film, opening a new methodology for the structural and mechanical characterization of these systems. Complementary rheological experiments at higher temperatures and structural determinations by X-ray diffraction or ellipsometry could help to enlighten these results. In addition to fundamental implications and in a biological context, the results are plausibly relevant to the previously conjectured mechanical role of ceramide in membrane functioning.

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ASSOCIATED CONTENT

S Supporting Information *

An additional appendix. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (F.M.). Present Address ∥

L.R.A.: Department of Physics, Harvard University, Cambridge, MA. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by MICINN under Grants FIS200914650-C02-01T, FIS2012-35723, Consolider-Ingenio 2010 en J


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Shear and Compression Rheology of Langmuir Monolayers of Natural

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