AFM-Based Force-Clamp Monitors Lipid Bilayer Failure Kinetics

Mar 23, 2012 - atomic force microscopy (AFM)-based force clamp, for the first time to our ... means of AFM-FS, it has been well established that the v...
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AFM-Based Force-Clamp Monitors Lipid Bilayer Failure Kinetics Lorena Redondo-Morata,†,‡,§ Marina I. Giannotti,*,†,‡,§ and Fausto Sanz*,†,‡,§ †

Institute for Bioengineering of Catalonia (IBEC), 15-21 Baldiri I Reixac, 08028 Barcelona, Spain Physical Chemistry Department, University of Barcelona (UB), 1-3 Martí i Franquès, 08028 Barcelona, Spain § CIBER de Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Campus Río Ebro, Edificio I+D, Poeta Mariano Esquillor s/n, 50018 Zaragoza, Spain ‡

S Supporting Information *

ABSTRACT: The lipid bilayer rupture phenomenon is here explored by means of atomic force microscopy (AFM)-based force clamp, for the first time to our knowledge, to evaluate how lipid membranes respond when compressed under an external constant force, in the range of nanonewtons. Using this method, we were able to directly quantify the kinetics of the membrane rupture event and the associated energy barriers, for both single supported bilayers and multibilayers, in contradistinction to the classic studies performed at constant velocity. Moreover, the affected area of the membrane during the rupture process was calculated using an elastic deformation model. The elucidated information not only contributes to a better understanding of such relevant process, but also proves the suitability of AFM-based force clamp to study model structures as lipid bilayers. These findings on the kinetics of lipid bilayers rupture could be extended and applied to the study of other molecular thin films. Furthermore, systems of higher complexity such as models mimicking cell membranes could be studied by means of AFM-based force-clamp technique.

1. INTRODUCTION Biological membranes are known to perform their function under a complex combination of forces. Recently, there has been a growing interest in the studies of mechanical stress on lipid bilayers. Several techniques have been employed to quantitatively investigate the mechanical properties of lipid membranes. At the microscopic level, the micropipet aspiration technique has shown to be valuable to gain quantitative mechanical information.1 Due to the chemical diversity of cell membranes, techniques with nanometric resolution, such as optical tweezers,2 atomic force microscopy (AFM),3 and AFMbased force spectroscopy (FS),4 emerged as an excellent approach to probe the local properties of lipid bilayers. By means of AFM-FS, it has been well established that the vertical force applied to supported lipid bilayers (SLBs) is a direct measurement of the lateral interactions between phospholipid neighbor molecules.5 Force−distance curves show a discontinuity in the approaching curve that marks the penetration of the AFM tip through the bilayer. The force at which this process occurs has been interpreted as the maximum force the bilayer is able to stand before breaking, the so-called breakthrough force, Fb. According to previous studies, subtle variations in the chemical structure of the phospholipid molecules6 as well as in the physicochemical environment7,8 give rise to differences in the Fb value, which can therefore be considered as the fingerprint of the mechanical stability of a specific lipid membrane in a determined environment. The breakthrough of lipid bilayers is a complex process in which © 2012 American Chemical Society

more than a single molecular determinant (tail, headgroup) is involved. From the physical perspective, the penetration of the AFM tip has been modeled as a barrier limited two-state process.9 In 1965, Zhurkov opened up a new avenue in the field of mechanics of materials suggesting a universal rate relation between lifetime, stress, and temperature.10 Studying the stress and failure of solids, he adopted a new concept of fracture: a kinetic concept. Basically, his hypothesis relied on the idea that thermal fluctuations provoke stress in interatomic bonds. This implies that a certain amount of time is required for a solid to fracture. The essential conclusion of Zhurkov’s studies was that mechanical rupture of solids is of thermal-fluctuation nature and that the application of external force facilitates and directs the destructive action of the thermal fluctuations. In a related embodiment, the formation of holes in liquid films has been a considerable focus of interest since the early 1970s.11−14 Specifically, the penetration of the cantilever tip into the lipid bilayer has been modeled and widely conceived as a two-state activated process.9 In addition to the general approach, Butt and Franz proposed two specific models for the activation process: one is a continuum nucleation model (CNM) that considers a molecular thin homogeneous film (a twodimensional fluid layer) between the solid substrate and the solid surface of the tip, and the other is a model that explicitly Received: February 3, 2012 Revised: March 23, 2012 Published: March 23, 2012 6403

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organic solvent traces. Then, multilamellar vesicles (MLVs) were obtained by hydration with buffer solution to give a final phospholipid concentration of 500 μM, by subjecting the vial to 30 s cycles of vortex mixing and heating to ca. 60 °C. MLVs were used as obtained in the case of surface planar multibilayer preparations. In the case of surface planar bilayers, the MLV solutions were kept in an ultrasound bath for 30 min in order to have unilamellar vesicles. Phospholipid containing preparations were always protected from light. Circular mica surfaces were used as substrates for AFM experiments (Ted Pella, Redding, CA). Prior to use, mica surfaces were glued onto Teflon discs with epoxy-based mounting glue. Phospholipid supported bilayers and multibilayers were prepared by the deposition of small unilamellar and large multilamellar lipid dispersion, respectively, on freshly cleaved mica surface following the method described elsewhere.18 In brief, 50 μL of the corresponding liposome suspension were applied to cover the freshly cleaved mica for a deposition time of 35 min at a temperature ca. 15 °C above the transition temperature of the lipid. After that, the mica substrates were thoroughly rinsed with the buffer solution. AFM imaging was used to control the quality of the obtained supported layers and to determine the number of lipid bilayers in the SLMs. AFM-Based Measurements. AFM images, FS, and FC experiments were performed with an MFP-3D instrument (Asylum Research, Santa Barbara, CA). Force curves (force spectroscopy and force-clamp) were acquired in force map (FM) mode with an array of 32 × 32 over a 5 × 5 μm2 area. All the measurements were performed in buffer solution of 20 mM HEPES and 150 mM NaCl, pH = 7.4. The probes used were V-shaped Si3N4 cantilevers with sharped silicon tips (SNL, Bruker AFM Probes, Camarillo, CA) with a nominal spring constant of 0.35 N·m−1 and a nominal tip radius of 2 nm. For FS and FC experiments, individual spring constants were calibrated using the equipartition theorem (thermal noise routine)19 after having correctly measured the piezo sensitivity (V·m−1). Constant-velocity mode experiments were performed at 1 μ·s−1. Approach and retract velocity in the FC experiments was also 1 μ·s−1, with a dwell time of 8−12 s, optimized depending on the applied force. Longer dwell times, up to 500 s, were checked, and no events at longer times were detected. In the case of FC measurements, the force feedback of MFP-3D AFM consists of a standard proportional, integral, and differential (PID) amplifier, whose output feeds to the piezoelectric positioner. The measured peak-to-peak noise was ≈50 pN. The feedback recovery time was usually ranging between 40 and 70 ms, but it is intrinsically different for each FC curve. The feedback recovery time depends on the mechanical properties of the sample, but also on a wide variety of parameters, such as the Z flexure dynamics, the transfer function of the Z-feedback circuit, the Z piezo response, the tip holder mass, the time constant filter, and even the cantilever itself can limit this time response in the case of damping.

takes into account the molecular nature of the lipid film. As they proposed, each molecule in the lipid bilayer has certain binding sites, which are energetically favorable positions. When the tip is away, these sites are energetically equivalent, but once the tip is pressed onto the lipid film, the energy of the molecules increases drastically and it is energetically favorable to jump apart and form a hole under the tip. Once a critical number of phospholipids have jumped out of the contact area, the pressure on the remaining molecules is so high that at certain time the bilayer ruptures and the tip pierces. Hence, it is of great interest to characterize the barriers of the energy landscape governing the system, in order to precise the extent of the lateral interactions in the bilayer. Considering the dependence of the Fb on the loading rate, the activation energy of the bilayer rupture in the absence of an external force can be derived by means of dynamic force spectroscopy.15 However, it remains a challenge to experimentally determine the location of the energy barrier maximum along the reaction coordinate (Δx). In the present work, we describe a new experimental approach based on AFM to directly characterize the kinetics of SLBs (and multibilayers) failure. In a traditional AFM-FS experiment, the tip is driven toward to and away from the surface through vertical motion of the piezo positioner at a constant velocity while the resulting force is measured. It is in the force−displacement curve recorded during the approaching step where the aforementioned Fb value can be determined. In this kind of configuration, force is measured but not controlled and the determined Fb is loadingrate dependent. Because force is the measurable and controllable magnitude of the mechanical rupture, it is appealing to study the bilayer rupture process under constant force conditions. In this framework, other AFM-based configurations work by controlling the applied force, using a feedback system that locks the cantilever deflection to the set point. This forceclamp mode was implemented by the group of Fernandez to study the stepwise unfolding of proteins16 and capture conformational changes in polysaccharides17 at a constant pulling force. Therefore, force-clamp spectroscopy represents an ideal platform to study the lipid film rupture kinetics. Herein, we use, for the first time to our knowledge, AFM-based force-clamp (AFM-FC) to probe SLBs and supported lipid multibilayers (SLMs) under different forces in order to determine the rate of the lipid bilayer failure and calculate both Δx and the activation energy that characterize the barrier limiting the rupture process of one-component membranes based on the Arrhenius−Bell two-state model.

3. RESULTS AND DISCUSSION For this study, model DPPC (1,2-dipalmitoyl-sn-glycero-3phosphocholine) SLBs and SLMs were prepared by the deposition of small unilamellar and large multilamellar lipid vesicle dispersions, respectively, on a freshly cleaved mica surface following the method described elsewhere18 and detailed in the Experimental Section. Experimentally, the lipid bilayers spread onto the planar substrate (mica) are identified by means of AFM imaging. Then, a set of force curve measurements in the constant velocity mode is performed in the center of the bilayer domains in order to determine the corresponding Fb distribution. The recorded events are represented in a histogram, and the distribution obtained can be fitted to the continuum nucleation model.20 Once the Fb mean value is determined, FC experiments can be performed setting the constant applied force (Fc) to be below the mean Fb. Alternatively, in a FC experiment, the AFM tip approaches the surface at a constant velocity (Figure 1Aa) until the set Fc is reached

2. EXPERIMENTAL SECTION Materials. 1,2-Dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) (specified as 99% pure) was purchased from Avanti Polar Lipids (Alabaster, AL) and used without further purification. Ethanol, CHCl3, methanol, NaCl, and NaOH were all purchased from Sigma-Aldrich (Spain). Sample Preparation. All the experiments were performed in buffer solution of 20 mM HEPES and 150 mM NaCl, pH = 7.4, prepared with ultrapure water (Milli-Q reverse osmosis system, 18.3 mΩ·cm resistivity) and filtered before use with an inorganic membrane filter (0.2 μM pore size, Whatman Internacional Ltd., England, U.K.). To prepare liposomes in solution, phospholipids were dissolved in chloroform/methanol (3:1) to give a final phospholipid concentration of 3 mM. An aliquot was poured in a glass vial and evaporated to dryness under a nitrogen flow. The resulting thin lipid film was kept under reduced pressure overnight to ensure the absence of 6404

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Figure 1. (A) Schematics of the lipid bilayer rupture process under force-clamp spectroscopy and force-clamp curves on a SPB. (a) AFM tip is approached to a SPB island. (b) The tip is kept deflected toward the surface under a constant force Fc. (c) SPB is not able to withstand the applied force and the AFM tip breaks through the lipid film. The sudden penetration makes the tip lose the set deflection, and consequently, a drop in force can be observed in the plot. (d) AFM tip recovers the deflection previously set due to the feedback system. (e) AFM tip is retracts away from surface. (B) Representative force-time and separation−time curves obtained via AFM-FC for DPPC SLBs in 20 mM HEPES and 150 mM NaCl, pH = 7.4. The inset shows the correlation of force failure with the unequivocal step in the separation versus time plot that marks the penetration of the AFM tip through the lipid bilayer.

Figure 2. (a) Histogram plotting the breakthrough force (Fb) for each constant-velocity force curve of a DPPC lipid bilayer rupture in AFM-FS experiments in 20 mM HEPES and 150 mM NaCl, pH = 7.4. The obtained distribution was fitted to the continuum nucleation model (continuous blue line). The inset shows a representative force curve performed on a DPPC SLB under constant velocity conditions. (b) Histogram plotting the time to breakthrough (tb), that is, the time the SLB withstand before failure, under a given constant force (10 nN) for a DPPC bilayer rupture in AFM-FC experiments. The obtained distribution was normalized and fitted to an exponential decay (continuous black line). The inset shows a forceclamp curve performed on an SLB under constant force (10 nN) conditions.

and kept constant (clamped) by continuous readjustments of the tip−surface distance (Figure 1Ab). A sudden decrease of the force (and the tip−surface separation) (Figure 1B) caused by

the lipid failure (Figure 1Ac) triggers the movement of the piezo to reinstate the tip position, consequently restoring the force to the Fc set value (Figure 1Ad). This is evidenced as a 6405

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single-step in the separation versus time trace (Figure 1B) that corresponds to the average height of the lipid bilayer observed in force−separation plots for constant velocity experiments (ca. 3 nm). As the SLB is already compressed when the rupture occurs, this value is generally slightly lower than the typical average height obtained in the section profile of AFM imaging. The time the SLB withstands before failure is defined as the time to breakthrough (tb). After the rupture event, the AFM tip keeps on compressing against the mica substrate, and once the set dwell time is reached, the tip retracts at constant velocity (Figure 1Ae). Due to the cantilever drift and the peak-to-peak noise in our experiments (ca. 50 pN), force should be considered to be approximately constant. Despite this technical limitation, well-defined rupture or failure events were observed in the force versus time recording, which correspond well with an unequivocal step in the separation versus time plot (Figure 1B), evidencing the penetration of the AFM tip through the lipid film (Figure 1B inset). As shown in Figure 1Aa, the Fb distribution obtained in constant velocity mode for the mica-DPPC SLBs gave an average value of 14.0 ± 1.3 nN. Accordingly, for the AFM-FC experiments, a range of Fc below 13 nN was chosen. The lower limit was set in 6 nN, and as for lower Fc values almost no rupture event was observed out of ca. 1000 curves recorded for dwell times up to 200 s. Moreover, it is important to point out that, for Fc higher than 11 nN, many rupture events were already observed to occur before the Fc was achieved; that is, the bilayer breakthrough was noticed in the approach trace of the force−time curve (constant-velocity part of the curve). This is not unexpected, as it is visible for the constant-velocity Fb distribution displayed in Figure 2a that a number of the rupture events fall in the 11−13 nN range. For each particular Fc, the tb shows an exponential decay distribution, as it is exemplified in Figure 2b for Fc = 10 nN. By fitting the corresponding histograms of tb to an exponential decay function, a mean lifetime (τ) is obtained for each Fc value studied (distributions and fittings for each Fc are displayed in Figure S1 and the corresponding fitting parameters in Table S1, in the Supporting Information). The inverse of τ is defined as the rate of the rupture process, α. For the Fc range studied, we found an exponential dependence of the rate of the rupture process on the applied Fc, as evidenced in the linear plot of ln α versus Fc in Figure 3a. As described by Butt and Franz,9 the rupture of a lipid membrane may be modeled as an activated process, with an associated energy barrier that follows the Arrhenius law.21 The probability for lipid bilayer rupture by thermal fluctuations is then proportional to the Boltzmann factor: (t ) = A e−(ΔU (t )/ kBT )

Figure 3. Logarithm of the rupture rate, α = 1/τ, black circles, as a function of the compression force, Fc, for DPPC SLBs (a) and SLMs (b). A fitting of the Arrhenius−Bell equation to the data (dashed line) gives values of α0 = 1.9 × 10−3 s−1, Δx = 3.74 pm for SLBs, and α0 = 0.21 s−1, Δx = 0.38 pm for SLMs (T = 300 K). In (a), blue triangles correspondent to high Fc values are excluded from the fitting, since the statistics of the tb for these applied forces does not take into consideration that several breakthrough events occur before Fc is reached, thus underestimating the α value.

lateral interactions will fail.22 The corresponding Arrhenius law then becomes the Arrhenius−Bell expression: α(F ) = A e−((E0 −ΔxFc) kBT )

(2)

where E0 is the activation energy (height of the energy barrier) of the process in absence of external force. This expression can be rearranged into: ln α(F ) = ln α 0 +

ΔxFc kBT

(3)

where α0 is the rupture rate constant in the absence of external applied force. The model implies a probabilistic behavior of the process with a single rate constant, which can be obtained from the single exponential fit to the average lipid failure trajectory, normalized by the total number of breakthrough events. Fitting the experimental data to the eq 2 gives rise to values of α0 = 1.9 × 10−3 s−1 and Δx = 3.74 pm (Figure 3a). The data corresponding to Fc of 12 and 13 nN have not been included in the fitting, since, as we mentioned previously, the statistics of the tb for these applied forces does not take into consideration that several breakthrough events occur before Fc is reached, giving an underestimated α value. In the approximation by Franz and Butt, the frequency factor A in eq 2 is estimated as the resonance frequency of the cantilever.20A cannot be significantly higher than the resonance frequency because even if holes form with higher frequency, the tip would not be

(1)

where the pre-exponential factor A is defined as the frequency at which the AFM tip attempts to penetrate the bilayer, ΔU is the activation energy required for the formation of a hole in the bilayer that is large enough to initiate rupture and lead the tip breakthrough, kB is the Boltzmann constant, and T is the absolute temperature. When the membranes are subjected to a constant compression force Fc, the energy barrier height is reduced by an amount that equals Δx·Fc, for Δx representing the distance from the native conformation to the transition state conformation along the reaction coordinate, beyond which phospholipid 6406

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able to use them for a breakthrough. Considering a value of 6 kHz for the cantilever resonance frequency, we estimated the energy barrier for the DPPC bilayer rupture at zero external force, E0 = 14.97kBT. The E0 value obtained by means of AFMFC is comparable to the value obtained by the traditional constant-velocity AFM-FS method taking into account the dependence of the Fb value to the loading rate. For this system, a value of about 12kBT was obtained by varying the loading rate in dynamic force spectroscopy experiments (detailed in the Supporting Information, Figure S2). Furthermore, the values characterizing the energy barrier (E0 and Δx) obtained by AFM-FC are in agreement with the ones reported for the penetration of lipid bilayers with hydrophilic and hydrophobic functionalized AFM probes that insert and anchor within the lipid bilayer core.23,24 Those experiments, however, were not performed at force-clamp conditions, but via applying an initial force to a lipid bilayer stack and keeping the piezo position constant, while monitoring the cantilever deflection evolution as it penetrates the film, showing a stepwise decrease of force with time. Still, the value of Δx obtained is surprisingly small. In the molecular reaction theory, Δx can be directly assigned to an interatomic (or intermolecular) distance along the reaction coordinate. However, in larger systems, it is the stress rather than the total force that determines the failure at a particular location and, if we consider that the effective area is implicitly included in the Δx value, then it may no longer represent molecular phenomena. Moreover, the artificial selection of a reaction coordinate constraint, in general, may not coincide with the true transition pathway involving local lipid rearrangements, leading to Δx values that lack of true physical meaning. Here, the mechanical force applied to the system is, in fact, perpendicular to the intermolecular forces needed to rupture the lipid bilayer, that is, the interactions between phospholipid neighboring molecules. In order to understand the extent of the area that is affected by the force applied during indentation, a simple model that we proposed elsewhere,25,26 which takes into account the lateral interactions while the surface is being deformed by an AFM tip, was used to determine the area of the lipid membrane perturbed before breaking. We have previously established that the deformed area of the membrane before breaking is greater than the contact radius of the tip itself; that is, many molecules are involved in the membrane deformation before breaking.25,26 The lateral interactions are modeled by the dynamics of the deforming surface as n coupled springs. According to this model, the dependence of the surface counterforce opposing the AFM tip penetration follows the expression: ⎛ 1 − ds F(δ) = k δ⎜⎜ 2 2 ⎝ (δ + d s )

⎞ ⎟ ⎟ ⎠

Figure 4. Force−indentation graph obtained by AFM-FS for a DPPC SLB in 20 mM HEPES and 150 mM NaCl, pH = 7.4. The continuous line corresponds to the fitting to the eq 4, with k = 5.54 ± 1.12 N·m−1 and ds = 3.82 ± 0.66 nm.

parameters. From the average of the fitting of seven curves, we obtained a ds value of 3.41 ± 1.04 nm. By using this model to describe the elastic part of the constant-velocity force curves on DPPC SLBs, the whole perturbed length before breaking was calculated to be 3.41 ± 1.04 nm, which corresponds to an affected area of 36 nm2. Taking 63 Å2 as the average area per DPPC lipid molecule,27 the affected area would correspond to about 58 lipid molecules. Then, the Δx value of 3.74 pm adjusted over the 58 lipid molecules would give a per-molecule value of 2.2 Å, slightly higher than the values reported for a vesicle fusion process (0.4−0.6 Å)28 and in the order of the lateral distance between the phospholipid neighboring molecules. Recent studies have demonstrated that the nanomechanical properties of SLBs are highly dependent on the substrate material and porosity, which influences the assembly of the phospholipids in the bilayer.29−32 In addition, membranes supported on a soft polymer cushion have been shown to decouple the membrane from the solid substrate allowing the membrane to naturally flow and deform. These polymer cushioned lipid bilayers have different local mechanical properties than the SLBs on solid substrates, as it has been demonstrated for 1-palmitoyl-2-oleoyl-phosphatidilcholine/1palmitoyl-2-oleoyl-phosphatidilserine (POPC/POPS) bilayers.33 Besides, there are reports that suggest that the stability of SLBs and SLMs may be different as a result of mainly two interactions: those with the solid support and, in the case of SLMs, the interbilayer interactions. These are both affected by the surrounding conditions such as surface and lipid head charges, ionic strength, and type of counterions.34 However, it is not fully understood which changes the solid support introduces in the lipid bilayer system. To date, it has been almost impossible to experimentally address such changes as extremely high resolution data is required. Here, SLMs were studied by means of force-clamp spectroscopy in order to investigate the kinetic process of their rupture following two main objectives. On the one hand, we wish to deepen into the understanding of the influence of the substrate in the mechanical stability of SLBs. Likewise, we consider of fundamental importance to determine whether the kinetics of the SLMs failure is comparable to the one observed

(4)

where k indicates the stiffness of the surface upon deformation, δ is the vertical deformation (indentation in this case), and ds is the distance (perpendicular to the applied force) between the contact point and the zero elongation (the whole perturbed length before breaking) (see Figure S3 in the Supporting Information). This expression describes the elastic deformation in a constant-velocity AFM-FS curve, that is, the indentation part of the force curve before failure of the membrane. Here, we have used eq 4 to fit the indentation curves from 100 pN to the force before the breakthrough, for DPPC SLBs. An example is shown in Figure 4. From the fitting, k and ds can be obtained as 6407

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for SLBs, just like the kinetics of protein unfolding using a polyprotein construct is reported to reproduce the kinetics to unfold the corresponding protein monomer.35 Given that both E0 and Δx reflect properties of the transition state of the rupture, we expect these variables to be strongly affected by altering the phospholipid ordering and the consequent mechanical properties of the system. The formation of DPPC SLM consisting of three to nine bilayers was first identified using AFM imaging (Figure 5a). Force−separation plots obtained

Figure 6. (a) Typical separation versus time plot for DPPC SLM compressed at a constant force Fc = 20 nN. Under constant driving force, AFM tip penetrates one by one each lipid bilayer that forms the whole SLM, thus generating a steplike penetration of the tip through the lipid film. From the step size, the thickness of each layer can be measured (ca. 4.5 nm each). (b) Average time course (ATC) of lipid failure obtained by summation and normalization of five recordings (black trace). The failure time course is well described by a single exponential decay (red trace) with a time constant of τ = 0.76 s.

separation value of 3.53 ± 0.47 nm, the population mean of both the layer facing the mica substrate and the layer toward the liquid interface are significantly different (Student’s test, p = 0.05). For the intermediate layers, the population means are not significantly different with the test mean. Therefore, this allows for summation and normalization of several separationtime recordings to be performed in order to obtain the average time course (ATC) of lipid failure (Figure 6b). The ATC obtained for each Fc value, ranging from 10 to 30 nN, was fitted to a single exponential decay assessing the corresponding τ values (Supporting Information Figure S5 shows individual ATCs and the corresponding fittings, with fitting parameters detailed in Table S3). Again, α was derived from τ, and ln α versus Fc was fitted to a linear function, giving values of α0 = 0.21 s−1, Δx = 0.38 pm, and E0 = 10.26kBT (Figure 3b). Once more, the value of Δx is extremely small to have a physical meaning. In order to obtain the value-per-molecule, the approximate number of molecules being affected by the compression and rupture process is needed. However, the elastic-deformation region of the constant-velocity force− separation curves cannot be used here to calculate this number, as it is not possible to distinguish the onset point of the breakthrough process and separate the elastic deformation part form the plastic one, as it has been discussed before. An approximation, but still underestimation, of the value of permolecule Δx value could be obtained by adjusting it over the 58

Figure 5. (a) 5 × 5 μm2 AFM 3D image of a DPPC SLM acquired in AC-mode, liquid environment (pH = 7.4). Four stacked surface planar bilayers can be distinguished from the topographic image showing a typical averaged height of ca. 5 nm, as it can be seen in the section profile. (b) Typical force−separation graph obtained by AFM-FS for a DPPC SLM system in 20 mM HEPES and 150 mM NaCl, pH = 7.4. In this case, single brittle ruptures of individual bilayers cannot be fully assigned, in contradistinction with plots obtained by means of AFM-FC.

in constant-velocity FS onto these multibilayers show a progressive penetration profile until the tip reaches the mica substrate at forces ca. 40 nN, depending on the number of bilayers (Figure 5b). A limitation of these AFM-FS experiments is that single brittle ruptures of individual bilayers cannot be fully assigned from the force−separation traces. Remarkably, AFM indentation on an SLM under constant force conditions (AFM-FC) yields a staircase-like penetration, with each step in the separation-time trace marking the lipid failure of a single bilayer (Figure 6a). The height of the different steps (separation) observed was analyzed (Supporting Information Figure S4, Table S2). While the bilayer in direct contact with the mica substrate shows a separation step of 2.75 ± 0.48 nm, the bilayer in contact with the liquid (lipid−liquid interface) displays a separation step of 4.00 ± 1.12 nm. For a mean 6408

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determination of the activation energy (E0) as well as the distance to the transition state along the reaction coordinate (Δx). Still, for the SLMs, these parameters can not be obtained by AFM-FS; therefore, AFM-FC represents a further advantage for the characterization of such multilayer systems. This approach opens a new trench for the study of the kinetics behind the lipid bilayer failure process. It becomes clear that further systematic experimental analysis on the trend of Δx as a function of the lipid ordering, for instance, varying the temperature or phospholipid molecular determinants may be valuable in order to shed more light into the molecular interpretation of the process. Moreover, from the theoretical treatment of the data exposed in this work, it is revealed that consider the lipid bilayer rupture as a two-state activated process may be an oversimplification of the phenomena’s nature, so more realistic models that include more representative transition pathways involving local lipid rearrangements would be interesting to develop in the near future. Finally, this kind of study on the kinetics of lipid bilayers rupture could be extended and applied to the study of other molecular thin films, including systems of higher complexity such as models mimicking cell membranes.

lipid molecules as in the SLB case. By this means, a value of 0.22 Å would be assigned to the SLMs rupture. The significant shift of the E0 and Δx to lower values for the SLM system (represented in Scheme 1) may indicate that the Scheme 1. Representation of the Energy Barrier Limited Two-State Process for the SLM and SLB Rupturea

a Upon Fc application to the systems, the energy barrier decreases an amount that equals ΔxFc (dark areas) respect to the undisturbed lipid system activation energy (E0).

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failure in the lipid multibilayers does not correspond to the simple serial failure of the individual bilayers. Instead, the kinetics of the entire process of the SLM penetration by the AFM tip is described. This result is not surprising, and it may be ascribed to the strong influence of the substrate and the interbilayer interactions. In the case of SLB, the hard underlying substrate may have a major influence in the lipid ordering and the interleaflet coupling than in the case of SLMs.36 Besides, each bilayer in the SLMs may perceive the substrate differently according to the increasing distance to it. The substrateinduced greater molecular packing would be reflected in the higher energy barrier value obtained for the SLB rupture process (E0 = 14.97kBT for the SLB vs E0 = 10.26kBT for the SLM). More strikingly, there is a large decrease in the distance to transition state when comparing the SLB rupture and the SLM rupture processes. Although its physical meaning in terms of the reaction coordinate is still not well understood, Δx determines the sensitivity of the rupture rate to the applied compressing force. While the energy barrier is lower for the SLM system, the force-dependency of the rupture rate is dramatically decreased, associated to the compression of softer material when compared to the SLBs.

ASSOCIATED CONTENT

S Supporting Information *

Time to breakthrough distributions for each individual force and fitting parameters for SLBs and SLMs, activation energy calculation by means of constant-velocity force spectroscopy, schematic diagram of the deformation model, and statistical analysis of the separation steps in AFM-FC for SLMs. 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] (M.I.G.); [email protected] (F.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Prof. C. Bustamante and Prof. B. Samori ̀ for helpful discussions and valuable suggestions. Support from Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) through SGR 2009 is acknowledged. We also thank Dr. G. Oncins from Nanometric Techniques Unit of the Scientific and Technical Center of the University of Barcelona (CCiTUB) for technical support and Dr. M. A. Edwards (IBEC) for help in data analysis.

4. CONCLUSIONS In conclusion, our results illustrate a well-defined approach to study kinetics of lipid membranes rupture at the nanoscale. By means of AFM-FC, we followed the kinetics of bilayer failure of model SLBs and SLMs for the first time to our knowledge. In contrast to the classical AFM-FS, the AFM-FC has the advantage to resolve the individual rupture events occurring during the penetration of SLMs. We were able to determine the parameters, E0 and Δx, characterizing the energy barrier that governs the lipid bilayer rupture when assumed as two-state process with a single energy barrier, for SLBs as well as SLMs. Both E0 as well as Δx were found to be higher for SLBs. This finding supports previous suspicion that the mechanical properties of lipid bilayers obtained from nanoindentation are strongly influenced by the underlying hard substrate. Although the activation energy has been previously determined by means of AFM-FS at various velocities, AFM-FC allowed for the

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