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B: Biomaterials and Membranes

Stability of Biological Membranes upon Mechanical Indentation Florian Franz, Camilo Andrés Aponte-Santamaría, Csaba Daday, Vedran Mileti#, and Frauke Gräter J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01861 • Publication Date (Web): 13 Jun 2018 Downloaded from http://pubs.acs.org on June 14, 2018

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The Journal of Physical Chemistry

Stability of Biological Membranes upon Mechanical Indentation Florian Franz,† Camilo Aponte-Santamar´ıa,‡,¶ Csaba Daday,† Vedran ¨ ∗,†,¶ Miletić,† and Frauke Grater †Molecular Biomechanics Group, Heidelberg Institute for Theoretical Studies, 69118 Heidelberg, Germany ‡Max Planck Tandem Group in Computing, University of Los Andes, 111711 Bogotá, Columbia ¶Interdisciplinary Center for Scientific Computing, 69120 Heidelberg, Germany E-mail: [email protected] Phone: +49-6221-533267

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Abstract Mechanical perturbations are ubiquitous in living cells, and many biological functions are dependent on the mechanical response of lipid membranes. Recent force-spectroscopy studies have captured the stepwise fracture of stacks of bilayers, avoiding substrate effects. However, the effect of stacking bilayers, as well as the exact molecular mechanism of the fracture process, is unknown. Here, we use atomistic and coarse-grained force-clamp Molecular Dynamics simulations to assess the effects of mechanical indentation on stacked and single bilayers. Our simulations show that the rupture process obeys the laws of force-activated barriercrossing, and stacking multiple membranes stabilizes them. The rupture times follow a log-normal distribution which allows the interpretation of membrane rupture as a pore-growth process. Indenter hydrophobicity determines the type of pore formation, the preferred dwelling region, and the resistance of the bilayer against rupture. Our results provide a better understanding of the nanomechanics underlying the plastic rupture of lipid membranes.

INTRODUCTION During the life of a cell, its membrane has to endure strong perturbations of chemical, electrical and mechanical nature, due to cellular processes such as endo- and exocytosis, membrane trafficking and the division of cells. 1 Throughout these processes, cell membranes need to preserve their integrity for cellular compartments to stay intact. Membrane failure, or rupture, therefore, can have devastating effects on the cell itself, which is, for example, the case for antimicrobial peptides. 2 In this context, pore formation is attracting more and more scientific interest and has been investigated both, computationally 3–7 and experimentally. 8,9 Also, local distortion of bilayers is linked to membrane fusion. 7,10 Moreover, membrane tension and bending guide numerous biological processes, such as pain sensation and hearing, via mechanosensitive embedded proteins. 11 Therefore, the stability of lipid bilayers, and in particular the resistance to pore formation, is of major importance. Hence, the nanomechanics of lipid membranes are subject to extensive experimental investigation. In the recent past, the so-called force-clamp technique emerged as a 2


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well-suited candidate for the characterization of force-induced processes like protein unfolding or bond rupture. 12 Lately, this technique has also been used to probe the rupture of biological membranes: by application of a constant force via an active control loop feedback mechanism, these force-clamp atomic force microscopy (AFM) experiments provide time-resolved measurements of the cantilever position while a biological model membrane is ruptured. 8,13,14 However, these experiments require the membrane to be supported by an underlying stiff substrate. It has been proposed that this membrane-supporting substrate, which is absent in biological systems, might have a non-negligible impact on the membrane mechanics and rupture dynamics. 15 To circumvent any substrate-based influence, Relat-Goberna et al. 13 performed force-clamp spectroscopy on a hydrated multi-bilayer phospholipid stack. Instead of one single bilayer, stacks of large numbers (over 1000) of individual bilayers were subjected to a constant indenting force, which causes the membranes to rupture one after another. These stacked systems are however not just an experimental workaround; indeed, they can be found in biological systems like the nuclear envelope, mitochondria, or myelin sheaths. Despite these considerable advances in setups however, the underlying molecular mechanisms of membrane rupture remain elusive to experiments. Furthermore, it remains unclear whether the rupture dynamics of stacked membranes resemble the dynamics of the – biologically more abundant – single bilayers, or gives rise to other unexpected effects. Finally, how the chemical nature of the indenter, hydrophobic or hydrophilic, influences the rupture process through the alternating lipid and solvated head group layers, has not been addressed. To elucidate these questions, we set out to investigate the rupture of single and stacked lipid bilayers via atomistic and coarse-grained molecular dynamics (MD) simulations. We can reproduce the step-wise layer-by-layer indentation observed in experiments. We find that stacking of bilayers to increases mechanical resistance. Importantly, the nature of the indenter strongly decides upon the rupture mechanism and the preferred sites of dwelling. Our results have implications for how mechanical perturbations distinctly impact membrane integrity in different environments.

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METHODS Coarse-grained simulations Single and multi-layer Systems For the simulation setup, we created bilayers consisting of 2048 DPPC lipids each using the INSANE python tool. 16 We solvated the bilayers and included a 0.2 M NaCl concentration. The indenter sphere was modeled inflating the structure of a 180-atom buckyball by a factor of 2.1 resulting in a indenter diameter of 2.5 nm. To obtain a stable sphere, we generated a topology that contains bonds between direct neighbors and second neighbors (2.1 N/m) as well as angles (0.1 N/m) and dihedrals (0.5 N/m). Initially, the indenter was positioned 1 nm above the bilayer. For the multi-bilayer setup, four periodic DPPC layers were stacked on top of each other. The ideal spacing between these layers was determined via an additional simulation: a lipid disc was placed 1.5 nm above a position restrained periodic bilayer. Subsequently, the lipid disc was pulled towards the ground layer at a constant velocity of 0.01 nm/ps with a harmonic force constant of 0.84 N/m. After the COM of the lipid disc came to a halt, the system was allowed to reach an equilibrium position in a subsequent 50 ns. In this simulation a constant COM distance between the bilayers was reached after approximately 20 ns. MD simulation without any forces acting upon the lipid disc. We an average spacing between the tow COMs of the layers of 5.9 nm which was used subsequently for the stacks of four periodic layers. We solvated the stack in a box of 25 nm × 25 nm × 31.9 nm.

Molecular Dynamics Simulations For molecular dynamics simulations, we used the GROMACS 2016.4 simulation suite 17 extended with a conditional stop code that stops the simulation when the bead has reached the bottom of the simulation box (explained in more detail in Conditional Stop). The initial systems were energy minimized and, subsequently, equilibrated and heated to 320 K for 10 ns using a time step 10 fs. For production runs, we applied a 20 fs time step. Lennard-Jones and Coulomb interaction were shifted to zero at 1.1 nm. Long-range dipole-dipole interactions were treated with the reaction-field method. Temperature coupling was done with the v-rescale 18 algorithm and pressure was set to 1 bar semiisotropically with the Parinello-Rahman 19 algorithm.

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All-atom simulations Single and multi-layer systems For the all-atom single layer, we generated a system with a total of 1152 DPhPC lipids by arranging a 128-lipid bilayer sample 20 in a 3 × 3-grid. Here, we used the SPC/E water model and added 0.2 M NaCl to mimic experimental conditions. For the all-atom stack, we followed a similar pathway as for the coarse-grained counterpart. We created the sphere which poses the atomistic model of the AFM indenter based on a 360-atom fullerene and replaced all carbon atoms by the G ROMOS force-field CH1 particle. The topology was created in an analogous manner as for the coarse-grained version.

Molecular Dynamics Simulations A 100,000 step energy minimization was followed by a 100 ps NVT solvent equilibration using the v-rescale thermostat with position restrained sphere and bilayer. Subsequently, we equilibrated the system for 10ns as a NPT-ensemble with Parinello-Rahman pressure coupling to 1 atm and Nosé-Hoover temperature 21 coupling to 293 K. Coulomb and Lennard-Jones cut-off were set to 1.2 nm.

Analysis MD trajectories were analyzed with the VMD visualization package 22 and custom scripts to extract the dwell times and contacts numbers. Fitting of the data was performed with the SciPy package. 23 The survival probability S(t) is calculated from the distribution of dwell times d(t), which can be interpreted as an absolute density of rupture events, via 1 S(t) = 1 − · N

Z

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(1)

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where σ and µ are standard deviation and the mean of the logarithm of the distribution.

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(2)


Conditional Stop To end the simulation gracefully when the indenter has passed through the box (instead of ending at a particular simulated time or a wall clock time), the conditional stop code in GROMACS is used. This functionality has been developed by the authors; GROMACS was extended as we now describe. A conditional group is a group of atoms specified using their indices (not unlike a pull group 24 ). A trigger specifies a condition involving one or two groups and an action that will be executed if the condition is satisfied. Presently, a number of distance-based conditions (minimal, maximal, and center of coordinates distance between groups can be checked for being greater than or smaller than the user specified threshold) for the stop action are supported. Distance-based conditions can operate either on the positions of the atoms of two groups or the positions of the atoms of one group and the initial positions of those atoms. The frequency of checking for the satisfaction of the conditions is also specified by the user in terms of number of steps between the consecutive checks. Specifically, if at any time step, when the check is done, at least one of the stop conditions is found to be satisfied, the simulation will notify the user about the condition that was satisfied and stop after that step is complete.

RESULTS AND DISCUSSION Multi-bilayer rupture Firstly, we carried out a series of multi-bilayer (MBL) rupture simulations using the M ARTINI force field. 25 We constructed stacks from periodic bilayers to reduce finite-size effects. To choose the thickness of the water and ion layer in between each pair of stacked bilayers, we performed additional simulations of finite bilayer stacks, during which the inter-bilayer solvation layer was equilibrated (see Methods for details) and taken as a reference for the infinite stack. We obtained for the zwitter-ionic DPPC bilayers a preferred average distance of 5.9 nm between the center-ofmass of the two layers, i.e. a solvation layer with an average thickness of 1.4 nm. The equilibrium spacing between adjacent bilayers arises from an interplay of long-range van-der-Waals attraction and short-range repulsion and is in good agreement with experiments for the MARTINI force

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field. 26 The AFM experiments 13 used the highly similar DPhPC lipid, which only differs in the tail from the lipid used in the simulations. Thus, we predict a similar solvation layer in the experimentally probed system. We modeled an AFM indenter tip with a 180-atom buckyball which either features 90 positively and 90 negatively charged M ARTINI beads, or 180 neutral, nonpolar beads. This results in a ’hydrophilic’ and ’hydrophobic’ topology, respectively. We note that these simplified coarsegrained AFM tip representations do not directly model the molecular properties of experimental tips but instead represent extreme types of tips with different chemistries. Both indenter topologies were used to mechanically probe the membrane stack with a series of pulling simulations including three different forces: 0.58 nN, 0.64 nN, and 0.75 nN. Figure 1A-D show the indenter position versus time curve for every combination of force and indenter topology for example trajectories (cf. SI Video 1). In all simulations, the rupture process is characterized by well-defined steps in the indenterposition. The displacement-time traces compare well to the AFM experiments, and were similarly also observed in stacks of finite size bilayer discs (Figures S1 and S2) as well as in atomistic simulations (Figure S3). These simulations show that the observation of stepwise rupture is not dependent on the boundary condition nor on the in- and outflow of water between layers. We find an average step size of (6.20 ± 0.02) nm and (6.93 ± 0.04) nm for the hydrophilic and hydrophobic indenter, respectively. The hydrophilic indenter gives step sizes which compare better to but are larger than the value of 5.4 nm from AFM experiments. We believe that the coarse-grained MARTINI model is not the cause of the ∼1 nm discrepancy, as MARTINI simulations of intermembrane repulsion were shown to be in good agreement with experiments. 26 As a more likely scenario, the small size of the indenter (2.5 nm as compared to the 24 nm indenter of the experimental setup) leads to an only minor compression of the bilayers and inter-bilayer water layers before rupture. In contrast, the comparably large experimental indenter dwells for significantly longer times (seconds) even at much higher forces (nN), likely resulting in stronger narrowing of the stack and thus smaller indentation steps.

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7.5

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time [ns] Figure 1: Coarse-grained multi-bilayer rupture process. A) Indenter sphere position versus time curves. For three forces, we show one example rupture curve for the hydrophilic (red), and the hydrophobic (blue) indenter. An indenter position of zero corresponds to the position of the first head-group layer before it makes contact with the sphere. B) Snapshot of the hydrophilic indenter at its second dwelling region. C) Hydrophobic indenter at its second dwelling region. (all snapshots created with VMD 22 ) D) Average step size between two subsequent dwelling regions for the hydrophilic indenter and its hydrophobic counterpart.

The difference in stepsizes for different indenter types points towards a fundamental difference between the rupture processes. As evident from Figure 2, a hydrophilic indenter dwells inside a water layer before rupturing a full membrane (head-groups–tails–head-groups). The hydrophobic indenter instead dwells inside the hydrophobic regions of the membranes and then ruptures a purely polar layer consisting of head-groups, sandwiched water, and the first head-group-layer of the subsequent membrane. The hydrophilic indenter – in contrast to the hydrophobic one – does not get in contact with any lipid tails, but passes through a pore in the membrane. The pore is formed by the two head-group layers of one bilayer which gives rise to a peak in indenter– 8


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time [ns]

Figure 2: Indenter–membrane contacts during the rupture of stacked bilayers. Number of contacts (number of lipid beads within 0.6 nm of any indenter bead) while rupturing the MLB with a hydrophilic (top) and a hydrophobic (bottom) indenter. Contacts with lipid head-groups and tails are colored in red and blue, respectively. The pulling force for both example trajectories is 0.58 nN and the respective indenter position (dotted line) is given for orientation.

head-group contacts. Hydrophobic rupture, on the other hand, involves a hydrophobic ”pore” for which lipid tails bridge the way to the inside of the subsequent membrane. Thus, one step in indentation position corresponds in both cases to the crossing through two head-group layers, but the chemical nature of the indenter decides on the preferred dwelling region. The impact of the indenter properties is also evident for the very first rupture event. We find that the initial rupture process at the first head-group layer caused by the hydrophobic is very short (cf. Figure S4). The first long dwelling occurs only subsequently, when the indenter passes from the inside of the first membrane to the inside of the second membrane. The initial rupture of the hydrophilic indenter,

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instead, resembles the subsequent rupture event with a comparably long dwelling time.

Figure 3: Survival probability of stacked membrane layers under force. Data is shown for stacked membrane layers indented by a hydrophilic (H-phil) and a hydrophobic (H-phob) indenter sphere. The hydrophobic indenter produces an additional initial rupture, where the first headgroup layer is penetrated (dotted line). The survival probability corresponds to the complement of the cumulative distribution of membrane failure which we obtained from a total of 70 rupture events per force and indenter topology. The top plot shows the distribution of dwell times for a force of 0.66 nN.

To quantitatively investigate the force-dependent rupture dynamics, we recorded and statistically analyzed 70 rupture processes for the three different constant forces and both indenter types. The survival probabilities shown in Figure 3 were obtained directly form the cumulative distribution function of dwell times. It shows how long an individual layer in the stack is expected to survive once subjected to an indenting force. As expected, dwell times increase with decreasing force (Figure 3), again in line with experiments or the simplest theoretical prediction of a onebarrier crossing process. 27 Our simulations yield a distribution of dwell times which can be best fitted with a log-normal distribution (cf. Equation (2)), for the whole range of forces probed in the simulations and for both indenter types. This is in close agreement with the AFM experiments 10


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and consistent with a pore-growth mechanism as suggested previously 13 (Figures S5 and S6). The model is based on the assumption that while the membrane is under force, the number of lipids that newly partake in the pore-formation is proportional to the circumference of the pore at that point. This leads to an increasing growth rate of the number of involved lipids and gives rise to the log-normal distribution of dwell times. To probe the influence of the system size on our results, we carried out a series of simulations with approximately twice the membrane area (from 625 nm2 to 1225 nm2 , Figure S7). Here, we observe that the average time required for rupture decreases by 32% and the stepsize increases by 11%. We account this to the increased deformations that come with the increased system size: for a membrane stack of a twofold area the vertical deformation also increases twofold. Evidently, stronger membrane bending speeds up the rupture process. This will be further discussed in the following section.

Figure 4: Force dependence of rupture rates for in membrane stacks is consistent with the Bell-model. The mean rupture rate are fitted to a single exponential of the form kr,f it = kr,0 ·exp(b· F ). The inset shows an extrapolation from experimental data. Experimentally obtained rupture rates were extrapolated into the simulated force range via the Bell-model. The force component of the experimental values obtained by Relat-Goberna et al. 13 was rescaled by a factor of 0.0108 according to the difference in force per area due to the different indenter diameters.

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From a theoretical point of view, membrane failure is commonly interpreted as a simple all-ornothing, barrier-limited reaction, in which the applied force causes a reduction of the energy barrier height. 28,29 Under these assumptions, the rupture rates k(F ) can be fitted to the Bell model: 27 σ k (F ) = k0,r · exp F kB T

(3)

where k0,r is the rate of rupture k(F ) in absence of force, σ is the distance from the free energy minimum to the transition state, F is the force on the bond, kB is Boltzmann’s constant, and T is the absolute temperature. Overall, our results are consistent with the Bell model. Within the two orders of magnitude of rupture rates sampled in our MD simulations, the rates follow exponentially the constant external force (Figure 4). The simulated force range impedes a direct comparison of survival probabilities to experimental values. Relat-Goberna et al. 13 use indenting forces ranging from 24 to 36 nN which are applied with AFM cantilevers that exhibit diameters of up to 24 nm. In our simulations we use a sphere with a diameter of 2.5 nm. Overall, our force per area is higher by a factor of about 50-100. If we take this into account, we can extrapolate the experimental data for a comparison to the computational data (Figure 4, inset) and observe the extrapolations partly covers the the range of the simulations albeit with different slopes. This extrapolation should be considered as no more than an order of magnitude estimations; M ARTINI timescales are typically sped up by a system-dependent factor which usually lies between 4 and 8, 25 and the limited extension of the simulation box entails finite size effects. As pointed out before, the system size influences the membrane stack’s susceptibility to bending which, in turn, influences the rupture rate. In AFM experiments bending is not limited by the finite size of the membranes but the use of hundreds of membranes in a stack deposited on a solid surface. These factors hamper a quantitative comparison between simulations and experiments. For this reason as well, the values from the Bell fit [σMBL,phob = (4.502 ± 0.009) pm and σMBL,phil =

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(4.511 ± 0.001) pm] are too small when compared to experiments (σexp = 12 pm). Overall, the picometer regime is surprisingly small compared to the dimensions of the system and suggests a very steep free energy potential for membrane rupture. Nonetheless, we have to keep in mind that the direction of force application does not coincide with the direction along which molecular interaction are being broken, so there is no straightforward physical interpretation of the σ values. 8,13,30 Interestingly, membranes withstand forces longer if they are pushed by a hydrophobic as opposed to a hydrophilic indenter. This can be seen by significantly smaller rupture rates (Figure 3 and Figure 4). Hence, the change in stepsize is also accompanied by an increased resistance towards rupture. Our data suggest that the solvated double head-group layer, with the strong electrostatic interactions between the oppositely charged functional groups, constitutes a higher barrier for the hydrophobic indenter than the weakly interacting double lipid-tail layer constitutes for the hydrophilic indenter. We note that our results depend on the details of the indenter model, which on a coarse-grained level cannot be expected to capture the actual indenter chemistry of the experiments. In this light, we conclude that independent from the indenter properties, system size and boundary condition, we observe well-defined steps of similar sizes, with dwell times and sites strongly depending on the details of the indenter and the extend of membrane deformation.

Single-bilayer rupture To compare the rupture dynamics of stacked system, as probed experimentally and in the simulations described above, to a single layer and to further elucidate the differences between the hydrophilic and hydrophobic indenter topologies, we carried out a series of single bilayer (SBL) rupture simulations. Vertical displacement was hindered via harmonic restraints on the center of mass of the bilayer. Also, we extended the probed force range by an additional force of 0.50 nN and again simulated 70 rupture processes per force. Figure 5 depicts the survival probabilities for the SBL simulation series. We observe that the survival probability of the membrane rupture induced by an hydrophilic indenter behaves similarly 13



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as in membrane stacks. Here as well, a log-normal distribution can be fitted to the distribution of dwell times (Figure S8 and S9). Overall, these dwell times are shorter than for MBLs, as can be seen from a shift in the survival probabilities (cf. Figure 4). We conclude that, in case of a hydrophilic indenter, stacking of membranes increases the resistance of the individual membranes against rupture. The difference in rupture dynamics brought upon by the indenter hydrophobicity is even stronger than for MBLs. A log-normal distribution does not yield a good fit for the distribution of dwell times of single bilayers ruptured by a hydrophobic indenter. The underlying reason for this is that here, we observe two distinct dwelling regions: firstly, a long-lived one originating from the rupture of the top leaflet of head-groups; secondly, a short-lived dwelling that occurs as the indenter is inside the tail region of the membrane pushing the membrane downward (Figure S10). The latter cannot be directly interpreted as rupture process since indenter–tail contacts are maintained as the indenter pushes downward and deforms the membrane, and the respective survival probability is not included in Figure 5. The first dwelling region corresponds to the initial rupture observed for the stacked system, since for both, SLBs and MLBs, the first head-group sheet is ruptured and sub-

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sequently, the indenter dwells inside the membrane. Nevertheless, for the SBLs, the initial dwell time is much longer and the respective distribution is much broader compared to the MBL. From this, we conclude that membrane bending influences the rupture significantly. Single layers deform strongly which, for hydrophobic indenters, postpones the loss of membrane integrity due to rupture. Membrane bending not only delays the rupture but also influences its dynamics. Therefore, more sampling would be required to identify the underlying distribution. In contrast to this, the initial rupture in MBLs, where bending is strongly diminished by underlying layers, occurs faster and follows a log-normal distribution. This becomes obvious when comparing the membrane deformations that occur during the rupture process (Figure S11). The indentation of SBLs results in a vertical deformation which is approximately twice as large as for MBLs. This data can be fit to a simple model proposed by Fraxedas et al. 31 which yields a stiffness of (2.47 ± 0.07) nN/nm for MBLs and (0.20 ± 0.01) nN/nm for SBLs. To prevent the bilayer from solely being displaced by the indenting force, we restrained the position of the bilayer centre of mass (COM) along the z-axis. In contrast to the mica substrate used in AFM experiments, this allows for membrane bending since the restoring force is distributed equally over all the lipids in the bilayer. Thereby, the deformation does not depend significantly on the strength of the restraint (Figure S12). In total, the timescale of hydrophobic rupture for SBL is up to one order of magnitude faster than for MBLs. Evidently, stronger membrane bending is responsible for the differences between the rupture of MBLs and SBLs. Surprisingly, these differences are strongly dependent on the indenter chemistry. Bending induced by a hydrophilic indenter speeds up the rupture process, whereas bending originates from a hydrophobic indenter delays the loss of membrane integrity. To investigate how these contrasting effects come about, we monitor the contacts between the lipids and the indenting sphere (Figure 6). For both topologies, contacts with lipid head-groups are established as the indenter pushed onto the membrane. At the same time, the distance between the head-group layers decreases which can be attributed to a thinning of the membrane by bending. At the point of rupture, the ’hydrophobic’ indenter loses head-group contacts and makes contact with lipid tails instead. This indicates that the two head-group leaflets rupture successively. The ’hydrophilic’ in-

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Figure 6: Head-group–head-group distance and indenter-bilayer contacts during the rupture of single lipid bilayers. Minimal distance between the two head-group layers, and the number of contacts between the indenter and the lipid head are shown during rupture by a hydrophilic (top) and hydrophobic (bottom) indenter. The stars indicate the rupture events and the snapshots show the respective position of the hydrophilic (red) and the hydrophobic (blue) indenter within the bilayer at the point of rupture.

denter, however, maintains a high number of head-group contacts throughout the rupture process. The rupture manifests itself in a sudden decrease of the minimal distance between the head-group layers: head-groups of both leaflets get in contact with each other to form a pore through which the hydrophilic indenter can pass the membrane without excessive tail contact. We conclude that the bending of the membranes facilitates the formation of a pore, as the distance between head-group leaflets decreases. In order to verify our results obtained with coarse-grained simulations, we also carried out a series of all-atom single layer simulations (Figures S13 and S14) using a hydrophobic indenter 16


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sphere. The all-atom simulations are consistent with our M ARTINI simulations: they also produce two distinct dwelling regions; a long-lived one at the first head-group leaflet and a short-lived one while leaving the membrane. However, membrane deformation and adherence between the lipid tails and the indenter are less pronounced in the all-atom simulations. All-atom simulations of single layers with a hydrophobic indenter (Figure S15) are consistent with the proposed poreformation mechanism: One single dwell is observed during which the bilayer is deformed until head groups of both leaflets get in contact with each other to allow the passage of the indenter.

CONCLUSION We here have probed the mechanical stability of single and stacked lipid bilayers by a spherical indenter. We find good agreement with recent AFM experiments. The exponential dependence of the rupture rates on the applied force indicates that the rupture of membrane leaflets is a forceactivated barriercrossing process. Interestingly, we observe single layers to show less resistance to rupture, with approximately one order of magnitude higher rates at a given indentation force, a finding that has not been accessibly by AFM experiments due to the challenge of working with free-standing lipid bilayers. In this context, we have revealed that membrane bending accelerates the rupture and that stacking of membranes inhibits membrane deformation which, hence, stabilizes the system. In our simulations, bending is inhibited by finite membrane sizes and facilitated by the limited number of layers in the stack. This impedes an exact comparison to experiments. The underlying mechanism of rupture and the log-distribution of dwell times, however, are very robust with respect to simulation parameters and coincide well with experiments. For this reason, we also conclude that the model of the AFM indenter as a simple sphere is a valid approximation, even though an AFM tip would rather be cone-shaped. The membrane rupture itself, however, is mainly dependent on the region below the indenter, and the lower half of the indenter sphere approximates well the topology of an AFM tip.

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We conclude that multi-layer systems as they occur e.g. in the myelin sheaths of neuronal axons, are more robust against vertical mechanical perturbations than single membranes. Finally, we find stacked bilayers to show higher resistance against rupture by a hydrophobic as compared to a hydrophilic indenter model. While the coarse-grained indenter models do not directly represent experimental AFM tips, our observation suggests that the choice of AFM tip chemistry, being it hydrophobic or rather polar, to strongly impact the observed rupture mechanisms of forces for systems with distinct and varying charge or polarity distributions.

Acknowledgement The authors acknowledge support by the Klaus-Tschira-Foundation the state of Baden-Württemberg through bwHPC and the German Research Foundation (DFG) through grant INST 35/1134-1 FUGG.

Supporting Information Available Videos of the rupture simulations, rupture of stacks of lipid discs, distributions of dwell times, experimental rupture rates, rupture curves of single-bilayer rupture, simulations at atomistic detail.

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