Permeability modes in fluctuating lipid membranes with DNA-translocating pores

Accepted Manuscript Permeability modes in fluctuating lipid membranes with DNAtranslocating pores

L.H. Moleiro, M. Mell, R. Bocanegra, I. López-Montero, P. Fouquet, Th. Hellweg, J.L. Carrascosa, F. Monroy PII: DOI: Reference:

S0001-8686(17)30334-2 doi: 10.1016/j.cis.2017.07.009 CIS 1794

To appear in:

Advances in Colloid and Interface Science

Received date: Revised date: Accepted date:

3 July 2017 10 July 2017 10 July 2017

Please cite this article as: L.H. Moleiro, M. Mell, R. Bocanegra, I. López-Montero, P. Fouquet, Th. Hellweg, J.L. Carrascosa, F. Monroy , Permeability modes in fluctuating lipid membranes with DNA-translocating pores, Advances in Colloid and Interface Science (2017), doi: 10.1016/j.cis.2017.07.009

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DNA-pore permeability

Permeability modes in fluctuating lipid membranes with DNA-translocating pores L.H. Moleiro1,2,5, M. Mell1, R. Bocanegra3, I. López-Montero1, P. Fouquet4, Th. Hellweg5, J.L. Carrascosa3,6 and F. Monroy1,7,* 1

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3BHub, Biophysics for Biotechnology and Biomedicine, Departamento de Química Física I, Universidad Complutense, Ciudad Universitaria s/n, 28040 Madrid, Spain, EU 2 Physikalische Chemie I, Univeristät Bayreuth, Universitätsstraße 30, D95447 Bayreuth, Germany, EU 3 Unidad Asociada CNB-Instituto Madrileño de Estudios Avanzados (IMDEA) Nanoscience, Faraday 9, E28049 Madrid, Spain, EU 4 TOF/HR Group, Institut Laue Langevin, 6 rue Jules Horowitz, BP156, F38042 Grenoble Cedex 9, France, EU 5 Physikalische und Biophysikalische Chemie I, Universität Bielefeld, Universitätsstraße 25, D33615 Bielefeld, Germany, EU 6 Departamento de Estructura de Macromoléculas, Centro Nacional de Biotecnología, CSIC, Darwin 3, E28049 Cantoblanco, Spain, EU 7 Unit of Translational Biophysics, Instituto de Investigacion Biomédica del Hospital Doce de Octubre (i+12), E28041 Madrid, Spain, EU

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* Corresponding author: [email protected]. Correspondence address: Department of Physical Chemistry, Complutense University, Ciudad Universitaria, 28040 Madrid. Spain. Tel.: (34) 91 394 4128, Fax: (34) 91 394 4135

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DNA-pore permeability

Abstract

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Membrane pores can significantly alter not only the permeation dynamics of biological membranes but also their elasticity. Large membrane pores able to transport macromolecular contents represent an interesting model to test theoretical predictions that assign active-like (nonequilibrium) behavior to the permeability contributions to the enhanced membrane fluctuations existing in permeable membranes [Maneville et al. Phys. Rev. Lett. 82, 4356 (1999)]. Such highamplitude active contributions arise from the forced transport of solvent and solutes through the open pores, which becomes even dominant at large permeability. In this paper, we present a detailed experimental analysis of the active shape fluctuations that appear in highly permeable lipid vesicles with large macromolecular pores inserted in the lipid membrane, which are a consequence of transport permeability events occurred in an osmotic gradient. The experimental results are found in quantitative agreement with theory, showing a remarkable dependence with the density of membrane pores and giving account of mechanical compliances and permeability rates that are compatible with the large size of the membrane pore considered. The presence of individual permeation events has been detected in the fluctuation time-series, from which a stochastic distribution of the permeation events compatible with a shot-noise has been deduced. The non-equilibrium character of the membrane fluctuations in a permeation field, even if the membrane pores are mere passive transporters, is clearly demonstrated. Finally, a bio-nanotechnology outlook of the proposed synthetic concept is given on the context of prospective uses as active membrane DNA-pores exploitable in gen-delivery applications based on lipid vesicles.

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Key words: neutron spin-echo; lipid vesicles; bending elasticity; membrane tension; permeability modes; membrane permeation dynamics

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DNA-pore permeability

Introduction

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Protein pores are found in biological membranes, where they act as permeability channels for transporting ions and hydrophilic molecules across hydrophobic barriers. Such a permeation transport constitutes a transport process that produces forces on the membrane where the pores are supported (1). The dynamics of the process is driven by the global permeability of the pores, which occurs in a time scale determined by a permeability kinetic coefficient (). Biological membranes are quite rigid under thermal fluctuations, which are essentially restored by bending elasticity ( kBT) and by subsidiary lateral tension ().The force created by the permeability flow produces a transverse stress in the pore that is opposed by the rigidity of the supporting membrane. Because the pores produce (transversal) transport of mass across the membrane, they induce additional transverse fluctuations, whose local amplitude is determined by the areal density of protein pores inserted in the membrane,  (2). Ionic channels represent the prototypical case of narrow pores with a high specificity for the transported species. Cells have also evolved wider channels to facilitate membrane transport of larger hydrophilic metabolites -such as sugars and aminoacids (3). However, scaling transmembrane transport up to macromolecular sizes requires the assembly of multimeric protein complexes working as gating nano-machineries (48). In the case of nucleic acid polymers (DNA and RNA’s), the translocation motors have to overcome a number of problems to achieve a selective gating followed by an efficient translocation of the polynucleotide molecules, basically those related to the charged nature of the polyanion and its high intrinsic rigidity (9, 10). Consequently, these multimeric pores organize as conformationally open structures able to accommodate the topological variability of the transported macromolecule along the translocation process (4, 6).

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DNA-translocating pores are paradigmatic, particularly those involved in the packaging of the genome in bacteriophages (11, 12), a work-consuming process performed by active macromolecular portals able to translocate the large DNA strand inside the viral capside (9, 12). The DNA-packaging machinery in phages -the so-named portal complex, defines a hollow channel located at a unique vertex of the prohead and comprises an oriented head−tail connector and the terminases, which are not only involved in the recognition of the DNA to be packaged but also in its ATP-driven translocation (4, 13). In the phage ϕ29, the connector is a multimeric complex formed by self-assembly of identical p10-protein units (11, 13). The monomers assemble in a propeller-like dodecamer with an external diameter of 14.6nm and a height of 7.5nm (6). The dodecamer forms a toroidal structure, with a stalk and a wing structural domain, which shows a conspicuous wide channel (ϕ = 3.5 nm diameter) that runs along the axis of the particle (13). In a recent work (14), we reported on an efficient synthetic route for the orthogonal integration of the pre-assembled connector of the native p10 protein of ϕ29 in lipid bilayers. Here, following the integration procedure described in ref. (14), we have prepared p10-pored lipid vesicles and we have tested for enhanced membrane permeability of water and small solutes in an osmotic field. To this purpose, we performed quantitative measurement of the thermal shape fluctuations in pored vesicles. On the one hand, optical videomicroscopy provided us with a powerful method to assess membrane dynamics by direct observation of the shape fluctuations in giant unilamellar vesicles (GUVs) (15, 16). By using flickering spectroscopy (FS), not only the spectral amplitudes but also the relaxation dynamics of the fluctuation modes can be determined in the continuous regime (q < 1/2), where the density distribution of permeation pores () is statistically averaged. From FS experiments, we determined the presence of permeability motions

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DNA-pore permeability

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and measured its relation with the surface density of the membrane pores. On the other hand, neutron spin echo (NSE) was alternatively exploited to explore microscopic permeability at the single-pore level, at wavevectors similar to the characteristic pore size (q a >> 1/2). Indeed, NSE provides the adequate q-range to quantitatively probe fast membrane dynamics over small length scales in nanometer-sized vesicles (see Ref. (17) for a recent review). For NSE experiments, we considered large unilamellar vesicles (LUVs) prepared by extrusion, which are comparatively smaller and more monodisperse than GUVs, a set up clearly advantageous in order to optimize observations in a statistical ensemble average. In the next section, we describe the minimal theory needed to rationalize how the dynamics of bending fluctuations is affected by pore permeability in an elastic lipid bilayer. In this contribution, we review the active theory of membrane fluctuations driven by permeability transport, and the only application reported to date with bacterio-rhodopsine channel. Our original contribution comprises both the synthetic biology of functional DNA-pore integration in the membrane of lipid giant vesicles, and the analytical tools developed to interpret NSE scattering functions in view of the theory of permeable membranes (see the new theory settled in the appendices).

Theory

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In deformable membranes, the height fluctuations h(r,t) are described by the usual CanhamHelfrich (CH) hamiltonian, which accounts for the elastic energy of the bending/tension modes in the Hookean approximation (18). In the presence of membrane pores, an additional strain field (r,t) accounting for the local imbalance of permeability might be considered, i.e. (r,t) = [(r,t) (r,t)]/.* To resolve this mechanical problem, Manneville et al. (19) proposed an extension of the CH-hamiltonian as: 2 1 2 (1) F  h,     h      2 h   2  2w   2 h   dA  2 The two first terms in Eq. (1) account for the usual CH-contributions from surface tension () and bending elasticity (, being the "bare" bending modulus). The third term in the right-hand side of Eq. (1) accounts for the mechanical energy due to changes in the permeation field. This is described as a Hookean contribution from the permeability imbalance strain, which is characterized by the linear susceptibility . The last contribution is a coupling term that links net permeability imbalance with local curvature (19), devoid higher curvature induces higher permeability. The coupling term, which is treated as an hybrid oscillator characterized by a coupling constant,  , represents a stabilizing contribution that reduces the bending energy due to pore aperture. This coupling term is assumed to scale linearly with membrane thickness (18). Such stabilizing coupling can be interpreted as an active-like component causing effective membrane softening due to the reaction force stressed by the open pores on the membrane after each permeation event occurs (eff = w(2h) ). By considering an elasticitypermeability Hamiltonian equivalent to Eq. (1) within the fluctuation-dissipation formalism, the analytic expression for the spectral amplitudes of the thermal fluctuations were previously obtained in ref. (19); in k-space, one obtains two summed contributions to the spectrum:

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The dimensionless permeation field (r,t) is defined as the local difference between the surface density of pores transferring mass outwards (r,t) and the density of them transferring mass backwards (r,t), which are referred to the average surface density of membrane pores inserted in the membrane, .

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hk2 

kBTw  w    kBT  , k 2  eff  k 4   eff k 2   eff  k 2

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where two effective bending moduli are involved: eff    w2

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 (4)  In the absence of net permeability (w), the mechanical-permeation spectrum in Eq. (2) describes regular tension-bending fluctuations; in that case, the usual Helfrich spectrum is recovered (the first term in Eq. 2), although the effective bending constant could be effectively decreased by the curvature-permeability term (> 0 in Eq. 3). At high permeability compliances (w), membrane fluctuations become amplified by permeability effects (the second term in Eq. 2), which become dominant in the regime of high wavevectors. 2

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eff    2w2  w2

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To complete the theoretical framework, the permeability transport must be considered within the evolution equation for the relevant strain field, h. The corresponding Langevin equation reads as: h  F  2 (5)  t        0 Fp   0 Fp h   th , t  h  where t stands for the hydrodynamic compliance (Oseen tensor), which accounts for the transverse component of the viscous flow field that is determined by the sum of frictional drag and permeability (in k-space, t(q) = 4k), with  being the permeability kinetic coefficient and  the bulk viscosity of the solvent). The hydrodynamic flow in the left hand of Eq. (4) is equaled to the sum of the flow field describing a permeation stream across the membrane (~ which is driven by net differences in osmotic pressure ) plus the local force exerted by the permeation imbalance (~ 0Fp) plus an additional transport term describing the sensitivity of the permeation stress to curvature (~ 0F´p2h) and finally, the stochastic thermal fluctuations th. This equation describes the dynamics of an overdamped transverse mode driven by membrane tension and bending elasticity and dissipating energy by two in parallel mechanisms, bulk friction and pore permeability. When solutions are found as planar waves, in the case that the osmotic flow is locally balanced by pore permeability, i.e.  0Fp, one expects mode relaxation at a rate (19):  1   4 2 2 h     (6)  k  eff k  0Fpk , 4k   which, at low permeability rates ( 0), recovers the usual form for pure tension-bending modes in an elastic membrane, i.e. h  (k+k3)/4.

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Materials and Methods Chemicals. 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC), 1,2-dioleoyl-sn-glycero-3phophoglycerol (DOPG) and 1-palmitoyl-2-azelaoyl-sn-glycero-3-phosphocholine (PAzPC) were from Avanti Polar Lipids (Alabaster, AL). Solvents and other analytical grade chemicals were from Sigma. Deionized water was used from a Milli-Q source (resistivity higher than 18 MOhm  cm; organic content < 5 ppb). Deuterated water from Sigma (99.9%) was used in NSE and DLS experiments as dispersion solvent ( = 1.2010 MPas at 22ºC).

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Connector Production. The connector complex was obtained from the protein p10 of Bacillus subtilis bacteriophage ϕ29. The gene coding for p10 was cloned in a recombinant plasmid pRSET-p10, which was overexpressed in E. coli. Protein p10 was purified by a two-step ion exchange chromatography, following the procedures described previously (20). Protein p10 purified according to this protocol was found assembled as a dodecameric complex (7).

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Sample Preparation. To achieve orthogonal integration of the ϕ29 connector in lipid bilayers, we follow the method previously reported in ref. (14). Briefly, the native connector was incubated with the lipid membranes in the presence of PAzPC, an oxidized lipid with the short saturated chain (C0:9) tailored with a carboxylic acid group susceptible to react with the arginine residues exposed at the outer surface of the connector protein. The lipid composition of the membrane was DOPC/DOPG/PAzPC with a proportion 80/10/10 per cent molar, a formulation enabling sufficient p10 reactivity with a maximum of structural flexibility and lateral fluidity (10). Lipids were mixed at this proportion and dissolved in chloroform/methanol (3/1) mixture.

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Large unilamellar vesicles. LUVs were prepared by the extrusion method using a commercial extruder (Avestin Liposofast Inc.). The lipid blend dissolved in chloroform/methanol mixture (3:1) is spread to form a precursor film. The solvent is slowly removed by evaporation in a dry nitrogen stream, yielding a homogenous lipid film, consisting of multiple lamellae. Then, the precursor film is hydrated with the protein solution by pouring the aqueous phase (with or without protein). The concentration of the vesicle suspensions was fixed constant at 2 mg/mL (final concentration). The suspension was buffered moderately basic (pH 8; the optimal condition for maximal reactivity of p10-arginines against carboxylated lipids in aqueous solution). During the hydration phase (1h) the suspension was frequently vortexed and maintained above the melting temperature of the lipid mixture (Tm  17ºC). Then, lipids are coextruded with the protein solution through a polycarbonate filtering membrane with a defined pore size (Whatmann; 200 nm), producing unilamellar proteoliposomes with a diameter similar to the pore size. Extrusion is performed at room temperature. Eleven extrusion cycles ensure a homogeneous dispersion of LUV’s with a constant size and low polydispersity (21). The proteoliposome dispersion was then filtered through a 0.2m teflon filter and poured into quartz tubes. To avoid differences between DLS and NSE experiments with lipoprotein LUVs, we always used D2O as aqueous solvent.

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Giant unilamellar vesicles. GUVs were prepared by the electro-formation method invented by Angelova (22) using the optimized protocol described by Mathivet et al. (23). The precursor lipid film is prepared as described above for preparing LUVs. Briefly, 10 μL of LUV buffer dispersion (10 mg/mL total lipid) was spread in an ITO (indium tin oxide)-coated glass slide. The fabrication chamber is composed of two parallel slides separated by a Teflon spacer (1 mm thickness). After solvent evaporation, the film was rehydrated with a sucrose solution (300 mM). The chamber was then connected to an AC power supply (1.1 V, 8 Hz; 90 min). The soluble dyes were added to the sucrose solution (0.5 mM) just before the re-hydratation step. Vesicle suspensions are stored in the dark at 5 °C, remaining stable for several days. Slow dynamics: Flickering Spectroscopy: Membrane fluctuations in GUVs were tracked at the equatorial plane of the vesicle with an inverted microscope working in the bright field mode (Nikon 80i). The microscope station is equipped with an ultrafast CMOS camera (Photron FastCAM SA3, 200 kfps max. rate, 1 Mpixel; 8 Mbytes RAM). Instantaneous fluctuations are decomposed as a discrete series of Fourier modes, h(t) = lhk(t)exp(iklx), where kl = l/R is the

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equatorial projection of the fluctuation wavevector (R being the radius and l = 2, 3, 4, . . . 1 being the azimuthal number). The dynamics of the equatorial fluctuations is experimentally probed through the autocorrelation function defined as Gk(t) = k(tt0) k(t0), where  indicates time-average over the time series obtained from a given fluctuation sequence. Good statistics are achieved only if time averaging is performed over long time intervals (typically, 5 s long at 20 kHz sampling; n  105 frames). The present ultrafast method is able to track fluctuations over very long periods of time, thus allowing a coherent detection of different components appearing correlated over very different time scales.

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Fast dynamics: Neutron Spin Echo (NSE) + Dynamic Light Scattering (DLS). Scattering methods provide a powerful tool to probe experimentally the relaxation dynamics of thermal fluctuations (24). NSE is adequate for studying the fast relaxation dynamics of the curvature undulations of LUVs giving rise to scattering in the regime of high wavevectors where fluctuations are short as compared to vesicle dimensions (qR  1; being q the 3D-scattering wavevector and R the vesicle radius) but comparable to membrane thickness (qh  1). For dilute dispersions (2 mg/ml vesicle concentration), the NSE intermediate scattering function takes the general form: (8) S (q t ) S (q 0)  ST  t   Aq  1  Aq  S fluct  t  ,

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which describes membrane fluctuations by considering internal motions coupled to diffusional translation (25). Both motions, diffusional translation and shape undulations, are essentially decoupled at the NSE spectroscopic window. In the present study, the prepared vesicles have a diameter of about 200nm, so the translational motion is non-relaxed at the q-window probed in NSE experiments, thus ST(t)  exp(Tt)  1  o(Tt) (if qR  1), with a translational decay rate T = DTq2, which is governed by the Stokes-Einstein diffusion coefficient of the bare vesicle DT = kBT/6Rh with the hydrodynamic radius Rh. Consequently, Eq. (8) can be approximated as a linear combination of two uncoupled exponential decays: (9) S (q t ) S (q 0)  Aq exp  T t   1  Aq  S fluct t  ,

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where the first component in Eq. 9 accounts for slow diffusional translation. For Rh  100nm, the translational component is essentially unrelaxed in the NSE window (T << tNSE1). In practice, this defines the baseline of the observed relaxation decay at a near constant value Aq.

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Intermediate Scattering Function of bending-dominated shape fluctuations: bulk friction vs. permeability control. The approximated expression in Eq. (9) has been successfully used for fitting experimental NSE relaxation curves with a Zilman-Granek (ZG) structure factor Sfluct(t) = SZG(t) accounting for membrane fluctuations in a rigid membrane dominated by bending elasticity (17, 25). For bending modes dissipating against bulk friction, the ZG-fluctuation structure factor is expected to vary with time as a stretched exponential profile (26, 27): 23 SZG  q,t   exp    t   , (10)   with a decay rate controlled by bulk viscosity ():

k T  k T    0.025  B   B  q3       12

(11)

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12 S q , t  S 0  exp     t    ,

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The stretched decay in Eq.10-Eq.11 indicates summed correlations over all the bending modes contributing to scattering, with correlation times determined by the dominant hydrodynamic impedance, which is given by the frictional flow resistance of the bulk fluid dragged as a consequence of membrane motion; thus, proportional to the bulk viscosity (see Appendix A). However, if pores make the membranes permeable, then the hydrodynamic impedance is reduced by the permeability compliance of the membrane allowing the fluid to flow across the pores. In the case of permeability control (by opposition to frictional control), the hydrodynamic impedance of the bending fluctuations becomes controlled by membrane permeability, so, the relaxation profile of the intermediate scattering function is (see Appendix B): (12)

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which is even more stretched than in the case of pure-frictional control (Eq. 10); here, the permeability-controlled decay rate is given as (see Appendix B): k T   q   0.045  B  kBT q 4   , (13)

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which should be found, even at equal bending rigidity, different than the viscosity-controlled decay rate in Eq. 11.

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NSE/DLS experiments. The reported NSE experiments for the NSE intermediate scattering function were performed on the spectrophotometer IN15 at the ILL, Grenoble (28). This instrument provides the longest Fourier times currently available at NSE instruments worldwide. The samples were poured into quartz cells (1mm thickness; Hellma). The instrument was equipped with a thermostated holder for these cells and all measurements were done at a temperature of 22 C. A Fourier time range up to 170 ns was explored at different q-values from 0.119 nm 1 to 1.102 nm. To achieve this, measurements at a wavelength of  = 12Å and 15Å had to be performed. The wavelength distribution in both cases had a FWHM of / = 0.15. DLS measurements of the hydrodynamic radius were carried out in the laboratory of the Partnership for Soft Condensed Matter (PSCM@ILL). Measurements have been performed using an ALV CGS-3 DLS/SLS Laser Light Scattering Goniometer System (ALV GmbH Langen, Germany). This instrument allows for a simultaneous measurement of static and dynamic light scattering in an angular range from 25º up to 155º. It is equipped with a HeNe laser operating at a wavelength of 633nm with a power of 22mW. An ALV/LSE-5004 Light Scattering Electronics is used together with an ALV-7004 Fast Multiple Tau Digital Correlator. For NSE/DLS measurements, a small aliquot of the same vesicle suspension prepared for NSE experiments is diluted in D2O (1:10 v/v). DLS (0.2mg/mL) and NSE (2mg/mL) experiments were indeed performed with the same vesicle suspension, DLS running immediately before NSE beamtime. The samples are poured into quartz cells (10mm O.D., Hellma). Then, they were placed in the measurement cell which is filled with decaline to match the refractive index of the quartz sample cells. Temperature inside this cell is measured by a Pt-100 sensor and kept constant at 25.0ºC with a precision of 0.1 degrees. The hydrodynamic radius of the vesicles Rh, is obtained by analyzing the relaxation rates of the DLS autocorrelation functions as diffusional translation, i.e. T(q) = DT q2 with DT = kBT/6Rh. Within this approach, the distribution bandwidths are related with the size polydispersity as R = R/R = T/T = DT/DT. For the considered cases, we found

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from DLS experiments DT = (2.0 ± 0.2) 1012 m2/s, a value compatible with the nominal radius Rh  100nm with a 10% size polydispersity.

Results

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Flickering spectroscopy in GUVs. The static spectra reveal effective softening due to membrane permeability. Figure 1 compares the amplitude spectra of the equatorial fluctuations of GUVs at increasing pore densities. At a first sight, one easily sees how the presence of pores in the membrane causes an increase in the amplitude of the spectrum. For the bare-lipid membrane, a regular spectrum is detected (see inset; Fig. 1b). The spectral analysis with Eq. 2 provides us with the experimental values of the mechanical parameters. For the bare-lipid membrane, one gets values:  = (7.5 ± 0.8) 1020 J = (18 ± 2) kBT and  = (5±3) 107 N/m (errors correspond to the standard deviation; N = 30 vesicles). This result assigns the bare lipid membrane with a relatively high bending rigidity,   20kBT, typical of most phospholipids in the fluid state (29-32). The surface tension is affected by a large variance, which is intrinsic to the natural variability in excess area of the vesicles fabricated by the electroswelling method. However, their absolute values are found relatively high (  5 107 N/m), as compared with GUVs made of neutral lipids ( 109108 N/m, typically; (29-32)), a fact probably related with the presence of the charged lipid causing lateral repulsion (POPG) (33). When the protein p10 is present, profound changes are observed in the fluctuation spectra with respect to the strongly boost up with increasing protein concentration. This change is measurable as an increase of the spectral amplitudes by nearly two orders of magnitude at the lowest wavevectors. Second, a marked change is observed in the spectral tails: although a regular decay is observed at low wavevectors, a near-constant tail is reached at high wavevectors. Such a high-amplitudes of the high-k modes correspond to enhanced high-curvature fluctuations, which have no explanation in the context of the regular Helfrich spectrum (see Eq. 2). Third, the amplitude of the non-decaying tail is strongly dependent on the protein concentration, a fact clearly pointing to a correlation between permeabilitymediated motions and the absolute amplitudes of the high-k fluctuations. Finally, a strong increase of the level of noise is detected in those tails with increasing protein, which could be related to an additional stochasticity introduced by the permeability process. Therefore, these experimental spectra have been analyzed with the extended expression in Eq. 2, which accounts for permeability motions that superposed to the regular tension-bending modes produce an enhancement of the membrane fluctuations (see fitting lines in Fig. 1A). Fitting convergence to Eq. 2 over the whole range of wavevectors were only possible by fixing w = 4nm (34) and eff() = 0, then working with the two moduli (, eff()) and with the global amplitude (w) considered as adjustable parameters.

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Figure 1. A) Power spectra of the shape fluctuations of GUVs made of the ternary lipid blend (DOPC/DOPG/PAzPC). In the absence of p10-pore protein (); In the presence of p10-pore protein [P/L ratio; ( in pores/m2): 1/37,000; ( 34) (). 1/10,000 ( 122) (). 1/7,500 ( 162) ()]. The density of pores () is estimated from the protein-to-lipid ratio (P/L) assuming that all the p10-protein in the preparation is incorporated to the lipid membrane:  (in pores/m2) = 106/[aP + (L/P) aL] with aP = 167 nm2 and aL = 0.8 nm2 being the cross-sectional areas of the protein and lipid molecules, respectively. The lines represent the best fits to the theoretical spectrum (see text for details). B) Inset with a reproducibility plot; several spectra obtained for different liposomes superpose in a master plot that is describe by the Helfrich spectrum (dashed line) with best fit parameters, 0 = (18 ± 2) kBT and  = (5±3) 107 N/m (errors correspond to standard deviations; N = 30 vesicles). C) Compositional dependence of the average membrane tension ( as obtained from the fits of the experimental spectra to Eq. 2. Error bars are standard deviations. A 20% typical error is assumed as a typical error of the density variable. C) Compositional dependence of the amplitude of the “active” contribution in Eq. 2. The global amplitude (w) represents a net compliance of the membrane due to the appearance of permeability forces that drive the membrane with enhanced fluctuations at high-k. A characteristic permeation energy (Ep  12 kBT per pore) can be obtained as the ratio of the spectral amplitude of the permeability component to the density of “driving” permeable pores (19).

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The dependence of the adjustable parameters on the protein concentration is shown in Fig. 1c () and Fig. 1d (w). First, a remarkable decrease is detected in the membrane tension (by more than two orders of magnitude; see Fig.1c), which suggests not only protein integration but strong dilating interaction with the membrane. The permeation amplitude (w; see Fig.1d) increases roughly linear with the protein concentration. From the slope, the elemental energy corresponding to the permeation event can be estimated, Ep = (w)/ = (12  2) kBT per pore (see Fig. 1d). However, no dependence on the protein concentration is detected for the effective bending modulus (within its experimental error); in this case, we obtain eff() = (2  1) kBT, independently of the protein concentration. Since eff()  2kBT, in comparison with   18kBT, using Eq. 3, one gets  1kBT/nm2, a value compatible with previous estimations (19). As the membrane tension as the effective moduli (eff() and eff()  0) are strongly reduced by the presence of protein, which indicates strong softening upon protein integration. Although such a material softening barely contributes to the increase of the fluctuation amplitudes, however, the non-decaying high-k tail in the experimental spectra (see Fig. 1a) can only be explained arising from the net permeation term in Eq. 2. Such enhanced fluctuations are detected in the regime of high wavevectors, just where bending modes might prevail over tension-mediated fluctuations. In this high-k regime, short-wavelength curvature fluctuations (in sites containing open pores) elicit the expulsion of the luminal water inside the pores, thus causing an additional amplitude of the membrane fluctuation. In the present case, the effective bending moduli effectively vanish (eff(i)  0), so high-k bending fluctuations become naturally enhanced, which contributes to the dominance of the permeability effects on the membrane fluctuations. Here, the permeation contribution in the second term of Eq. 2 becomes essentially constant, which explains the shortwavelength fluctuations of a permeable membrane that are noteworthy detected in the spectra as a non-decaying tail at high-k with near-constant amplitude given as h2perm  kBTw(w)/2. This amplitude is essentially higher with increasing membrane permeation, and is significantly enhanced with decreasing membrane tension. Both circumstances occur in the present case with increasing protein content, which explains the colossal enhancement of the high-k fluctuations, by more than two order of magnitude, due to membrane permeation (notice the high-k tails in Fig. 1A). Every individual permeation event displaces the luminal water contained in the pore channel, which immediately causes a reaction force in the membrane (Newton’s Third Law). These forces are cumulative, causing comparatively stronger fluctuations over increasingly larger

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distances, and at sufficient permeation and low tension, they could even become dominant over regular mechanical restoring. In the present case, at high pore densities, the membrane fluctuations seem to be clearly dominated by these permeation events.

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Enhanced permeability fluctuations driven by concentration gradients. In order to verify the permeation nature of the enhanced fluctuations, we performed additional experiments with pored membranes subjected to increasing concentration gradients of permeable solute (glucose). In practice, we fixed the protein concentration (constant pore density thus constant permeability), but increased the concentration of glucose in the outer medium, thus creating a hypertonic gradient that favors permeability across the pores. The results are shown in Figure 2. Regarding the high-k tail supposedly attributed to permeability events, an evident increase is detected with increasing the hypertonic gradient. Indeed, one observes a global enhancement of the membrane fluctuations with increasing the osmotic gradient, even for the bare lipids not containing the permeable pores (see the control case in Fig. 2). The hypertonic gradient causes the vesicles to deflate, creating larger excess areas with increasing gradient, which results in lower membrane tensions, thus higher fluctuations at higher gradients. This is clearly the effect observed in Fig. 2 for the fluctuations of the non-pored membranes with increasing the osmotic gradient (see Fig. 2; bare lipids): the higher the gradient, the larger the excess created thus the higher the spectral amplitudes. This excess-area effect is markedly higher in the regime of low-k’s where membrane tension dominates, although at high-k’s, where the bending rigidity dominates independently of the lateral tension of the membrane, the spectra are quite insensitive to the sugar gradient. An analysis of those data in terms of the Helfrich spectrum points out that the lateral tension largely decreases with increasing the osmotic gradient (see bare lipids in Fig. 2), whereas the bending rigidity remains essentially constant at its bare value (0  18 kBT). However, the effect of the osmotic gradient in the fluctuations of the pored membranes is much more dramatic, affecting all the spatial scales probed in the spectra of the vesicle fluctuations. The presence of large pores allow: 1) a decrease of the lateral tension (see Fig. 1C); 2) an effective softening of the membrane, measurable as an effective lower bending rigidity (eff  2 kBT); and 3) the existence of permeation events with a cumulative effect over all scales. Factors 1) and 2) are purely mechanical, contributing to inhibit, or at least inducing to decrease, the regular control of the fluctuations by rigidity restoring, thus contributing to increase the amplitude of the membrane fluctuations. Factor 3) is permeation-specific, and induces in the pored membranes increasingly larger fluctuations with increasing osmotic gradients. The effects of permeation are especially visible in the regime of high-k where the spectral tail due to the “active” membrane permeation (which varies as h2perm  kBTw(w)/2) is clearly dominant over the regular elastic restoring by bending rigidity (which would decrease with k as h2reg  (kBT/k2). This result points out the control of the permeability transport upon the fluctuations of the membrane containing the p10-protein which, obviously, is functioning as a transport gate permeable to water and glucose (14). Although the osmotic gradient is orientated from outwards to inwards, the molecular transport is bidirectional, composed by the diffusion of glucose inside the diluted lumen of the vesicle and an osmotic outflow of water outwards the hypertonic outer medium. Because a mass imbalance is produced in each permeability event, an effective force Fc appears resulting in an apparently active process, which enhances the amplitude of the membrane fluctuations above the basal level of the thermal noise. Consequently, the higher the gradient, the higher is the permeation susceptibility Fc, which neatly results in an increasing spectral tail with increasing gradient (see Fig. 2).

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Figure 2. Dependence on the osmotic gradient () of the experimental power spectra of the shape fluctuations of GUVs with p10-pore protein inserted on the membrane (L/P = 10,000;   120 pores/m2; filled symbols). The hypertonic gradient is defined as the positive difference between the concentration of glucose in the suspending milieu and the concentration of sucrose inside the vesicles, this is  = [glucose]out – [sucrose]in: 8 mM (); 80 mM (); and 400 mM (). All these spectra are describable as a same Helfrich contribution to fluctuations (eff 2kBT,  = 109 N/m) plus a variable component due to pore permeability (w, which makes the high-k tail to increase with the pore-density. The lines correspond to fits to Eq. 2 with fixed mechanical parameters (bending and membrane tension) and variable amplitude of the permeability term. Control experiments with bare lipids (no protein; hollow symbols): hypertonic gradient  = 8 mM (); 80mM (); and 400 mM (). No permeability effects (long tails) are detected with these impermeable membranes in the absence of protein, even when subjected to high osmotic stress. Dashed lines correspond to the best fits to Helfrich spectrum, taking  18kBT (fixed), which describes the terminal high-k tail, and fitting for the optimal value of , which best fits the low-k tension-dominated regime (rounded average values indicated below the data; from 106 N/m at low hypertonic gradient up to 108 N/m at the highest studied).

Correlation function: dynamic crossover from the regular bulk friction to the permeability regime. For the sake of example, Figure 3A shows the height-to-height autocorrelation functions

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(ACF) obtained from the flickering time series for the equatorial modes of fluctuation of a given vesicle. The ACF-relaxation is reasonably described by a single exponential decay, from whose fits the relaxation rates of the fluctuation modes are obtained. Figure 3B shows the k-dependence of the experimental rates. For the bare lipids (left panel), the data are found in good quantitative agreement with the theoretical prediction for tension/bending modes in a flexible membrane with no-permeability, this is 0  (k+k3)/4 (taking  = 5 107 N/m and = 018kBT, the values obtained from the static spectra of the bare lipid membrane).

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Figure 3. A) Height-to-height autocorrelation functions of the membrane fluctuations in a typical GUV, ACF(t) = h(t-t’) h(t’). The exponential profile ACF(t) ~ exp(ht) is characterized by a single relaxation rate h that is determined by the balance between restoring forces and hydrodynamic compliance (see text for details). B) Experimental relaxation rates of the ACFs obtained for: non-pored membranes made of bare lipids (left panel; the different dataset correspond to different vesicles); pored membranes with p10-protein integrated in the lipid bilayer (right panel). The data correspond to the three pore-densities considered in Fig. 1:  (in pores/m2)  34 ();  122 (); and  162 (). The evident decrease of the relaxation rates is primarily due to membrane softening. The dashed lines represent the best fits to permeability model in Eq. 6 with F’p = 0. C) Excess rate due to permeability, (=0), where the experimental relaxation rates of the pored membranes (Fig. 3B; right) are divided by the value expected for the equivalent non-permeable membrane, i.e.(=0) = (k+k3)/4, with  and  being the mechanical parameters obtained from the fits of the experimental spectra (see Fig. 1). No excess is detected in the non-pored cases, i.e. (=0) = 1 for bare-lipids, whereas a positive excess ((=0) > 1) is observed in the pored membranes (symbols as in Fig. 3B). The continuous lines represents the best fits to a linear dependence describing the excess rate due to permeability; from Eq. 6, one gets (=0) = 1 + 4k. The calculated values of the permeability kinetic coefficient are plotted in the inset, together with the values obtained from the NSE experiments discussed in Fig. 4B. A linear dependence with the pore-density is clearly inferred (dashed line).

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We also analyzed the autocorrelation functions that correspond to the pored vesicles. The results are shown in Fig. 3B (right panel), which show the relaxation rates obtained at different protein concentration. In this case, the relaxation rates are found meaningfully slower than in the nonpored case (left panel), as expected for softened membranes characterized by lower values of the mechanical moduli. Furthermore, a systematic dependence of the relaxation rates with the protein concentration is observed in these cases. For the sake of analysis, we compare in Fig. 3C the different cases with the relaxation rates reduced by the value at zero permeability, this is (=0) (= (k+k3)/4 calculated by taking the effective values of the mechanical moduli obtained in every case from the corresponding static spectra). As expected, no excess rate is detected for the bare lipid membranes. However, for the pored membranes, a clear excess rate is observed increasing with the protein content. Such an excess is found with a clear k-dependence, which is compatible with Eq. 6 corresponding to the relaxation rates of the fluctuation modes in the permeable membrane with a combined hydrodynamic compliance ( =  + 1/4k). No influence of the current term in Eq. 6 due to curvature is detected in this excess rate, i.e. Fp’  0. The absolute values of the compliance factor are obtained in the range 4 = (1 – 5) 106 m; taking  103 kg/m s, one obtains values of the permeability coefficient that range the interval  = (3 – 10) 104 m2 s/kg for the protein concentrations considered. As expected, near-linearly increasing values of the permeability kinetic coefficient are obtained with increasing pore-density (see inset in Fig. 3C).

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Neutron Spin echo in LUVs. Permeability motions are detected in the intermediate relaxation function. The NSE relaxation functions contain dynamical information occurring at times below 100 ns corresponding to shortrange membrane fluctuations. Figure 4 shows the time dependence of the normalized intermediate scattering function S(q,t)/S(q,0) measured for LUVs (100nm radius) made of the same lipid mixture than above, both in the absence- (Fig. 4A) and in the presence (Fig. 4B) of inserted pores in the membrane (right panels in Fig. 4B, corresponding to two protein-to-lipid ratios, P/L = 1/37,000 (equivalent to   34 pores/m2) and P/L = 1/10,000 ( 120 pores/m2)). We perform a multidimensional analysis that consists of the simultaneous fitting of the experimental series obtained at different q’s to the approximate expression in Eq. 9. First, we fix the diffusional translation rates T = DTq2, at the values expected from the diffusion coefficient of LUVs with 200nm diameter, i.e. D = 2 1012 m2/s, as previously measured in DLS experiments performed on the same samples (see Methods and refs. (17, 25) for details). Then, we choose a given model to describe the dynamic structure factor of the bending-dominated shape fluctuations: A) The ZG-model for bending modes dissipating against bulk friction, in the case of bare lipids (left panel in Fig. 4); or B) the permeability-model developed in Appendix B, in the case of putative pore permeability expected in the presence of p10 proteins. Finally, in every case, we fit all the normalized curves corresponding to different q’s using Eq. 9 in the whole qrange probed by NSE. In practice, this procedure allows for fitting all the curves in the NSE-plot to their respective terminal baselines (Aq), which correspond to the amplitudes of the translational components, and with variable decay rates (fluct(q)), which, with the corresponding parametric dependence, increase with the wavevector as: A) () ~ (kBT/)½ (kBT/) q3, in the case of a purely rigid membrane; and B) () ~ (kBT/) (kBT ) q4, for the pore-containing softened/permeable membrane. On the one hand, the relaxation profiles in the NSE-plot corresponding to the bare lipid membrane are perfectly reproduced by the Zilman-Granek

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structure factor (Fig. 4A; no pores, no permeability), taking Eqs. 10-11 with the bulk viscosity fixed at  = 1.201 MPa s and with a fitted value of the bending rigidity of  = (16 ± 5) kBT, in quantitative agreement with the value obtained from GUVs by flickering spectroscopy (see Fig. 1A). On the other hand, the NSE-plots obtained for the softened membranes with inserted proteins have been fitted to the permeability model (Fig. 4B); using Eqs. 12-13, where a value of   eff = 2 kBT (the value obtained from GUVs by FS; see Fig. 1A) has been assumed, one gets to fit the NSE-plot with a same value of the permeability kinetic coefficient in every one of the two cases explored (see legends in Fig. 4B). The fitted values are in rough agreement with the absolute values of  previously obtained from the analysis of the flickering spectroscopy data in Fig. 3C, and point out a relative increase with protein concentration that is compatible with a linear dependence on the pore-density, i.e. , as pointed out in the inset of Fig. 3C.

Figure 4. NSE scattering intermediate functions of the shape fluctuations of LUVs (200nm diameter) based on the membrane systems considered in this study. A range of scattering wavevectors was probed [q (nm1) =: 0.330 (); 0.454 (); 0.723 (); 0.913 ()]. A) Bare lipid membrane without protein. The lines correspond to the best fit to Eq. 9 with the ZG-expressions in Eqs. 10-11 for the bending fluctuations in a rigid membrane (see refs. (26, 27, 31, 35)). Fitting is performed simultaneously to all wavevectors following the procedure described in ref. 14; B) Pored lipoprotein membrane with p10-pores inserted in the lipid membrane. Two different pore-densities were measured (L/P = 200,000 (left panel) and 37,000 (right panel)), corresponding to two different pore-densities (see legends). Simultaneous fitting to the different q’s was performed with Eqs. 12-13 corresponding to the scattering model for a permeable membrane (se Appendix B). Both, the experimental data and the best fits to the permeability model reveal a slightly faster relaxation for the denser protein system, which suggests an influence of the permeability transport on the microscopic dynamics probed by NSE.

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Discussion

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The above results point out an enhancement of the membrane fluctuations due to the permeability transport occurred across membrane-inserted protein pores. On the one hand, the amplitude of the averaged fluctuations increases with increasing both, the protein content (Fig. 1) and the osmotic gradient (Fig. 2). Such effects suggest the chief role that permeation forces play in driving “active” fluctuations with a higher amplitude than the pure mechanical modes excited by thermal energy and restored by membrane elasticity. On the other hand, the influence of permeability transport is also manifested on the fluctuation dynamics, not only in the slow collective dynamics at low wavevectors (tracked in GUVs by FS) but also in the fast microscopic dynamics as probed by NSE (in LUVs). Such dynamical effects, measured as an increase of the relaxation rates of the membrane fluctuations, both at low q’s (Fig. 3) and at high q’s (Fig. 4), are induced by the permeability of the membrane, which facilitates a faster flow of membrane matter in the permeable membranes than the frictional resistance opposed by the bulk fluid on the impermeable membranes. The insertion of open pores causes a profound impact on the membrane mechanics. Indeed, increasing membrane permeability causes effective membrane softening, larger amplitudes of the membrane fluctuations and faster relaxation rates. The fluctuation model proposed by Manneville et al. (19) captures not only the essentials of this behavior but also more specific details, such as the high spectral tails describing the enhanced permeability-driven fluctuations induced by membrane curvature at high wavevectors (see Fig. 1 and Fig. 2), and the progressive acceleration of the correlations in the fluctuations facilitated by the highest hydrodynamic compliance provided by membrane permeability.

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Permeation forces and membrane mechanics. Within the static version of the Maneville’s model, the linear susceptibility Fpmight arise from the elementary force per area unit, Fp, transmitted by a pore to the membrane in a steady permeation event. From a microscopic standpoint, upon an elementary event, the membrane is displaced in the normal direction by a distance  (of the order of the membrane thickness), so the energy involved on the unitary permeability event is Ep = Fp. Consequently, the susceptibility coefficient should be related to the elemental force as Ep Fa. From the data in Fig. 1D the permeation energy has been evaluated to be Ep  12 kBT per pore, so assuming 7.5nm (the length of the pore), one estimates a permeation force Fp  10 pN per pore, of the same order as microscopic forces involved in conformational changes of mechanoactive proteins (2). This permeation force is comparable to the external force exerted by the hypertonic gradient; for a gradient  = 400 mOsM, one gets an osmotic pressure  = kBT   1pN/nm2, which, referred to the sectional area of the permeation channel (a  10nm2) corresponds to an osmotic force Fosm  10 pN. Additionally, one can estimate the permeation energy per unitary area as fp  Ep/a  3 104 N/m. This parameter defines the tension induced by the active elements on the membrane, which is largely exceeding the membrane tension (fp ) that will be strongly reduced by the action of the “active” permeation elements applying their force on the membrane. Furthermore, such active elements inject on the membrane an additional energy of around Ep  12kBT, so consequently, the bending stiffness would be effectively reduced by a comparable amount, as it is indeed observed. To summarize, in addition to a global enhancement of the membrane fluctuations, a mechanical softening is also expected as the collective effect of permeation events occurring sparsely along the membrane but persistently sustained by the continuous action of thermal fluctuations. Detection of single permeation-events. The emergence of permeation forces on the macroscopic

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membrane fluctuations might arise from the existence of single permeability events occurring in the microscale. In order to detect such events, we tracked the fluctuation time-series of single points in the membrane of giant vesicles. A typical example is shown in Figure 5, where we plot typical single-point trajectories at three different states with increasing content of p10-pores. At first sight, the expected increase of the amplitude of the fluctuations is clearly visible with increasing membrane permeability. A detailed inspection reveals the presence of spikes in the time series, which are detected as -peaks (shots) of very short duration (, compatible with the sampling time (t = 1/fps = 50s). These shots appear suddenly, with a random distribution of the lag-time between consecutive events. The shots always happen towards the vesicle interior, which correspond to membrane displacements that occur inwards as a consequence of the hypertonic imbalance that transports heavy glucose from outwards displacing lighter luminal water. No reverse experiment is possible (shots outwards) as the vesicles blowup in hypotonic gradients. Only a few shot events are visible at low pore-density (L/P = 20,000; Fig. 5B), but much more and more intense are detected with increasing pore-density (L/P = 5,000; Fig. 5C). However, no shots are detected in the time series corresponding to the fluctuations in an impermeable membrane (bare lipids; Fig. 5A). A similar behavior is detected with increasing the hyperosmotic gradient at a given protein density (data not shown).

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Figure 5. Membrane fluctuation time-series tracked at a single-point of the membrane of giant vesicles at different degree of p10-protein orthogonal integration: A) bare-lipids (no protein); B) Integrated protein at L/P = 20,000 (  60 pores / m2); and C) L/P = 7,500 (  160 pores / m2). The appearance of shots due to single permeation-events is manifest with increasing pore-density. The respective probability distributions of the membrane displacements are plotted in the lower panels. An evident non-Gaussianity is clearly visible at high pore-density (column C).

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The histograms of the time series (Fig. 5; bottom panels), which determine the probability distributions of the membrane displacements that occur as a consequence of the vesicle fluctuations. In the absence of permeation events (Fig. 5A; impermeable membrane), or when only a few events are present (Fig. 5B; low pore density), the probability of the membrane fluctuations nearly follows a Gaussian distribution, which corresponds to thermal fluctuations occurring in an effective harmonic potential that describes a mean-field of membrane elasticity, i.e. Helast = (1/2) keff h2. The distributions broaden with increasing permeation, which indicates that larger fluctuations are progressively more probable. In other words, the effective spring constant keff(), which encompass bending and tension components, decreases with increasing permeation, which indicates global membrane softening allowing larger membrane excursions upon thermal energy. These evidences are compatible with the previous results in this paper. However, a clear deviation from Gaussian statistics is detected for the time series with a high number of shots due to permeation events occurring in the membrane (see Fig. 5C). In this case, deviations happen as a non-Gaussian in the left tail (negative displacements) of the probability distribution, which correspond to large excursions of the membrane displacing inwards during the permeation events. Such a long-tail should be interpreted as the statistical trace of an out-ofequilibrium process occurring in these systems, arguably the permeation transport driven by the hypertonic gradient and occurring across the membrane pores.

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Dynamical characteristics of the permeability process. Once orthogonally inserted in a lipid membrane (14), the p10-portal could work as an integral protein with a wide hydrophilic channel adequate for active DNA-transport, prior incorporation of the translocation motor (5, 11, 36). The p10-portal, alone, is a passive channel that allows the traffic of water, ions and small soluble biomolecules, such as sugars, under osmotic gradients. However, the protein p10 produces important changes in the membrane, not only causing mechanical (structural) softening but also inducing important dynamical effects related to the passive mechanism of pore permeability. We have probed the nanoscopic dynamics of the membrane with NSE, detecting permeability-related relaxation in the time window of hundred nanoseconds (see Fig. 4). In this nanoscopic domain, if one assumes the fluctuations with an amplitude comparable to the channel length L, the velocity of permeation might be of the order of vP  0.1-1 nm/ns. During such a permeation event in the hypertonic field created as an excess of glucose in the outer medium, a permeation force Fp  10 pN is put into play, making the fluid inside the channel to be ejected from this space. From the dynamic mesoscopic data (see Fig. 3), the kinetic permeability coefficient has been estimated  103 m2 s/kg, so the net permeability flow rates obtained from the analysis of the fluctuations are vP =   Fp  1 nm/ns, of the same order of magnitude as estimated from the nanoscopic dynamics. Such pore-favored permeability rates to water, ions and small hydrophilic molecules is very fast as compared with the low permeability (and practical impermeability) of lipid membranes to water (and to polar molecules), thus opening a promise of opportunities in the use of these membrane pores in the field of wet nano-technology. Implications in nanotechnology. Under the form of multimeric self-assembled complexes, such as the portal complex of ϕ29, these protein nanopores are robust, easily obtainable at low cost, and easy to modify with nanotechnological purposes. In particular, pore proteins incorporated to lipid membranes could be used as smart gates for specific solute transport in artificial vesicle-based cargo devices or bioreactors. During recent years, a large number of studies have focused on the use of biological nanopores for diverse applications, from counting single molecules (37) to

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genome sequence approaches (38, 39). Indeed, the high specificity of the viral connector for DNA translocation, together with its well-known structure (13), makes it an attractive system to bridge material engineering and synthetic structural biology in the context of the use of DNAnanopores in synthetic tools and devices (14). Furthermore, the synthetic approach offers unique possibilities for the analysis of the physical mechanisms involved in polymer translocation along pore-like structures.

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At thermodynamic equilibrium, passive membranes fluctuate because of thermal noise, i.e. the Brownian motion of the bilayer. In this paper, we have shown how a permeation field is able to modify the membrane fluctuations in a way such that they become dominated by “active-like” motions originated from individual permeation events that occur as a result of the passive transport of solvent and solutes through the membrane pores in an osmotic field. The presence of wide open pores, able to transport mass at big amounts under an external osmotic field, is sufficient to cause on the membrane: A) an effective softening, measurable as a lower bending rigidity that explains the actual enhancement of the thermal fluctuations; and B) an increase of permeability kinetic rates, measurable as an acceleration of the relaxation dynamics of the membrane fluctuations. These effects have been congruently found in experiments with permeable membranes with inserted pores engineered for macromolecular (DNA) transport. The enhancement of the membrane fluctuations is due to the presence of permeation motions, which are superimposed on the pure mechanical modes excited by thermal energy and restored by membrane tension and bending rigidity. Consequently, a coupling between mechanical modes and permeation modes there exists in permeable membranes, which is responsible for energy transfer between both modes in a way such the higher the permeation susceptibility, the lower the effective bending stiffness, and the higher the amplitude of the fluctuations, in agreement with experimental results, which are found in accordance with theory. Therefore, the thermal fluctuations in the permeable membrane are deeply altered by the presence a nonequilibrium noise source, which arises from single permeation events. The presence of these permeation events has been detected in the fluctuation time-series as isolated spikes with a well-defined duration (ca. 0.1ms) and a stochastic (near Poissonian) distribution of the delay times between consecutive events that is compatible with a shot-noise caused by the permeation events, which is superposed to the Brownian noise caused by the thermal energy on the deformation modes of the permeable membrane. Such a noise superposition explains why the fluctuations of the permeable membrane do not follow a Gaussian distribution, with non-Gaussianity arising from the nonequilibrium displacements due to permeation motions. The present experimental results, and their theoretical consequences, show how membrane fluctuations could be exploited either to store or to transfer energy from an osmotic 3D field to the elasticity 2D field in flexible membranes with a high permeability. Although no active DNA transport through the 29 portal has been considered in this work, the present conclusions point out the crucial role that will be eventually played by membrane elasticity on the mechanics of the translocation process in possible artificial microsystems for DNA transport across membranes that integrate the 29 DNA-translocation machinery.

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Acknowledgments

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F.M. thanks to Dominique Langevin for always guiding by the way of rigorous physics with the flavor of soft matter and the color of biology. Many thanks for your example, which has been always present alongside my scientific career. This work was partially supported by grants FIS2015-70339-C2-1-R from MINECO and S2013/MIT-2807 (NanoBIOSOMA from CAM) (to FM), and BFU2014-54181-P from MINECO and S2009/MAT-1507 from CAM (to JLC). M. Mell was supported by FPU Program (MEC, Spain) and L.H. Moleiro by CSD2007-0010 (MICINN, Spain). I. López-Montero thanks to “Programa Ramón y Cajal” granted by MINECO (Spain; RYC-2013-12609) and an ERC Starting Grant by European Commission (EU; ERC2013-StG38133). We gratefully acknowledge ILL Soft Matter Partnership Lab (PSCM@ILL) for DLS-time in its facility and especially to Ralf Schweins for technical assistance.

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Appendix A. Zilman-Granek formalism for the intermediate scattering function of the bending fluctuations in the bulk friction regime.

(A1)

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The ZG theory provide us with the analytic formalism for interpreting the dynamic structure factor corresponding to the membrane fluctuations (26, 27). In a continuous description, assuming ergodocity within the thermal modes, hq(t)hq(0) = hq2 eqt (with hq2 being the rms amplitude and (q) a relaxation rate), in the ZG formalism the two-point correlation function reads (26, 27):

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which is the relevant quantity for the subsequent calculation of the intermediate scattering function of the shape fluctuations observed at a scattering wavevector k, this is (26, 27): (A2)

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In the ZG theory, only the time-dependent component of the two-point correlations is considered in the relevant calculation; a dynamic correlator is defined as (26, 27): (A3)

in a way such that Eq. (A1) can be re-written as the sum of the two terms, h2(rr', t) = 0(rr') + (rr', t), with 0(rr') being the static part of the fluctuations. Here, the relevant result concerns to (rr',t) in Eq. A3, which determine the time dependence of the fluctuation structure factor. The original ZG theory deals with pure bending fluctuations restored by bending elasticity () and relaxing through bulk friction (which is determined by the bulk viscosity ). For bending thermal modes characterised by exponential correlations hq(t)hq(0) = hq2 eqt, one expects amplitudes varying as hq2bend = kBT/Ezqwith Ezqq4 being the transverse component of the elastic energy density tensor), and relaxation rates defined by a q-dependent dispersion, bend

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= (/4)q3. Consequently, after making a variable change (z = q) in terms of a characteristic, time-dependent, viscous length, = (t/4)1/3, the integral in Eq. A3 can be rewritten as follows (26, 27): (A4)

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where the scaling function F[u(t)] was defined in ZG (27) as:

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with J0[u(t)] being the zero-th order Bessel function of the first kind which is a monotonically decaying function of the dimensionless distance u(t) = z(rr')/.

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The scaling function F[u(t)] can be calculated numerically, although the relevant asymptotic limit can be analytically discussed. Over short distances (u  0), the kernel J0(u)  1, thus, the scaling function asymptotically converges to the constant value independent of time, F(u0)  1.34 ~ t0 (27). Consequently, the point-to-point correlations are expected with the time dependence arisen from the variable change implicit to Eq. A4. Therefore, for the two-point correlations in rigid membranes governed by bending modes ( kBT; u  0), one expects a sub-diffusive trajectory varying with time as (27, 35): (A6)

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Consequently, if one looks at the time dependence of the dynamic structure factor of the bending fluctuations in the viscous dissipation regime, substituting Eq. A6 into Eq. A2, one finds a stretched exponential profile as: (A7)

(A8)

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with a viscosity-dominated decay rate for the bending modes:

This constitutes the major result of the ZG theory, which introduces the sub-diffusive character of the bending fluctuations in rigid membranes as a main feature defining the relaxation of the dynamic structure factor.

Appendix B. Extension to generalized hydrodynamic compliance including permeability transport. By considering a generalized hydrodynamic compliance embedded in a generic Oseen tensor (q), the ZG formalism could be easily extended to bending modes relaxing through other different dissipation mechanisms. In the case considered here, where bulk friction competes with permeation transport for energy dissipation; in that case, the specific Oseen tensor reads as:

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(B1) Consequently, the relaxation rate (which is defined as a dynamical ratio of the corresponding restoring force to the energy dissipation -characterized by the Oseen tensor) can be expressed as: (B2)

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which reduces to the usual value in the viscous frictional regime, bend  q3/4 (at low permeability  (4q)).

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However, in viscous solvents, if the membrane permeability is high enough, the bending modes relax as bend  q4 (if 4q 1). In that case, the system predominantly dissipates energy through permeation transport, which becomes a more compliant dissipative process than bulk friction. Such a permeability regime is naturally dominant at high wavevectors, where a renormalized dispersion ~ q4 is expected for the relaxation rates of the bending modes with respect to the usual  ~ q3 scaling. Consequently, for bending modes dissipating energy in the permeability regime, the time-dependent component of the two-point correlations re-writes as follows:

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In this case, performing the relevant change of variable (z = q with  = (t)1/4), the dynamic correlator is expected with the sub-diffusive form: (B4)

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with the corresponding scaling function F[u(t)] defined in this case as: (B5)

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Assuming identical conditions as those considered by ZG in the viscous dissipation regime, the present scaling function can be also calculated numerically in the high-q dynamic scale (u  0; J0(u)  1). From the numerical calculation, one obtains a time independent asymptote taking a constant value F(u0)  0.886 ~ t0. Consequently, if one looks at the dynamic structure factor of the bending fluctuations in the permeation regime, substituting the new results into Eq. A2, one finds a stretched exponential profile as: (B6) with a permeability-controlled decay rate: (B7)

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This result represents the natural extension to permeability-mediated dissipation of the ZG theory of the dynamic structure factor of the bending fluctuations in the rigid membrane. Similarly to the ZG-case of pure viscous dissipation (stretching exponent  = 2/3, dynamic scaling  ~ k3), the theory above also predicts a sub-diffusive relaxation defined by a small stretching exponent ( = 1/2) and relaxation rates characterized by  ~ k4 scaling. Intermediate relaxation regimes are expected from hybrid dissipation ( (4q)); in those cases, the dynamic parameters should take intermediate values  = 2/ and  ~ k with the exponent  varying in the range 3()  4().

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References

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1. Alberts, B. 2002. Cell biology interactive. Garland Science,, New York. 2. Girard, P., J. Prost, and P. Bassereau. 2005. Passive or Active Fluctuations in Membranes Containing Proteins. Physical Review Letters 94:088102. 3. Nelson, D. L., and M. M. Cox. 2013. Lehninger Principles of Biochemistry. W.H. Freeman. 4. Valpuesta, J. M., and J. L. Carrascosa. 1994. Structure of viral connectors and their function in bacteriophage assembly and DNA packaging. Quarterly Reviews of Biophysics 27:107-155. 5. Cuervo, A., and J. L. Carrascosa. 2011. Viral connectors for DNA encapsulation. Current Opinion in Biotechnology. 6. Valpuesta, J. M., J. J. Fernández, J. M. Carazo, and J. L. Carrascosa. 1999. The threedimensional structure of a DNA translocating machine at 10 Å resolution. Structure (London, England : 1993) 7:289-296. 7. Floch, A. G., B. Palancade, and V. Doye. 2014. Fifty years of nuclear pores and nucleocytoplasmic transport studies: multiple tools revealing complex rules. Methods in cell biology 122:1-40. 8. Costa, T. R., C. Felisberto-Rodrigues, A. Meir, M. S. Prevost, A. Redzej, M. Trokter, and G. Waksman. 2015. Secretion systems in Gram-negative bacteria: structural and mechanistic insights. Nature reviews. Microbiology 13:343-359. 9. Bustamante, C., Z. Bryant, and S. B. Smith. 2003. Ten years of tension: single-molecule DNA mechanics. Nature 421:423-427. 10. Smith, D. E., S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante. 2001. The bacteriophage [phis]29 portal motor can package DNA against a large internal force. Nature 413:748-752. 11. Guasch, A., J. Pous, B. Ibarra, F. X. Gomis-Rüth, J. M. Valpuesta, N. Sousa, J. L. Carrascosa, and M. Coll. 2002. Detailed architecture of a DNA translocating machine: the highresolution structure of the bacteriophage [phi]29 connector particle. Journal of Molecular Biology 315:663-676. 12. Cuervo, A., and J. L. Carrascosa. 2012. Viral connectors for DNA encapsulation. Current Opinion in Biotechnology 23:529-536. 13. Valpuesta, J. M., J. J. Fernández, J. M. Carazo, and J. L. Carrascosa. 1999. The threedimensional structure of a DNA translocating machine at 10 Å resolution. Structure (London, England : 1993) 7:289-296. 14. Moleiro, L. H., I. López-Montero, I. Márquez, S. Moreno, M. Vélez, J. L. Carrascosa, and F. Monroy. 2012. Efficient Orthogonal Integration of the Bacteriophage ϕ29 DNA-Portal Connector Protein in Engineered Lipid Bilayers. ACS Synthetic Biology 1:414-424.

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15. Faucon, J. F., M. D. Mitov, P. Méléard, I. Bivas, and P. Bothorel. 1989. Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements. J. Phys. France 50:2389-2414. 16. Méléard, P., T. Pott, H. Bouvrais, and J. H. Ipsen. 2011. Advantages of statistical analysis of giant vesicle flickering for bending elasticity measurements. Eur. Phys. J. E 34:1-14. 17. Mell, M., L. H. Moleiro, Y. Hertle, P. Fouquet, R. Schweins, I. Lopez-Montero, T. Hellweg, and F. Monroy. 2013. Bending stiffness of biological membranes: what can be measured by neutron spin echo? The European physical journal. E, Soft matter 36:75. 18. Helfrich, W. 1973. Elastic properties of lipid bilayers: theory and possible experiments. Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie 28:693-703. 19. Manneville, J. B., P. Bassereau, S. Ramaswamy, and J. Prost. 2001. Active membrane fluctuations studied by micropipet aspiration. Physical Review E 64:021908. 20. Ibanez, C., J. A. Garcia, J. L. Carrascosa, and M. Salas. 1984. Overproduction and purification of the connector protein of Bacillus subtilis phage 29. Nucleic Acids Research 12:2351-2365. 21. Frisken, B. J., C. Asman, and P. J. Patty. 2000. Studies of Vesicle Extrusion. Langmuir 16:928-933. 22. Angelova, M. I., S. Soléau, P. Méléard, F. Faucon, and P. Bothorel. 1992. Preparation of giant vesicles by external AC electric fields. Kinetics and applications. In Trends in Colloid and Interface Science VI. C. Helm, M. Lösche, and H. Möhwald, editors. Steinkopff. 127-131. 23. Mathivet, L., S. Cribier, and P. F. Devaux. 1996. Shape change and physical properties of giant phospholipid vesicles prepared in the presence of an AC electric field. Biophysical Journal 70:1112-1121. 24. Berne, B. J., and R. Pecora. 1976. Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics. Dover Publications. 25. Arriaga, L. R., I. López-Montero, F. Monroy, G. Orts-Gil, B. Farago, and T. Hellweg. 2009. Stiffening Effect of Cholesterol on Disordered Lipid Phases: A Combined Neutron Spin Echo + Dynamic Light Scattering Analysis of the Bending Elasticity of Large Unilamellar Vesicles. Biophysical Journal 96:3629-3637. 26. Zilman, A. G., and R. Granek. 1996. Undulations and Dynamic Structure Factor of Membranes. Physical Review Letters 77:4788-4791. 27. Zilman, A. G., and R. Granek. 2002. Membrane dynamics and structure factor. Chemical Physics 284:195-204. 28. Schleger, P., G. Ehlers, A. Kollmar, B. Alefeld, J. F. Barthelemy, H. Casalta, B. Farago, P. Giraud, C. Hayes, C. Lartigue, F. Mezei, and D. Richter. 1999. The sub-neV resolution NSE spectrometer IN15 at the Institute Laue–Langevin. Physica B: Condensed Matter 266:49-55. 29. Gracia, R. S., N. Bezlyepkina, R. L. Knorr, R. Lipowsky, and R. Dimova. 2010. Effect of cholesterol on the rigidity of saturated and unsaturated membranes: fluctuation and electrodeformation analysis of giant vesicles. Soft Matter 6:1472-1482. 30. Nagle, J. F. 2013. Introductory lecture: basic quantities in model biomembranes. Faraday discussions 161:11-29; discussion 113-150. 31. Mell, M., L. H. Moleiro, Y. Hertle, I. Lopez-Montero, F. J. Cao, P. Fouquet, T. Hellweg, and F. Monroy. 2015. Fluctuation dynamics of bilayer vesicles with intermonolayer sliding: experiment and theory. Chemistry and physics of lipids 185:61-77. 32. Nagle, J. F., M. S. Jablin, S. Tristram-Nagle, and K. Akabori. 2015. What are the true values of the bending modulus of simple lipid bilayers? Chemistry and physics of lipids 185:3-10.

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33. Shoemaker, S. D., and T. K. Vanderlick. 2002. Intramembrane electrostatic interactions destabilize lipid vesicles. Biophys J 83:2007-2014. 34. Boal, D. H. 2005. Mechanics of the cell. Cambridge University Press, Cambridge etc. 35. Hu, J. G., and R. Granek. 1996. Buckling of Amphiphilic Monolayers Induced by Head-Tail Asymmetry. J. Phys. II France 6:999-1022. 36. Feiss, M., and V. B. Rao. 2012. The bacteriophage DNA packaging machine. Advances in experimental medicine and biology 726:489-509. 37. Wendell, D., P. Jing, J. Geng, V. Subramaniam, T. J. Lee, C. Montemagno, and P. Guo. 2009. Translocation of double-stranded DNA through membrane-adapted ϕ29 motor protein nanopores. Nat Nano 4:765-772. 38. Wallace, E. V. B., D. Stoddart, A. J. Heron, E. Mikhailova, G. Maglia, T. J. Donohoe, and H. Bayley. 2010. Identification of epigenetic DNA modifications with a protein nanopore. Chemical Communications 46:8195-8197. 39. Olasagasti, F., K. R. Lieberman, S. Benner, G. M. Cherf, J. M. Dahl, D. W. Deamer, and M. Akeson. 2010. Replication of individual DNA molecules under electronic control using a protein nanopore. Nat Nano 5:798-806.

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Graphical abstract

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Highlights  Membrane pores alter not only the permeation dynamics of biological membranes but also their elasticity. DNA-translocating pores of viruses can be used to transport macromolecular contents across membranes.

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They also represent an interesting model to test theoretical predictions that assign active-like (non-equilibrium) behavior to membrane permeability

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The presence of individual permeation events has been detected in the time-series of the membrane fluctuations.

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The out-of-equilibrium character of the membrane fluctuations in a permeation field is demonstrated.

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