Eulalie J Lafarge

Pierre Muller

André P Schroder

Ekaterina Zaitseva

Jan C Behrends

Carlos M Marques

Activation energy for pore opening in lipid membranes under an electric field

The standard model of pore formation was introduced more than 50 years ago and it has been since, despite some refinements, the cornerstone for interpreting experiments related to pores in membranes. A central prediction of the model concerning pore opening under an electric field is that the activation barrier for pore formation is lowered proportionally to the square of the electric potential. However, this has only been scarcely and inconclusively confronted to experiments. In this paper we study the electropermeability of model lipid membranes composed of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC) containing different fractions of POPC-OOH, the hydroperoxidized form of POPC, in the range [0-100] mol %. By measuring ion currents across a 50 µm diameter black lipid membrane (BLM) with picoampere and millisecond resolution, we detect hydroperoxidation-induced changes to the intrinsic bilayer electropermeability and to the probability of opening angstrom-size or larger pores. Our results over the full range of lipid compositions show that the energy barrier to pore formation is lowered linearly by the absolute value of the electric field, in contradiction with the predictions of the standard model.

). This jeopardizes progress in the field, particularly when one considers that every aspect of the widespread phenomenology that relates to lipid membranes with pores refers to or stands on the framework provided by the standard model. In particular, the standard model assumes that pore nucleation under an electric field is a direct consequence of membrane tension changes; since there is evidence that tension depends quadratically on the electric field (3), the model predicts a quadratic decrease of the activation barrier of pore formation with V , the electric potential jump across the membrane -please see table in the Materials and Methods section for all quantities and their units. Results from numerical simulations do provide a molecular view of the first steps of pore formation, but have only very rarely been compared to experiments or developed to a point where an operational model of pore formation can be elaborated (4). In this paper we test the predicted V 2 reduction of the activation barrier of pore formation in lipid membranes assembled from mixtures of POPC and its hydroperoxidized form POPC-OOH.

.

Biomembranes allow water molecules to cross their ∼ 5 nm-thick barrier with permeability coefficients Pm as high as Pm ∼ 10 -5 m•s -1 while being almost impermeable to the majority of hydrophilic solutes (13). For charged species, permeability

is many orders of magnitude smaller at 10 -12 m•s -1 for Cl -, and 10 -14 m•s -1 for K + , two common bio-relevant ions [START_REF] Hannesschlaeger | Intrinsic membrane permeability to small molecules[END_REF].

Permeability values for water and other molecules can be rationalized within a simple picture where a molecule driven by a chemical potential gradient climbs the membrane barrier of free-energy height Um with probability ∼ exp(-Um/kBT ), where kB is the Boltzmann constant and T the absolute temperature, and moves over the barrier top with velocity D/ , thus leading to Pm = (D/ ) exp(-Um/kBT ). With typical diffusion coefficients in oil D ∼ 10 -9 m2 .s -1 a molecule takes a few tens of nanoseconds to cross the barrier once it has climbed it [START_REF] Hille | Ionic Channels of Excitable Membranes[END_REF]. For water, the partition coefficient Kw = exp(-Um/kBT ), measured often between water and hexadecane is given by Kw ∼ 10 -5 (barrier Um of order of ten kBT ), with correspondingly much smaller values for ions, K Cl -∼ 10 -12 and K K + ∼ 10 -14 (and barriers ∼ three times larger than for water). As a practical consequence, charge gradients can be indefinitely maintained across lipid membranes, even for large cell-sized lipid vesicles of R ∼10 µm radius that can equilibrate an osmotic imbalance of ∆C ∼ 20 mM within a thousand seconds (τw ∼ R/(Pmνw∆C) ∼ 1000 s), with νw the water molar volume.

In our quest to understand charge transport across lipid membranes, we performed experiments in a black lipid membrane (BLM) geometry -see Fig. S1, carefully identifying and quantifying charge transport events and determining ionic permeabilities in membranes assembled from POPC/POPC-OOH mixtures in a solution of 100 mM KCl. For all bilayers we witnessed the emergence of angstrom-size single pore opening as the field strength was increased, thus allowing to quantify the influence of the field strength on the probability of initial pore formation. Our results do not only bring a new and extensive set of data to the field of electroporation, but also challenge some of the prevailing views in the field.

Significance Statement

Why does a pore open when a high enough electric field is applied to a lipid bilayer? Despite almost a century of efforts we do not have a clear answer to this question, in part due to scarcity of data from experiments designed to probe this phenomenon. Here, we report results from electropermeation experiments on black lipid membranes assembled from different mixtures of a common lipid, POPC, and its hydroperoxidized form POPC-OOH. By carefully identifying pore formation events, we were able to quantify the influence of the applied electric field and of the hydroperoxidation degree on the frequency of pore opening. Our results disagree with the standard model of pore formation and bring new significant insight into the factors controlling pore opening under an electric field. Under no (i) or small (ii) applied voltages, the current fluctuates smoothly about a small (∼ pA) average current. Charges accumulate on both sides of the membrane that acts as a capacitor, a small amount of ions cross the membrane. Under larger applied voltages, the opening of short lifetime pores (iii) and long lifetime pores (iv) can be detected by the sudden rise of the current. Pores can accommodate lipid heads along the pore rim, in a conformation referred to as hydrophilic pores. Small numbers of simultaneous pores still allow for identifiable membrane geometries (v).

I c1 I c2 Time V 0 = 0 V 2 > V 1 V 1 > V 0 (i) (ii) (iii) (iv) (v
Our experiments focus on the analysis of the ionic current crossing phospholipid membranes composed of various mole fractions (X OOH ) of POPC-OOH. In the following we will first describe and characterize conduction events as a function of applied voltage and hydroperoxidation degree and determine membrane ability to withstand the electric field without rupturing. We then perform a quantitative analysis of intrinsic (pore-free) electropermeability. Finally we quantify the membrane propensity to open pores as a function of applied voltage, identifying the opening of single pores, and studying their characteristic lifetimes, intensities and frequency of formation.

Traces of electric current.

In our experiments, the information on charge transport is contained in the time series of the measured current I(t) for a given applied voltage, see Fig. S2 for our voltage ramping protocol and Fig. S3 for the equivalent electric circuit. Given the typical values for the membrane capacitance in the picofarad range -see Fig. S4 for measured values -and the series resistance of order of a few tenths of a megaohm, the response time of the equivalent electric circuit is a few microseconds, see sections S3 and S4. Thus, relaxation phenomena in our traces, associated for instance with the decay time τ of the capacitance peaks and current increase after pore opening, is a result of the filtering process implemented in the D R A F T recording apparatus and in the software, typically on the order of a few milliseconds, τ 2.7 ms, see Fig. S5 for filtering and Fig. S6 for chosen examples of current traces.

Fig. 2 proposes a classification of conductance events based on the shape of the observed current fluctuation and assigns each class to a hypothetical mechanism on the level of membrane structure and dynamics. The average current that we designate as Ic is present in all traces. In the absence of an applied voltage V , one has Ic = 0; the membrane simply separates two volumes of the ionic solution. When a voltage V is applied the membrane acts as a capacitor of a few picofarad with a "leakage" current Ic of order of several picoamperes. The lipid bilayer bears thus, under an applied potential of 100 mV, roughly one charge per 200 nm 2 corresponding to 350 lipids. The same area also lets one charge per second cross the membrane barrier. Sections (iii) and (iv) of Fig. 2 show current fluctuations when a large enough V induces a sudden rise of the current above its baseline value Ic, reaching a maximum and then immediately -case (iii) -or after a plateau phase -case (iv) -returns to the baseline. This is the signature of pore opening, the number of charges conveyed through a pore being a function of the applied voltage, of the ion concentration in the solution and, importantly for the interpretation of the results, of the pore size. Under our conditions, for an applied voltage of 100 mV, a simple conduction model [START_REF] Sw Kowalczyk | Modeling the conductance and dna blockade of solid-state nanopores[END_REF] predicts that a pore of Dp = 1 nm diameter generates a stationary current Ip of 20 pA with intensity values Ip for pores of different sizes scaling as Ip ∝ D 2 p . Since pore opening and closing is much faster than the characteristic instrument response time τ , model variations for pore opening can be taken as square gate functions for Dp(t) such as Dp(t) = Dp for ti < t < ti + τp and Dp(t) = 0 otherwise, with ti and τp the pore initial time and lifetime, respectively, see also Fig. S4. Section (iii) shows an example of short pore, i.e. τp < τ , while section (iv) shows the opposite example of a long-lived pore where τp τ and thus a stationary plateau can be reached before the pore closes, see also section S3. Section (v) of Fig. 2 shows a more complex signal where individual events are nevertheless still identifiable. We name trace segments complex when the state of the membrane cannot be inferred from the current traces.

Membrane rupture under an applied voltage. As explained before, experiments were performed by ramping up V as shown in Fig. S2. Voltage values at which membrane breakage occurred were collected and averaged to build the membrane survival probability under an imposed voltage -see Fig. S12. While pure POPC membranes (0 % -OOH) have a 50 % probability of breaking at 300 mV in a time span of six seconds, both for positive and negative applied voltages, for nearly fully hydroperoxidized membranes (96 % -OOH), the 50 % rupture probability is reached at 175 mV. Hydroperoxidation, as we will below quantify for all investigated phenomena, renders the membranes increasingly vulnerable to electric fields.

Membrane intrinsic conductivity.

If one pictures the lipid membrane as a one dimensional barrier restricting ionic mobility in the direction perpendicular to the bilayer, the standard formulations by Goldman, Hodgkin and Katz [START_REF] Hille | Ionic Channels of Excitable Membranes[END_REF][START_REF] Hannesschlaeger | Intrinsic membrane permeability to small molecules[END_REF][START_REF] De Goldman | Potential, impedance, and rectification in membranes[END_REF][START_REF] Al Hodgkin | The effect of sodium ions on the electrical activity of the giant axon of the squid[END_REF] can be used to predict the ion current density ic = Ic/S where S is the effective membrane area contributing to the electric measurement (that we infer from the measured capacity) and Ic is the current measured on all trace sections devoid of pores. A simple step-like potential that depends only on the barrier height Um and on the barrier thickness leads to a linear relationship between the current and the applied potential. Current-voltage relations ic(V ) with a supralinear component can be obtained from barrier functions of a more complex shape. The simpler of these is the trapezoidal barrier, where the basis of the barrier has thickness while the top of the barrier at height Um is thinner, with thickness b ≤ [START_REF] Hall | A barrier model for current flow in lipid bilayer membranes[END_REF]. Conductivity predictions from the trapezoidal barrier can be written as a cubic expansion of the applied potential:

ic = e c Pm u 1 + 1 - b 2 2 u 2 24 [1]
with u = eV /(kBT ), e the elementary charge and c the ion concentration. Fig. 3 A presents ic(V ) data and fitted curves for all the hydroperoxidation degrees. Results are plotted as a function of both the normalized voltage u and the actual voltage V . For better comparison with results from the literature we provide two Y-axis scales, for both the measured current density (left) and the current crossing a membrane with 42 µm diameter, the average diameter of our membranes as inferred above from capacity measurements.

Eq. ( 1) fits well the data over a voltage range (shown by full lines in the figure) that depends on the peroxidation degree but that is always large enough to allow for determination of the two fitting parameters, the permeability Pm and the ratio b/ . Pm for pure POPC is measured at 2.8±2.5×10 -12 m•s -1 , consistent with reported permeability values for the anion Cl - that dominates charge transport across the lipid membrane [START_REF] Hannesschlaeger | Intrinsic membrane permeability to small molecules[END_REF]. Values of Pm increase steadily with the peroxidation level, as shown in Fig. 3 B, up to 11±9×10 -12 m.s -1 for the fully hydroperoxidized bilayer, an increase of roughly a factor 4 of the average values. Fittings return an almost constant value for the ratio b/ = 0.87 ± 0.05, typical for values reported in the literature for lipid membranes [START_REF] Fuks | Permeability and electrical properties of planar lipid membranes from thylakoid lipids[END_REF]. As stated above, membrane permeability is well described by Pm = (D/ ) exp(-Um/kBT ). Observed changes of membrane permeability cannot be explained by the small decrease (∼ 20%) of membrane thickness [START_REF] De | Hydroperoxide and carboxyl groups preferential location in oxidized biomembranes experimentally determined by small angle x-ray scattering: Implications in membrane structure[END_REF], and it is unlikely that the diffusion coefficient D of the ions across the membrane increases dramatically with hydroperoxidation, given the small volume fraction occupied by the added organic hydroperoxide. The observed increase is thus better interpreted as due to a lowering of the membrane barrier potential ∆Um = -1.4 kBT , at least with respect to anion Cl -that dominates transport here, consistently with the known increase of polarity of the inner membrane region [START_REF] Junqueira | Molecular organization in hydroperoxidized popc bilayers[END_REF].

Pore formation correlates with changes in the barrier to ions. As V increases, the traces show the emergence of ionic transport across the membrane through pores, as depicted above in sections (iii), (iv) and (v) of Fig. 2.

We evaluate first the probability for a membrane to remain free of pores during the six seconds when a constant voltage is applied. Fig. 4 shows this probability for each membrane composition. As the figure shows increasing X OOH results, at any D R A F T imposed voltage, in an increase of the probability for the membrane to create pores. For instance, hardly any pore can be detected for pure POPC membranes at applied voltages lower than 50 mV, while for the same voltage in a half of the 96 % POPC-OOH membranes at least one pore was observed. Interestingly, the range of voltage over which Eq. ( 1) fits well data in Fig. 3 A correlates with voltages at which pore opening probability reaches values higher than 0.90 -see Fig. S13. Thus, the trapezoidal model behind Eq. (1) stops to be valid when the electric fields are high enough to bring the membrane to the verge of pore opening conditions.

Lifetime distribution of identifiable pores. We developed a threshold method -see section S7 -to detect identifiable pores with a well defined opening and closing current jump. Using the results from this pore-detection routine we built the distribution of pore lifetimes τp displayed in Fig. 5. Since no variation of pore lifetimes was observed with applied voltage (Fig. S14), the results in Fig. 5 are computed by grouping all pores detected for a given -OOH composition irrespective of voltage.

The distribution of lifetimes is shown in Fig. 5 with 0.8 ms time bins. As the figure shows, there is no noticeable difference in the distributions for the various peroxidation degrees. If one excludes the first bin that is at the limit of time resolution, the combined distribution follows a single exponential decay with a time constant of 1.8±0.1 ms (error computed from a 90 % confidence interval of the fit), similar to experiments recorded with 1 ms time resolution under BLM geometry in 100 mM KCl for diphytanoylphosphatidylcholine (DPhPC) membranes [START_REF] Kc Melikov | Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer[END_REF]. It is remarkable that the lifetime is independent of X OOH , suggesting that for these pores, lifetime is determined by phenomena extrinsic to the lipid bilayer. Indeed, as we recently showed [START_REF] Paez-Perez | Directly imaging emergence of phase separation in peroxidized lipid membranes[END_REF], hydroperoxidation impacts both the chain and the head region of the membrane, making it unlikely that intrinsic bilayers contributions to the lifetime would be independent of hydroperoxidation degree. A relevant remark in this context is that at the pore site the flow of charges creates an inhomogeneous electric field: the electrical potential difference across the membrane is strongly lowered close to the pore -it would vanish in the center of the pore for the case of a free flow of charges ( 22) -and it recovers far from the pore to its homogeneous value. Charge rearrangement must therefore take place laterally also, a process with a characteristic time that depends on the size of the region that is perturbed by the flow. This certainly calls for further modeling efforts of the electrical stresses acting on a membrane in the presence of pore flow.

In the following, we discriminate between short and long-lived pores, as defined in section S4, in order to better determine their characteristics and abundance.

Size of short lifetime pores. Given the average lifetime of short-lived pores τp = 1.8 ± 0.1 ms obtained by the threshold method, most of the pores detected in this category cannot reach a stationary conducting state which requires that the lifetime of the pore τp is larger than τ , the time needed to reach the stationary value Ip. It is nevertheless possible to obtain Ip values as explained in section S3. Corresponding values of pores sizes can be computed [START_REF] Sw Kowalczyk | Modeling the conductance and dna blockade of solid-state nanopores[END_REF] from Dp = (4bIp/πV σ) 1/2 with b = 5 nm the length of the pore and σ the solution conductivity, σ = 1.29 S.m -1 for a 100 mM KCl solution [START_REF] Haynes | CRC handbook of chemistry and physics[END_REF]. We obtained an average diameter Dp = 6.4 ± 2.0 Å independently of applied voltage and hydroperoxidation degree, comparable to the lower range of reported radii [START_REF] Ra Böckmann | statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations[END_REF][START_REF] Kc Melikov | Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer[END_REF][START_REF] Glaser | Reversible electrical breakdown of lipid bilayers: formation and evolution of pores[END_REF][START_REF] Sengel | Imaging the dynamics of individual electropores[END_REF], see also Fig. S16.

Opening frequency of short lifetime pores. We measure the frequency of detection of short lifetime pores using the threshold method mentioned above. Fig. 6 A shows the opening frequency of short lifetime pores expressed as the average number Ns of pore openings detected per second for a given applied voltage. As the figure shows, the frequency increases with both voltage and X OOH .

The semi-logarithmic representation of Fig. 6 A reveals a nearly linear dependence of ln Ns with applied voltage for all the samples, with an almost identical slope for all X OOH . This suggests that under our conditions, frequency of pore opening follows the empirical relation:

Ns = fp|u| exp(α|u|) [2]
with all the information on X OOH being carried by fp alone. The master curve in Fig. 6 B was obtained by finding fp(X OOH ) values that minimize vertical distance in the semi-logarithmic representation of all curves with respect to X OOH = 0. Fits of this master plot give the pair of values (α + = 0.50±0.05, f + p (0) = 1.1±0.1×10 -3 s -1 ) and (α -= 0.56±0.06, f - p (0) = 1.5±0.1×10 -3 s -1 ) for respectively the positive and the negative branches (errors from a 90 % fit confidence interval). Fig. S19 displays the influence of X OOH on the frequency fp, which shows both the positive and negative branches are well described by the function ln(fp(X OOH )/fp(0)) = -1.2 + 0.055X OOH for all points except the first.

The number of short lifetime pores that we detect is a function of applied voltage and hydroperoxidation degree. The voltage dependence that we observe does not follow the predictions of the standard model for pore formation in lipid bilayers, nor those from the many variants of the model [START_REF] Kotnik | Membrane electroporation and electropermeabilization: mechanisms and models[END_REF][START_REF] Glaser | Reversible electrical breakdown of lipid bilayers: formation and evolution of pores[END_REF][START_REF] Abidor | Electric breakdown of bilayer lipid membranes: I. the main experimental facts and their qualitative discussion[END_REF][START_REF] Powell | Transient aqueous pores in bilayer membranes: a statistical theory[END_REF]. Central to those predictions, is the dependence of the activation barrier for the pore creation rate with V 2 , the square of the applied potential. Incidentally, to our knowledge, this dependence has never been confirmed. Scarce data exists (21) that has been interpreted as a proof of such quadratic variation [START_REF] Vasilkoski | Membrane electroporation: The absolute rate equation and nanosecond time scale pore creation[END_REF], but a strong confirmation of this effect has not been reported. Our empirical form Eq. 2 suggests rather a direct dependence of the attempt rate with the voltage and an activation energy that is lowered proportionally to |V |. Such dependence has been reported in a publication combining experiments and numerical simulations, and qualitatively discussed in terms of the action of the field on the dipolar state of the lipids (4). If we interpret our observations within this frame and estimate the field strength by V / , the effective dipolar moment µ lowering the pore nucleation barrier is µ = αe where α is the coefficient in Eq. 2, e the elementary charge and = 5 nm the membrane thickness. Given the value provided by our experiments α = 0.5 and the (non-SI but widely used) measure of dipolar strength strength by a Debye unit D = 0.02 nm•e, we get µ = 125 D, one order of magnitude

D R A F T

larger than values reported from simulations (4). A similar analysis performed on data [START_REF] Kc Melikov | Voltage-induced nonconductive pre-pores and metastable single pores in unmodified planar lipid bilayer[END_REF] from DPhPC membranes gives α = 0.42, denoting a slightly smaller sensitivity of these bilayers to the formation of pores under an applied electric potential.

The voltage effect on the pore formation rate is not, in our experiments, a function of hydroperoxidation degree, contrary to the pore formation rate itself, which dependence on X OOH is shown in Fig. S19. Thus, a fully hydroperoxidized POPC bilayer sees its activation barrier for pore formation lowered by about 5 k B T , with a roughly linear dependence on X OOH . Simply put, full hydroperoxidation lowers the barrier for pore formation by as much as an electric field of ∼250 mV, a rule of thumb that would be interesting to correlate with the molecular transformations induced by the insertion of the -OOH group in the POPC unsaturated chain [START_REF] Siani | An overview of molecular dynamics simulations of oxidized lipid systems, with a comparison of elba and martini force fields for coarse grained lipid simulations[END_REF][START_REF] Boonnoy | Bilayer deformation, pores, and micellation induced by oxidized lipids[END_REF].

Long lifetime pores. Currents associated with large lifetime pores τp τ reach a stationary value which, despite the ever present fluctuations, provides a clear distinct visual aspect to the traces. They evoke the signature of currents carried by ionic channels, which correspond in general to rather long lived pores of a well-defined size [START_REF] Heimburg | Lipid ion channels[END_REF]. In practice, we developed a squared gating method -see section S7 -to filter the signal I(t) in order to remove noise, short lifetime pores and complex signals.

Long-lived pores are much scarcer than short-lived pores -see also Fig. 5; thus pore sizes and lifetimes collected for these pores have a larger statistical uncertainty that does not allow, in particular, to assert the influence of voltage or oxidation degree on the frequency of pore opening. We did not find any statistical support for asserting that pores open with a fixed size -and thus conduct a fixed current -for membranes of a given composition. There is rather a disperse distribution of currents, from where an average value can nevertheless be extracted. Significantly, the average current values follow a linear relation with applied voltage, thus enabling to compute an average pore conductance corresponding to an average pore size of Dp = 7.4 ± 2.8 Å, a value close to the one found for short lifetime pores. We did not find either a statistically significant variation of average currents with oxidation degree. The lifetime distribution of pores lasting more than 20 ms show, similarly to short lifetime pores, an exponential decay with however a different time constant of 160 ms, see Fig. S18.

Conclusion

By studying conductive events across several hundreds of membranes with different hydroperoxidation degrees and by detecting and analyzing many thousands of those events, we contribute to the discussion about pore formation in lipid membranes with a new set of statistically relevant data that challenges the widely accepted V 2 dependence of the reduction of the barrier for pore nucleation and brings fresh insight to the field.

Our first finding is that the pores start opening at a voltage where the barrier model describing the intrinsic permeability of the membrane to ions stops being valid. Indeed, for low enough voltages the membrane maintains the nature of its permeation barrier to the ions, well described in our case by a trapezoidal model with two lengths and one height. Such barrier corresponds to the molecular organization of the bilayer in the absence of an applied potential. When the pore formation probability becomes finite at high enough voltages, the permeation barrier changes, implying that the lipid organization in the bilayer has changed as well. This validates numerical simulations approaches where the state of the lipids is carefully tracked, for instance with respect to their polarization state, before opening of pores is detected.

For the large majority of events that we detected, the pore lifetime is independent of membrane oxidation. This points to explanations of pore lifetime extrinsic to the lipid membrane such as those related to the lateral relaxation of the electric stresses at the pore site, calling for further studies on the electro-dissipation effects in conductive pores in lipid bilayers [START_REF] Winterhalter | Effect of voltage on pores in membranes[END_REF], and thus challenging whether a configuration walk in a free-energy landscape can capture the essentials of this phenomenon.

Most of the pores that we detected had small diameters, around 0.7 nm, independently of voltage or hydroperoxidation degree. The survival of such small pores over milliseconds or more suggests that they correspond to the so called hydrophilic pores: indeed, lipid head re-organization allowing for the head-carpeting of the inner pore canal is expected to occur tens of nanoseconds only after a water channel nucleates across the membrane [START_REF] Za Levine | Life cycle of an electropore: field-dependent and field-independent steps in pore creation and annihilation[END_REF]. Geometrically, such robust result indicates also that these pores adopt the smallest possible diameter compatible with the constraints of lipid packing in the semi-toroidal inner pore surface, also supporting the anticipated deviation at small diameters of the pore line tension from its constant value.

Our results rule out a key prediction from the standard model of pore formation, namely that the barrier for pore nucleation is reduced proportionally to V 2 . Indeed this would imply an increase of the number of pores formed during a given period of time as ∼ exp(constant • V 2 ). Under our experimental conditions we observe instead a growth with the electric potential of the form ∼ exp(α|V |). Although this is compatible with explanations based on the field effect on the lipids electric dipoles, we find a dipolar moment one order of magnitude larger than those extracted from simulations. We anticipate much fruitful future developments along these lines to better decipher the molecular forces and membrane properties that control pore opening.

Finally, our results reinforce the picture that has been unraveling over the last decade to describe hydroperoxidized lipid membranes: despite the strong molecular modifications that induce a larger area per lipid, a smaller thickness and a weaker stretching modulus, we find that these membranes retain their integrity, even under an applied electric potential. The work in this paper further shows that hydroperoxidized bilayers behave in a quantitatively different yet standard manner with respect to electropermeation and pore formation: they display a four-fold larger permeability with respect to the anion Cl -, and open pores with a larger frequency at weaker electric fields.

Materials and Methods

D R A F T

Materials. 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC, 16:0-18:1) was purchased in chloroform (25 mg.mL -1 ) from Avanti Polar Lipids. Lipids were stored at -20 • C and used without further purification. 1,9-Dimethyl-Methylene Blue (MB), KCl, KOH and Hepes were provided as powder from Sigma Aldrich. Cellulose membrane dialysis tubing with a molecular cut-of of 14000 Da and octane are also bought from Sigma Aldrich. All NMR analysis were performed in 99.8 % deuterated methanol (MeOD) supplied by Acros Organics. 10 µL pipettes tips, provided from STARLAB, were used to paint the free-standing lipid membranes.

Lipid hydroperoxydation. Batch solutions of POPC from fresh, i.e. sealed, POPC vials, were systematically controlled by NMR before the hydroperoxidation procedure. The two hydroperoxidized isomers of POPC-OOH shown in Fig. 1, were synthesized photochemically using MB as a photosensitizer. Briefly, 6 mL of a MeOD solution of POPC at 5 mg•mL -1 (6.6 mM) containing MB at 20.8 µg•mL -1 (50 µM) were placed inside a home-made device composed of red LEDs (λ=625 nm, 600 W•m -2 ), under a constant dioxygen flux and stirred for 10 min. Resulting conversion rates (97 ± 3 mol %) were monitored by 1 H NMR. MB, the photosensitizer, was removed by a 4 h dialysis in water. The obtained lipid in water solution was dried and lipids redispersed in MeOD to perform a NMR control. Hydroperoxidized lipid solutions were kept in MeOD at -20 • C for further use.

Mixtures of POPC and POPC-OOH. MeOD solutions of POPC and of POPC-OOH were mixed as required to obtain the three targeted values of 25, 50, and 75 mol % of POPC-OOH. For each mixture, the exact POPC-OOH fraction was checked by 1 H NMR, always within ± 5 mol % of the target value. Solvent was then evaporated, and dried lipids were dissolved in octane at 10 mg•mL -1 . Pure POPC and pure POPC-OOH samples were prepared in a similar manner. Lipids in octane solutions were kept at -20 • C and used within a few weeks.

Here below, results are grouped by number weighted averages of the measured OOH content.

The measurement device. Experiments were performed on an Orbit Mini miniaturized bilayer workstation (Nanion Technologies, Munich, Germany), with an inserted microelectrode cavity array (MECA 4) recording chip (Ionera Technologies, Freiburg, Germany) as shown in Fig. S1. The chip contains four wells with diameter 50 µm and depth 30 µm, each cavity corresponding to a recording channel. A chloridized silver microelectrode (Ag/AgCl) is present at the bottom of each well and a single, macroscopic common counter electrode is found at the top of the chip.

The Orbit Mini operates in voltage-clamp mode using the Elements 4 (e4) channel-amplifier (Elements SRL, Cesena, Italy). Voltage can be imposed to only selected channel(s), but with a common value, in the range -500 mV to +500 mV. The current intensity across each well I(t) is measured independently, allowing in principle to record simultaneously the current across four different membranes. However, since the current saturation due to a membrane rupture in one of the channels induces artifact signals in the neighboring channels of the e4 amplifier, we chose to work with a single well at a time. I(t) was measured with a sampling rate of 1.2 kHz and bandwidth 0.6 KHz. The Orbit Mini is piloted by elements data reader 3 (EDR 3) software, offering several measurement gains. Capacitance Cm determination uses a predefined instrument routine working with the [-20, 20] nA measurement gauge. We acquired all current signals with the smallest gain, within the range [-200, 200] pA.

Free standing bilayer preparation. Experiments were conducted at room temperature ( 20 • C). The MECA 4-chip was filled with 150 µL of a fresh buffer solution composed of 100 mM KCl and 10 mM HEPES in milli-Q water, adjusted to pH 7 by addition of 1 M KOH solution, typically 10 µL for a total of 5 mL solution. Special attention was given to the complete air removal from each of the four cavities. A bilayer was painted on the top of the cavity by the air bubble method described elsewhere [START_REF] Zaitseva | Electrophysiology on channel-forming proteins in artificial lipid bilayers: Next-generation instrumentation for multiple recordings in parallel in Patch Clamp Electrophysiology[END_REF]. Briefly, an air bubble is formed above the chosen cavity with a 10 µL micropipette tip previously immersed in the lipid-in-octane solution. Contact with the well and further removal of the air bubble leaves attached to the rim of the aperture a thin octane film stabilized by lipids. Molecular forces lead to the thinning of the film, resulting -as schematically depicted in Fig. S1 -in a free standing bilayer of area S in the center of the well, surrounded by a thick oil annulus attached to the rim [START_REF] Sh White | Analysis of the torus surrounding planar lipid bilayer membranes[END_REF]. Presence, stability, and quality of the free standing bilayer were monitored with EDR 3 under the application of ±20 mV: a negligible current (<0.1 pA) was seen when a sealing membrane was formed, while a saturated current (± 200 pA) was displayed otherwise. When formed, the membrane was left to equilibrate for at least 1 min while continuously checking the stability of the current. In case of an unstable current, the membrane was destroyed and reformed. Afterwards, membrane capacitance Cm was measured. Capacitance variability was observed, we found that reproducible measurements were obtained for membranes with a stable capacitance ranging from roughly 6 to 13.5 pF.

Conductance measurements. Once a membrane was formed, EDR 3 software was used to follow and record current intensity traces I(t) for various imposed voltages V . A defined protocol for increasing applied voltages was applied as shown in Fig. S2. The protocol was manually stopped at membrane rupture, corresponding to sudden irreversible current saturation. If ever a membrane resisted until reaching the sequence where V = 500 mV, it was not considered as a valid bilayer and the experiment was discarded. The EDR 3 functionalities were first used to manually acquire a small fraction of our data, before acquisition was fully automatized with a home-written macro (Pulover's Macro Creator).

We acquired currents from more than 50 membranes of each targeted lipid composition: 95 membranes for POPC containing 0 % of POPC-OOH, 94 for 25 %, 53 for 50 %, 76 for 75 %, and 55 for 100 %. Statistical analysis of our data required the development of homemade Python scripts implemented on Visual Studio. Signal treatment and pore detection techniques are further detailed in Supplemental Material, where methods to identify and measure the different conductive modes are also discussed.

Summary of physical quantities.

D R A F T

Fig. 1 .

 1 Fig. 1. POPC and POPC-OOH isomers.

  E.J.L. and E.Z. performed experiments. E.J.L., P.M., A.P.S. and C.M.M. analyzed data from experiments. A.S., P.M., J.C.B. and C.M.M. designed and conducted the project. E.J.L., A.S. and C.M.M wrote the paper. All authors interpreted the data and commented and reviewed the manuscript.

Fig. 2 .

 2 Fig. 2. Current traces and associated membrane geometry. (A) Identifiable segments of I(t) along with (B) their schematic representation and (C) their presumed membrane conformation.Under no (i) or small (ii) applied voltages, the current fluctuates smoothly about a small (∼ pA) average current. Charges accumulate on both sides of the membrane that acts as a capacitor, a small amount of ions cross the membrane. Under larger applied voltages, the opening of short lifetime pores (iii) and long lifetime pores (iv) can be detected by the sudden rise of the current. Pores can accommodate lipid heads along the pore rim, in a conformation referred to as hydrophilic pores. Small numbers of simultaneous pores still allow for identifiable membrane geometries (v).

Fig. 3 . 9 DFig. 4 .Fig. 5 . 11 DFig. 6 .

 3945116 Fig. 3. Intrinsic membrane electropermeability. (A) ic -V characteristics in a pore-free membrane. Left axis measures current density, right axis expresses current across a patch of 42 µm diameter. X-axis displays normalized voltage units u = eV /(k B T ), voltage is shown in top horizontal axis. Full lines drawn in the range where Eq. (1) adequately fits the data, dashed lines extrapolate the fit over the whole range as a guide to the eyes; error bars measure the standard deviation. (B) Permeability of POPC membranes as a function of X OOH , the molar fraction of hydroperoxidized lipids. The data is displayed as box-plots representing the distribution of membrane permeability based on first quartile, median, mean (filled square symbol), third quartile, with whiskers showing standard deviation. Lafarge et al. PNAS | November 21, 2023 | vol. XXX | no. XX | 9

To whom correspondence should be addressed. E-mail: carlos.marques@ens-lyon.fr 2 | www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Lafarge et al.

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Lafarge et al.

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Lafarge et al.

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Lafarge et al.

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Lafarge et al.

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Lafarge et al.

ACKNOWLEDGMENTS. E.J.L. thanks the Franco-German University and the French Ministry of High Education for a PhD grant.

The team is beholden to M. Basler for the development of equipment allowing fast lipid hydroperoxidation and to C. Gicquel and L. Fayolle for help with pore data analysis. Y. Moskalenko is gratefully acknowledged for support with the protocol for lipid synthesis.


Akila Abdellaziz

Jennifer Papuchon

Safia Khaled

Dalila Ouerdane

Herve´fleury

Patricia Recordon-Pinson

Predominance of CRF06_cpx and Transmitted HIV Resistance in Algeria: Update 2013-2014

Since 2008, no data on HIV diversity or the transmission rate of HIV resistance mutations in naive patients have been presented for Algeria, a country of MENA region. Between 2013 and 2014, we studied 152 samples including 89 naive patients. The current study describes the change in HIV diversity in Algeria with the predominance of CRF06_cpx and the huge increase of transmitted HIV resistance, which now reaches 15%.

Introduction

L geRIa, T ogeTHeR W I T H 22 coUNTRIes, belongs to the A Middle East and North Africa (MENA) region. Data on the HIV epidemic are sparse in this region, especially for drug users, but recently some countries have increased their HIV surveillance; nevertheless, in others, HIV prevalence data are still not available. [START_REF] Mumtaz | HIV among people who inject drugs in the Middle East and North Africa: Systematic review and data synthesis[END_REF][START_REF] Bozicevic | HIV surveillance in MENA: Recent developments and results[END_REF] According to UNAIDS in 2013 3 there were 230,000 (160,000-330,000) people living with HIV in the MENA region, with an estimated 25,000 (14,000-41,000) new HIV infections, including 2,300 (1,500-3,400) among children. In this area in 2013, 15,000 (10,000-21,000) people died of AIDS-related causes. Treatment coverage is 11% (8-16%) for people living with HIV.

For Algeria, 3 country reports indicated in 2013 that 25,000 people were living with HIV (13,000-43,000) with an adult prevalence rate of 0.1% for 36.5 million inhabitants. According to the Algerian Ministry of Health and Hospital Reform, 8,258 cases were reported in 2013 with 1,460 AIDS cases and 6,798 HIV-positive cases. [START_REF] Ministe | re de la Sante´de la Population et de la Re´forme Hospitalie[END_REF] The number of new infections has been stable for years with 700-800 cases per year. Only 19% of infected people have received antiretroviral (ARV) drugs in national reference centers.

In previous studies [START_REF] Bouzeghoub | High diversity of HIV type 1 in Algeria[END_REF][START_REF] Bouzeghoub | First observation of HIV type 1 drug resistance mutations in Algeria[END_REF] we observed a high diversity of HIV type 1 in Algeria, with a complicated pattern of subtypes and circulating recombinant forms (CRFs), particularly in the southern part of the country. Although the B subtype was predominant, CRF06_cpx and CRF02_AG were widely represented. Concerning drug resistance mutations, some transmitted mutations to nucleoside reverse transcriptase inhibitors (NRTIs) and protease inhibitors (PIs) occurred in untreated patients. In 2008, we did not observe any resistance mutation to nonnucleoside reverse transcriptase inhibitors (NNRTIs) because of the recent introduction of this class of drugs in Algeria. Since 2008, no study has pointed out the diversity of HIV in Algeria or the transmission rate of resistance mutations in naive patients.

Materials and Methods

We studied 152 samples collected between 2013 and 2014 from either untreated or ARV-treated patients under clinical failure of therapy from El Hadi Flici hospital in Algiers. Blood was collected in ethylenediaminetetraacetic acid (EDTA) tubes and plasma was separated and stored at -80°C. One hundred and ten plasma samples were spotted using Whatman 903 paper (Dried Plasma Spot: DPS). Viral RNA was extracted from plasma or DPS. From plasma, RNA extraction was carried out using the High Pure Viral RNA Kit (Roche Diagnostics Systems) and from DPS, RNA extraction was carried out using the Nuclisens kit (BioMe´rieux).

The viral RNA was used in reverse transcription polymerase chain reaction (RT-PCR) of RT and Prot genes followed by a nested PCR, using two sets of primers in a GeneAmp PCR System 9700 (Applied Biosystems, Foster City, CA) thermal cycler. The outer and inner primers for RT are described in a previous publication. [START_REF] Marechal | Increasing HIV type 1 polymorphic diversity but no resistance to antiretroviral drugs in untreated patients from Central African Republic: A 2005 study[END_REF] The fragments obtained were sequenced on both strands using the Big Dye Terminator v 3.1 Cycle Sequencing Kit with a DXL 3500 DX sequencer (Applied Biosystem, Courtaboeuf, France). The primers of the nested PCR were used for sequencing the RT and Prot regions. The derived nucleotide sequences of the RT and Prot regions were aligned with Clustal W2 alignment program with known reference strains of M and N pooled from the HIV-1 gene databank (http://hiv-web-lanl.gov/).

Phylogenetic trees were inferred using the neighbor-joining method from matrix distances calculated after gapstripping of

Results

Among the 152 collected samples, 89 were obtained from naive patients. Their mean age was 38 years (5-81) and the M/W sex ratio was 1.4. The median viral load was 5,017,844 copies/ml (102-100 million). From the 152 samples studied, 124 were amplified, with 119 sequenced on the Prot gene and 110 on the RT gene.

The molecular characterization of the viruses, based on genomic sequence analysis, is presented in Fig. 1. The predominant subtype was largely CRF06_cpx, followed by the B subtype, CRF02_AG, and other non-B strains (A1, recombinant B-CRF02, CRF07_BC, CRF22_01A1, recombinant BF, and recombinant BG).

Figure 2 indicates the proportion of resistance mutations in naive patients. Viruses harboring mutations were present in 28 of 89 samples from naive patients. Some were major alignments, with a Kimura two-parameter algorithm. Phylogenetic trees were visualized using ITOL (Interactive Tree of LIFE) software. [START_REF] Letunic | Interactive Tree of Life v2: Online annotation and display of phylogenetic trees made easy[END_REF] The mutations involved in antiretroviral resistance were recorded according to the algorithm of the Agence Nationale de Recherche sur le SIDA (ANRS/France) (http://hivfrenchresistance.org, 2014, version 24). GenBank accession numbers for the sequences reported in this study are KT339064 to KT339174 for RT and KT338945 to KT339063 for Prot. ). Boxed mutations are listed on the drug resistance mutations for surveillance of transmitted HIV-1 drug resistance. [START_REF] Bennett | drug resistance mutations for surveillance of transmitted HIV-1 drugresistance: 2009 update[END_REF] resistance mutations such as M184V for NRTI, K103N for NNRTI, and V82F for PI. The prevalence of HIV-1 resistance-associated mutations in this study was found to be 31% (according to Drug Resistance Algorithms, Stanford HIVDB 7.0.1 and ANRS 2014.v24). This significant prevalence is similar to that reported in a recent update on HIV-1 transmitted drug resistance in Africa or in other countries. [START_REF] Letunic | Interactive Tree of Life v2: Online annotation and display of phylogenetic trees made easy[END_REF][START_REF] Ssemwanga | Update on HIV-1 acquired and transmitted drug resistance in Africa[END_REF][START_REF] Pereira | Primary drug resistance at diagnosis of HIV-1 infection: A Portuguese cohort[END_REF][START_REF] Zeng | HIV-1 genotypic diversity and prevalence of drug resistance among treatment na¨ıve HIVinfected individuals in Chengdu of China[END_REF] However, if we consider the list established by Bennett et al., [START_REF] Bennett | drug resistance mutations for surveillance of transmitted HIV-1 drugresistance: 2009 update[END_REF] the percentage of transmitted mutations was 15%.

Discussion

In previous studies published in 2006 and 2008, we observed high HIV-1 diversity in Algeria with a predominance of the B subtype followed by CRF02_AG and CRF06_cpx. [START_REF] Bouzeghoub | High diversity of HIV type 1 in Algeria[END_REF][START_REF] Bouzeghoub | First observation of HIV type 1 drug resistance mutations in Algeria[END_REF] In the current study, the diversity was maintained, but CRF06_cpx became widely predominant. The evolution of the HIV infection, previously originating primarily in Europe and now from others neighboring countries, surely explains this epidemiological change.

In this study, we observed a prevalence of 31% of HIV-1 resistance-associated mutations, 15% considering the list established by Bennett et al. [START_REF] Bennett | drug resistance mutations for surveillance of transmitted HIV-1 drugresistance: 2009 update[END_REF] : this was a huge increase compared to the previous analysis. [START_REF] Bouzeghoub | First observation of HIV type 1 drug resistance mutations in Algeria[END_REF] Nevertheless, this result is not surprising and has already been observed elsewhere. [START_REF] Ssemwanga | Update on HIV-1 acquired and transmitted drug resistance in Africa[END_REF][START_REF] Pereira | Primary drug resistance at diagnosis of HIV-1 infection: A Portuguese cohort[END_REF][START_REF] Zeng | HIV-1 genotypic diversity and prevalence of drug resistance among treatment na¨ıve HIVinfected individuals in Chengdu of China[END_REF] In Africa, the prevalence of drug resistance mutations varies across countries, reaching 54.9% in Central Africa. [START_REF] Ssemwanga | Update on HIV-1 acquired and transmitted drug resistance in Africa[END_REF] In other countries where access to antiretroviral therapy increased for years, such as Portugal or China, the same number of mutations is noted. [START_REF] Pereira | Primary drug resistance at diagnosis of HIV-1 infection: A Portuguese cohort[END_REF][START_REF] Zeng | HIV-1 genotypic diversity and prevalence of drug resistance among treatment na¨ıve HIVinfected individuals in Chengdu of China[END_REF] However, these mutations are perfectly correlated with the HIV treatments proposed in Algeria and in all the countries of the MENA region.

These results support the recommendation for epidemiological monitoring of the entire national territory; also recommended is routine resistance testing before the initiation of antiretroviral therapy in Algeria to investigate transmitted drug resistance in naive populations represented by recently infected individuals and/or pregnant women.

F I G . 1 .

 1 Subtype distribution of HIV-1-infected patients in Algeria in 2013-2014. ''Others'' represented one A1 subtype, two CRF22_01A1, one CRF07_BC, two recombinant forms BF, one recombinant form BG, and one recombinant form B-CRF02. F I G . 2. Number of viruses bearing reverse transcriptase (RT) and protease (PROT) mutations in the 89 naive patients analyzed (Drug Resistance Algorithms, Stanford HIVDB 7.0.1 and ANRS 2014.v24

Acknowledgment

This work has been funded by French Ministry of National Education through a quadrennial grant to UMR5234.

Author Disclosure Statement

No competing financial interests exist.