Reduction in Tension and Stiffening of Lipid Membranes in an Electric Field Revealed by X-Ray Scattering

Arnaud Hemmerle, Giovanna Fragneto, Jean Daillant, and Thierry Charitat

Phys. Rev. Lett. 116, 228101 – Published 2 June 2016

Abstract

The effect of ac electric fields on the elasticity of supported lipid bilayers is investigated at the microscopic level using grazing incidence synchrotron x-ray scattering. A strong decrease in the membrane tension up to $1 mN / m$ and a dramatic increase of its effective rigidity up to $300 k_{B} T$ are observed for local electric potentials seen by the membrane $≲ 1 V$ . The experimental results are analyzed using detailed electrokinetic modeling and nonlinear Poisson-Boltzmann theory. Based on a modeling of the electromagnetic stress, which provides an accurate description of the bilayer separation versus pressure curves, we show that the decrease in tension results from the amplification of charge fluctuations on the membrane surface whereas the increase in bending rigidity results from the direct interaction between charges in the electric double layer. These effects eventually lead to a destabilization of the bilayer and vesicle formation. Similar effects are expected at the tens of nanometers length scale in cell membranes with lower tension, and could explain a number of electrically driven processes.

Received 5 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.228101

Physics Subject Headings (PhySH)

Membranes Surface tension effects

Lipids

Grazing-incidence X-ray diffraction

Physics of Living Systems

Authors & Affiliations

Arnaud Hemmerle^1,*, Giovanna Fragneto², Jean Daillant³, and Thierry Charitat^1,†

¹UPR 22/CNRS, Institut Charles Sadron, Université de Strasbourg, 23 rue du Loess, BP 84047 67034 Strasbourg Cedex 2, France
²Institut Laue-Langevin, 71 avenue des Martyrs, BP 156, 38042 Grenoble Cedex, France
³Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, F-91192 Gif-sur-Yvette Cedex, France

^*Present address: Max Planck Institute for Dynamics and Self-Organization (MPIDS), Göttingen 37077, Germany.
^†thierry.charitat@ics-cnrs.unistra.fr

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Vol. 116, Iss. 22 — 3 June 2016

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Images

Figure 1
Schematic representation of the effect of the electric field (a). Top: freely fluctuating bilayer. Middle: the interaction between the induced charges and the external electric field leads to an electric force that is amplifying the undulation, acting as a destabilizing negative surface tension. Bottom: bending brings the charges closer increasing the electrostatic interactions, mainly in the electric double layer (black arrows) and leads to an increase in the bending rigidity. Calculated electric potential as a function of the distance for 10 Hz (black solid curve) and 50 Hz (red dotted line) (b). The inset of (b) shows the local voltage at the membrane boundaries as a function of frequency and for different Debye lengths $κ_{D}^{- 1} = 800 nm$ (red curve), 300 nm (green curve), and 150 nm (black curve) using $d_{m} = 5 nm$ . $z = 0$ corresponds to the middle plane of the floating bilayer.
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Figure 2
Schematic view of the experiment and electrokinetic model of the supported bilayers (a). The incident beam at grazing incidence (direction $k_{in}$ ) is scattered in direction $k_{sc}$ , giving access to in-plane fluctuations. The off-specular reflectivity curves and the associated best fits (b).
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Figure 3
Effect of an ac field on a supported bilayer. Filled symbols are data from this work. The black squares, green circles, and red triangles correspond to different experiments. The solid lines correspond to the full electrostatic contribution (Poisson-Boltzmann theory) to $Γ_{el}$ and $K_{el}$ , which can be decomposed into a membrane contribution (dotted line) and an electric double layer contribution (dashed line). The linear Debye-Hückel theory is shown as dashed-dotted lines. $κ_{D}^{- 1} = 800 nm$ (red curves), $κ_{D}^{- 1} = 300 nm$ (green curves), and $κ_{D}^{- 1} = 150 nm$ (black curves). Mechanical pressure as a function of distance (a). The blue stars are from Ref. [24] where the pressure was applied by osmotic stress on similar double bilayers. The empty symbols are from Ref. [28] (osmotic stress on multilayer stacks). The solid line is calculated after Ref. [24] using dispersive, electrostatic, and entropic contributions to the interbilayer potential. Number of water molecules per lipid $n_{w}$ as a function of electrostatic pressure $Π$ (b). The blue circles were obtained by NMR spectroscopy for osmotically stressed 1,2-dimyristoyl-sn-glycero-3-phosphocholine multilayer stacks [29]. Electrostatic contribution to the membrane tension $Γ_{el}$ as a function of frequency for a fixed voltage $V_{0} = 5 V$ (c) and as a function of the local voltage $V_{loc}$ at the membrane (d). Electrostatic contribution to the membrane rigidity $K_{el}$ as a function of frequency for a fixed voltage $V_{0} = 5 V$ (e) and $K_{el} κ_{D} / k_{B} T$ as a function of the local potential difference $V_{loc}$ (f).
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Figure 4
$Γ_{el}$ as a function of $K_{el}$ (a). The destabilization limits for $U^{''} = 1 0^{12.5}$ and $1 0^{11.5} J \cdot m^{- 4}$ are given as light and dark pink domains, respectively. Vesicle formation under an electric field (5 V, 5 Hz) from a single supported bilayer of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (b). Observation by fluorescence microscopy at 5 min (left) and 85 min (right) after the application of the field.
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