Line Tension of Pore Edge in Membrane on Solid Support

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Abstract

Controlled formation of through pores in bilayer lipid membranes is a key stage of various biotechnological techniques. Excess energy of the pore edge is characterized by line tension, the value of which determines the overall stability of the membrane with respect to pore formation. The practically important pore size is on the order of a few nanometers. It is impossible to study such pores by direct optical methods, but they can, in principle, be visualized by atomic force microscopy. This method uses a solid support on which the lipid bilayer is held due to the interaction of one of the monolayers with it. In this work, we theoretically investigated the effect of the presence of the support on the value of the line tension of the pore edge. It was assumed that the line tension is determined by the energy of elastic deformations of the membrane at the edge. Various regimes of membrane interaction with the support were considered: from a free-standing membrane (complete absence of interaction) to the case of infinitely strong adhesion of the membrane to the support. The calculation results show that the relative change in the line tension of the pore edge within such variation of the intensity of the interaction of the membrane with the support is less than 3.5%. Thus, the developed theoretical model predicts an extremely weak effect of the interaction with the support on the magnitude of the line tension–the main energy characteristic of the pore edge.

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About the authors

D. I. Kostina

National University of Science and Technology “MISiS”

Email: akimov@misis.ru
Russian Federation, Moscow, 119049

M. V. Sumarokova

Research Institute of System Biology and Medicine of Rospotrebnadzor

Email: akimov@misis.ru
Russian Federation, Moscow, 117246

S. P. Dudik

Research Institute of System Biology and Medicine of Rospotrebnadzor

Email: akimov@misis.ru
Russian Federation, Moscow, 117246

P. V. Bashkirov

Research Institute of System Biology and Medicine of Rospotrebnadzor

Email: akimov@misis.ru
Russian Federation, Moscow, 117246

S. A. Akimov

National University of Science and Technology “MISiS”

Author for correspondence.
Email: akimov@misis.ru
Russian Federation, Moscow, 119049

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2. Fig. 1. Schematic representation of a one-dimensional pore edge in a membrane on a substrate. The substrate is shown by an oblique hatching. The Oz axis of the Cartesian coordinate system is perpendicular to the plane of the substrate; the Ox axis is perpendicular to the pore edge line. The shape of the neutral surfaces of the upper and lower monolayers, as well as the intermonolayer surface, is described by the functions Hu(x), Hl(x), and M(x), respectively. The thick red line shows the neutral surface of the vertical monolayer; its shape is described by the function Hv(z). The neutral surface of the vertical monolayer section is continuously contiguous with the neutral surface of the lower monolayer at the point {X1, Z1}, of the upper monolayer at the point {X2, Z2}. The thickness of the hydrophobic part of the monolayer h.

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3. Fig. 2. Calculated shape of the neutral surfaces of the monolayers and the intermonolayer surface of the membrane near the one-dimensional pore edge. The edge has translational symmetry along the Oy axis perpendicular to the xz plane of the figure. The position of the origin of coordinates is chosen so that the leftmost point of the membrane corresponds to the coordinate x = 0. The shapes are calculated at different values of the steepness of the interaction potential with the substrate: a - Ks = 0 (free membrane); b - Ks = 10 kBT/nm4; c - Ks = +∞ (infinitely strong adhesion of the membrane to the substrate). In panel c, arrows show the calculated director direction nu(x) in the upper horizontal monolayer, nl(x) in the lower horizontal monolayer, and nv(z) in the vertical monolayer.

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4. Fig. 3. Dependence of the linear tension of the pore edge on the steepness of the membrane-substrate interaction potential: a - in linear scale; b - in semi-logarithmic scale. Ks = 0 corresponds to a free membrane, Ks = +∞ - to the case of infinitely strong adhesion of the membrane to the substrate. The relative change of linear tension in the full range of variation of Ks is less than 3.5%.

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