Influence of Membrane Curvature on the Energy Barrier of Pore Formation

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Formation of through conducting defects — pores — in the lipid bilayer affects many processes in living cells and can lead to strong changes in cellular metabolism. Pore formation is a complex topological rearrangement and occurs in several stages: first, a hydrophobic through pore is formed, then it is reconstructed into a hydrophilic pore with a curved edge, the expansion of which leads to membrane rupture. Pore formation does not occur spontaneously, since it requires significant energy costs associated with membrane deformation. The evolution of the system is associated with overcoming one or two energy barriers, the ratio of their heights affects the stability of the pore and the probability of its formation. We study the effect of membrane curvature on the height of the energy barrier for the transition of a pore to a metastable hydrophilic state. We apply the theory of elasticity of lipid membranes and generalize the model of pore formation in flat membranes to the case of arbitrary curvature. We show that the barrier for pore formation decreases by 8 kBT when the radius of curvature decreases from 1000 to 10 nm, which facilitates the formation of a metastable pore. Our results are consistent with experimental data and can be used to model complex processes occurring in curved regions of living cell membranes.

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作者简介

R. Molotkovsky

Institute of Systems Biology and Medicine of Rospotrebnadzor

编辑信件的主要联系方式.
Email: rodion.molotkovskiy@gmail.com
俄罗斯联邦, Moscow, 117246

P. Bashkirov

Institute of Systems Biology and Medicine of Rospotrebnadzor

Email: rodion.molotkovskiy@gmail.com
俄罗斯联邦, Moscow, 117246

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2. Fig. 1. Schematic representation of a hydrophobic (panel a) and hydrophilic (panel b) pore in a planar lipid bilayer.

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3. Fig. 2. Schematic representation of the initial state of the system. A segment of radius Rs is cut out from the membrane with radius of curvature Rc and replaced by the deformed membrane. The radius Rc is determined from the intermonolayer surface. The directors and neutrals are cross-linked at points with coordinates , where = arcsin(Rs/Rc) - half of the angle of solution of the spherical segment.

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4. Fig. 3. Calculated dependence of Ha(0) - Ha(Rs - hasin(g)) functions on r at Rs = 3, 6 and 8 nm. The sphere radius Rc = 20 nm; the monolayer thickness h = 1.5 nm. The elastic parameters of the system are as follows: B = 10 kBT, Kt = 40 mN/m and Ka = 120 mN/m per monolayer.

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5. Fig. 4. Schematic representation of a pore of radius r0 and thickness 2L in a curved membrane. The “horizontal” bilayer section of the membrane is highlighted in orange, the “vertical” monolayer sections are highlighted in blue. The pore is highlighted with a large dashed line. The shape of the membrane in the initial position is highlighted by a small dotted line.

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6. Fig. 5. Dependences of the energy change Wtot (panel a) and the equilibrium half-length of the hydrophobic pore edge site Lmin (panel b) on the pore radius r0. Curves for crosslinking radius Rs = 5 nm are shown in red; curves for crosslinking radius Rs = 50 nm; membrane radius of curvature Rc = 1000 nm are shown in blue. Green color indicates curves for membrane radius of curvature Rc = 10 nm; solid line corresponds to crosslinking radius Rs = 4 nm; dashed line corresponds to crosslinking radius Rs = 5 nm. The equilibrium membrane thickness is h = 1.5 nm; the dimensionless surface tension is 0 = 0.001. The monolayer elastic moduli are B = 10 kBT, Kt = 40 mN/m, and Ka = 120 mN/m. The spontaneous curvature is zero.

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7. Fig. 6. Results of varying the radius of curvature of the membrane Rc. a - Dependence of the system energy Wtot on the pore radius at different values of Rc (signed on the graph, values are given in nm). b - Dependence of the barrier height E1 on the transition of the system from the hydrophobic pore state to the hydrophilic pore state on Rc. For all curves the cross-linking radius Rs = 5 nm. Values of elastic parameters are given in the text.

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8. Fig. 7. Equilibrium shape of the membrane with hydrophobic (a) and hydrophilic (b) pores. The radius of curvature of the membrane Rc = 10 nm. The bilayer section is shown in blue, the monolayer “vertical” sections are shown in green, and the vertical dashed line shows the edge of the hydrophobic pore. The hydrophobic pore has the following parameters: r0 = 0.5 nm, Lmin = 1.05 nm, Ha = 2 nm. The hydrophilic pore has the following parameters: r0 = 1.8 nm, = 2.14 nm, Ha = 2 nm, Hb = - 0.5 nm, Za = 1 nm.

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