Influence of Membrane Curvature on the Energy Barrier of Pore Formation

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 8k_BT 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.