Shape of the membrane neck around a hole during plasma membrane repair

Plasma membrane damage and rupture occurs frequently in cells, and holes must be sealed rapidly to ensure homeostasis and cell survival. The membrane repair machinery is known to involve recruitment of curvature-inducing annexin proteins, but the connection between membrane remodeling and hole closure is poorly described. The induction of curvature by repair proteins leads to the possible formation of a membrane neck around the hole as a key intermediate structure before sealing. We formulate a theoretical model of equilibrium neck shapes to examine the potential connection to a repair mechanism. Using variational calculus, the shape equations for the membrane near a hole are formulated and solved numerically. The system is described under a condition of fixed area, and a shooting approach is applied to fulfill the boundary conditions at the free membrane edge. A state diagram of neck shapes is produced describing the variation in neck morphology with respect to the membrane area. Two distinct types of necks are predicted, one with conformations curved beyond π existing at positive excess area, whereas flat neck conformations (curved below π) have negative excess area. The results indicate that in cells, the supply of additional membrane area and a change in edge tension is linked to the formation of narrow and curved necks. Such necks may be susceptible to passive or actively induced membrane fission as a possible mechanism for hole sealing during membrane repair in cells.