Abstract
In various biological processes such as endocytosis and caveolae formation, the cell membrane is locally deformed into curved morphologies. Previous models to study membrane morphologies resulting from locally induced curvature often only consider the possibility of axisymmetric shapes-an indeed unphysical constraint. Past studies predict that the cell membrane buds at low resting tensions and stalls at a flat pit at high resting tensions. In this work, we lift the restriction to axisymmetry to study all possible membrane morphologies. Only if the resting tension of the membrane is low, we reproduce axisymmetric membrane morphologies. When the resting tension is moderate to high, we show that 1) axisymmetric membrane pits are unstable and 2) nonaxisymmetric ridge-shaped structures are energetically favorable. Furthermore, we find the interplay between intramembrane viscous flow and the rate of induced curvature affects the membrane's ability to transition into nonaxisymmetric ridges and axisymmetric buds. In particular, we show that axisymmetric buds are favored when the induced curvature is rapidly increased, whereas nonaxisymmetric ridges are favored when the curvature is slowly increased. Our results hold relevant implications for biological processes such as endocytosis and physical phenomena like phase separation in lipid bilayers.