Fig. 1: Description of the model. Yellow rectangles represent caveolin disks.

The part/s of the distal monolayer contacting the hydrophobic plane/s of the disc/s (monolayer I) is/are shown in red color. The monolayer fragment/s that do not contact the disc plane/s (monolayers II and III) is/are shown in dark blue colour. A The reference state preceding the relaxation of the system. The dashed lines represent the monolayer neutral planes. B A decrease of the number of lipid molecules contacting the disc leads to the area stretching of the monolayer I. C Relaxation of the monolayer I stretching that leads to tilt and splay in the monolayers I and II. The axes \({{{\rm{x}}}}_{{{\rm{I}}}}\) and \({{{\rm{x}}}}_{{{\rm{II}}},{{\rm{III}}}}\) are chosen to describe, respectively, the monolayer I and the monolayers II and III; (D) Kinking of the membrane profile, which generates the tilt and splay in the monolayer III but results in an overall relaxation of the system’s elastic energy. E Membrane with multiple disks. Notations: \({{{\rm{\phi }}}}_{{{\rm{B}}}}\) and \({{\rm{\varphi }}}\) in (C–E) are, respectively, the boundary tilt and kink angles; \({{\rm{R}}}\) and \({{\rm{L}}}/2\) in (E) represent, respectively, the disc radius and the half-distance between adjacent disks determined along the system’s mid plane; the dashed lines in (E) show the boundaries of the building block defined as the system and at the same time represent the radius of the effective curvature, \({{{\rm{\rho }}}}_{{{\rm{eff}}}}=\frac{1}{{{{\rm{J}}}}_{{{\rm{eff}}}}}\).