Extended Data Fig. 8: Model of droplet autophagy and parameters used for calculations.

a, The LIR interaction controls bending direction during droplet autophagy (Fig. 4, Extended Data Fig. 7). Two coexisting liquids are characterized by dissimilar physicochemical properties and molecule concentrations. This implies that the spontaneous curvatures of membranes in contact with either the cytosol or the droplet will be different (\({m}_{{\rm{c}}}\ne {m}_{{\rm{d}}}\)). Thus, symmetric sheets fully immersed in homogeneous liquids (corresponding to dewetting and complete wetting in this manuscript, Extended Data Fig. 2a) have an equal probability of bending in both directions because a spontaneous curvature contrast between both sheet sides does not exist. Any membrane asymmetry introduced (indicated by the blue line), for example, by membrane-binding proteins and complexes, can induce a preferred bending direction by generating a spontaneous curvature contrast⁵. During droplet autophagy, both sheet sides contact two different liquids (the cytosol and the droplet). Thus, it is very unlikely that the spontaneous curvatures of both sides of a sheet are equal, that is, m_cd = 0. In general, a wetting sheet can therefore be considered asymmetric, that is, \({m}_{{\rm{cd}}}\ne 0\). b, Geometric parameters for numerical calculations. Pinned shapes are determined by the sheet curvature radius R_sh and angle θ_sh, and the droplet curvature radius R_d and angle θ_d. To determine unpinned shapes, the angle θ_co, which defines the location of the three-phase contact line, is also required. For unpinned shapes, the intrinsic contact angle θ_in (between the tangents of the two circles) imposes a relation between θ_co and θ_d, as given by Supplementary equation (12) in the Supplementary Methods for the two possible (+) shapes, and by Supplementary equation (13) in the Supplementary Methods for the (−) shape.