a, On the basis of the close similarity of the G domains and BSE domains of Mgm1 and dynamin (Extended Data Fig. 2b), we propose that Mgm1 and dynamin perform similar power strokes. Dimerization of the G domain would link neighbouring Mgm1 filaments. The power stroke would then result in negative torque in the direction of the membrane normal. In b, a circle with a dot indicates a vector towards the viewer and a circle with an x indicates vector in the opposite direction. The arrow represents the direction of the torque. Note that power-stroke torque is independent of membrane curvature and helix handedness. During the power stroke, the helix pitch remains constant because of the G domain contacts. Unwinding or winding of filaments then translates into a change in helix diameter. Inter-paddle contacts must be weak or absent as the filaments slide past each other. b, The power-stroke torque applies an equal and opposite force between neighbouring turns. For outside decoration, the surface normal points outward. The resulting forces would constrict a right-handed helix and expand a left-handed helix. For inside decoration, the surface normal points inward, reversing the sign of the power-stroke torque. This reverses the resultant forces on the filament, which would expand a right-handed helix and constrict a left-handed helix. See also Supplementary Video 1. c, Modelling an example helical Mgm1 filament on an inner-tube surface. Although the Mgm1 tetramer on the inside lattice observed by cryo-ET resembled the crystal tetramer closely, formation of a continuous filament on the inside of a narrow tube would require curvature changes in the tetramer relative to the crystal structure. Using an all-atom structure-based model, we explore how the tetramer structure might change as part of a tight filament. The modelling parameters ensured that a short filament (4 dimers) fits within the steric constraints of a 30-nm-radius tube, and that the pitch results in a 1-start helix (left-handed pitch angle of 3.6°). Otherwise, the shape of the tetramer is free to find its optimal shape. Changes in the interface bending angles result in a transition from positive curvature (θ 2 > θ 1 ) to negative curvature (θ 2 < θ 1 ) (Extended Data Fig. 7d). d, Comparison of the constrained tetramer shown in c (central dimers) with the crystal structure. Minor changes in interface-1 and larger changes in interface-2 (with minimal changes to atomic packing, see insets) enable a conformational switch within the tetramer from binding to a concave surface (as in the crystal packing geometry) to binding to a convex surface. In this case, θ 1 = 128° and θ 2 = 117°. See also Extended Data Fig. 7g for comparison to explicit solvent simulations. e, Schematic overview of mitochondrial inner membrane remodelling. f–h, Models of mitochondrial membrane remodelling by Mgm1 and OPA1 filaments. f, During inner-membrane fusion, Mgm1 or OPA1 filaments may assemble on opposing membrane buds to stabilize the membrane curvature at the fusion site, as previously proposed62. g, On the inner surface of cristae, Mgm1 or OPA1 filaments may assemble into left-handed helical filaments to constrict the crista junction in a GTPase-dependent fashion. Alternatively, they may assemble into right-handed helical filaments that expand the crista volume to prevent their collapse. In this way, Mgm1 filaments may counteract the membrane-constricting activity of the ATPase synthase dimers63 or the MICOS complex64,65,66,67 to pull lipids into cristae and enable the dynamic transition from a tight crista state with reduced oxidative phosphorylation to an expanded active state with high oxidative phosphorylation activity. In agreement with this model, cristae have been shown to collapse when a GTPase-deficient OPA1 variant is expressed14. h, Similar to dynamin assemblies at the neck of clathrin-coated pits, Mgm1 or OPA1 may assemble in a right-handed helix around the neck of an inner membrane junction, resulting in constriction and membrane scission upon GTP hydrolysis. The assembly geometry of the Mgm1 or OPA1 filaments may depend on lipid composition, interaction partners or the specific Mgm1 or OPA1 isoform. Consistent with the latter assumption, inner membrane fusion requires the long form of OPA1, but the short OPA1 isoforms are sufficient for stabilizing crista membranes68.