F₁F_o-ATP synthase (ATP synthase) is a central membrane protein that synthetizes most of the ATP in the cell through a rotational movement driven by a proton gradient across the hosting membrane. In mitochondria, ATP synthases can form dimers through specific interactions between some subunits of the protein. The dimeric form of ATP synthase provides the protein with a spontaneous curvature that sustain their arrangement at the rim of the high-curvature edges of mitochondrial membrane (cristae). Also, a direct interaction with cardiolipin, a lipid present in the inner mitochondrial membrane, induces the dimerization of ATP synthase molecules along cristae. The deletion of those biochemical interactions abolishes the protein dimerization producing an altered mitochondrial function and morphology. Mechanically, membrane bending is one of the key deformation modes by which mitochondrial membranes can be shaped. In particular, bending rigidity and spontaneous curvature are important physical factors for membrane remodelling. Here, we discuss a complementary mechanism whereby the rotatory movement of the ATP synthase might modify the mechanical properties of lipid bilayers and contribute to the formation and regulation of the membrane invaginations.

F ₁ F _o -ATP 合酶（ATP 合酶）是一种中心膜蛋白，通过跨宿主膜的质子梯度驱动的旋转运动合成细胞中的大部分 ATP。在线粒体中，ATP 合酶可以通过蛋白质某些亚基之间的特定相互作用形成二聚体。 ATP 合酶的二聚体形式为蛋白质提供了自发曲率，从而维持其在线粒体膜（嵴）高曲率边缘边缘的排列。此外，与心磷脂（线粒体内膜中存在的一种脂质）的直接相互作用会诱导 ATP 合酶分子沿嵴二聚化。这些生化相互作用的缺失消除了蛋白质二聚化，从而改变了线粒体功能和形态。从机械角度来说，膜弯曲是线粒体膜成形的关键变形模式之一。特别是，弯曲刚度和自发曲率是膜重塑的重要物理因素。在这里，我们讨论了一种补充机制，ATP 合酶的旋转运动可能会改变脂质双层的机械特性，并有助于膜内陷的形成和调节。