Adenosine triphosphate (ATP) synthases populate the inner membranes of mitochondria, where they produce the majority of the ATP required by the cell. From yeast to vertebrates, cryoelectron tomograms of these membranes have consistently revealed a very precise organization of these enzymes. Rather than being scattered throughout the membrane, the ATP synthases form dimers, and these dimers are organized into rows that extend for hundreds of nanometers. The rows are only observed in the membrane invaginations known as cristae, specifically along their sharply curved edges. Although the presence of these macromolecular structures has been irrefutably linked to the proper development of cristae morphology, it has been unclear what drives the formation of the rows and why they are specifically localized in the cristae. In this study, we present a quantitative molecular-simulation analysis that strongly suggests that the dimers of ATP synthases organize into rows spontaneously, driven by a long-range attractive force that arises from the relief of the overall elastic strain of the membrane. The strain is caused by the V-like shape of the dimers, unique among membrane protein complexes, which induces a strong deformation in the surrounding membrane. The process of row formation is therefore not a result of direct protein-protein interactions or a specific lipid composition of the membrane. We further hypothesize that, once assembled, the ATP synthase dimer rows prime the inner mitochondrial membrane to develop folds and invaginations by causing macroscopic membrane ridges that ultimately become the edges of cristae. In this way, mitochondrial ATP synthases would contribute to the generation of a morphology that maximizes the surface area of the inner membrane, and thus ATP production. Finally, we outline key experiments that would be required to verify or refute this hypothesis.