As the place where the fuel of the cell, namely ATP, is synthesized, mitochondria are crucial organelles in eukaryotic cells. The shape of the invaginations of the mitochondria inner membrane, known as cristae, has been identified as a signature of the energetic state of the organelle. However, the interplay between the rate of ATP synthesis and the cristae shape remains unclear. In this work, we describe the cristae membrane using a pH-dependent Helfrich model, maintained out-of-equilibrium by a diffusive flux of protons. We show that such a model captures the shape change of the invagination, in particular the formation of necks between wider zones under variable, and especially oscillating, proton flux.