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The inner membrane of mitochondria presents folds, the cristae, which are the production place of ATP. This synthesis is catalized by transmembrane proteins and relies on a flow of protons confined to the surface of the membrane. We posit that, in turn, the proton flux shapes the crista membrane in a way that suits these proteins. To study this hypothesis, we model a crista as a spherical vesicle submitted to a diffusive proton gradient flowing from the poles to the equator. Using Helfrich model, we introduce a pH-dependent spontaneous curvature for the membrane and determine the shape of the vesicle, in the regime of small deformations. We show that the pH gradient can produce shapes featuring flat zones at the poles and curved zones at the equator. These correspond to the geometry of the proteins involved in the process. Based on biophysical arguments, we define a functionality score for the vesicle and construct a phase diagram identifying the zones of “well-functioning” cristae, which we compare to experimental measurements.
PHYSICAL REVIEW E
By: Yorgos Chatziantoniou and Hélène Berthoumieux.
Phys. Rev. E 113, 034404 – Published 10 March, 2026
DOI:https://doi.org/10.1103/g6fm-frk4