pH gradient-driven deformation of a crista-like vesicle

Abstract

The inner membrane of mitochondria presents folds, the cristae, which are the production place of ATP. This synthesis is driven by a flow of protons confined to the surface of the membrane, which also shapes the crista to ensure a high synthesis rate. 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, when submitted to the pH gradient, in the regime of small deformations. 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.