Proton Motive Force–Driven Curvature as a Determinant of Cristae Architecture and Bioenergetic Function

Mitochondrial cristae are highly curved invaginations of the inner mitochondrial membrane (IMM) that optimize oxidative phosphorylation (OXPHOS) by concentrating respiratory complexes and adenosine triphosphate (ATP) synthase. The mechanistic relationship between membrane curvature, proton motive force (PMF), and cristae morphogenesis remains incompletely understood. Here, we integrate theoretical arguments, experimental evidence, and quantitative energetic estimates to propose that PMF is not merely a biochemical driver of ATP synthesis but also a mechanical determinant of IMM shape. Local proton gradients and voltage differences generate intense electric fields and electrochemical free energy at cristae ridges, where ATP synthase dimers assemble into curvature-stabilizing rows. Modeling and reconstitution experiments demonstrate that proton flux, cardiolipin, protein enrichment, and electrostatics can induce cristae-like invaginations that may modulate membrane bending rigidity. Reaction diffusion–based Helfrich models further show that proton fields couple directly to membrane curvature, producing spatially heterogeneous deformation patterns that mirror metabolic state–dependent transitions between orthodox and condensed mitochondrial morphologies. This hypothesis supports a mechanochemical model in which proton flow not only powers ATP synthesis but also actively shapes cristae architecture through electrostatic stress and curvature-dependent energetics. To formalize this coupling, we incorporate a PMF–dependent surface integral into the Helfrich free-energy functional, capturing how spatial variations in proton density and electrochemical potential may lower the effective bending energy in regions of high flux. The suggested framework explains how cristae may maintain curvature while dynamically remodeling in response to bioenergetic demand. While the analysis is intentionally pedagogical, it opens several avenues for further theoretical and experimental investigation.