A model of membrane deformations driven by a surface pH gradient

TL;DR

This paper presents a theoretical model linking membrane lipid composition and shape deformations driven by pH gradients, specifically applied to mitochondrial cristae, revealing how biochemical states influence membrane morphology.

Contribution

The study introduces a generalized Helfrich free energy model coupling lipid composition and membrane shape, providing insights into pH-driven membrane deformations in mitochondria.

Findings

Model predicts membrane tube deformations under pH gradients.

Deformation patterns resemble observed mitochondrial cristae changes.

Highlights role of cardiolipins in shape regulation.

Abstract

Many cellular organelles are membrane-bound structures with complex membrane composition and shape. Their shapes have been observed to depend on the metabolic state of the organelle, and the mechanisms that couple biochemical pathways and membrane shape are still actively investigated. Here, we study a model coupling inhomogeneities in the lipid composition and membrane geometry via a generalized Helfrich free energy. We derive the resulting stress tensor, the Green's function for a tubular membrane and compute the phase diagram of the induced deformations. We then apply this model to study the deformation of mitochondria cristae described as membrane tubes supporting a pH gradient at its surface. This gradient in turn controls the lipid composition of the membrane via the protonation/deprotonation of cardiolipins, which are acid-based lipids known to be crucial for mitochondria shape and functioning. Our model predicts the appearance of tube deformations resembling the observed shape changes of cristea when submitted to a proton gradient.