On the Gaussian modulus of lipid membranes

The Gaussian modulus is a crucial property that influences topological transformations in lipid membranes. However, unlike the bending modulus, estimating the Gaussian modulus has been particularly challenging due to the constraints imposed by the Gauss-Bonnet theorem. Despite this, various theoretical, computational, and experimental approaches have been developed to estimate the Gaussian modulus, though they are often complex, and analytical estimates remain rare. In this work, we present a minimalist model inspired by the folding of a sheet of paper, which provides an exact calculation of the Gaussian modulus. Remarkably, the induced deformation does not affect the Gaussian curvature or alter the system's topology, yet it yields the modulus that governs these geometric properties.