Simultaneous interferometric determination of Gaussian, tilt and bending moduli of biomimetic membranes

Cell membrane remodelling during key processes such as endocytosis, exocytosis, pore formation, and cell division involves large changes in the curvature, which are governed by bending, Gaussian and tilt moduli. While bending rigidity has been extensively studied, it has been a major challenge to experimentally measure Gaussian and tilt moduli due to fundamental limitations imposed by the Gauss-Bonnet theorem on closed membranes and the nanometric size of the constituents. We address these issues by studying a fluid monolayer model membrane consisting of aligned, micron-length rod-like particles, known as colloidal membranes. Their continuum deformation follows the Helfrich curvature energy, while their micron-scale thickness allows easy observation of tilt deformation modes at optically resolvable length-scales. We use high-speed interference reflectance microscopy to measure complete 3D surface profiles of fluctuating membranes with nanometer precision, which offers significant advantages over conventional fluctuation spectroscopy that measures membrane cross-section dynamics. We detect both tilt and bending modes and extract the corresponding moduli from the thermal fluctuation spectrum. We also demonstrate that these moduli can be tuned by varying the self-assembly conditions and particle geometry. The open membrane edges exhibited enhanced long-wavelength fluctuations with a negative Gaussian curvature, enabling experimental determination of the elusive Gaussian modulus.