Estimation of Membrane Curvature for Cryo-Electron Tomography

Curvature is an important morphological descriptor of cellular membranes. Cryo-electron tomography (cryo-ET) is particularly well-suited to visualize and analyze membrane morphology in a close-to-native state and high resolution. However, current curvature estimation methods cannot be applied directly to membrane segmentations in cryo-ET. Additionally, a reliable estimation requires to cope with quantization noise. Here, we developed and implemented a method for membrane curvature estimation from tomogram segmentations.\n\nFrom a membrane segmentation, a signed surface (triangle mesh) is first extracted. The triangle mesh is then represented by a graph (vertices and edges), which facilitates finding neighboring triangles and the calculation of geodesic distances necessary for local curvature estimation. Here, we present several approaches for accurate curvature estimation based on tensor voting. Beside curvatures, these methods also provide robust estimations of surface normals and principal directions.\n\nWe tested the different methods on benchmark surfaces with known curvature, demonstrating the validity of these methods and their robustness to quantization noise. We also applied two of these approaches to biological cryo-ET data. The results allowed us to determine the best approach to estimate membrane curvature in cellular cryo-ET data.