Spectral connectivity descriptors separate inner from outer mitochondrial membranes in cryo-electron tomography

Abstract

The Surface Morphometrics pipeline enables quantitative analysis of organellar membrane ultrastructure from cryo-electron tomography (cryo-ET) data, measuring curvature, thickness, and inter-membrane distances. Here we extend this pipeline with a family of spectral connectivity descriptors derived from graph Laplacian and cotangent Laplace–Beltrami operators applied to triangulated membrane surface meshes. Using 15 inner mitochondrial membrane (IMM), 15 outer mitochondrial membrane (OMM), and 7 endoplasmic reticulum (ER) meshes extracted from publicly deposited cryo-ET data (EMPIAR-11370), we show that these operator-level descriptors provide a global connectivity layer complementary to local curvature and thickness measurements. In matched within-mitochondrion comparisons, the geometry-aware cotangent operator separated outer from inner mitochondrial membranes in all 15 pairs (Wilcoxon p = 6.1 × 10⁻⁵), whereas the normalized graph operator separated 11 of 15 (p = 0.018). The four reversal cases—where the graph metric does not separate IMM from OMM but the cotangent metric does—show that the dual-operator approach resolves topology-sensitive and geometry-sensitive aspects of membrane bottleneck architecture. Across membrane classes, both operators recover the biologically expected hierarchy (IMM < OMM < ER connectivity; Kruskal–Wallis p < 0.001 for the cotangent branch), and vertex-count normalization effectively removes mesh-density confounds. These spectral descriptors are computationally lightweight, straightforwardly compatible with existing Surface Morphometrics outputs, and provide a global connectivity characterization complementary to local morphometric measurements.

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