Abstract

Morphological analysis of organelle and cell shapes has long been used to infer cellular function, identify cell states, and understand biological processes. With advances in three-dimensional electron microscopy modalities, quantitative characterization of membrane ultrastructure has emerged as an approach to interrogate how organization of proteins and other components around the membrane drive structure and function. Hindering these efforts, the confident reconstruction of geometric features such as membrane curvature is challenging since it requires the calculation of higher-order derivatives from discrete membrane representations. Modern advances in using neural networks to learn continuous implicit representations of complex shapes present a promising solution to this problem. Here, we describe a physics-informed neural network framework for reconstructing membrane geometries from images using an implicit neural representation. By modeling the membrane as a continuous phase field, our approach enables direct estimation of its biophysically relevant geometric quantities, including mean and Gaussian curvature. The use of physics-based regularization during training improves accuracy of recovered curvature measurements of synthetic datasets, especially under noisy imaging conditions. Application to experimental datasets further shows that our framework generalizes to complex cellular structures, such as the Golgi apparatus and mitochondria. Notably, the phase-field representation handles the complex membrane topologies without additional constraints. We further perform three-dimensional curvature analysis of endocytic pits in cells to reveal anisotropic curvatures at the pit neck, previously predicted to be a lower-energy pathway for neck constriction. Our work provides a unified framework for reconstructing three-dimensional membrane shape, including curvature, from volumetric imaging data. By capturing membrane geometry more accurately, our approach yields mechanical insights that can be linked to molecular-scale interactions.