Towards improved particle averaging for single-molecule localization microscopy using geometric deep learning

Single-molecule localization microscopy (SMLM) can resolve intracellular structures down to the nanoscale, but often produces sparse and incomplete data. Particle averaging (PA) can aid with the reconstruction of complete structures, but traditional PA methods can suffer from template bias or the high computational costs of geometric alignment. To address these limitations, we developed a geometric deep learning (GDL) framework for enhanced, template-free 3D particle averaging. Our pipeline uses a GDL autoencoder, trained on realistic simulated data, to map incomplete point clouds into a robust latent space. By averaging feature vectors directly within this space, our method bypasses the need for explicit 3D alignment. We validated our approach on simulated DNA origami and experimental nuclear pore complex (NPC) data. The latent space averaging successfully reconstructed NPC structures with key metrics (ring radius {approx} 46 nm, ring distance {approx} 52 nm) that are comparable to state-of-the-art methods. This work establishes a viable GDL pipeline for SMLM analysis, offering an efficient alternative to traditional PA. While the current model requires structure-specific training, our results highlight the significant potential of GDL for quantitative structural biology.