Orientation Estimation of Cryo-EM Images for Molecules with Arbitrary Symmetry by Semidefinite Programming

Single-particle cryo-electron microscopy (cryo-EM) pose estimation is traditionally solved anew for each dataset, where iterative refinement is done from scratch while the estimator learns to store the molecule in its weights. In this work, we show that pose inference is a generalizable, specimen-agnostic operation when conditioned explicitly on a reference volume. We introduce ARCHER, an amortized contrastive classifier that models the pose posterior over a discrete rotation grid. Trained across a variety of protein structures, it operates zero-shot without retraining per structure. This transferability is grounded in Fourier-space information mechanics, where all specimen dependence is captured by the reference structure's power spectrum and spatial extent. ARCHER achieves a median angular error of 5.0° on 100 held-out test structures and 2.5° on experimental particles, matching dedicated estimators within 0.16 Å in 3D reconstruction. Crucially, downstream conformational signal is preserved. The leading conformational coordinate correlates at 0.97 with deposited benchmarks, faithfully reconstructing free-energy basins and mobile domains. These results overall demonstrate that cryo-EM pose estimation can be generalized across different structures.

Crystal-orientation maps are physical fields defined only up to crystal symmetry; electron backscatter diffraction (EBSD) resolves them experimentally, but acquisition-time constraints limit spatial resolution. Unlike conventional images, EBSD data lie on the quotient space $\mathrm{SO}(3)/G$, where $G$ is the crystal-symmetry group. Standard Euclidean interpolation can therefore mix symmetry-equivalent representations and blur grain boundaries. We introduce the Symmetry-Group-Aware Super-Resolution Attention Network (SG-SRAN), which incorporates crystal symmetry and boundary preservation by design. A frozen, locally isometric encoder maps equivalent orientations to a common latent representation in which Euclidean distance approximates misorientation. Super-resolution is performed in this space, with each high-resolution token restricted to a feature-consistent local support to prevent cross-boundary mixing. A dictionary-based decoder then recovers valid orientations. Across FCC and HCP benchmarks, SG-SRAN matches 15-16 million parameter backbones using only 27-49k trainable parameters, while achieving the lowest p68 errors, highest inverse-pole-figure fidelity, and zero-shot transfer to unseen alloys.

We present a geometry-aware method for heterogeneous single-particle cryogenic electron microscopy (cryo-EM) reconstruction that predicts atomic backbone conformations. To incorporate protein-structure priors, we represent the backbone as a graph and use a graph neural network (GNN) autodecoder that maps per-image latent variables to 3D displacements of a template conformation. The objective combines a data-discrepancy term based on a differentiable cryo-EM forward model with geometric regularization, and it supports unknown orientations via ellipsoidal support lifting (ESL) pose estimation. On synthetic datasets derived from molecular dynamics trajectories, the proposed GNN achieves higher accuracy compared to a multilayer perceptron (MLP) of comparable size, highlighting the benefits of a geometry-informed inductive bias.