A Novel Machine-Learning Based Method for Resolving Secondary Structure Topology in Medium-Resolution Cryo-EM Density Maps

Medium-resolution cryo-electron microscopy (cryo-EM) density maps preserve substantial information about protein secondary-structure organization; however, accurately recovering the topology and connectivity of α-helices and β-strands remains challenging due to noise, structural heterogeneity, and the intrinsic resolution limitations that obscure residue-level detail. Topology determination is a key intermediate step toward building atomic protein models from medium-resolution cryo-EM density maps. It requires identifying the correct correspondence and orientation between secondary-structure elements (SSEs), i.e., α-helices and β-strands, predicted from the amino-acid sequence and those detected in the three dimensional (3D) density map. Despite significant advances in cryo-EM reconstruction and molecular modelling, this correspondence problem remains a challenging task, particularly in the presence of noisy density maps and in large, topologically complex α/β proteins. To address this issue, we propose a fully automated, classification-based framework that infers protein secondary-structure topology directly from medium-resolution cryo-EM density maps. Specifically, we cast topology determination as a supervised classification problem in three-dimensional space, leveraging geometric learning on model-derived Cα coordinate representations to establish SSE correspondences, and a Dynamic Time Warping (DTW)-based procedure to resolve density-stick directionality. Validation on a benchmark of 38 proteins spanning both simulated and experimental cryo-EM maps and covering diverse fold classes (α, β, and α/β) demonstrates strong and consistent performance. Among the evaluated predictors, the Voronoi (1-NN) classifier achieves the highest average correspondence quality, with a mean F1-score of 96.82% across the full benchmark. The framework also scales to large, topologically dense targets containing up to 65 secondary-structure elements while preserving very fast correspondence inference (<3 ms), offering a substantial improvement over prior baselines in both accuracy and computational cost. Overall, the classification-driven strategy provides reliable SSE-to-density matching and, when coupled with DTW-based direction selection, yields stronger topology constraints that directly support model building and refinement from medium-resolution cryo-EM reconstructions, while remaining easy to integrate into existing structural interpretation pipelines.