CryoTriplane: Triplane-based Neural Radiance Field Representation for High-resolution Cryo-EM 3D Homogeneous Reconstruction.

MOTIVATION: Determining the three-dimensional (3D) structure of proteins is a cornerstone of structural biology, providing essential insights into their underlying biological mechanisms and functional roles. Cryogenic electron microscopy (cryo-EM) single-particle analysis allows researchers to investigate biomolecules at near-atomic resolutions, unraveling the structure of biomolecular complexes. However, reconstructing high-fidelity 3D volumes from extremely noisy projections, particularly under the interference of structural heterogeneity, remains a challenging task. Traditional Fourier-domain methods often suffer from frequency-dependent signal attenuation and uneven information distribution. While recent deep-learning-based frameworks attempt to predict high-frequency components directly in frequency space, they are highly susceptible to noise and often introduce artifacts. State-of-the-art (SOTA) real-space method circumvents Fourier-domain defects, yet remains constrained by the inherent spectral bias of multi-layer perceptrons, as fixed positional encoding fails to sufficiently capture intricate high-frequency details. RESULTS: We propose cryoTriplane, a real-space 3D homogeneous reconstruction network that utilizes a hybrid spatial representation to adaptively capture fine structural details. By combining fixed positional encoding for noise-robust structural initialization with structure-aware positional encoding for high-frequency refinement, our method achieves 3D reconstructions that are simultaneously globally consistent and locally fine-grained. Comprehensive qualitative and quantitative evaluations across five simulated and four real-world datasets demonstrate that cryoTriplane significantly outperforms existing methods in resolving fine structural features. Furthermore, validation through downstream atomic modeling underscores cryoTriplane's ability to recover high-quality density maps. Specifically, our method achieves sequence coverage improvements of 4.6% and 5.5% on the EMPIAR-10005 and EMPIAR-10492 datasets over the SOTA approach, respectively. AVAILABILITY AND IMPLEMENTATION: Our code is available at  https://github.com/chengyr1999/CryoTriplane. The real datasets used in this study are publicly available from EMPIAR.