A Robust Hierarchical Linear Model for Cryo-EM Map Analysis

Cryo-electron microscopy (cryo-EM) has become a pivotal tool for determining the atomic structures of biological macromolecules. In this study, we introduce a robust hierarchical linear (RHL) model to estimate key atom-specific parameters: the amplitude and width of Gaussian functions, which are typically simplified using uniform widths and amplitudes scaled by atomic number in cryo-EM map related studies. Our RHL framework incorporates minimum density power divergence estimation (MDPDE) to account for heteroscedasticity and enhance robustness against outliers. Through both simulation studies and real data analysis, we demonstrate that the proposed method effectively reduces the influence of outliers and yields reliable parameter estimates. When applied to cryo-EM data of human apoferritin (PDB ID: 6Z6U; EMDB ID: 11103), our model reveals that the estimated Gaussian parameters are stable across most amino acids, with nitrogen atoms consistently displaying lower amplitude and width values than predicted by conventional Gaussian modeling. These results underscore the need for a systematic analysis of paired cryo-EM maps and atomic models from the EMDB and PDB to gain deeper insights into atom-specific features embedded in cryo-EM data.