Density Estimation Using Gaussian Mixture Modeling for Cryogenic Electron Microscopy Heterogeneity Analysis

Abstract

Cryogenic electron microscopy (cryo-EM) produces large collections of noisy observations of biomolecules with structural heterogeneity. The central challenge is to estimate the underlying distribution of confor- mational states from these observations. In our approach, high-dimensional data are first mapped into a low-dimensional latent space, where conformational variability is more directly represented but the noise becomes heterogeneous and anisotropic. In this work, we study density estimation in this latent space using Gaussian mixture models (GMMs) as an approximation. We develop an expectation–maximization (EM) algorithm that incorporates per-observation noise covariances, allowing for probabilistic denoising when fit- ting the mixture model. We evaluate the algorithm’s effectiveness for both approximating a GMM as well as capturing the underlying conformational density in cryo-EM data. Using synthetic datasets with known ground truth, we assess the performance of the algorithm’s GMM-based estimates via quantitative error metrics. The results characterize the conditions under which GMMs provide accurate density estimates and highlight limitations using a GMM for density estimation in cryo-EM heterogeneity analysis.