Cryo-EM skips the density-map detour: EB-FM learns atomic-coordinate conformational distributions straight from 2D projections
Synopsis
Standard cryo-EM pipelines first reconstruct a 3D density from 2D projections and only then fit an atomic model, so atomic-coordinate priors never reach the most under-determined stage. EB-FM trains a flow-matching prior inside a Monte Carlo stochastic-approximation expectation-maximization loop, repeatedly inverting the nonlinear imaging forward model during training, so no clean structures are needed for pretraining. On simulated cryo-EM data with known poses it recovers conformational distributions directly in atomic-coordinate space for four proteins, though predicted motion amplitudes stay below the molecular-dynamics ground truth.
Interpretation
Cryo-EM conformational heterogeneity can be learned directly as a generative prior in atomic-coordinate space, without passing through a 3D density map as an intermediate product. Classical pipelines target a single consensus structure and handle heterogeneity only through discrete clustering; deep methods such as cryoDRGN and 3DFlex learn continuous latent representations but still work in two stages, reconstructing 3D density or voxel grids from 2D projections and fitting atomic models to those densities afterward, so the density stage has no atomic-coordinate prior and the fitting stage no longer sees the raw images. On simulated data for four ATLAS proteins, EB-FM's EMD-RMSD beats cryoDRGN-guided AlphaFold3 on all four proteins, with nearly identical performance on 3rjs_A; coverage RMSD is better on three of four, and fidelity RMSD better on only one.
The prior can be trained without clean 3D conformations, using only noisy 2D projections, by repeatedly inverting the forward model during training. The standard flow-matching objective requires drawing clean samples from the target distribution, and in de novo discovery clean conformations are never directly observed, so that objective is intractable. On the 2D two-moons benchmark, as measurement dimension falls and posterior uncertainty grows, DiEM-iso loses structure and mode-collapses at smaller dimensions, EB-FM without persistent latents loses structure at still smaller dimensions, and only full EB-FM with persistent latents resolves non-collapsed distributions at the lowest dimension.
In practice each observation carries a persistent latent, updated by stochastic approximation into a moving average of the posterior mean, and the flow-matching prior is retrained on this stabilized latent ensemble. Single-sample Monte Carlo posterior sampling is high-variance, while drawing many samples per observation is prohibitive for flow models that need multi-step guided sampling. On simulated cryo-EM data, optimization with only rendering and backbone losses diverges to degenerate structures, whereas training the prior in parallel lets information flow across observations and gradually capture the conformational distribution; optimized latents improve substantially over initialization for all proteins, and unconditional samples reach RMSD values close to the optimized latents.
Perspective
The demonstrated scope is four ATLAS proteins simulated with molecular dynamics and a transmission-electron-microscope simulator under known poses, using backbone atoms only; the method targets differentiable nonlinear forward models, and code is available.
In real data the pose is an unknown parameter of the forward model, and mismatch between simulated and real data remains an open challenge; predicted ensembles underestimate the absolute magnitude of conformational change across all four proteins, identifying flexible regions without fully recovering motion amplitude; the method also remains computationally expensive at the current scale.