The recent breakthrough of AlphaFold3 in modeling complex biomolecular interactions, including those between proteins and ligands, nucleotides, or metal ions, creates new opportunities for protein design. In so-called inverse protein folding, the objective is to find a sequence of amino acids that adopts a target protein structure. Many inverse folding methods struggle to predict sequences for complexes that contain non-protein components, and perform poorly with complexes that adopt multiple structural states. To address these challenges, we present ADFLIP (All-atom Discrete FLow matching Inverse Protein folding), a generative model based on discrete flow-matching for designing protein sequences conditioned on all-atom structural contexts. ADFLIP progressively incorporates predicted amino acid side chains as structural context during sequence generation and enables the design of dynamic protein complexes through ensemble sampling across multiple structural states. Furthermore, ADFLIP implements training-free classifier guidance sampling, which allows the incorporation of arbitrary pre-trained models to optimise the designed sequence for desired protein properties. We evaluated the performance of ADFLIP on protein complexes with small-molecule ligands, nucleotides, or metal ions, including dynamic complexes for which structure ensembles were determined by nuclear magnetic resonance (NMR). Our model achieves state-of-the-art performance in single-structure and multi-structure inverse folding tasks, demonstrating excellent potential for all-atom protein design. The code is available at https://github.com/ykiiiiii/ADFLIP .

Electron cryo-microscopy (cryo-EM) is a powerful method for investigating the structures of protein molecules, with important implications for understanding the molecular processes of life and drug development. In this technique, many noisy, two-dimensional projection images of protein molecules in unknown poses are combined into one or more three-dimensional reconstructions. The presence of multiple structural states in the data represents a major bottleneck in existing processing pipelines, often requiring expert user supervision. Variational auto-encoders (VAEs) have recently been proposed as an attractive means for learning the data manifold of data sets with a large number of different states. These methods are based on a coordinate-based approach, similar to Neural Radiance Fields (NeRF), to make volumetric reconstructions from 2D image data in Fourier-space. Although NeRF is a powerful method for real-space reconstruction, many of the benefits of the method do not transfer to Fourier-space, e.g. inductive bias for spatial locality. We present an approach where the VAE reconstruction is expressed on a volumetric grid, and demonstrate how this model can be trained efficiently through a novel backpropagation method that exploits the sparsity of the projection operation in Fourier-space. We achieve improved results on a simulated data set and at least equivalent results on an experimental data set when compared to the coordinate-based approach, while also substantially lowering computational cost. Our approach is computationally more efficient, especially in inference, enabling interactive analysis of the latent space by the user.