XDXD: End-to-end crystal structure determination with low resolution X-ray diffraction

TL;DR

XDXD addresses the bottleneck of solving crystal structures from low-resolution X-ray diffraction by delivering an end-to-end diffusion-based model that outputs a full atomic model conditioned on the diffraction pattern. Trained on about $3.95\times 10^5$ simulated patterns and tested on approximately 24,000 experimental COD structures, it handles unit cells with up to 200 non-hydrogen atoms. At data limited to $2.0$ Å, XDXD achieves a match rate of about 70.4% with RMSE below $0.05$, using 16 candidate structures ranked by cosine similarity to the observed pattern. The method generalizes to peptides (backbone RMSD < $1.5$ Å) without peptide-specific training, indicating potential for macromolecular crystallography and fully automated structure solution in challenging cases.

Abstract

Determining crystal structures from X-ray diffraction data is fundamental across diverse scientific fields, yet remains a significant challenge when data is limited to low resolution. While recent deep learning models have made breakthroughs in solving the crystallographic phase problem, the resulting low-resolution electron density maps are often ambiguous and difficult to interpret. To overcome this critical bottleneck, we introduce XDXD, to our knowledge, the first end-to-end deep learning framework to determine a complete atomic model directly from low-resolution single-crystal X-ray diffraction data. Our diffusion-based generative model bypasses the need for manual map interpretation, producing chemically plausible crystal structures conditioned on the diffraction pattern. We demonstrate that XDXD achieves a 70.4\% match rate for structures with data limited to 2.0~Å resolution, with a root-mean-square error (RMSE) below 0.05. Evaluated on a benchmark of 24,000 experimental structures, our model proves to be robust and accurate. Furthermore, a case study on small peptides highlights the model's potential for extension to more complex systems, paving the way for automated structure solution in previously intractable cases.

Figures (5)

• Figure 1: XDXD model architecture. The X-ray diffraction (XRD) signal is first preprocessed and then passed through an XRD encoder to obtain the corresponding XRD embedding. In parallel, the molecular graph embedding layer encodes atom types and bonds. Subsequently, the embeddings from the XRD encoder and the molecular graph embedding layer are jointly fed into the Diffraction Signal Conditioned Crystal Structure Prediction (DCSP) module. Within the DCSP module, pair embeddings are computed via outer-product, tri-multiplication, Graphormer layers, and edge aggregation operations. The final structure prediction is derived from the atom node embeddings. Meanwhile, atom node embeddings interact with pair embeddings through outer-product operations and Graphormer modules. Additionally, the XRD embeddings and atom node embeddings are integrated through a cross-attention mechanism.
• Figure 2: Evaluation results on experimental data.a. The match rate is analyzed across various atom-count intervals. b. The Root Mean Square Error (RMSE) is evaluated across different atom-count intervals. c. The generation process for C16H13NO2 with the space group 'P b c a'. d. Electron density is simulated using the experimental amplitude and a simulated phase derived from the predicted structure. e. The experimental structure is compared with the structure factor simulated from the predicted structure.
• Figure 3: Evaluation of diffraction pattern consistency.a, b. Cosine similarity between structure factors simulated from the predicted structure and the experimental structure, evaluated for signal resolutions lower than 2 Å. c, d. R1 value between structure factors simulated from the predicted structure and the experimental structure, for signal resolutions below 2 Å.
• Figure 4: Evaluation Results Based on Space Group and Elemental Composition.a. Evaluation of match rate and RMSE for crystals containing only non-metal elements. b. Evaluation of match rate and RMSE for crystals containing metal elements. c. Heatmap of RMSE as a function of the number of atoms and space groups. The number in parentheses under RMSE denotes the number of samples in the test set. d. Evaluation of match rate and RMSE across different space groups.
• Figure 5: XDXD predictions of small molecule and peptide structures. Predicted structures are shown in darker colors, while reference structures from the COD or RCSB are shown in lighter colors.a-c. Small molecule structure with chemical composition C$_{12}$H$_{19}$NO$_{2}$ and space group P -4 21 c. d-f. Small molecule structure with space group P a -3 and chemical composition C$_{24}$H$_{48}$Cl$_{6}$Fe$_{3}$O$_{7}$. h-j. Small molecule structure with space group P 42 b c and chemical composition C$_{11}$H$_{12}$BrNO$_{2}$. b,c,e,f,i,j. Scatter plots of observed versus simulated structure factors for the COD-retrieved structure and the predicted structure of the corresponding row. k. Predicted protein structure for PDB ID 5zmz (peptide) compared with the reference structure from RCSB. l. Predicted protein structure for PDB ID 2olx (peptide) compared with the reference structure from RCSB.