Protein structure determination has long been one of the primary challenges of structural biology, to which deep machine learning (ML)-based approaches have increasingly been applied. However, these ML models generally do not incorporate the experimental measurements directly, such as X-ray crystallographic diffraction data. To this end, we explore an approach that more tightly couples these traditional crystallographic and recent ML-based methods, by training a hybrid 3-d vision transformer and convolutional network on inputs from both domains. We make use of two distinct input constructs / Patterson maps, which are directly obtainable from crystallographic data, and "partial structure" template maps derived from predicted structures deposited in the AlphaFold Protein Structure Database with subsequently omitted residues. With these, we predict electron density maps that are then post-processed into atomic models through standard crystallographic refinement processes. Introducing an initial dataset of small protein fragments taken from Protein Data Bank entries and placing them in hypothetical crystal settings, we demonstrate that our method is effective at both improving the phases of the crystallographic structure factors and completing the regions missing from partial structure templates, as well as improving the agreement of the electron density maps with the ground truth atomic structures. This work has been accepted in Acta Crystallographic section D.

Determining protein structures at an atomic level remains a significant challenge in structural biology. We introduce $\texttt{RecCrysFormer}$, a hybrid model that exploits the strengths of transformers with the aim of integrating experimental and ML approaches to protein structure determination from crystallographic data. $\texttt{RecCrysFormer}$ leverages Patterson maps and incorporates known standardized partial structures of amino acid residues to directly predict electron density maps, which are essential for constructing detailed atomic models through crystallographic refinement processes. $\texttt{RecCrysFormer}$ benefits from a ``recycling'' training regimen that iteratively incorporates results from crystallographic refinements and previous training runs as additional inputs in the form of template maps. Using a preliminary dataset of synthetic peptide fragments based on Protein Data Bank, $\texttt{RecCrysFormer}$ achieves good accuracy in structural predictions and shows robustness against variations in crystal parameters, such as unit cell dimensions and angles.

Determining the structure of a protein has been a decades-long open question. A protein's three-dimensional structure often poses nontrivial computation costs, when classical simulation algorithms are utilized. Advances in the transformer neural network architecture -- such as AlphaFold2 -- achieve significant improvements for this problem, by learning from a large dataset of sequence information and corresponding protein structures. Yet, such methods only focus on sequence information; other available prior knowledge, such as protein crystallography and partial structure of amino acids, could be potentially utilized. To the best of our knowledge, we propose the first transformer-based model that directly utilizes protein crystallography and partial structure information to predict the electron density maps of proteins. Via two new datasets of peptide fragments (2-residue and 15-residue) , we demonstrate our method, dubbed \texttt{CrysFormer}, can achieve accurate predictions, based on a much smaller dataset size and with reduced computation costs.

This work demonstrates that, for a simple case of 10 randomly positioned atoms, a neural network can be trained to infer atomic coordinates from Patterson maps. The network was trained entirely on synthetic data. For the training set, the network outputs were 3D maps of randomly positioned atoms. From each output map, a Patterson map was generated and used as input to the network. The network generalized to cases not in the test set, inferring atom positions from Patterson maps. A key finding in this work is that the Patterson maps presented to the network input during training must uniquely describe the atomic coordinates they are paired with on the network output or the network will not train and it will not generalize. The network cannot train on conflicting data. Avoiding conflicts is handled in 3 ways: 1. Patterson maps are invariant to translation. To remove this degree of freedom, output maps are centered on the average of their atom positions. 2. Patterson maps are invariant to centrosymmetric inversion. This conflict is removed by presenting the network output with both the atoms used to make the Patterson Map and their centrosymmetry-related counterparts simultaneously. 3. The Patterson map does not uniquely describe a set of coordinates because the origin for each vector in the Patterson map is ambiguous. By adding empty space around the atoms in the output map, this ambiguity is removed. Forcing output atoms to be closer than half the output box edge dimension means the origin of each peak in the Patterson map must be the origin to which it is closest.