Using a Graph Transformer Network to Predict 3D Coordinates of Proteins via Geometric Algebra Modelling

EasyChair Preprint 8695

Abstract

Protein Structure Prediction (PSP) is the computational estimation of the three-dimensional (3D) shape of a protein. This is a challenging problem in com- putational biology, but can significantly reduce times and costs compared with traditional experimental meth- ods. The state of the art in PSP is currently achieved by complex deep learning pipelines, composed of mul- tiple networks. The final step in the pipeline is gener- ally the prediction of the 3D coordinates of some atoms in the protein chain. In the recent literature, this last step has been performed successfully via a graph trans- former (GT) architecture. In this paper, we present a novel metric based on the relative orientations of amino acid residues and instantiated using geometric algebra (GA). We then encode this metric in matrix form and establish its relationship to the secondary structures of proteins. Lastly, we employ this matrix as an additional input feature to aid the prediction of the 3D coordinates of a protein via the GT. Adding orientational informa- tion in the form of a single additional feature in this way, significantly improves the quality of the predicted coordinates, even after few learning iterations and on a small dataset. Hence, we are able to use GA as a power- ful tool to describe protein geometry in a compact way and to improve the accuracy of PSP.

Keyphrases: Geometric Algebra, Graph Transformer, pose estimation, protein structure prediction

@booklet{EasyChair:8695,
  author    = {Alberto Pepe and Joan Lasenby and Pablo Chacon},
  title     = {Using a Graph Transformer Network to Predict 3D Coordinates of Proteins via Geometric Algebra Modelling},
  howpublished = {EasyChair Preprint 8695},
  year      = {EasyChair, 2022}}