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Modeling orientational features via Geometric Algebra for 3D protein coordinates prediction
  • Alberto Pepe,
  • Joan Lasenby
Alberto Pepe
University of Cambridge Department of Engineering

Corresponding Author:ap2219@cam.ac.uk

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Joan Lasenby
University of Cambridge Department of Engineering
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By protein structure prediction (PSP) we refer to the prediction of the 3-dimensional (3D) folding of a protein, known as tertiary structure, starting from its amino acid sequence, known as primary structure. The state-of-the-art in PSP is currently achieved by complex deep learning pipelines that require several input features extracted from amino acid sequences. It has been demonstrated that features that grasp the relative orientation of amino acids in space positively impacts the prediction accuracy of the 3D coordinates of atoms in the protein backbone. In this paper, we demonstrate the relevance of Geometric Algebra (GA) in instantiating orientational features for PSP problems. We do so by proposing two novel GA-based metrics which contain information on relative orientations of amino acid residues. We then employ these metrics as an additional input features to a Graph Transformer (GT) architecture to aid the prediction of the 3D coordinates of a protein, and compare them to classical angle-based metrics. We show how our GA features yield comparable results to angle maps in terms of accuracy of the predicted coordinates. This is despite being constructed from less initial information about the protein backbone. The features are also fewer and more informative, and can be (i) closely associated to protein secondary structures and (ii) more readily predicted compared to angle maps. We hence deduce that GA can be employed as a tool to simplify the modeling of protein structures and pack orientational information in a more natural and meaningful way.
14 Jan 2023Submitted to Mathematical Methods in the Applied Sciences
18 Jan 2023Assigned to Editor
18 Jan 2023Submission Checks Completed
23 Jan 2023Review(s) Completed, Editorial Evaluation Pending
25 Jan 2023Reviewer(s) Assigned