Geometric Algebra Models of Proteins for Three-Dimensional Structure Prediction: A Detailed Analysis

A protein can be regarded as a chain of amino acids with a unique folding in the three-dimensional (3D) space. Knowing the folding of a protein is highly desirable since the folding controls the protein properties. However, determining it experimentally is expensive and time consuming: estimating the 3D structure of a protein computationally—known as protein structure prediction (PSP)—can overcome these issues. In this paper, we explore the advantage of using Geometric Algebra (GA) to model proteins for PSP applications. In particular, we employ GA to define a metric over the orientations of the amino acids in the chain. We then encode this metric in matrix form and show how patterns in these images mirror folding patterns of proteins. Lastly, we prove that this metric is predictable through a standard deep learning (DL) architecture for the inference of pairwise amino acid distances. We demonstrate that GA is a powerful tool for obtaining a compact representation of the protein geometry with potential to improve the prediction accuracy of standard PSP pipelines.