A Reversible Spherical Geometric Conversion of Protein Backbone Structure Coordinate Matrix to Three Independent Vectors of ρ, θ and φ

Due to the vast conformational space proteins can adopt, accurate and efficient prediction of protein structure remains still a challenging task, coupled with the intricacies of interatomic interactions and the limitations of current computational models in effectively navigating this complex molecular landscape. Additionally, the lack of comprehensive experimental data for all protein structures further exacerbates the difficulty in reliable machine learning-based prediction of the three-dimensional conformations of the proteios building block of life. Geometrically, Cartesian coordinate system (CCS, X, Y and Z) and spherical coordinate system (SCS, , and ) are two interconvertible coordinate systems, and are like two sides of one coin. Since the beginning of Protein Data Bank (PDB) in 1971, CCS has been the default approach to specify atomic positions with X, Y and Z in PDB. In this manuscript, therefore, I present a novel method for the reversible spherical geometric conversion of protein backbone structure coordinate matrices to three independent vectors: , and . This reversible conversion facilitates lossless extraction of essential structural features from protein backbone structural data, enabling the development of advanced novel algorithms for protein structure prediction in future. In short, this inter-atomic SCS approach offers a comprehensive yet efficient means of representing protein backbone geometry, leveraging spherical coordinates to capture spatial relationships in a compact and intuitive inter-atomic manner, and to provide a robust framework for reversible feature extraction for the ongoing efforts in advancing the field of protein structure prediction, the holy grail of computational structural biology.