Protein Structure Description with ρ, θ and ϕ : A Case Study with Caenopore-5

Since its establishment in 1971, the Protein Data Bank (PDB) has been using Cartesian coordinate system (CCS) as the standard framework for protein structure description with x, y, z . Despite the interconvertibility of CCS and spherical coordinate systems (SCS, ρ, θ and ϕ ), CCS remains to date the default and the only framework for protein structure description in PDB. Recent advances in protein structure prediction (e.g., AlphaFold) revolutionized the field by integrating deep learning algorithms with experimental structural data, achieving unprecedented accuracy of protein structure prediction and relying on Cartesian representation of protein structures to extract geometric features. To this end, questions remain about what drives the next stage of continued performance improvement of protein structure prediction. Therefore, this article introduces an alternative coordinate system for protein structure description and feature extraction. Using Caenopore-5 as an example, this article redefines protein backbone structures using atomic bonding networks (ABN) within the SCS framework (ABN-SCS), leading to the extraction of a set of spherical parameters ( ρ, θ and ϕ ) from the NMR ensemble of Caenopore-5, encompassing 477 covalent bonds and 80 peptide bonds within its backbone for each structural model in its NMR ensemble. Finally, this work demonstrates that ABN-SCS enables characterization of spherical bond-level geometries, expanding the feature space available for computational pipelines such as AlphaFold2, and argues that integrating ABN-SCS features into protein structure prediction pipelines can enhance geometric fidelity, and that the time is now ripe for the trapped spherical features [ ρ, θ, ϕ ] to be integrated into algorithms such as AF2 towards protein structure prediction with improved performance.