On correlation between protein secondary structure, backbone bond angles, and side-chain orientations

Abstract: We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C$\alpha$ carbon of a protein backbone, and for this we develop new visualization techniques to analyze high resolution X-ray structures in Protein Data Bank. We observe that there is a correlation between the deformations of the ideal tetrahedral symmetry and the local secondary structure of the protein. We propose a universal coarse grained energy function to describe the ensuing side-chain geometry in terms of the C$\beta$ carbon orientations. The energy function can model the side-chain geometry with a sub-atomic precision. As an example we construct the C$\alpha$-C$\beta$ structure of HP35 chicken villin headpiece. We obtain a configuration that deviates less than 0.4 .A in root-mean-square distance from the experimental X-ray structure.