Recent advances in protein 3D structure prediction using deep learning have focused on the importance of amino acid residue-residue connections (i.e., pairwise atomic contacts) for accuracy at the expense of mechanistic interpretability. Therefore, we decided to perform a series of analyses based on an alternative framework of residue-residue connections making primary use of the TOP2018 dataset. This framework of residue-residue connections is derived from amino acid residue pairing models both historic and new, all based on genetic principles complemented by relevant biophysical principles. Of these pairing models, three new models (named the GU, Transmuted and Shift pairing models) exhibit the highest observed-over-expected ratios and highest correlations in statistical analyses with various intra- and inter-chain datasets, in comparison to the remaining models. In addition, these new pairing models are universally frequent across different connection ranges, secondary structure connections, and protein sizes. Accordingly, following further statistical and other analyses described herein, we have come to a major conclusion that all three pairing models together could represent the basis of a universal proteomic code (second genetic code) sufficient, in and of itself, to "encode" for both protein folding mechanisms and protein-protein interactions.