Mean-Field Coupling Between Local Interactions in Proteins in Relation to Chirality, Secondary, and Supersecondary Structure Formation, and Allostery.

Coarse graining is usually considered as a tool to extend the time and size scale of simulations. However, leaving out the atomistic details to keep their fingerprints in a coarse-grained model also enables us to understand better structure formation and dynamics. In this chapter, by using our scale-consistent theory of coarse graining, we demonstrate that the coarse-grained terms corresponding to the coupling between local conformational states of amino-acid residues explain secondary-structure propagation along polypeptide backbone to stabilize -helices and -strands in proteins and direct the loops preceding and following such segments of protein structure. These and related correlations are probably the still missing terms in both physics- and knowledge-based approaches to protein-structure modeling, including AlphaFold. We also show that the chirality of coarse-grained torsional potentials and, thereby, that of polypeptide backbone emerge from putting together achiral site-based torsional potentials given the phase shift due to residue chirality, and that the improper-torsional potentials that correspond to the coupling between local conformational states of the sites adjacent to a given -carbon atom enable us to model amino-acid-residue enantiomerization.