Revisiting The Ramachandran Plot: Hard-Sphere Repulsion, Electrostatics, And H-Bonding In The Alpha-Helix

What determines the shape of the allowed regions in the Ramachandran plot?
Although Ramachandran explained these regions in terms of 1-4 hard-sphere
repulsions, there are discrepancies with the data where, in particular, the
alphaR, alphaL, and beta-strand regions are diagonal. The alphaR-region also
varies along the alpha-helix where it is constrained at the center and the amino
terminus but diffuse at the carboxyl terminus. By analyzing a high-resolution
database of protein structures, we find that certain 1-4 hard-sphere repulsions
in the standard steric map of Ramachandran do not affect the statistical
distributions. By ignoring these steric clashes (NH(i+1) and O(i-1)C), we
identify a revised set of steric clashes (CbetaO, O(i-1)N(i+1), CbetaN(i+1),
O(i-1)Cbeta, and O(i-1)O) that produce a better match with the data. We also find
that the strictly forbidden region in the Ramachandran plot is excluded by
multiple steric clashes, whereas the outlier region is excluded by only one
significant steric clash. However, steric clashes alone do not account for the
diagonal regions. Using electrostatics to analyze the conformational dependence
of specific interatomic interactions, we find that the diagonal shape of the
alphaR and alphaL-regions also depends on the optimization of the NH(i+1) and
O(i-1)C interactions, and the diagonal beta-strand region is due to the alignment
of the CO and NH dipoles. Finally, we reproduce the variation of the Ramachandran
plot along the alpha-helix in a simple model that uses only H-bonding
constraints. This allows us to rationalize the difference between the amino
terminus and the carboxyl terminus of the alpha-helix in terms of backbone
entropy.