Reply to: Comment on “Revisiting the Ramachandran plot from a new angle”

Dear Brian,

With this letter, we reply to Porter and Rose, who in a recent paper¹ and in their Comment on “Revisiting the Ramachandran plot from a new angle” assert that sidechain hydrogen bonding is the primary determinant of the observed population of φ/ψ backbone dihedral angles in the “bridge region” (φ ≤ 0° and −20° ≤ ψ ≤ 40°). Our manuscript “revisiting the Ramachandran plot from a new angle”² shows that steric considerations alone predict the observed backbone dihedral angle distributions. In this response, we reinterate three main points.

1. The calcuated Ramachandran plot depends critically on the value of the bond angle τ (between C^′, C_α, and N). Specifically, as τ increases within the range 100° ≤ τ ≤ 120°, configurations in the “bridge region” with φ ≤ 0° and −20° ≤ ψ ≤ 40° change from being disallowed at τ = 100° to be allowed at τ = 115° and above. In fact, this result dates back to 1965,³ but most often Ramachandran plots are drawn for a single value of τ, typically τ = 110°. The τ dependence is generally not considered.

2. We analyzed a database⁴ of high-resolution protein structures and plotted the backbone dihedral angles of all amino acids on Ramachandran plots as a function of their bond angle τ. (See Fig. 2 in Ref.2) In agreement with the predictions of Ramachandran and colleagues,³ the bridge region is populated by amino acids with large values of τ, while φ and ψ combinations in the bridge region are not frequently observed for amino acids with smaller values of τ. Thus, an increased population of structures in the bridge region at large τ is consistent with the predictions from steric interactions alone for every amino acid type.

3. The analysis and conclusions of Porter and Rose suggest that hard–sphere interactions alone cannot explain the observed distribution of backbone dihedral angles. For example, they state in the abstract that the “forbidden [bridge] region is well-populated in folded proteins, which can provide longer-range intramolecular hydrogen-bond partners.” However, using only a hard sphere model, Ramachandran and colleagues predicted the φ and ψ combinations as a function of τ that are observed in proteins of known structure. In particular, they showed that φ and ψ combinations in the bridge region are not forbidden at large τ.

It is certainly possible that hydrogen-bonding may influence the adopted value of τ (which in turn may then influence the allowed values of φ and ψ), but the existence of φ and ψ combinations within the bridge region is not on its own prime facia evidence of the role of hydrogen bonding.