# Why isn't the Ramachandran plot symmetric?

Since only relative position of groups along a bond is considered while calculating torsional strain and considering "+" and "-" means clockwise and anti clock wise rotation, shouldn't any set of $$\phi$$ and $$\psi$$ angle say (x, y) satisfying the energy consideration have correspondingly (-x,-y) since they are relatively the same configuration? But only the Ramachandran plot for glycine shows this symmetry, see below, why doesn't this show for all the proteins?

• Not what you are looking for per se, but note that the Ramachandran plot is a field over a subset of $\mathbb{R}^2$. Such a field will have a parity decomposition which relates to reflection invariance (symmetry) and reflection equivariance (i.e. odd "symmetry"). Apr 29, 2022 at 18:20
• Welcome to SE Biology. However . I can't understand your question as it stands, and I've published papers with Ramachandran plots in them. To explain something like this you absolutely need a diagram and you need to explain exactly what Ramachandran plot you are referring to. (And please do not give links to common terms from Wikipedia — we don't need to know what glycine is, but a plot of glycine in some context showing symmetry would help.) Apr 30, 2022 at 21:15
• Wikipedia has a Rama plot of glycine. Is that representative of the symmetry you mentioned? May 2, 2022 at 19:24
• @AgnesianOperator yes
– veke
May 3, 2022 at 14:24

but only the Ramachandran plot for glycine shows this symmetry

With the exception of glycine, all the common amino acids exhibit chirality at the carbon atom adjacent to the carboxyl group.

Except for glycine, the amino acids exist as chiral molecules in two forms, the L- and D-enantiomers. Although the two enantiomers exhibit identical physical and chemical properties, living organisms use only amino acids of L-chirality.

Jeong, Y., Kim, H.W., Ku, J. et al. Breakdown of chiral recognition of amino acids in reduced dimensions. Sci Rep 10, 16166 (2020).

• +1 I thought of this but wasn't confident. In principle if we switched the left-right handedness of each chiral center, would we expect to see the reflection of the original Rama plot on the Rama plot of the reflected molecule? Apr 29, 2022 at 18:23
• That sounds correct to me. Apr 29, 2022 at 18:25

It's awkward answering your own question, but I think I have now realized where my misconception arose from. If we look at the 3 dimensional structure of a protein

and consider the third alpha carbon to visualize. Let us take phi and psi as (x, y) and (-x, -y), then the groups associated with nitrogen and carbonyl carbon attached to alpha carbon are relatively in same configuration for both (x, y) and (-x, -y) but here we are missing to consider the relative configuration of groups attached to carbonyl carbon and nitrogen with respect to the group attached to the alpha carbon, since if a clockwise rotation of psi brings the oxygen attached to the nitrogen closer to hydrogen, then the anticlockwise rotation will bring the oxygen closer to the side group, thus clockwise rotation and anticlockwise rotation of phi or psi is not symmetric when considering it with respect to the alpha carbon. Since the alpha carbon of glycine has another hydrogen attached to it instead of a side chain both clockwise and anticlockwise rotation become equivalent leading to a symmetric graph. If we say that (x, y) is stable for an L- amino acid chain then (-x, -y) will be stable for D- amino acid chain (we can imagine this as R and H on alpha carbon switching places for L and D amino acids, thus the once stable counter clockwise orientation for L- amino acids will now have to be clockwise for D-amino acids for it to be stable again)

• It's awkward answering your own question - actually it's encouraged! If you find an answer to your own question otherwise, please include it as an answer. Apr 30, 2022 at 9:21