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Take a look at the following image:

enter image description here

Is there any special meaning to the angle between two peptide planes (marked with red arrow heads)?

If so, why isn't a specific name (like phi, psi, etc.) given?

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    $\begingroup$ Hmm, I'm pretty sure that angle is just $\phi - \psi$ (or $\psi - \phi$; I guess it depends which way round you define your angle, but my point is that it's not a 'new' value). $\endgroup$ Commented Mar 23, 2023 at 0:56
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    $\begingroup$ There is an angle defined by three consecutive alpha-carbon positions, and pseudo-torsion angles defined by four consecutive alpha-carbons (for course-grained modeling). Because this is a 3-dimensional structure, the angle shown in the picture is unrelated to the angle of intersection between the peptide planes (which is about 90 deg for a alpha-helical segment and maybe 50 deg for a beta strand). $\endgroup$
    – Karsten
    Commented Mar 23, 2023 at 1:23
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    $\begingroup$ @orthocresol It is more complicated. Plus, the angle shown is ill-defined (is it a proper angle, or a dihedral, and does it depend on the position of the amide proton - which is ill-defined itself). $\endgroup$
    – Karsten
    Commented Mar 23, 2023 at 1:25
  • $\begingroup$ I stared at it again, and to be honest, I still think it is some kind of combination of $(\psi, \phi)$; but I'm fully willing to accept that I'm missing something, so I'll defer to you. I don't have a proof, it's just a strong intuition, which may be wrong. FWIW, my reading of it is this: if the peptide units are indeed planar, then the angle between them is the angle between the two normal vectors (= $\arccos(\vec{n}_1 \cdot \vec{n}_2/|\vec{n}_1||\vec{n}_2|)$). There's an ambiguity in that $\cos(x)$ is symmetric about 180°, but that can be resolved through careful definition (I think). $\endgroup$ Commented Mar 23, 2023 at 13:51
  • $\begingroup$ @orthocresol If the angle at the alpha carbon were 180 deg, then I would agree. In the conformation shown, the peptide planes are almost coplanar. If you rotate both planes by 90 deg (so that there are far outside of the plane of the paper), they would have an angle closer to 60 deg. The figure can be found here and is ambiguous about the direction of rotation (what are we keeping constant and what are we rotating). $\endgroup$
    – Karsten
    Commented Mar 25, 2023 at 3:21

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