Find amino acids in unusual regions of the Ramachandran diagram
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Ramachandran diagram (https://en.wikipedia.org/wiki/Ramachandran_plot)
is a great tool to check the quality of the protein model (of course,
one of the quality aspects). In the R. diagram, each amino acid (a.r.)
is assigned point in a two-dimensional plane using that a.r. dihedral
angles φ and ψ as the coordinates of this point. Is it possible to
apply the diagram of R. not to individual a.r., but to evaluate the
entire protein chain, i.e. according to R.  chart to count one number
that represents that circuit "quality"?

Questions:

- how to estimate how much a.r. are in the "authorized" ones, and how
  many others R. in chart areas? How can zone shapes be approximated?
  How estimate the errors we will make in approximating R. permissible
  district borders in rectangles? circles? Ellipses?

- How does the approximation of the allowed zone affect the
  calculation speed?

- In all structures described in the PDB, do a.r. are allowed R. in
  the chart districts? What is the average a.r. "forbidden" zones?
  What is this a.r. number distribution?

- Are there proteins in the PDB archive with more than usual
  a.r. located in the disallowed areas of the R. chart? If so, is it
  real, physically possible structures? Are such structures found in
  living nature? How to classify such structures?

Program:

This research requires a program that reads PDB archive files and
determines a number of a.r. residues for each protein chain that are
in disallowed regions of the R. diagram. For debugging and program
verification purposes, it would be worthwhile to provide the
possibility to output all values of the φ and ψ angles.