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Why do we consider the normal and extreme limits for Ramachandran plots to be less than the Van Der Waal distances between two atoms?

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  • $\begingroup$ The calculations are done on the basis of steric hindrance faced by the side chains when the angles are changed. For instance almost at all times (0,0) for (phi,psi) are not allowed because there is clash in between the side chains. This steric clash is calculated based on the normal limit and extreme limit the maximum and minimum distance allowed between the two atoms for the conformation to be deemed stable. Both these distances though are smaller than Van Der Waal distances. $\endgroup$ Oct 20 '20 at 9:32
  • $\begingroup$ Do you have a source for this algorithm? Which is the minimum and maximum distance? I am also confused by these definitions. It would help to have a source for the table. Where did you get these numbers? $\endgroup$
    – Buck Thorn
    Oct 20 '20 at 9:40
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    $\begingroup$ I got the table itself as a part of a question paper, for reference material I suppose you could read this: skuld.bmsc.washington.edu/~merritt/bc530/local_copies/… $\endgroup$ Oct 20 '20 at 10:10
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A remarkable aspect of the Ramachandran plots is that the implementation of a hard-sphere potential with flexibility limited to the two backbone dihedrals proved sufficient to largely explain the conformational range sampled by real polypeptides. Take for instance the following map from a seminal article by Ramachandran (from Ref. 1; dashed line encloses the partially allowed region):

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The map was generated with the following set of restraints:

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In the article Ramachandran et al. explain how they selected the range of vdW distances used to generate their maps:

The next step towards working out the allowed conformations is to choose a set of permitted minimum contact distances between the different types of atoms. Only those conformations (4,4') which do not have any of the contact distances less than these minimum values now become allowed. Two such sets are given in Table II, termed "normally allowed" and "outer limit" contact distances. These are essentially the same as those given by Ramachandran, Ramakrishnan, and Sasisekha-ran (1963) arrived at from a study of the contact distances observed in structures of various organic compounds. Contact distances inbetween the two limits have also been observed in actual crystals, but not as frequently as the normally allowed values.

van der Waals radii are meant to define distances of closest approach. They are useful to identify conformational regions forbidden due to steric clashes. However, tabulated vdW radii are representative values. In real molecules the internuclear potential can vary somewhat depending on atomic types and the local electronic environment.

In addition, molecules are fairly flexible and can to a degree circumvent potential clashes by changing internuclear distances and angles, but a rigid model does not capture that. That a simple rigid model suggests a steric clash, because one or more vdW distance restraints are violated, does not guarantee that a conformation (phi/psi pair) is forbidden. Therefore, if you use a rigid model to generate a Ramachandran plot, that is, if only phi and psi are allowed to change, then you should allow "wiggle room", for instance by setting a lower threshold for the allowed values of the vdW distances. The use of "tolerances" in vdW radii should therefore not be surprising.

Close contacts can be energetically costly even with compensating rearrangements, so the associated configurational space - marked as "partially allowed" in a traditional diagram - is more sparse. In a modern approach a more descriptive potential for the protein backbone is employed, and ideally degrees of freedom other than the dihedral angles are relaxed, and energy isolines are displayed. The following, from Ref. 2, shows roughly how such a diagram might look:

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References

  1. G.N.Ramachandran, C.M. Venkatachalam, and S.Krimm. Stereochemical Criteria for Polypeptide and Protein Conformations II. Helical and Hydrogen-Bonded Polypeptide Chains. Biophysical Journal 6 (1966) 849-872.
  2. ibid, 909-933.
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