While going through the paper titled "GEOMETRIC ANALYSIS OF THE CONFORMATIONAL FEATURES OF PROTEIN STRUCTURES" by Manish Dutt, I came to know that there is a correlation between the radius of gyration and the number of layers of convex hull of each proteins 3D structure (convex hull layers are formed by forming the convex hull of a set of points, which forms the first layer, then removing them, and recalculating another set of boundary points, i.i., second convex hull, which form the second layer).

Now my questions is, what is the biological significance of this correlation? Or is there any?

  • $\begingroup$ What is a 'layer' of a convex hull? As far as I know, there is just one hull layer (the minimal bounding surface containing all the points) $\endgroup$ – gilleain Sep 15 '16 at 10:45
  • $\begingroup$ Never mind I'm guessing that you can nest hulls by removing the points on the outer hull and re-calculating. Still worth describing this in your question, I think $\endgroup$ – gilleain Sep 15 '16 at 10:52
  • $\begingroup$ @gilleain I have edited the question. Hope you can understand it now... $\endgroup$ – girl101 Sep 15 '16 at 11:27

From reading the paper, I don't see any obvious biological significance. The abstract says:

Proteins exhibit intriguing diversity in their three-dimensional conformations that enables them to perform different functions

Which is great, but there is no connection in this paper between conformation and function - not surprisingly as this is a large part of structural protein analysis!

The way I look at this work is similar to the idea of a "descriptor" from the field of Cheminformatics. The radius of gyration is a descriptor, and so is this hull number. The author claims a correlation between these two descriptors, so... is one easier to calculate than the other?

This is interesting work, but I'm not sure at this point what the significance of hull number is for protein structural analysis. However I can say that the correlation between these two descriptors is not biologically significant - it's just a geometric relationship that would presumably hold for any set of 3D points.

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