Firstly, let me review previous works on DDG and protein structure analysis.
As for DDG of protein backbone, the pioneer work of Rackovsky and Scheraga in 1978 is known. In their method, proteins are represented as spatial broken lines and they defined curvature and torsion at each vertex. In particular, they defined tangent vector at vertex ri as shown on the right.
But, protein backbone structure is usually studied via classification and differential geometrical approach is not taken these days.
On the other hand, since proteins are a molecule, they have surface. And a bunch of works on DDG of surface are known.
To name a few, Forman proposed a discrete version of Morse theory.
And the BioGeometry project at Duke univ. and others studied geometry of protein in general.
In Germany, there is a MATHEON project on dis. surface parametrizations.
If you visit the homepage of the MSRI, you will find some video lectures on related topics.