TITLE:
Discrete Differential Geometry of n-Simplices and Protein Structure Analysis
AUTHORS:
Naoto Morikawa
KEYWORDS:
Differential Geometry, n-Simplex, Discrete Mathematics, Protein Structure, Tetrahedron
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.16,
August
29,
2014
ABSTRACT: This paper proposes
a novel discrete differential geometry of n-simplices.
It was originally developed for protein structure analysis. Unlike previous
works, we consider connection between space-filling n-simplices. Using cones of an integer lattice, we introduce
tangent bundle-like structure on a collection of n-simplices naturally. We have applied the mathematical framework
to analysis of protein structures. In this paper, we propose a simple encoding
method which translates the conformation of a protein backbone into a 16-valued
sequence.