Discrete Differential Geometry of n-Simplices and Protein Structure Analysis

Naoto Morikawa

Genocript, Zama, Japan.

DOI: 10.4236/am.2014.516237                

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.

Keywords

Differential Geometry, n-Simplex, Discrete Mathematics, Protein Structure, Tetrahedron

Conflicts of Interest

The authors declare no conflicts of interest.

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