Discrete Differential Geometry of <i>n</i>-Simplices and Protein Structure Analysis

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.