TITLE:
Discrete Differential Geometry and the Structural Study of Protein Complexes
AUTHORS:
Naoto Morikawa
KEYWORDS:
Discrete Differential Geometry, n-Simplices, Hamiltonian Cycle Problem, Protein Complexes, Vector Bundle
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.7 No.3,
July
10,
2017
ABSTRACT: This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices (n=2,3,4...), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find “a set of” closed trajectories of n-simplices which fills the n-dimensional region defined by a given pair of n+1 -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of n=2 using the discrete differential geometry of triangles (i.e., 2-simplices).