Discrete Differential Geometry and the Structural Study of Protein Complexes

• 作者: Naoto Morikawa
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: DISCRETE Differential GEOMETRY n-Simplices HAMILTONIAN Cycle Problem Protein COMPLEXES Vector BUNDLE
• 年，卷（期）: 2017,（3）
• 页码范围: 148-164
• 页数: 17页
• 分类号: O1

摘要

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).