%0 Journal Article
%T Discrete Differential Geometry and the Structural Study of Protein Complexes
%A Naoto Morikawa
%J Open Journal of Discrete Mathematics
%P 148-164
%@ 2161-7643
%D 2017
%I Scientific Research Publishing
%R 10.4236/ojdm.2017.73014
%X 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 <em>n</em>-simplices (<em>n</em>=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 <em>n</em>-simplices which fills the <em>n</em>-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 <em>n</em>=2 using the discrete differential geometry of triangles (<em>i.e.</em>, 2-simplices).
%K Discrete Differential Geometry
%K &lt
%K i&gt
%K n&lt
%K /i&gt
%K -Simplices
%K Hamiltonian Cycle Problem
%K Protein Complexes
%K Vector Bundle
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=77508