Discrete Differential Geometry and the Structural Study of Protein Complexes

Naoto  Morikawa

doi:10.4236/ojdm.2017.73014

Naoto Morikawa

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).

Keywords: Discrete Differential Geometry, n-Simplices, Hamiltonian Cycle Problem, Protein Complexes, Vector Bundle

Cite this paper: Morikawa, N. (2017) Discrete Differential Geometry and the Structural Study of Protein Complexes. Open Journal of Discrete Mathematics, 7, 148-164. doi: 10.4236/ojdm.2017.73014.

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