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Gerstein, M and Richards, F.M. (2001) Protein Geometry: Volumes, Areas, and Distances. In: Rossman, M.G. and Arnold, E., Eds., The International Tables for Crystallography, Vol. F, Chap. 22, Kluwer, Dordrecht, 531-539.

has been cited by the following article:

• 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).