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Updated: Jul 13, 2026

Spatial Separation of Molecular Conformers and Clusters
Published on: January 9, 2014
Generation and enumeration of compact conformations on the two-dimensional triangular and three-dimensional fcc
Myron Peto1, Taner Z Sen, Robert L Jernigan
1Department of Biochemistry, Biophysics and Molecular Biology, Iowa State University, Ames, Iowa 50011-3020, USA.
Abstract:
We enumerated all compact conformations within simple geometries on the two-dimensional (2D) triangular and three-dimensional (3D) face centered cubic (fcc) lattice. These compact conformations correspond mathematically to Hamiltonian paths and Hamiltonian circuits and are frequently used as simple models of proteins. The shapes that were studied for the 2D triangular lattice included mxn parallelograms, regular equilateral triangles, and various hexagons. On the 3D fcc lattice we generated conformations for a limited class of skewed parallelepipeds. Symmetries of the shape were exploited to reduce the number of conformations. We compared surface to volume ratios against protein length for compact conformations on the 3D cubic lattice and for a selected set of real proteins. We also show preliminary work in extending the transfer matrix method, previously developed by us for the 2D square and the 3D cubic lattices, to the 2D triangular lattice. The transfer matrix method offers a superior way of generating all conformations within a given geometry on a lattice by completely avoiding attrition and reducing this highly complicated geometrical problem to a simple algebraic problem of matrix multiplication.
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