Long proteins with unique optimal foldings in the H-P model

Authors:
Oswin Aichholzer;David Bremner;Erik D. Demaine;Henk Meijer;Vera Sacristán;Michael Soss
Affiliations:
Institut fur Grundlagen der Informationsverarbeitung, Technische Universität Graz, Inffeldgasse 16b, A-8010 Graz, Austria;Faculty of Computer Science, University of New Brunswick, P.O. Box 4400, Fredericton, N.B. E3B 5A3, Canada;MIT Laboratory for Computer Science, 200 Technology Square, Cambridge, MA;Department of Computing and Information Science, Queen's University, Kingston, Ontario K7L 3N6, Canada;Department de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain;Chemical Computing Group, 1010 Sherbrooke St. West, Suite 910, Montreal, Quebec H3A 2R7, Canada
Venue:
Computational Geometry: Theory and Applications - Special issue: The European workshop on computational geometry -- CG01
Year:
2003

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Abstract

It is widely accepted that (1) the natural or folded state of proteins is a global energy minimum, and (2) in most cases proteins fold to a unique state determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic) model is a simple combinatorial model designed to answer qualitative questions about the protein folding process. In this paper we consider a problem suggested by Brian Hayes in 1998: what proteins in the two-dimensional H-P model have unique optimal (minimum energy) foldings? In particular, we prove that there are closed chains of monomers (amino acids) with this property for all (even) lengths; and that there are open monomer chains with this property for all lengths divisible by four.