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Algorithmic computation of knot polynomials of secondary structure elements of proteins

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)1503-1512
Number of pages10
JournalJournal of Computational Biology
Issue number8
Publication statusPublished - 1 Oct 2006
Externally publishedYes
Publication typeA1 Journal article-refereed


The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure - α-helix, antiparallel β-sheet, and parallel β-sheet - and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm - not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.


  • Knot polynomial, Planar graph, Protein structure, Topological invariant, Tutte polynomial