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Helices for mathematical modelling of proteins, nucleic acids and polymers

Journal Article


Abstract


  • Helices occur in modelling a range of structures including ropes, fibers, polymers and biopolymers. In a recent paper with Thamwattana and Hill, the authors derived Euler-Lagrange equations for the protein folding problem, where the energy being minimised was assumed to depend only on the curvature and torsion of the protein backbone space curve and their first derivatives. Such a model is applicable to helices occurring in other scenarios and in this article the author considers more generally which energies will yield helices as solutions of their corresponding Euler-Lagrange equations. He finds in particular classes of energy for which all circular helices are solutions and an energy depending on curvature and its derivative which generates conical helices as solutions of the Euler-Lagrange equations. Also included are some new results for energies depending only on curvature, extending previous investigations by Feoli et al. (2005).

Publication Date


  • 2008

Citation


  • McCoy, J. A. (2008). Helices for mathematical modelling of proteins, nucleic acids and polymers. Journal of Mathematical Analysis and Applications, 347 (1), 255-265.

Scopus Eid


  • 2-s2.0-46449111071

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2565

Has Global Citation Frequency


Number Of Pages


  • 10

Start Page


  • 255

End Page


  • 265

Volume


  • 347

Issue


  • 1

Abstract


  • Helices occur in modelling a range of structures including ropes, fibers, polymers and biopolymers. In a recent paper with Thamwattana and Hill, the authors derived Euler-Lagrange equations for the protein folding problem, where the energy being minimised was assumed to depend only on the curvature and torsion of the protein backbone space curve and their first derivatives. Such a model is applicable to helices occurring in other scenarios and in this article the author considers more generally which energies will yield helices as solutions of their corresponding Euler-Lagrange equations. He finds in particular classes of energy for which all circular helices are solutions and an energy depending on curvature and its derivative which generates conical helices as solutions of the Euler-Lagrange equations. Also included are some new results for energies depending only on curvature, extending previous investigations by Feoli et al. (2005).

Publication Date


  • 2008

Citation


  • McCoy, J. A. (2008). Helices for mathematical modelling of proteins, nucleic acids and polymers. Journal of Mathematical Analysis and Applications, 347 (1), 255-265.

Scopus Eid


  • 2-s2.0-46449111071

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2565

Has Global Citation Frequency


Number Of Pages


  • 10

Start Page


  • 255

End Page


  • 265

Volume


  • 347

Issue


  • 1