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Energy density functions for protein structures

Journal Article


Abstract


  • In this paper, we adopt the calculus of variations to study the

    protein folding problem with an energy functional dependent on the

    curvature, torsion and the derivatives of both the curvature and

    torsion of the protein backbone. Minimizing this energy amongst

    smooth normal variations yields two Euler-Lagrange equations, which

    can be reduced to a single equation. In the case when the energy depends only on

    the curvature and torsion, it can be shown that the free energy

    density is the form of a homogeneous function of degree one. Another

    simple special solution for this case is shown to coincide with an

    energy density linear in curvature which has been examined in detail

    by previous authors. The Euler-Lagrange equations are illustrated

    with reference to certain simple special cases of the energy density

    function, and a family of conical helices, which has not been

    studied previously, is examined in some detail.

Authors


  •   Thamwattana, Ngamta (external author)
  •   McCoy, James A.
  •   Hill, Jim M. (external author)

Publication Date


  • 2008

Citation


  • Thamwattana, N., McCoy, J. A. & Hill, J. (2008). Energy density functions for protein structures. Quarterly Journal of Mechanics and Applied Mathematics, 61 (3), 431-452.

Scopus Eid


  • 2-s2.0-48849113967

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2568

Has Global Citation Frequency


Number Of Pages


  • 21

Start Page


  • 431

End Page


  • 452

Volume


  • 61

Issue


  • 3

Abstract


  • In this paper, we adopt the calculus of variations to study the

    protein folding problem with an energy functional dependent on the

    curvature, torsion and the derivatives of both the curvature and

    torsion of the protein backbone. Minimizing this energy amongst

    smooth normal variations yields two Euler-Lagrange equations, which

    can be reduced to a single equation. In the case when the energy depends only on

    the curvature and torsion, it can be shown that the free energy

    density is the form of a homogeneous function of degree one. Another

    simple special solution for this case is shown to coincide with an

    energy density linear in curvature which has been examined in detail

    by previous authors. The Euler-Lagrange equations are illustrated

    with reference to certain simple special cases of the energy density

    function, and a family of conical helices, which has not been

    studied previously, is examined in some detail.

Authors


  •   Thamwattana, Ngamta (external author)
  •   McCoy, James A.
  •   Hill, Jim M. (external author)

Publication Date


  • 2008

Citation


  • Thamwattana, N., McCoy, J. A. & Hill, J. (2008). Energy density functions for protein structures. Quarterly Journal of Mechanics and Applied Mathematics, 61 (3), 431-452.

Scopus Eid


  • 2-s2.0-48849113967

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2568

Has Global Citation Frequency


Number Of Pages


  • 21

Start Page


  • 431

End Page


  • 452

Volume


  • 61

Issue


  • 3