Energy density functions for protein folding structures

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dc.contributor.authorThamwattana, N.
dc.contributor.authorMcCoy, J.
dc.contributor.authorHill, J.
dc.date.issued2008
dc.description.abstractIn this paper, we adopt the calculus of variations to study the structure of protein with an energy functional F(κ, τ, κ0, τ 0) dependent on the curvature, torsion and their derivatives with respect to the arc length of the protein backbone. Minimising this energy among smooth normal variations yields two Euler–Lagrange equations, which can be reduced to a single equation. This equation is identically satisfied for the special case when the free-energy density satisfies a certain linear condition on the partial derivatives. In the case when the energy depends only on the curvature and torsion, it can be shown that this condition is satisfied if the free-energy density is 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 is examined in some detail.
dc.description.statementofresponsibilityNgamta Thamwattana, James A. Mccoy and James M. Hill
dc.identifier.citationQuarterly Journal of Mechanics and Applied Mathematics, 2008; 61(3):431-451
dc.identifier.doi10.1093/qjmam/hbn012
dc.identifier.issn0033-5614
dc.identifier.issn1464-3855
dc.identifier.urihttp://hdl.handle.net/2440/63871
dc.language.isoen
dc.publisherOxford Univ Press
dc.rightsCopyright The author 2008. Published by Oxford University Press; all rights reserved.
dc.source.urihttps://doi.org/10.1093/qjmam/hbn012
dc.titleEnergy density functions for protein folding structures
dc.typeJournal article
pubs.publication-statusPublished

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