Energy density functions for protein folding structures
Date
2008
Authors
Thamwattana, N.
McCoy, J.
Hill, J.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
Quarterly Journal of Mechanics and Applied Mathematics, 2008; 61(3):431-451
Statement of Responsibility
Ngamta Thamwattana, James A. Mccoy and James M. Hill
Conference Name
Abstract
In 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.
School/Discipline
Dissertation Note
Provenance
Description
Access Status
Rights
Copyright The author 2008. Published by Oxford University Press; all rights reserved.