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Energy functions for stringlike continuous curves, discrete chains, and space-filling one dimensional structures
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
Shanghai University.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2013 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 87, no 10, 105011- p.Article in journal (Refereed) Published
Abstract [en]

The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the case of continuous curves, we demand that the energy function must be invariant under local frame rotations, and it should also transform covariantly under reparametrizations of the curve. This leads us to consider energy functions that are constructed from the conserved quantities in the hierarchy of the integrable nonlinear Schrödinger equation. We point out the existence of a Weyl transformation that we utilize to introduce a dual hierarchy to the standard nonlinear Schrödinger equation hierarchy. We propose that the dual hierarchy is also integrable, and we confirm this to the first nontrivial order. In the discrete case the requirement of reparametrization invariance is void. But the demand of invariance under local frame rotations prevails, and we utilize it to introduce a discrete variant of the Zakharov-Shabat recursion relation. We use this relation to derive frame-independent quantities that we propose are the essentially unique and as such natural candidates for constructing energy functions for piecewise linear polygonal chains. We also investigate the discrete version of the Weyl duality transformation. We confirm that in the continuum limit the discrete energy functions go over to their continuum counterparts, including the perfect derivative contributions.

Place, publisher, year, edition, pages
APS , 2013. Vol. 87, no 10, 105011- p.
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:uu:diva-199941DOI: 10.1103/PhysRevD.87.105011ISI: 000319117300008OAI: oai:DiVA.org:uu-199941DiVA: diva2:621887
Available from: 2013-05-17 Created: 2013-05-17 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Dynamics of Discrete Curves with Applications to Protein Structure
Open this publication in new window or tab >>Dynamics of Discrete Curves with Applications to Protein Structure
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In order to perform a specific function, a protein needs to fold into the proper structure. Prediction the protein structure from its amino acid sequence has still been unsolved problem. The main focus of this thesis is to develop new approach on the protein structure modeling by means of differential geometry and integrable theory. The start point is to simplify a protein backbone as a piecewise linear polygonal chain, with vertices recognized as the central alpha carbons of the amino acids. Frenet frame and equations from differential geometry are used to describe the geometric shape of the protein linear chain. Within the framework of integrable theory, we also develop a general geometrical approach, to systematically derive Hamiltonian energy functions for piecewise linear polygonal chains. These theoretical studies is expected to provide a solid basis for the general description of curves in three space dimensions. An efficient algorithm of loop closure has been proposed.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2013. 41 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1054
Keyword
Frenet equations, integrable model, folded proteins, discrete curves
National Category
Physical Sciences Biophysics
Research subject
Physics; Physical Biology
Identifiers
urn:nbn:se:uu:diva-199987 (URN)978-91-554-8694-5 (ISBN)
Public defence
2013-09-02, Å10132, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Supervisors
Available from: 2013-06-11 Created: 2013-05-17 Last updated: 2013-08-30Bibliographically approved

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Hu, ShuangweiNiemi, Antti J.

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