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On bifurcations in framed curves and chains.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A closed framed curve can be characterized by the value of its self-linking number. However, in general the self-linking number is not uniquely determined. In particular, it depends on the way how the curve has been framed. Moreover, the self-linking number can also change, when a bifurcation called perestroika takes place. Here we devise a simple Hamiltonian energy function to study perestroikas during the time evolution of a closed, piecewise linear polygonal chain. We analyze several examples to follow the progress of the discrete Frenet framing during the time evolution of the chain, and we observe how self-linking number changing perestroikas occur whenever there is an inflection point along the chain.

National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:uu:diva-199983OAI: oai:DiVA.org:uu-199983DiVA: diva2:621890
Available from: 2013-05-17 Created: 2013-05-17 Last updated: 2013-08-30
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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Shuangwei, Hu

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