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On Coarse Grained Representations And the Problem of Protein Backbone Reconstruction
CNRS, France.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
CNRS, France.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Crystallographic protein structures reveal that generically, only two of the Ramachandran angles are flexible. The third Ramachandran angle, all the backbone bond angles, and also all the covalent bond lengths are quite rigid, displaying only insignificant deviations from their optimal values. This empirical observation is among the rationale for the construction of coarse grained force fields where only a subset of the full set of atomic coordinates is utilized as dynamically active variables. The present article addresses in a systematic manner the question, to what extent the various angles andbond lengths can be replaced by their optimal values. In the case of bond lengths, it is found that the optimal values are in practice sufficient. But a coarse graining where a subset of angular variables is replaced by optimal values, commonly yields geometrically incorrect protein structures. There appears to be an inherent numerical instability, which seems to reflect the presence of a positive Liapunov exponent in the iterative reconstruction algorithm. Besides the full and complete set of individual atomic angles, essentially only one numerically stable coarse grained subset of angular variables is found. It consists of variable virtual Cα backbone bond and torsion angles. In combination with fixed, constant valued virtual bond lengths these two angles reproduce the original structure with high precision. The present observations impose strong limitations on the subset of backbone coordinates that can be utilized, even in principle, for the development of coarse grained force fields.

National Category
Physical Sciences
Research subject
Physical Biology
Identifiers
URN: urn:nbn:se:uu:diva-199985OAI: oai:DiVA.org:uu-199985DiVA: diva2:621897
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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