Mathematical aspects of protein structure determination with NMR orientational restraints

J. R. Quine, Timothy A. Cross, Michael Chapman, Richard Bertram

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The field of structural biology is becoming increasingly important as new technological developments facilitate the collection of data on the atomic structures of proteins and nucleic acids. The solid-state NMR method is a relatively new biophysical technique that holds particular promise for determining the structures of peptides and proteins that are located within the cell membrane. This method provides information on the orientation of the peptide planes relative to an external magnetic field. In this article, we discuss some of the mathematical methods and tools that are useful in deriving the atomic structure from these orientational data. We first discuss how the data are viewed as tensors, and how these tensors can be used to construct an initial atomic model, assuming ideal stereochemistry. We then discuss methods for refining the models using global optimization, with stereochemistry constraints treated as penalty functions. These two processes, initial model building followed by refinement, are the two crucial steps between data collection and the final atomic model.

Original languageEnglish (US)
Pages (from-to)1705-1730
Number of pages26
JournalBulletin of Mathematical Biology
Volume66
Issue number6
DOIs
StatePublished - Nov 2004
Externally publishedYes

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Protein Structure
protein structure
nuclear magnetic resonance
Nuclear magnetic resonance
Proteins
Stereochemistry
protein
Peptides
peptide
Tensors
stereochemistry
Tensor
Protein
Crystal atomic structure
peptides
Nucleic acids
technological development
nucleic acid
Penalty Function
Global optimization

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)

Cite this

Mathematical aspects of protein structure determination with NMR orientational restraints. / Quine, J. R.; Cross, Timothy A.; Chapman, Michael; Bertram, Richard.

In: Bulletin of Mathematical Biology, Vol. 66, No. 6, 11.2004, p. 1705-1730.

Research output: Contribution to journalArticle

Quine, J. R. ; Cross, Timothy A. ; Chapman, Michael ; Bertram, Richard. / Mathematical aspects of protein structure determination with NMR orientational restraints. In: Bulletin of Mathematical Biology. 2004 ; Vol. 66, No. 6. pp. 1705-1730.
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