Bulletin of Mathematical Biology

, Volume 66, Issue 6, pp 1705–1730 | Cite as

Mathematical aspects of protein structure determination with NMR orientational restraints

  • J. R. Quine
  • Timothy A. Cross
  • Michael S. Chapman
  • Richard Bertram


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.


Nuclear Magnetic Resonance Dipolar Coupling Quine Residual Dipolar Coupling Nuclear Magnetic Resonance Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  • J. R. Quine
    • 1
    • 2
    • 4
  • Timothy A. Cross
    • 2
    • 3
    • 4
  • Michael S. Chapman
    • 3
    • 4
  • Richard Bertram
    • 1
    • 4
  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA
  2. 2.National High Magnetic Field LaboratoryFlorida State UniversityTallahasseeUSA
  3. 3.Department of ChemistryFlorida State UniversityTallahasseeUSA
  4. 4.Kasha Laboratory of BiophysicsFlorida State UniversityTallahasseeUSA

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