Bulletin of Mathematical Biology

, Volume 73, Issue 12, pp 2809–2836 | Cite as

Solving a Generalized Distance Geometry Problem for Protein Structure Determination

Original Article


We propose a new approach to the problem of determining an ensemble of protein structures with a set of interatomic distance bounds in NMR protein modeling. Similarly to X-ray crystallography, we assume that the protein has an equilibrium structure and the atoms fluctuate around their equilibrium positions. Then, the problem can be formulated as a generalized distance geometry problem, to find the equilibrium positions and maximal possible fluctuation radii for the atoms in the protein, subject to the condition that the fluctuations should be within the given distance bounds. We describe the scientific background of the work, the motivation of the new approach and the formulation of the problem. We develop a geometric buildup algorithm for an approximate solution to the problem and present some preliminary test results as a first step concept proofing. We also discuss related theoretical and computational issues and potential impacts of this work in NMR protein modeling.


Biomolecular modeling Protein structure determination Molecular distance geometry Linear and nonlinear systems of equations Constrained and unconstrained optimization 


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Copyright information

© Society for Mathematical Biology 2011

Authors and Affiliations

  1. 1.Department of MathematicsIowa State UniversityAmesUSA
  2. 2.Department of Mathematics, Program on Bioinformatics and Computational BiologyIowa State UniversityAmesUSA

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