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Fold Des. 1997;2(3):173-81.

Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential.

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Polymer Research Center, Bogazici University, Bebek, Istanbul, Turkey.



An elastic network model is proposed for the interactions between closely (< or = 7.0 A) located alpha-carbon pairs in folded proteins. A single-parameter harmonic potential is adopted for the fluctuations of residues about their mean positions in the crystal structure. The model is based on writing the Kirchhoff adjacency matrix for a protein defining the proximity of residues in space. The elements of the inverse of the Kirchhoff matrix give directly the auto-correlations or cross-correlations of atomic fluctuations.


The temperature factors of the C alpha atoms of 12 X-ray structures, ranging from a 41 residue subunit to a 633 residue dimer, are accurately predicted. Cross-correlations are also efficiently characterized, in close agreement with results obtained with a normal mode analysis coupled with energy minimization.


The simple model and method proposed here provide a satisfactory description of the correlations between atomic fluctuations. Furthermore, this is achieved within computation times at least one order of magnitude shorter than commonly used molecular approaches.

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