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

Background: An elastic network model is proposed for the interactions between closely (≤ 7.0 Å) located α-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. Results: The temperature factors of the Ca 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. Conclusions: 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.