Optimal modeling of atomic fluctuations in protein crystal structures for weak crystal contact interactions

The accurate modeling of protein dynamics in crystalline states holds keys to the understanding of protein dynamics relevant to functions. In this study, we used coarse-grained elastic network models (ENMs) to explore the atomic fluctuations of a protein structure that interacts with its crystalline environment, and evaluated the modeling results using the anisotropic displacement parameters (ADPs) obtained from x-ray crystallography. To ensure the robustness of modeling results, we used three ENM schemes for assigning force constant combined with three boundary conditions for treating the crystalline environment. To explore the role of crystal contact interactions in the modeling of ADPs, we varied the strength of interactions between a protein structure and its environment. For a list of 83 high-resolution crystal structures, we found that the optimal modeling of ADPs, as assessed by a variety of metrics, is achieved for weak protein-environment interactions (compared to the interactions within a protein structure). As a result, the ADPs are dominated by contributions from rigid-body motions of the entire protein structure, and the internal protein dynamics is only weakly perturbed by crystal packing. Our finding of weak crystal contact interactions is also corroborated by the calculations of residue-residue contact energy within a protein structure and between protein molecules using a statistical potential.