Linear response theory in dihedral angle space for protein structural change upon ligand binding

Coupling between proteins motion and ligand binding can be well explained by the linear response theory (Ikeguchi, M.; Ueno, J.; Sato, M.; Kidera, A. Phys Rev Lett 2005, 94, 078102.), in which the structural change is treated as a response to ligand binding. The prediction accuracy of structural change upon ligand binding has been improved by replacing the variables in the linear response theory from Cartesian coordinates to dihedral angles. The dihedral angle theory can more accurately describe the rotational motions of protein domains compared with the Cartesian theory, which tends to shift the coordinate to the tangential direction of the domain rotation. In this study, the ligand-bound form of Ferric-binding protein was predicted from its ligand-free form using the dihedral linear response theory. When the variance-covariance matrix, the key component in the linear response theory, was derived by linear conversion from Cartesian coordinates to dihedral angles, the dihedral linear response theory gave an improvement in the prediction. Therefore, the description of the rotational motion by dihedral angles is crucial for accurate prediction of protein structural change.