Satoshi Omori

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.

Latent dynamics of a protein molecule observed in dihedral angle space

Dihedral angles are alternative set of variables to Cartesian coordinates for representing protein dynamics. The two sets of variables exhibit extremely different behavior. Motions in dihedral angle space are characterized by latent dynamics, in which motion induced in each dihedral angle is always compensated for by motions of many other dihedral angles, in order to maintain a rigid globular shape. Using molecular dynamics simulations, we propose a molecular mechanism for the latent dynamics in dihedral angle space. It was found that, due to the unique structure of dihedral principal components originating in the globular shape of the protein, the dihedral principal components with large (small) amplitudes are highly correlated with the eigenvectors of the metric matrix with small (large) eigenvalues. Such an anticorrelation in the eigenmode structures minimizes the mean square displacement of Cartesian coordinates upon rotation of dihedral angles. In contrast, a short peptide, deca-alanine in this study, does not show such behavior of the latent dynamics in the dihedral principal components, but shows similar behaviors to those of the Cartesian principal components, due to the absence of constraints to maintain a rigid globular shape.

Extended string-like binding of the phosphorylated HP1α N-terminal tail to the lysine 9-methylated histone H3 tail

The chromodomain of HP1α binds directly to lysine 9-methylated histone H3 (H3K9me). This interaction is enhanced by phosphorylation of serine residues in the N-terminal tail of HP1α by unknown mechanism. Here we show that phosphorylation modulates flexibility of HP1α’s N-terminal tail, which strengthens the interaction with H3. NMR analysis of HP1α’s chromodomain with N-terminal tail reveals that phosphorylation does not change the overall tertiary structure, but apparently reduces the tail dynamics. Small angle X-ray scattering confirms that phosphorylation contributes to extending HP1α’s N-terminal tail. Systematic analysis using deletion mutants and replica exchange molecular dynamics simulations indicate that the phosphorylated serines and following acidic segment behave like an extended string and dynamically bind to H3 basic residues; without phosphorylation, the most N-terminal basic segment of HP1α inhibits interaction of the acidic segment with H3. Thus, the dynamic string-like behavior of HP1α’s N-terminal tail underlies the enhancement in H3 binding due to phosphorylation.

Normal mode analysis of protein dynamics in a non-Eckart frame.

Normal mode analysis, with the all-atom or coarse-grained elastic network model, represents the equilibrium fluctuation of protein molecule in the Eckart frame, where contributions from external motions (translation and rotation) of the entire protein molecule are eliminated. On the other hand, domain motion is frequently exhibited by the relative motion of one domain to the other. Such a representation of fluctuations in the non-Eckart frame cannot be achieved by conventional normal mode analysis. Here, we propose normal mode analysis in a non-Eckart frame, where the external degrees of freedom are fixed for any portion of the system. In this analysis, the covariance matrix in the Eckart frame is transformed into one in the non-Eckart frame. Using a molecular dynamics simulation, we have confirmed the validity of the transformation formula and discussed the physical implication of the formula.