Department of Supramolecular Biology, Yokohama City University, Yokohama 230-0045, Japan.
J Chem Phys. 2010 Mar 21;132(11):115103. doi: 10.1063/1.3360144.
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.
二面角是代表蛋白质动力学的笛卡尔坐标的另一组变量。这两组变量表现出截然不同的行为。二面角空间中的运动具有潜在动力学特征，在每个二面角的运动总是通过许多其他二面角的运动来补偿，以保持刚性的球状形状。我们使用分子动力学模拟提出了二面角空间中潜在动力学的分子机制。研究发现，由于二面角主分量的独特结构源于蛋白质的球状形状，因此具有大（小）幅度的二面角主分量与具有小（大）特征值的度量矩阵的特征向量高度相关。这种特征模式结构中的反相关在二面角旋转时最小化了笛卡尔坐标的均方位移。相比之下，由于缺乏保持刚性球状形状的约束，短肽（本研究中的 deca-alanine）在二面角主分量中不会表现出这种潜在动力学行为，但会表现出与笛卡尔主分量相似的行为。
