Altis Alexandros, Nguyen Phuong H, Hegger Rainer, Stock Gerhard
Institute of Physical and Theoretical Chemistry, J. W. Goethe University, Max-von-Laue-Strasse 7, D-60438 Frankfurt, Germany.
J Chem Phys. 2007 Jun 28;126(24):244111. doi: 10.1063/1.2746330.
It has recently been suggested by Mu et al. [Proteins 58, 45 (2005)] to use backbone dihedral angles instead of Cartesian coordinates in a principal component analysis of molecular dynamics simulations. Dihedral angles may be advantageous because internal coordinates naturally provide a correct separation of internal and overall motion, which was found to be essential for the construction and interpretation of the free energy landscape of a biomolecule undergoing large structural rearrangements. To account for the circular statistics of angular variables, a transformation from the space of dihedral angles {phi(n)} to the metric coordinate space {x(n)=cos phi(n),y(n)=sin phi(n)} was employed. To study the validity and the applicability of the approach, in this work the theoretical foundations underlying the dihedral angle principal component analysis (dPCA) are discussed. It is shown that the dPCA amounts to a one-to-one representation of the original angle distribution and that its principal components can readily be characterized by the corresponding conformational changes of the peptide. Furthermore, a complex version of the dPCA is introduced, in which N angular variables naturally lead to N eigenvalues and eigenvectors. Applying the methodology to the construction of the free energy landscape of decaalanine from a 300 ns molecular dynamics simulation, a critical comparison of the various methods is given.
最近，Mu等人[《蛋白质》58, 45 (2005)]建议在分子动力学模拟的主成分分析中使用主链二面角而非笛卡尔坐标。二面角可能具有优势，因为内坐标自然地提供了内部运动和整体运动的正确分离，这对于构建和解释经历大结构重排的生物分子的自由能景观至关重要。为了考虑角变量的循环统计，采用了从二面角空间{phi(n)}到度量坐标空间{x(n)=cos phi(n), y(n)=sin phi(n)}的变换。为了研究该方法的有效性和适用性，在这项工作中讨论了二面角主成分分析（dPCA）的理论基础。结果表明，dPCA相当于原始角度分布的一对一表示，其主成分可以很容易地通过肽的相应构象变化来表征。此外，引入了dPCA的复数形式，其中N个角变量自然地导致N个特征值和特征向量。将该方法应用于从300纳秒分子动力学模拟构建十肽丙氨酸的自由能景观，对各种方法进行了关键比较。
