Standard Tensorial Analysis of Local Ordering in Proteins from Residual Dipolar Couplings

详细信息    查看全文

• 作者：Eva Meirovitch ; Donghan Lee ; Korvin F. A. Walter ; Christian Griesinger
• 刊名：The Journal of Physical Chemistry B
• 出版年：2012
• 出版时间：May 31, 2012
• 年：2012
• 卷：116
• 期：21
• 页码：6106-6117
• 全文大小：766K
• 年卷期：v.116,no.21(May 31, 2012)
• ISSN：1520-5207

文摘

Residual dipolar couplings (RDCs) in proteins arise from independent external medium-related and internal protein-related ordering of the spin-bearing probe. Griesinger et al. developed a method for treating RDCs in proteins. The global ordering is given in the standard manner by a rank 2 tensor specified in a known molecular frame, MF. The local ordering is described by the spherical harmonic ensemble averages, Y_2m(胃, 蠁), m = 0, 卤1, 卤2, also given in MF. From these quantities, a method we call mf-RDC derives the squared generalized order parameter (S_rdc²), the amplitude (direction) of the anisotropic disorder, 畏 (Φ̅鈥?, and an approximation, (N鈥揌)_eff, to the average probe orientation, i.e., to the local director. (N鈥揌)_eff is determined through a frame transformation where Y₂₀ is maximized. Φ̅鈥?is associated with a subsequent frame transformation where Y₂₂ + Y_2鈥? is maximized. The mf-RDC method was applied previously to N鈥揌 and C鈥揅_methyl sites in ubiquitin. In this study, we convert the respective Y_2m(胃, 蠁)'s into a Saupe tensor, which is diagonalized. This is the standard procedure. It yields the eigenvalues, S_xx, S_yy, and S_zz, and the Principal Axis System (PAS) of the rank 2 local ordering tensor, S_l. S_rdc², 畏, and Φ̅鈥?can be recast as S_xx, S_yy, and S_zz. The mf-RDC frame transformations are not the same as the conventional Wigner rotation. The standard tensorial analysis provides new information. The contribution of local ordering rhombicity to S_rdc² is evaluated. For the 伪-helix of ubiquitin, the main local ordering axis is assigned as C_i鈥?^伪 鈥?C_i^伪; for the methyl sites, it is associated with the C鈥揅_methyl axis, as in mf-RDC. Ordering strength correlates with methyl type. The strength (rhombicity) of S_l associated with picosecond鈥搉anosecond local motions is reduced moderately (substantially) by nanosecond鈥搈illisecond local motions. A scheme for analyzing experimental RDCs based on the standard tensorial perspective, which allows for arbitrary orientation of the local director in the protein and of the PAS of S_l in the probe, is formulated.