Schurr J M, Babcock H P, Fujimoto B S
Department of Chemistry, University of Washington, Seattle 98195.
J Magn Reson B. 1994 Nov;105(3):211-24. doi: 10.1006/jmrb.1994.1127.
The effects of anisotropy of rotational diffusion and extent of dimerization on the performance of the simple and extended model-free formulas are investigated. Numerically exact 15N NMR R1, R2, and NOE data are simulated for cylindrically symmetric species and also for mixtures of spherical monomers and dimers with the same internal dynamics. The relevant internuclear vectors are assumed to move in isotropic deflection potentials fixed at different orientations in the molecule and to exhibit a single relaxation time in their internal correlation functions. The simple model-free formula is fitted to these simulated data in order to obtain the best-fit order parameter and internal relaxation time for each nucleus. Fitting is accomplished by the standard data-analysis protocol, in which a single common global correlation time is adjusted, and also by an alternative protocol, in which the global correlation time is adjusted separately for each nucleus. The extended model-free formula is likewise fitted to these same data. With noise-free data, the simple model-free formula and standard protocol yield remarkably good best-fit internal motion parameters up to moderate anisotropies (r = D parallel/D perpendicular = 2.0), but some or many of the NMR relaxation data are not fitted well even for quite modest anisotropies (r = 1.3). The extended model-free formula yields an improved fit to the NMR data, but predicts substantial amplitudes of nonexistent slow internal motions (tau approximately greater than 0.2 ns) for many of the nuclei for all r > or = 1.3. The simple model-free formula with the alternate protocol yields even better internal motion parameters than the standard protocol and also an excellent fit to the NMR relaxation data. The best-fit global correlation time for each nucleus corresponds very closely to the theoretical correlation time defined herein. Knowledge of these times would allow one not only to estimate the anisotropy of diffusion but also in favorable cases to infer the existence of slow internal motions. Inclusion of typical statistical errors in R1, R2, and NOE, or modest exchange contributions to R2, seriously degrades the performance of the simple model-free formula with either protocol, especially in regard to the internal relaxation times, which can exhibit very large deviations from their input value even for spherical diffusors. When the fraction of monomers existing as dimers lies in the range 0.1 < or = fd < or = 0.8, none of the three model-free approaches tested yields reliable internal motion parameters.
研究了旋转扩散各向异性和二聚化程度对简单和扩展的无模型公式性能的影响。针对圆柱对称物种以及具有相同内部动力学的球形单体和二聚体混合物，模拟了数值精确的(^{15}N) NMR (R_1)、(R_2)和NOE数据。假设相关的核间矢量在分子中固定于不同取向的各向同性偏转势中移动，并且在其内部相关函数中表现出单一的弛豫时间。将简单的无模型公式拟合到这些模拟数据，以获得每个核的最佳拟合序参数和内部弛豫时间。拟合通过标准数据分析协议完成，其中调整单个共同的全局相关时间，还通过另一种协议完成，其中为每个核分别调整全局相关时间。扩展的无模型公式同样拟合这些相同的数据。对于无噪声数据，简单的无模型公式和标准协议在中等各向异性（(r = D_{平行}/D_{垂直}= 2.0)）之前能产生非常好的最佳拟合内部运动参数，但即使对于相当小的各向异性（(r = 1.3)），一些或许多NMR弛豫数据也拟合得不好。扩展的无模型公式对NMR数据的拟合有所改进，但对于所有(r \geq 1.3)，许多核预测出不存在的缓慢内部运动（(\tau \approx > 0.2 ns)）的大幅振幅。采用替代协议的简单无模型公式产生的内部运动参数比标准协议更好，并且对NMR弛豫数据也有出色的拟合。每个核的最佳拟合全局相关时间与本文定义的理论相关时间非常接近。了解这些时间不仅可以估计扩散的各向异性，而且在有利的情况下还可以推断缓慢内部运动的存在。在(R_1)、(R_2)和NOE中包含典型的统计误差，或对(R_2)有适度的交换贡献，会严重降低采用任何一种协议的简单无模型公式的性能，特别是在内部弛豫时间方面，即使对于球形扩散体，其也可能与输入值有很大偏差。当作为二聚体存在的单体分数在(0.1 \leq f_d \leq 0.8)范围内时，所测试的三种无模型方法都无法产生可靠的内部运动参数。
