The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, Ramat-Gan 52900-02, Israel.
J Chem Phys. 2013 Dec 14;139(22):225104. doi: 10.1063/1.4838436.
We developed in recent years the two-body (protein and probe) coupled-rotator slowly relaxing local structure (SRLS) approach for elucidating protein dynamics from NMR spin relaxation. So far we used as descriptors the set of physical parameters that enter the SRLS model. They include the global (protein-related) diffusion tensor, D1, the local (probe-related) diffusion tensor, D2, and the local coupling∕ordering potential, u. As common in analyzes based on mesoscopic dynamic models, these parameters have been determined with data-fitting techniques. In this study, we describe structural dynamics in terms of the eigenmodes comprising the SRLS time correlation functions (TCFs) generated by using the best-fit parameters as input to the Smoluchowski equation. An eigenmode is a weighted exponential with decay constant given by an eigenvalue of the Smoluchowski operator, and weighting factor determined by the corresponding eigenvector. Obviously, both quantities depend on the SRLS parameters as determined by the SRLS model. Unlike the set of best-fit parameters, the eigenmodes represent patterns of motion of the probe-protein system. The following new information is obtained for the typical probe, the (15)N-(1)H bond. Two eigenmodes, associated with the protein and the probe, dominate when the time scale separation is large (i.e., D2 >> D1), the tensorial properties are simple, and the local potential is either very strong or very weak. When the potential exceeds these limits while the remaining conditions are preserved, new eigenmodes arise. The multi-exponentiality of the TCFs is associated in this case with the restricted nature of the local motion. When the time scale separation is no longer large, the rotational degrees of freedom of the protein and the probe become statistically dependent (coupled dynamically). The multi-exponentiality of the TCFs is associated in this case with the restricted nature of both the local and the global motion. The effects of local diffusion axiality, potential strength, and extent of mode-coupling on the eigenmode setup are investigated. We detect largely global motional or largely local motional eigenmodes. In addition, we detect mixed eigenmodes associated with correlated∕prograde or anti-correlated∕retrograde rotations of the global (D1) and local (D2) motional modes. The eigenmode paradigm is applied to N-H bond dynamics in the β-sheet residue K19, and the α-helix residue A34, of the third immunoglobulin-binding domain of streptococcal protein G. The largest contribution to the SRLS TCFs is made by mixed anti-correlated D1 and D2 eigenmodes. The next largest contribution is made by D1-dominated eigenmodes. Eigenmodes dominated by the local motion contribute appreciably to A34 and marginally to K19. Correlated D1 and D2 eigenmodes contribute exclusively to K19 and do not contribute above 1% to A34. The differences between K19 and A34 are delineated and rationalized in terms of the best-fit SRLS parameters and mode-mixing. It may be concluded that eigenmode analysis is complementary and supplementary to data-fitting-based analysis.
我们近年来开发了二体（蛋白质和探针）耦合旋转器缓慢弛豫局部结构（SRLS）方法，用于从 NMR 自旋弛豫中阐明蛋白质动力学。到目前为止，我们使用了进入 SRLS 模型的物理参数集作为描述符。它们包括全局（与蛋白质相关）扩散张量 D1、局部（与探针相关）扩散张量 D2 和局部耦合/有序势 u。与基于介观动力学模型的分析一样，这些参数是通过数据拟合技术确定的。在这项研究中，我们根据 Smoluchowski 方程的最佳拟合参数作为输入生成的 SRLS 时间相关函数 (TCF) 的本征模式来描述结构动力学。本征模式是具有衰减常数的加权指数，衰减常数由 Smoluchowski 算子的本征值给出，加权因子由相应的本征向量确定。显然，这两个量都取决于 Smoluchowski 模型确定的 SRLS 参数。与最佳拟合参数集不同，本征模式代表探针-蛋白质系统的运动模式。对于典型的探针（15）N-（1）H 键，获得了以下新信息。当时间尺度分离较大（即 D2 >> D1）、张量特性简单且局部势很强或很弱时，与蛋白质和探针相关的两个本征模式占主导地位。当在保持其余条件的情况下超过这些限制时，会出现新的本征模式。在这种情况下，TCF 的多指数性与局部运动的受限性质有关。当时间尺度分离不再很大时，蛋白质和探针的旋转自由度在统计上变得相互依赖（动态耦合）。在这种情况下，TCF 的多指数性与局部和全局运动的受限性质都有关。研究了局部扩散轴性、势强度和模式耦合对本征模式设置的影响。我们检测到主要是全局运动或主要是局部运动的本征模式。此外，我们还检测到与全局（D1）和局部（D2）运动模式的相关/前向或反相关/后向旋转相关的混合本征模式。本征模式范例应用于链球菌蛋白 G 第三免疫球蛋白结合域中β-折叠残基 K19 和α-螺旋残基 A34 的 N-H 键动力学。对 SRLS TCF 贡献最大的是混合反相关 D1 和 D2 本征模式。下一个最大的贡献来自于 D1 主导的本征模式。由局部运动主导的本征模式对 A34 的贡献相当大，对 K19 的贡献微不足道。相关的 D1 和 D2 本征模式仅对 K19 有贡献，对 A34 的贡献不超过 1%。根据最佳拟合 SRLS 参数和模式混合，区分并合理化了 K19 和 A34 之间的差异。可以得出结论，本征模式分析是基于数据拟合的分析的补充和补充。
