Hansen D Flemming, Led Jens J
Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.
J Magn Reson. 2003 Aug;163(2):215-27. doi: 10.1016/s1090-7807(03)00062-4.
The validity of a series of approximate solutions of the Bloch-McConnell equations normally applied in the analyses of chemically exchanging systems is evaluated, using the electron self-exchange (ESE) in the blue copper protein plastocyanin from Anabaena variabilis as an example. The evaluation is based on a comparison with the results of a complete analysis of the NMR signals of chemically exchanging nuclei that allows an independent and accurate determination of all the involved parameters. The complete analysis is based on the general solution of the Bloch-McConnell equations. It includes a simultaneous analysis of the chemical shift, and the transverse and longitudinal relaxation rates of the observed nuclei as well as the variation of these parameters with the molar fractions of the exchanging species and the rate of the chemical exchange process. The linear prediction model method was used in the data analysis to achieve the highest possible precision. Surprisingly, it is found that the fast exchange condition may not be fulfilled even in cases where a single exchange-averaged NMR signal is observed, and the Larmor frequency and relaxation rates depend linearly on the molar fractions of the exchanging species. In such cases the use of approximate solutions in the analysis of the transverse relaxation rates and the pseudo-contact shifts can lead to erroneous results. In limiting cases close to the fast exchange and slow exchange regimes correct values of some of the parameters can be obtained using the second order approximate solution of the Bloch-McConnell equations. In contrast, the complete analysis of the NMR signals results in an accurate determination of the exchange rates and the NMR parameters of the exchanging sites. This, in turn, can provide information about the structure and function of a protein undergoing chemically exchange. For the investigated plastocyanin the complete analysis results in an accurate determination of the paramagnetic enhancement of the nuclear relaxation rates, the paramagnetic chemical shift, the electron relaxation rate, the electron self-exchange rate, and the distances between the nuclei and the paramagnetic metal ion, viz. the Cu2+ ion.
以可变鱼腥藻蓝铜蛋白质体蓝素中的电子自交换（ESE）为例，评估了通常用于化学交换体系分析的一系列布洛赫 - 麦康奈尔方程近似解的有效性。该评估基于与化学交换核的NMR信号完整分析结果的比较，这种完整分析能够独立且准确地确定所有相关参数。完整分析基于布洛赫 - 麦康奈尔方程的通解。它包括对观测核的化学位移、横向和纵向弛豫率以及这些参数随交换物种摩尔分数和化学交换过程速率变化的同时分析。数据分析中使用线性预测模型方法以实现尽可能高的精度。令人惊讶的是，发现即使在观察到单个交换平均NMR信号的情况下，快速交换条件也可能不满足，并且拉莫尔频率和弛豫率与交换物种的摩尔分数呈线性关系。在这种情况下，在横向弛豫率和伪接触位移分析中使用近似解可能会导致错误结果。在接近快速交换和慢速交换区域的极限情况下，使用布洛赫 - 麦康奈尔方程的二阶近似解可以获得一些参数的正确值。相比之下，对NMR信号的完整分析能够准确确定交换速率和交换位点的NMR参数。这反过来又可以提供有关经历化学交换的蛋白质结构和功能的信息。对于所研究的质体蓝素，完整分析能够准确确定核弛豫率的顺磁增强、顺磁化学位移、电子弛豫率、电子自交换率以及核与顺磁金属离子（即Cu2 +离子）之间的距离。
