Algebraic expressions for Carr-Purcell-Meiboom-Gill relaxation dispersion for N-site chemical exchange.

The Carr-Purcell-Meiboom-Gill (CPMG) NMR relaxation dispersion experiment measures the effective relaxation rate constant during a train of spin-echo pulse sequence elements as a function of the echo time. The CPMG experiment is a powerful method for characterizing chemical and conformational dynamic processes, termed chemical and conformational exchange, on μs-ms time scales, comparable to the experimentally accessible echo times. Approximate theoretical expressions for the effective relaxation rate constant for N-site chemical exchange have been reported (H. Koss, M. Rance, and A. G. Palmer, Biochemistry 57, 4753-4763 (2018)). Expressions for the effective relaxation rate constant have been improved by using the Cayley-Hamilton theorem to obtain simple and accurate approximations of the average Liouvillian for the CPMG experiment. The improved accuracy of the results allows efficient analyses of experimental data. In addition, the relationship is clarified between the approach of Koss and coworkers and that of Jen (J. Jen, J. Magn. Reson. 30, 111-128 (1978)).

卡尔 - 珀塞尔 - 梅博姆 - 吉尔（CPMG）核磁共振弛豫弥散实验测量一系列自旋回波脉冲序列单元期间的有效弛豫速率常数随回波时间的变化。CPMG实验是一种在微秒 - 毫秒时间尺度上表征化学和构象动态过程（称为化学和构象交换）的强大方法，该时间尺度与实验可获取的回波时间相当。已经报道了N位点化学交换的有效弛豫速率常数的近似理论表达式（H. 科斯、M. 兰斯和A. G. 帕尔默，《生物化学》57，4753 - 4763（2018年））。通过使用凯莱 - 哈密顿定理来获得CPMG实验平均刘维尔算符的简单而精确的近似值，有效弛豫速率常数的表达式得到了改进。结果准确性的提高使得能够对实验数据进行高效分析。此外，科斯及其同事的方法与詹的方法之间的关系也得到了阐明（J. 詹，《磁共振杂志》30，111 - 128（1978年））