Nagle J F
Department of Biological Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213.
Biophys J. 1991 Feb;59(2):476-87. doi: 10.1016/S0006-3495(91)82241-X.
A direct nonlinear least squares method is described that obtains the true kinetic rate constants and the temperature-independent spectra of n intermediates from spectroscopic data taken in the visible at three or more temperatures. A theoretical analysis, which is independent of implementation of the direct method, proves that well determined local solutions are not possible for fewer than three temperatures. This analysis also proves that measurements at more than n wavelengths are redundant, although the direct method indicates that convergence is faster if n + m wavelengths are measured, where m is of order one. This suggests that measurements should concentrate on high precision for a few measuring wavelengths, rather than lower precision for many wavelengths. Globally, false solutions occur, and the ability to reject these depends upon the precision of the data, as shown by explicit example. An optimized way to analyze vibrational spectroscopic data is also presented. Such data yield unique results, which are comparably accurate to those obtained from data taken in the visible with comparable noise. It is discussed how use of both kinds of data is advantageous if the data taken in the visible are significantly less noisy.
本文描述了一种直接非线性最小二乘法，该方法可从在三个或更多温度下可见光范围内获取的光谱数据中得出n个中间体的真实动力学速率常数和与温度无关的光谱。一项与直接方法的实施无关的理论分析证明，温度少于三个时无法得到确定良好的局部解。该分析还证明，测量超过n个波长的数据是冗余的，尽管直接方法表明，如果测量n + m个波长（其中m为一阶量级），收敛速度会更快。这表明测量应集中于少数几个测量波长的高精度，而非许多波长的低精度。总体而言，会出现错误解，如明确示例所示，拒绝这些错误解的能力取决于数据的精度。本文还介绍了一种分析振动光谱数据的优化方法。此类数据产生独特的结果，与从具有可比噪声的可见光数据中获得的结果具有相当的准确性。文中讨论了，如果可见光数据的噪声明显较小，同时使用这两种数据将如何具有优势。
