Boeker E A
Department of Chemistry and Biochemistry, Utah State University, Logan 84322-0300.
Biochem J. 1987 Jul 1;245(1):67-74. doi: 10.1042/bj2450067.
The integrated rate equation for reactions with stoichiometry A----P + Q is: e0t = -Cf . ln(1-delta P/A0) + C1 delta P + 1/2C2(delta P)2 where the coefficients C are linear or quadratic functions of the kinetic constants and the initial substrate and product concentrations. I have used the 21 progress curves described in the accompanying paper [Cox & Boeker (1987) Biochem. J. 245, 59-65] to develop computer-based analytical and statistical techniques for extracting kinetic constants by fitting this equation. The coefficients C were calculated by an unweighted non-linear regression: first approximations were obtained from a multiple regression of t on delta P and were refined by the Gauss-Newton method. The procedure converged in six iterations or less. The bias in the coefficients C was estimated by four methods and did not appear to be significant. The residuals in the progress curves appear to be normally distributed and do not correlate with the amount of product produced. Variances for Cf, C1 and C2 were estimated by four resampling procedures, which gave essentially identical results, and by matrix inversion, which came close to the others. The reliability of C2 can also be estimated by using an analysis-of-variance method that does not require resampling. The final kinetic constants were calculated by standard multiple regression, weighting each coefficient according to its variance. The weighted residuals from this procedure were normally distributed.
对于化学计量式为A→P + Q的反应，其积分速率方程为：e0t = -Cf·ln(1 - ΔP/A0) + C1ΔP + 1/2C2(ΔP)²，其中系数C是动力学常数以及初始底物和产物浓度的线性或二次函数。我利用随附论文[考克斯和博克(1987年)《生物化学杂志》245卷，59 - 65页]中描述的21条进程曲线，开发了基于计算机的分析和统计技术，通过拟合此方程来提取动力学常数。系数C通过非加权非线性回归计算得出：首先通过t对ΔP的多元回归获得初步近似值，然后用高斯 - 牛顿法进行优化。该程序在六次或更少的迭代中收敛。通过四种方法估计了系数C中的偏差，结果似乎并不显著。进程曲线中的残差似乎呈正态分布，并且与产生的产物量不相关。Cf、C1和C2的方差通过四种重采样程序进行估计，这些程序得出的结果基本相同，还通过矩阵求逆进行估计，其结果与其他方法相近。C2的可靠性也可以通过使用一种无需重采样的方差分析方法来估计。最终的动力学常数通过标准多元回归计算得出，根据每个系数的方差对其进行加权。此程序得到的加权残差呈正态分布。
