Smith LH, McCarty PL, Kitanidis PK
Institute of Technology and Engineering, Massey University, Palmerston North, New Zealand.
Appl Environ Microbiol. 1998 Jun;64(6):2044-50. doi: 10.1128/AEM.64.6.2044-2050.1998.
A convenient method for evaluation of biochemical reaction rate coefficients and their uncertainties is described. The motivation for developing this method was the complexity of existing statistical methods for analysis of biochemical rate equations, as well as the shortcomings of linear approaches, such as Lineweaver-Burk plots. The nonlinear least-squares method provides accurate estimates of the rate coefficients and their uncertainties from experimental data. Linearized methods that involve inversion of data are unreliable since several important assumptions of linear regression are violated. Furthermore, when linearized methods are used, there is no basis for calculation of the uncertainties in the rate coefficients. Uncertainty estimates are crucial to studies involving comparisons of rates for different organisms or environmental conditions. The spreadsheet method uses weighted least-squares analysis to determine the best-fit values of the rate coefficients for the integrated Monod equation. Although the integrated Monod equation is an implicit expression of substrate concentration, weighted least-squares analysis can be employed to calculate approximate differences in substrate concentration between model predictions and data. An iterative search routine in a spreadsheet program is utilized to search for the best-fit values of the coefficients by minimizing the sum of squared weighted errors. The uncertainties in the best-fit values of the rate coefficients are calculated by an approximate method that can also be implemented in a spreadsheet. The uncertainty method can be used to calculate single-parameter (coefficient) confidence intervals, degrees of correlation between parameters, and joint confidence regions for two or more parameters. Example sets of calculations are presented for acetate utilization by a methanogenic mixed culture and trichloroethylene cometabolism by a methane-oxidizing mixed culture. An additional advantage of application of this method to the integrated Monod equation compared with application of linearized methods is the economy of obtaining rate coefficients from a single batch experiment or a few batch experiments rather than having to obtain large numbers of initial rate measurements. However, when initial rate measurements are used, this method can still be used with greater reliability than linearized approaches.
本文描述了一种评估生化反应速率系数及其不确定性的简便方法。开发此方法的动机在于现有生化速率方程分析统计方法的复杂性，以及线性方法（如Lineweaver - Burk图）的缺点。非线性最小二乘法可从实验数据中准确估计速率系数及其不确定性。涉及数据反演的线性化方法不可靠，因为违反了线性回归的几个重要假设。此外，使用线性化方法时，没有计算速率系数不确定性的依据。不确定性估计对于涉及不同生物体或环境条件速率比较的研究至关重要。电子表格法使用加权最小二乘法分析来确定积分Monod方程速率系数的最佳拟合值。尽管积分Monod方程是底物浓度的隐式表达式，但加权最小二乘法可用于计算模型预测与数据之间底物浓度的近似差异。利用电子表格程序中的迭代搜索例程，通过最小化加权误差平方和来搜索系数的最佳拟合值。速率系数最佳拟合值的不确定性通过一种也可在电子表格中实现的近似方法计算。该不确定性方法可用于计算单参数（系数）置信区间、参数之间的相关程度以及两个或多个参数的联合置信区域。给出了产甲烷混合培养物利用乙酸盐以及甲烷氧化混合培养物三氯乙烯共代谢的计算示例集。与线性化方法相比，将此方法应用于积分Monod方程的另一个优点是，从单个批次实验或少数批次实验中获取速率系数更为经济，而无需进行大量的初始速率测量。然而，当使用初始速率测量时，该方法仍然比线性化方法更可靠。
