SPREADSHEET METHOD FOR EVALUATION OF BIOCHEMICAL REACTION-RATE COEFFICIENTS AND THEIR UNCERTAINTIES BY WEIGHTED NONLINEAR LEAST-SQUARES ANALYSIS OF THE INTEGRATED MONOD EQUATION

A convenient method for evaluation of biochemical reaction rate coeffi cients and their uncertainties is described. The motivation for develo ping this method was the complexity of existing statistical methods fo r analysis of biochemical rate equations, as web as the shortcomings o f linear approaches, such as Lineweaver-Burk plots. The nonlinear leas t-squares method provides accurate estimates of the rate coefficients and their uncertainties from experimental data. Linearized methods tha t involve inversion of data are unreliable since several important ass umptions of linear regression are violated. Furthermore, when lineariz ed methods are used, there is no basis for calculation of the uncertai nties in the rate coefficients. Uncertainty estimates are crucial to s tudies involving comparisons of rates for different organisms or envir onmental conditions, The spreadsheet method uses weighted least-square s analysis to determine the best-fit values of the rate coefficients f or the integrated Monod equation. Although the integrated Monod equati on is an implicit expression of substrate concentration, weighted leas t-squares analysis can be employed to calculate approximate difference s in substrate concentration between model predictions and data. An it erative search routine in a spreadsheet program is utilized to search for the best-fit values of the coefficients by minimizing the sum of s quared weighted errors, The uncertainties in the best-fit values of th e rate coefficients are calculated by an approximate method that can a lso be implemented in a spreadsheet. The uncertainty method can be use d to calculate single-parameter (coefficient) confidence intervals, de grees 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 trichloro ethylene cometabolism by a methane-oxidizing mixed culture. An additio nal advantage of application of this method to the integrated Monod eq uation 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 initi al rate measurements. However, when initial rate measurements are used , this method can still be used with greater reliability than lineariz ed approaches.