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Appl Environ Microbiol, June 1998, p. 2044-2050, Vol. 64, No. 6
Institute of Technology and Engineering,
Massey University, Palmerston North, New
Zealand,1 and
Department of Civil
and Environmental Engineering, Stanford University, Stanford,
California 94305-40202
Received 24 September 1997/Accepted 19 March 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.
0099-2240/98/$04.00+0
Copyright © 1998, American Society for Microbiology. All rights reserved.
Spreadsheet Method for Evaluation of Biochemical Reaction Rate
Coefficients and Their Uncertainties by Weighted Nonlinear
Least-Squares Analysis of the Integrated Monod Equation
*
Corresponding author. Mailing address: Institute of
Technology and Engineering, Massey University, Palmerston North, New
Zealand. Phone: (64) 6-356-9099. Fax: (64) 6-350-5604. E-mail:
l.h.smith{at}massey.ac.nz.
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