TY - JOUR
T1 - Novel differential elimination method for determining kinetic coefficients under substrate self-inhibition
AU - Park, Seongjun
AU - Rittmann, Bruce
AU - Bae, Wookeun
N1 - Funding Information:
Acknowledgments ‘‘This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD).’’ (KRF-2006-352-D00122).
PY - 2010/4
Y1 - 2010/4
N2 - A differential elimination method (DEM) is developed to determine the kinetic coefficients for substrate self-inhibition. Finite differentiation of the equation eliminates either KI or KS, which enables the equation to be linearized so that q̂, KS, and KI can be estimated without using nonlinear least square regression (NLSR). The DEM options that eliminate KI or KS computed the parameter values exactly when the data did not contain any errors. If one-point or random errors were not too large, both DEM options worked as well as NLSR when data were acquired with geometric intervals for substrate concentration. The DEM was more accurate for fitting the data for the smallest and largest values of S, but relatively weaker in estimating the observed maximum substrate utilization rate, qmax. The estimates for Smax, the concentration at which the maximum specific substrate utilization rate is observed, were relatively invariant among the methods, even when KS and KI differed. When the intervals were arithmetic (i. e., equal intervals of substrate concentration) and the data contained errors, the DEM and NLSR estimated the parameters poorly, indicating that collecting data with an arithmetic interval greatly increases the risk of poor parameter estimation. Parameter estimates by DEM fit very well experimental data from nitrification or photosynthesis, which were taken with geometric intervals of substrate concentration or light intensity, but fit poorly phenol-degradation data, which were obtained with arithmetic substrate intervals. Besides providing a reasonable substitute for NLSR, the DEM also can be used as a tool to diagnose the quality of experimental data by comparing its estimates between the DEM options, or, more rigorously, to those from NLSR.
AB - A differential elimination method (DEM) is developed to determine the kinetic coefficients for substrate self-inhibition. Finite differentiation of the equation eliminates either KI or KS, which enables the equation to be linearized so that q̂, KS, and KI can be estimated without using nonlinear least square regression (NLSR). The DEM options that eliminate KI or KS computed the parameter values exactly when the data did not contain any errors. If one-point or random errors were not too large, both DEM options worked as well as NLSR when data were acquired with geometric intervals for substrate concentration. The DEM was more accurate for fitting the data for the smallest and largest values of S, but relatively weaker in estimating the observed maximum substrate utilization rate, qmax. The estimates for Smax, the concentration at which the maximum specific substrate utilization rate is observed, were relatively invariant among the methods, even when KS and KI differed. When the intervals were arithmetic (i. e., equal intervals of substrate concentration) and the data contained errors, the DEM and NLSR estimated the parameters poorly, indicating that collecting data with an arithmetic interval greatly increases the risk of poor parameter estimation. Parameter estimates by DEM fit very well experimental data from nitrification or photosynthesis, which were taken with geometric intervals of substrate concentration or light intensity, but fit poorly phenol-degradation data, which were obtained with arithmetic substrate intervals. Besides providing a reasonable substitute for NLSR, the DEM also can be used as a tool to diagnose the quality of experimental data by comparing its estimates between the DEM options, or, more rigorously, to those from NLSR.
KW - Differential elimination method
KW - Graphical plot method
KW - Kinetic coefficients
KW - Linear plot method
KW - Nonlinear least square regression
KW - Substrate inhibition
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U2 - 10.1007/s10532-009-9294-7
DO - 10.1007/s10532-009-9294-7
M3 - Article
C2 - 19768559
AN - SCOPUS:77950457887
SN - 0923-9820
VL - 21
SP - 203
EP - 216
JO - Biodegradation
JF - Biodegradation
IS - 2
ER -