### Abstract

A differential elimination method (DEM) is developed to determine the kinetic coefficients for substrate self-inhibition. Finite differentiation of the equation eliminates either K_{I} or K_{S}, which enables the equation to be linearized so that q̂, K_{S}, and K_{I} can be estimated without using nonlinear least square regression (NLSR). The DEM options that eliminate K_{I} or K_{S} 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, q_{max}. The estimates for S_{max}, the concentration at which the maximum specific substrate utilization rate is observed, were relatively invariant among the methods, even when K_{S} and K_{I} 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.

Original language | English (US) |
---|---|

Pages (from-to) | 203-216 |

Number of pages | 14 |

Journal | Biodegradation |

Volume | 21 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2010 |

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### Keywords

- Differential elimination method
- Graphical plot method
- Kinetic coefficients
- Linear plot method
- Nonlinear least square regression
- Substrate inhibition

### ASJC Scopus subject areas

- Environmental Engineering
- Pollution
- Environmental Chemistry
- Microbiology
- Bioengineering

### Cite this

*Biodegradation*,

*21*(2), 203-216. https://doi.org/10.1007/s10532-009-9294-7

**Novel differential elimination method for determining kinetic coefficients under substrate self-inhibition.** / Park, Seongjun; Rittmann, Bruce; Bae, Wookeun.

Research output: Contribution to journal › Article

*Biodegradation*, vol. 21, no. 2, pp. 203-216. https://doi.org/10.1007/s10532-009-9294-7

}

TY - JOUR

T1 - Novel differential elimination method for determining kinetic coefficients under substrate self-inhibition

AU - Park, Seongjun

AU - Rittmann, Bruce

AU - Bae, Wookeun

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

UR - http://www.scopus.com/inward/record.url?scp=77950457887&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950457887&partnerID=8YFLogxK

U2 - 10.1007/s10532-009-9294-7

DO - 10.1007/s10532-009-9294-7

M3 - Article

C2 - 19768559

AN - SCOPUS:77950457887

VL - 21

SP - 203

EP - 216

JO - Biodegradation

JF - Biodegradation

SN - 0923-9820

IS - 2

ER -