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.

Original languageEnglish (US)
Pages (from-to)203-216
Number of pages14
Issue number2
StatePublished - Apr 2010


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

ASJC Scopus subject areas

  • Environmental Engineering
  • Microbiology
  • Bioengineering
  • Environmental Chemistry
  • Pollution


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