Appl Microbiol Biotechnol (2003) 61:314–322 DOI 10.1007/s00253-002-1220-4 ORIGINAL PAPER E. A. Seagren · H. Kim · B. F. Smets Identifiability and retrievability of unique parameters describing intrinsic Andrews kinetics Received: 27 March 2002 / Revised: 27 November 2002 / Accepted: 6 December 2002 / Published online: 11 March 2003  Springer-Verlag 2003 Abstract A key factor contributing to the variability in the microbial kinetic parameters reported from batch assays is parameter identifiability, i.e., the ability of the mathematical routine used for parameter estimation to provide unique estimates of the individual parameter values. This work encompassed a three-part evaluation of the parameter identifiability of intrinsic kinetic parame- ters describing the Andrews growth model that are obtained from batch assays. First, a parameter identifia- bility analysis was conducted by visually inspecting the sensitivity equations for the Andrews growth model. Second, the practical retrievability of the parameters in the presence of experimental error was evaluated for the parameter estimation routine used. Third, the results of these analyses were tested using an example data set from the literature for a self-inhibitory substrate. The general trends from these analyses were consistent and indicated that it is very difficult, if not impossible, to simulta- neously obtain a unique set of estimates of intrinsic kinetic parameters for the Andrews growth model using data from a single batch experiment. Introduction The quantitative analysis and design of microbial pro- cesses requires estimation of the parameters in the kinetic expression chosen to represent the process of interest, such as microbial growth and substrate depletion. Of particular interest in this work is estimation of the parameters for the Andrews growth kinetics model (Andrews 1968), which has been found by several researchers, e.g., (D’Adamo et al. 1984; Edwards 1970; Hill and Robinson 1975; Pawlowsky and Howell 1973; Yang and Humphrey 1975) to describe the biodegradation kinetics for self-inhibitory substrates: q ¼ m Y ¼ m max Y  S K s þ Sþ S 2 K i 0 @ 1 A ð1Þ Here, q is the specific substrate removal rate, m is the specific growth rate, Y is the true growth yield, m max is the maximum specific growth rate, K s is the half-maximum rate coefficient, K i is the inhibition coefficient, and S is the substrate concentration. Determination of Andrews kinetic parameters is challenging in part because it must be done at relatively high and inhibitory substrate concentrations. Under these conditions, maintaining sta- ble steady-states may not be possible in continuous systems (e.g., chemostats; Andrews 1968). Therefore, some researchers estimate inhibition kinetic parameters in continuous cultures maintained at unstable steady-states (e.g., Schröder et al. 1997), but non-steady-state condi- tions in batch assays or washout experiments are more typically used. Unfortunately, standard procedures for determining kinetic parameters in non-steady-state batch assays do not exist. Consequently, the kinetic parameter values reported in the literature vary widely for a given compound, even with pure cultures (e.g., Monteiro et al. (2000). This variability appears to be attributable to three key factors (Grady et al. 1996): (1) culture history, i.e., the type and duration of the environmental conditions imposed on the culture prior to measuring the kinetics, which may E. A. Seagren ( ) ) Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742, USA e-mail: eseagren@eng.umd.edu Tel.: +1-301-4054828 Fax: +1-301-4052585 H. Kim Department of Environmental Engineering, The University of Seoul, Seoul 130-743, Korea B. F. Smets Department of Civil and Environmental Engineering, University of Connecticut, Storrs, CT 06269-2037, USA