A simple computer program with statistical tests for the analysis of enzyme kinetics.

A simple computer program that calculates the kinetic parameters of enzyme reactions is described. Parameters are determined by nonlinear, least-squares regression using either Marquardt-Levenberg or Gauss-Newton algorithms to find the minimum sum of squares. Three types of enzyme reactions can be analyzed: single substrate reactions (Michaelis-Menten and sigmoidal kinetics), enzyme activation at a fixed substrate value or enzyme inhibition at a fixed substrate value. The user can monitor goodness of fit through nonparametric statistical tests (performed automatically by the computer) and through visual examination of the pattern of residuals. The program is unique in providing equations for activator and inhibition analysis as well as in enabling the user to fix some of the parameters before regression analysis. The simplicity of the program makes it extremely useful for quickly determining kinetic parameters during the data-gathering process.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Kinetic analysis of the Ca2+-dependent, membrane-bound, macrophage phospholipase A2 and the effects of arachidonic acid

The kinetics of the Ca2+-dependent, alkaline pH optimum, membrane-bound phospholipase A2 from the P388D1 macrophage-like cell line were studied using various phosphatidylcholine (PC) and phosphatidylethanolamine (PE) substrates. This enzyme exhibits "surface dilution kinetics" toward PC in Triton X-100 mixed micelles, and the "dual phospholipid model" was found to adequately describe its kinetic behavior. With substrate in the form of sonicated vesicles, the dual phospholipid model should give rise to Michaelis-Menten type kinetics. However, the hydrolysis of dipalmitoyl-PC, 1-palmitoyl-2-oleoyl-PC, and 1-stearoyl-2-arachidonoyl-PC vesicles exhibited two distinct activities. Below 10 microM, the data appeared to follow Michaelis-Menten behavior, while at higher concentrations, the data could best be fit to a Hill equation with a Hill coefficient of 2. These PCs had Vmax values for the low substrate concentration range of 0.2-0.6 nmol min-1 mg-1 and Km values of 1-2 microM. At the high substrate concentration range, the Vmax values were between 5 and 7 nmol min-1 mg-1. PC containing unsaturated fatty acids had an apparent Km, determined from the Hill equation, of about 15 microM, while the apparent Km of dipalmitoyl-PC was 0.6 microM. When 70% glycerol was included in the assays, a single Michaelis-Menten curve was obtained for both dipalmitoyl-PC and 1-stearoyl,2-arachidonoyl-PC. Possible explanations for these kinetic results include reconstitution of the membrane-bound phospholipase A2 in the phospholipid vesicle or the enzyme has tow distinct phospholipid binding function. The kinetics for both dipalmitoyl-PC and dipalmitoyl-PE hydrolysis in vesicles was very similar, indicating that the enzyme does not greatly prefer one of these head groups over the other. The enzyme also showed no preference for arachidonoyl containing phospholipid. Enzymatic activity toward PC containing saturated fatty acids was linear to about 15% hydrolysis while the hydrolysis of PC containing unsaturated fatty acids was linear to only about 5%. This loss of linearity was due to inhibition by released unsaturated fatty acids. Arachidonic acid was found to be a competitive inhibitor of dipalmitoyl PC hydrolysis with a K1 of 5 microM. This tight binding suggests a possible in vivo regulatory role for arachidonic acid. Three compounds of the arachidonic acid cascade, prostaglandin F2 alpha, 6-keto-prostaglandin F1 alpha, and thromboxane B2, showed no inhibition of enzymatic activity.     

A combined method for determining inhibition type, kinetic parameters, and inhibition coefficients for aerobic cometabolism of 1,1,1-trichloroethane by a butane-grown mixed culture.

A combined method for determining inhibition type, kinetic parameters, and inhibition coefficients is developed and presented. The method was validated by applying it to data obtained from batch kinetics of the aerobic cometabolism of 1,1,1-trichloroethane (1,1,1-TCA) by a butane-grown mixed culture. The maximum degradation rates (k(max)) and half-saturation coefficients (K(s)) were independently determined in single compound tests, and compared with those obtained from inhibition tests. The inhibition type was determined using direct linear plots at various substrate and inhibitor concentrations. Kinetic parameters (k(max) and K(s)) and inhibition coefficients (K(ic) and K(iu)) were determined by nonlinear least squares regression (NLSR) fits of the inhibition model determined from the direct linear plots. Initial guesses of the kinetic parameters for NLSR were determined from linearized inhibition equations that were derived from the correlations between apparent maximum degradation rates (k(app)(max)) and/or the apparent half-saturation coefficient (K(app)(s)) and the k(max), K(s), and inhibitor concentration (I(L)) for each inhibition equation. Two different inhibition types were indicated from the direct linear plots: competitive inhibition of 1,1,1-TCA on butane degradation, and mixed inhibition of 1,1,1-TCA transformation by butane. Good agreement was achieved between independently measured k(max) and K(s) values and those obtained from both NLSR and the linearized inhibition equations. The initial guesses of all the kinetic parameters determined from linear plots were in the range of the values estimated from NLSR analysis. Overall the results show that use of the direct linear plot method to identify the inhibition type, coupled with initial guesses from linearized plots for NLSR analysis, results in an accurate method for determining inhibition types and coefficients. Detailed studies with pure cultures and purified enzymes are needed to further demonstrate the utility of this method.     

On the use of apparent kinetic parameters for immobilized enzyme with noncompetitive substrate inhibition

The use of a simple rate equation with apparent parameters to describe the kinetic behavior of an immobilized enzyme with noncompetitive substrate inhibition was assessed. To do so, the reaction rate was calculated as a function of the interfacial substrate concentration, and the results were used to identify the apparent kinetic parameters by nonlinear regression. This procedure was repeated for different values of the diffusional constraints and of the inhibition constant. The equation using apparent parameters can describe the global kinetic behavior, provided that the diffusional and inhibitory constraints are not too high. When the constraints are high, a Michaelis-Menten equation can be used to model the kinetics for interfacial concentrations lower than the concentration leading to the maximum reaction rate.     

A kinetic study of lipase-catalyzed reversible kinetic resolution involving verification at miniplant-scale

Lipase-catalyzed kinetic resolution of racemates is a popular method for synthesis of chiral synthons. Most of these resolutions are reversible equilibrium limited reactions. For the first time, an extensive kinetic model is proposed for kinetic resolution reactions, which takes into account the full reversibility of the reaction, substrate inhibition by an acyl donor and an acyl acceptor as well as alternative substrate inhibition by each enantiomer. For this purpose, the reversible enantioselective transesterification of (R/S)-1-methoxy-2-propanol with ethyl acetate catalyzed by Candida antarctica lipase B (CAL-B) is investigated. The detailed model presented here is valid for a wide range of substrate and product concentrations. Following model discrimination and the application of Haldane equations to reduce the degree of freedom in parameter estimation, the 11 free parameters are successfully identified. All parameters are fitted to the complete data set simultaneously. Six types of independent initial rate studies provide a solid data basis for the model. The effect of changes in substrate and product concentration on reaction kinetics is discussed. The developed model is used for simulations to study the behavior of reaction kinetics in a fixed bed reactor. The typical plot of enantiomeric excess versus conversion of substrate and product is evaluated at various initial substrate mixtures. The model is validated by comparison with experimental results obtained with a fixed bed reactor, which is part of a fully automated state-of-the-art miniplant.     

Soman inhibition of butyrylcholinesterase in the presence of substrate: pressure and temperature perturbations.

Irreversible inhibition of butyrylcholinesterase by soman was studied in the presence of the substrate (o-nitrophenyl butyrate). Inhibition was found of the competitive complexing type. Study at different temperatures and pressures showed that the behavior of the enzyme differs from that of the inhibitor-free enzyme. In the absence of inhibitor, enzyme kinetics displayed a non-linear temperature dependence with a break at 21 degrees C. In the presence of a non-inhibitor structural analog of soman (pinacolyl dimethylphosphinate and methyl dimethylphosphinate), the Arrhenius plot break is slightly shifted (18 degrees C). On the other hand, in the presence of soman this break is abolished. The pressure-dependence of the substrate hydrolysis revealed also differences between the native enzyme and the enzyme in the presence of soman: the sign and magnitude of the apparent activation volume (delta V not equal to) were different for the two reactions. Beyond 300 bar, in the presence of soman, a plateau (delta V not equal to approx. 0) was observed over a large pressure range depending on temperature. Such a behavior with respect to temperature and pressure can reflect a soman-induced enzyme conformational state. Thus, temperature and pressure perturbations of the kinetics allow to complete the inhibition scheme of butyrylcholinesterase by soman. Our data suggest that upon soman binding, the enzyme undergoes a long-lived soman-induced-fit conformational change preceding the phosphonylation step. However, an alternative hypothesis according to which the enzyme processes a secondary soman-binding site cannot be ruled out.     

Hepatic microsomal glucose-6-phosphatase of normal and alloxan-diabetic rats. Thermotropic effects on kinetics and interaction with deoxycholate and 1-anilino-8-naphthalene sulfonate

Thermotropic effects on the kinetics of glucose-6-phosphatase (D-glucose-6-phosphate phosphohydrolase, EC 3.1.3.9) activity of hepatic microsomes from normal and alloxan-diabetic rat liver were investigated by determining V, Km and Ki (substrate inhibition) values. Influence of deoxycholate (0.1%) and 1-anilino-8-naphthalene sulfonate (2.5 mM) on the kinetics was also evaluated. 1. Substrate inhibition occurred at 0.06 M for the enzyme from normal rats and at 0.0-0.025 M for the enzyme from diabetic rats. 2. The enzyme from diabetic rats showed a transition that extended between 22.7 and 27 degrees C in the Arrhenius plot (log V vs. T-1) instead of at 19.5 degrees C. 3. Deoxycholate increased the V value of both enzymes without affecting substrate inhibition at all the temperatures but did not completely abolish the transition in the Arrhenius plot of the enzyme from diabetic rats. 4. 1-Anilino-8-naphthalene sulfonate eliminated substrate inhibition and activated the enzyme of normal rats above 27.5 degrees C by increasing both V and Km values. Below this temperature, the enzyme showed biphasic or allosteric kinetics. At low substrate concentrations it was activated as both V and Km values were increased. The enzyme from diabetic rats, on the other hand, was activated at all the temperatures and exhibited linear kinetics. 5. Binding of 1-anilino-8-naphthalene sulfonate to the microsomal fraction increased with decreasing temperature as revealed by the increase of relative fluorescence. The microsomal fraction of diabetic rats showed a more anomalous fluorescence response between 13-18 degrees C. 6. Enthalpy changes for glucose 6-phosphate binding to the inhibition site were slightly larger than binding to the active site. Calculated entropies of activation for transition state complex of glucose-6-phosphatase reaction were fairly large and negative. The free energy of activation (28-30 kcal/mol) was independent of temperature and experimental conditions. 7. In the microsomal fraction (total as well as rough), phospholipid content and fatty acid unsaturation index of phospholipids were decreased after diabetes. The level of free cholesterol remained unchanged but the molar ratio of cholesterol to phospholipid increased. The different thermal response and 1-anilino-8-naphthalene sulfonate interaction to the enzyme from diabetic rat and liver could be ascribed to the altered lipid environment of the enzyme on the endoplasmic reticulum membrane.     

Phenylalanine ammonia-lyase: A model for the cooperativity kinetics induced by d- and l-phenylalanine

A preparation of l-phenylalanine ammonia-lyase (EC 4.1.3.5.) from soybean (Glycine max L. cv. Kanrich) showed negative cooperativity with respect to l-phenylalanine and competitive inhibition by d-phenylalanine. A two-protomer partially concerted model for inhibition kinetics is described. If cooperativity is associated with ligand binding but not k_cat, plots of v against log [S] at constant [I] are symmetrical. Such curves may be fitted by graphical or iterative least-squares methods. The experimental results conform to this restricted model. The three-substrate and three-inhibitor dissociation constants were estimated by a stepwise procedure. For substrate only the first and second dissociation constants were 12 and 78 μm, respectively, with a symmetry point value of 30.5 μm. To a first approximation, site occupancy determines the cooperativity. As d- and l-phenylalanine produce equivalent effects, they are assumed to pack into the same induced space. As ligand binding at one site has little influence on the relative d:l binding at the other and does not influence k_cat, cooperativity probably reflects changes in regions remote from the active site such as the interface between the protomers. The regulatory range in [S] of the enzyme in vivo may be indicated by the linearity range of the semilog plot for the isolated enzyme. The observed range corresponds to a 100-fold change in [S] compared to a 10-fold change for Michaelis-Menten kinetics.     

Computer analysis of enzyme-substrate-inhibitor kinetic data with automatic model selection using IBM-PC compatible microcomputers

A weighted nonlinear least-squares curve-fitting program, implemented in compiled BASIC for the IBM-PC is described to estimate the parameters of enzyme kinetics obeying Michaelis-Menten kinetics and seven inhibition models. The effects of the inhibitor on the maximal velocity (Vm) and the Michaelis-Menten constant (Km) are used to select automatically the most plausible model of inhibition and to calculate initial estimates of parameters. The program is used to demonstrate that the inhibition of carbamyl-phenylalanine hydrolase by the product phenylalanine is consistent with the pure mixed noncompetitive model.     

External and internal diffusion in heterogeneous enzymes systems

The intrusion of diffusion in heterogeneous enzyme reactions, which follow. Michaelis-Menten kinetics, is quantitatively characterized by dimensionless parameters that are independent of the substrate concentration. The effects of these parameters on the overall rate of reaction is illustrated on plots commonly employed in enzyme kinetics. The departure from Michaelis-Menten kinetics due to diffusion limitations can be best assessed by using Hofstee plots which are also suitable to distinguish between internal and external transport effects. A graphical method is described for the evaluation of the reaction rate as a function of the surface concentration of the substrate from measured data.     

Effects of some S-blocked glutathione derivatives on the prevalent glyoxalase II (a form) of rat liver

The prevalent glyoxalase II (S-2-hydroxyacylglutathione hydrolase, EC 3.1.2.6, a form) of rat liver cytosol has been studied with a series of seven S-blocked glutathione derivatives. At pH 7.4 and 20 degrees C, only p-nitrobenzyl-S-glutathione was found completely inactive. All the other derivatives are linear competitive inhibitors of the enzyme. Ki values using S-D-lactoylglutathione as substrate are reported. Alkyl-S-glutathiones are weak inhibitors and their inhibition increases with the decrease of the length of the alkyl chain. The best inhibitors are those glutathione derivatives which contain a thioester bond (carbobenzoxy- and p-nitrocarbobenzoxy-S-glutathione) or a carbonyl group (p-chlorophenacyl-S-glutathione). Inhibition by carbobenzoxy-S-glutathione seems to be more complex since the double reciprocal plot shows deviation from linearity at low substrate concentration.     

Cutting Edge: Coding single nucleotide polymorphisms of endoplasmic reticulum aminopeptidase 1 can affect antigenic peptide generation in vitro by influencing basic enzymatic properties of the enzyme

ER aminopeptidase 1 (ERAP1) customizes antigenic peptide precursors for MHC class I presentation and edits the antigenic peptide repertoire. Coding single nucleotide polymorphisms (SNPs) in ERAP1 were recently linked with predisposition to autoimmune disease, suggesting a link between pathogenesis of autoimmunity and ERAP1-mediated Ag processing. To investigate this possibility, we analyzed the effect that disease-linked SNPs have on Ag processing by ERAP1 in vitro. Michaelis-Menten analysis revealed that the presence of SNPs affects the Michaelis constant and turnover number of the enzyme. Strikingly, specific ERAP1 allele-substrate combinations deviate from standard Michaelis-Menten behavior, demonstrating substrate-inhibition kinetics; to our knowledge, this phenomenon has not been described for this enzyme. Cell-based Ag-presentation analysis was consistent with changes in the substrate inhibition constant K(i), further supporting that ERAP1 allelic composition may affect Ag processing in vivo. We propose that these phenomena should be taken into account when evaluating the possible link between Ag processing and autoimmunity.     

Use of nonlinear regression to analyze enzyme kinetic data: application to situations of substrate contamination and background subtraction

In a recent publication, A. Lundin, P. Arner, and J. Hellmér [Anal. Biochem. 177, 125-131 (1989)] describe a method whereby kinetic substrate assays can be performed when the assay mixture includes a significant contaminating levels of substrate. Their method requires various rearrangements of the data, and involves three separate linear regression calculations. We show how the same data may be analyzed directly, and far more simply, by nonlinear regression. Unlike the linear regression method, nonlinear regression allows direct calculation of the actual values for Km, Vmax, and the concentration of contaminating substrate (as well as estimates of their standard errors); the former method gives only apparent values. The nonlinear regression technique is also statistically a more valid means of analysis, as the rearrangements required to give linearized equations will considerably distort the error distribution and render simple unweighted linear regression inappropriate. The ease of incorporating extra parameters into standard equations when nonlinear regression is used is further illustrated by fitting enzyme reaction data which describe a first-order process when a significant nonspecific background is present. For this equation no simple rearranged linear plot is possible, but nonlinear regression is easily applied to determine the kinetic parameters.     

Ionic-strength-dependent substrate inhibition of the lysis of Micrococcus luteus by hen egg-white lysozyme

The kinetics of lysis of Micrococcus luteus by hen egg-white lysozyme in dilute buffer media is characterized by pronounced substrate inhibition. This effect occurs within the complete pH range where lysozyme activity is detectable. The electrostatic potential of the negatively charged cell-wall proteoglycan increases with decreasing ionic strength, resulting in an enhanced affinity between proteoglycan and lysozyme and probably favouring multipoint substrate attachment. For the lysozyme-catalyzed hydrolysis of cell-wall proteoglycan three plausible mechanisms of substrate inhibition can be postulated. Two out of the three models fit our experimental data, the simplest of the two providing the most rigorous information on the kinetic parameters Km, V and Ki. Three graphical methods consistent with the chosen model were applied for preliminary parameter estimation and the constants obtained were compared to those from nonlinear least-squares analysis. If substrate inhibition is neglected it is shown that serious bias is imposed upon the parameters.     

A cometabilic kinetics model incorporating enzyme inhbition, inactivation, and recovery: I. Model development, analysis, and testing

Cometabolic biodegradation prcesses are important for bioremediation of hazardous waste sites. However, these proceeses are not well understood and have not been modeled thoroughly. Traditional Michaelis-Menten kinetics models often are used, but toxic effects and bacterial responses to toxicity may cause changes in enzyme levels, rendering such models inappropriate. In this article, a conceptual and mathematical model of cometabolic enzyme kinetics i described. Model derivation is based on enzyme/growth-substrate/nongrowth-substrate interaction and incorporates enzyme inhibition (caused by the presence of a cometabolic compound), inactivation (resulting from toxicity of a cometabolic product), and recovery (associated with bacterial synthesis of new enbzyme in response to inactivation). The mathematical model consists of a system of two, nonlinear ordinary differential equations that can be solved implicitly using numerical methods, providing estimates of model parameters. Model analysis shows that growth substraate adn nongrowth substrate oxidation rates are related by a dimensionless constant. Reliability of tehy model solution prcedure is verifiedl by abnalyzing data ses, containing random error, from simulated experimentss with trichhloroethyylene (TCE) degradation by ammonia-oxidizing bacterialunder various conditions. Estimation of the recovery rate contant is deterimined to be sensitive to intial TCE concentration. Model assumptions are evaluated in a companion article using data from TCE degradation experiments with amoniaoxidizing bacteria. (c) 1995 John Wiley & Sons, Inc.     

Mathematical modeling of diffusion and reaction in the hydrolysis of vegetable protein in an immobilized enzyme recycle reactor

Experimental investigation is by far the most effective approach for studying the behavior of physical systems. However, an enzymatic solubilization of vegetable protein is a complex combination of intrinsic problems, of which many are not easily adaptable to experimental investigation. Experimental designs to study enzyme vegetable protein reactions yield data which describe the extramembraneous activity of the immobilized enzyme. In a continuous recycle immobilized enzyme reactor, the microenvironment concentration of the substrate or product in the membrane phase, or the concentrations along the reactor axial length in the bulk phase are not discernible to the experimenter. However, the knowledge of such concentration profiles is important in weighing the significance of such factors as intermembrane diffusion, enzyme loading, wet membrane size, and the mode of operation of the reactor. The simulation of mathematical models, which describe the physical system within the constraints imposed, yields information which is vital to the understanding of the process occurring in the reactor. The kinetics and diffusion of an immobilized thermophilic Penicillium duponti enzyme at pH 3.4-3.7 and 50 degrees C was modeled mathematically. The kinetic parameters were evaluated by fitting a model to experimental data using nonlinear regression analysis. Simulation profiles of the effects of reactor geometry, substrate concentration, membrane thickness, and enzyme leading on the hydrolysis rate are presented. From the profiles generated by the mathematical model, the best operational reactor strategy is recommended.     

Investigations of reaction kinetics for immobilized enzymes--identification of parameters in the presence of diffusion limitation

A method is proposed for identification of kinetic parameters when diffusion of substrates is limiting in reactions catalyzed by immobilized enzymes. This method overcomes conventional sequential procedures, which assume immobilization does not affect the conformation of the enzyme and, thus, consider intrinsic and inherent kinetics to be the same. The coupled equations describing intraparticle mass transport are solved simultaneously using numerical methods and are used for direct estimation of kinetic parameters by fitting modeling results to time-course measurements in a stirred tank reactor. While most traditional procedures were based on Michaelis-Menten kinetics, the method presented here is applicable to more complex kinetic mechanisms involving multiple state variables, such as ping-pong bi-bi. The method is applied to the kinetic resolution of (R/S)-1-methoxy-2-propanol with vinyl acetate catalyzed by Candida antarctica lipase B. A mathematical model is developed consisting of irreversible ping-pong bi-bi kinetics, including competitive inhibition of both enantiomers. The kinetic model, which fits to experimental data over a wide range of both substrates (5-95%) and temperatures (5-56 degrees C), is used for simulations to study typical behavior of immobilized enzyme systems.     

Model Testing in Radioligand/Receptor Interaction by Monte Carlo Simulation

Abstract

Monte Carlo simulations have been applied for evaluating the reliability of parameter estimates as well as for testing models in radioligand saturation binding experiments. Scatchard analysis was compared to the nonlinear least-square curve fitting method for one-site saturation binding curves. It was found that linear regression analysis from the transformed data in the Scatchard plot yielded generally less accurate parameter estimates than nonlinear regression analysis of untransformed data. The advantage of the nonlinear least-squares curve fitting method was especially pronounced in cases where the scatter and number of data points, as well as the radioligand concentration range, were chosen similar to less optimal experimental conditions. Under such circumstances, several K_D and B_max values derived by Scatchard analysis led to physically impossible negative values whereas the same data analyzed by nonlinear regression yielded reasonable parameter estimates. Furthermore, it was found that for both means of analysis, K_D and B_max correlated positively. In another set of Monte Carlo experiments, saturation binding curves involving two receptor sites were generated and subsequently analyzed according to both a one-site and a two-site model. The confidence with which one is able to distinguish the two-site model from nonlinear least-squares curve fitting was then estimated for optimal, as well as for, less ideal experimental condigions.     

Kinetic analysis of high-concentration isopropanol biodegradation by a solvent-tolerant mixed microbial culture

The ability of a previously enriched microbial population to utilize isopropanol (IPA) as the sole carbon source within a minimal salts medium is studied. The advantage of prior enrichment procedures for the improvement of IPA biodegradation performance is demonstrated for an IPA concentration of up to 24 g L(-1). Results showing the interrelationship between temperature and substrate utilization and inhibition levels at temperatures of between 2 degrees C and 45 degrees C are examined. Models of inhibition based on enzyme kinetics are assessed via nonlinear analysis, in order to accurately represent the growth kinetics of this solvent-tolerant mixed culture. The model that best describes the data is the Levenspiel substrate inhibition model, which can predict the maximum substrate level above which growth is completely limited. This is the first report of IPA treatment of up to 24 g L(-1) by an aerobic solvent-tolerant population.