Nonlinear estimation of the parameters of Monod kinetics that best describe mineralization of several substrate concentrations by dissimilar bacterial densities

The kinetics of mineralization of a wide range of concentrations of benzoate, glucose, and benzylamine by Pseudomonas sp., Salmonella typhimurium, and microorganisms in acclimated sewage was studied. The treatment of initial substrate concentration and population density as independent variables in nonlinear regression analysis permitted the estimation of a single value for each of the parameters of Monod kinetics that best described the mineralization of substrate at each concentration by the pure cultures and the sewage microflora. One value for each of the parameters of Monod kinetics was used for each of the three compounds to produce theoretical curves which lay close to the observed data on mineralization. Statistically significant differences existed in the values of the parameters of Monod kinetics that best described mineralization in cultures differing only in initial substrate concentration and cell density. However, for the compounds tested, the variance left by analyses using one value for each parameter of Monod kinetics was less than double the unexplained variance left by individual analyses of the data from each treatment. Although significant, this increase is small compared with the amount of variance that could be explained using only one value for each parameter of Monod kinetics.     

Nonlinear estimation of Monod growth kinetic parameters from a single substrate depletion curve.

Monod growth kinetic parameters were estimated by fitting sigmoidal substrate depletion data to the integrated Monod equation, using nonlinear least-squares analysis. When the initial substrate concentration was in the mixed-order region, nonlinear estimation of simulated data sets containing known measurement errors provided accurate estimates of the mu max, Ks, and Y values used to create these data. Nonlinear regression analysis of sigmoidal substrate depletion data was also evaluated for H2-limited batch growth of Desulfovibrio sp. strain G11. The integrated Monod equation can be more convenient for the estimation of growth kinetic parameters, particularly for gaseous substrates, but it must be recognized that the estimates of mu max, Ks, and Y obtained may be influenced by the growth rate history of the inoculum.     

Nonlinear estimation of Monod growth kinetic parameters from a single substrate depletion curve

Monod growth kinetic parameters were estimated by fitting sigmoidal substrate depletion data to the integrated Monod equation, using nonlinear least-squares analysis. When the initial substrate concentration was in the mixed-order region, nonlinear estimation of simulated data sets containing known measurement errors provided accurate estimates of the mu max, Ks, and Y values used to create these data. Nonlinear regression analysis of sigmoidal substrate depletion data was also evaluated for H2-limited batch growth of Desulfovibrio sp. strain G11. The integrated Monod equation can be more convenient for the estimation of growth kinetic parameters, particularly for gaseous substrates, but it must be recognized that the estimates of mu max, Ks, and Y obtained may be influenced by the growth rate history of the inoculum.     

Nonlinear estimation of monod growth kinetic parameters from a single substrate depletion curve

[This corrects the article on p. 1454 in vol. 45.].     

Models for mineralization kinetics with the variables of substrate concentration and population density.

The rates of mineralization of [14C]benzoate by an induced population of Pseudomonas sp. were measured at initial substrate concentrations ranging from 10 ng/ml to 100 micrograms/ml. Plots of the radioactivity remaining in the culture were fit by nonlinear regression to six kinetic models derived from the Monod equation. These models incorporate only the variables of substrate concentration and cell density. Plots of the mineralization kinetics in cultures containing low, intermediate, and high initial substrate concentrations were well fit by first-order, integrated Monod, and logarithmic kinetics, respectively. Parameters such as maximum specific growth rate, half-saturation constant, and initial population density divided by yield agreed between cultures to within a factor of 3.4. Benzoate mineralization by microorganisms in acclimated sewage was shown to fit logistic (sigmoidal), Monod, and logarithmic kinetics when the compound was added at initial concentrations of 0.1, 1.0, and 10 micrograms/ml, respectively. The mineralization of 10 micrograms of benzoate per ml in sewage also followed logarithmic kinetics in the absence of protozoa. It is concluded that much of the diversity in shapes of mineralization curves is a result of the interactions of substrate concentration and population density. Nonlinear regression with models incorporating these variables is a valuable means for analysis of microbial mineralization kinetics.     

Apparent zero-order kinetics of phenol biodegradation by substrate-inhibited microbes at low substrate concentrations

The reaction kinetics for phenol biodegradation at low substrate concentrations can be estimated based on the analysis of changes in the dissolved oxygen concentration in the bulk liquid during biodegradation. The measured oxygen concentration changes with an interesting behavior as biodegradation proceeds. The oxygen concentration in the bulk liquid decreases rapidly in the early stages of degradation and subsequently decreases linearly and then rapidly recovers to the initial saturated level. Taking into account the oxygen transfer rate between gas and liquid phases and oxygen consumption rate by microbes, the change in the dissolved oxygen concentration can be simulated with an unsteady state mass balance equation and three kinetic models for the rate of phenol metabolism: a substrate-inhibited model; a zero-order model; and a combined model. In the combined model, it is assumed that, at phenol concentrations above 10 mg/L, the degradation rate is expressed by a substrate-inhibited model; whereas at concentrations below 10 mg/L the zero-order model is applied. It was found that the characteristics of the change in the dissolved oxygen concentration, especially the rapid increase at the end of degradation, can only be described by the combined kinetic model. This result suggests that conventional Haldane-type kinetics would be unsuitable for estimating the phenol consumption rate at low phenol concentrations, in particular, at concentrations less than 10 mg/L. (c) 1996 John Wiley & Sons, Inc.     

STADEERS: a software package for the statistical design of experiments pertaining to the estimation of parameters in rate expressions that describe enzyme-catalyzed processes

This paper describes a computational algorithm (STADEERS-STAtisticalDesign of Exeriments in Enzyme ReactorS) for the statisticaldesign of biochemical engineering experiments. The type of experimentthat qualifies for this package involves a batch reaction catalyzedby a soluble enzyme where the activity of the enzyme decayswith time. Assuming that both the catalytic action and the deactivationof the enzyme obey known rate expressions, the present codeis helpful in the process of obtaining estimates of the kineticparameters by providing as output the times at which samplesshould be withdrawn from the reacting mixture. Starting D-optimaldesign is used as a basis for the statistical approach. ThisBASIC code is a powerful tool when fitting a rate expressionto data because it increases the effectiveness of experimentationby helping the biochemical kineticist obtain data points withthe largest possible informa tional content.     

Quasi-steady-state kinetics at enzyme and substrate concentrations in excess of the Michaelis-Menten constant

In vitro enzyme reactions are traditionally conducted under conditions of pronounced substrate excess since this guarantees that the bound enzyme is at quasi-steady-state (QSS) with respect to the free substrate, thereby justifying the Briggs-Haldane approximation (BHA). In contrast, intracellular reactions, amplification assays, allergen digestion assays and industrial applications span a range of enzyme-to-substrate ratios for which the BHA is invalid, including the extreme of enzyme excess. The quasi-equilibrium approximation (QEA) is valid for a subset of enzyme excess states. Previously, we showed that the total QSSA (tQSSA) overlaps and extends the validity of the BHA and the QEA, and that it is at least roughly valid for any total substrate and enzyme concentrations. The analysis of the tQSSA is hampered by square root nonlinearity. Previous simplifications of the tQSSA rate law are valid in a parameter domain that overlaps the validity domains of the BHA and the QEA and only slightly extends them. We now integrate the tQSSA rate equation in closed form, without resorting to further approximations. Moreover, we introduce a complimentary simplification of the tQSSA rate law that is valid in states of enzyme excess when the absolute difference between total enzyme and substrate concentrations greatly exceeds the Michaelis-Menten constant. This includes a wide range of enzyme and substrate concentrations where both the BHA and the QEA are invalid and allows us to define precisely the conditions for zero-order and first-order product formation. Remarkably, analytical approximations provided by the tQSSA closely match the expected stochastic kinetics for as few as 15 reactant molecules, suggesting that the conditions for the validity of the tQSSA and for its various simplifications are also of relevance at low molecule numbers.     

Degradation and mineralization of atrazine by a soil bacterial isolate.

An atrazine-degrading bacterial culture was isolated from an agricultural soil previously impacted by herbicide spills. The organism was capable of using atrazine under aerobic conditions as the sole source of C and N. Cyanuric acid could replace atrazine as the sole source of N, indicating that the organism was capable of ring cleavage. Ring cleavage was confirmed in 14CO2 evolution experiments with [U-14C-ring]atrazine. Between 40 and 50% of ring-14C was mineralized to 14CO2. [14C]biuret and [14C]urea were detected in spent culture media. Cellular assimilation of 14C was negligible, in keeping with the fully oxidized valence of the ring carbon. Chloride release was stoichiometric. The formation of ammonium during atrazine degradation was below the stoichiometric amount, suggesting a deficit due to cellular assimilation and metabolite-N accumulation. With excess glucose and with atrazine as the sole N source, free ammonium was not detected, suggesting assimilation into biomass. The organism degraded atrazine anaerobically in media which contained (i) atrazine only, (ii) atrazine and glucose, and (iii) atrazine, glucose, and nitrate. To date, this is the first report of a pure bacterial isolate with the ability to cleave the s-triazine ring structure of atrazine. It was also concluded that this bacterium was capable of dealkylation, dechlorination, and deamination in addition to ring cleavage.     

An algebraic model for the kinetics of covalent enzyme inhibition at low substrate concentrations

This article describes an integrated rate equation for the time course of covalent enzyme inhibition under the conditions where the substrate concentration is significantly lower than the corresponding Michaelis constant, for example, in the Omnia assays of epidermal growth factor receptor (EGFR) kinase. The newly described method is applicable to experimental conditions where the enzyme concentration is significantly lower than the dissociation constant of the initially formed reversible enzyme–inhibitor complex (no “tight binding”). A detailed comparison with the traditionally used rate equation for covalent inhibition is presented. The two methods produce approximately identical values of the first-order inactivation rate constant (k_inact). However, the inhibition constant (K_i), and therefore also the second-order inactivation rate constant k_inact/K_i, is underestimated by the traditional method by up to an order of magnitude.     

A new framework for the estimation of control parameters in metabolic pathways using lin-log kinetics.

The control properties of biochemical pathways can be described by control coefficients and elasticities, as defined in the framework of metabolic control analysis. The determination of these parameters using the traditional metabolic control analysis relationships is, however, limited by experimental difficulties (e.g. realizing and measuring small changes in biological systems) and lack of appropriate mathematical procedures (e.g. when the more practical large changes are made). In this paper, the recently developed lin-log approach is proposed to avoid the above-mentioned problems and is applied to estimate control parameters from measurements obtained in steady state experiments. The lin-log approach employs approximative linear-logarithmic kinetics parameterized by elasticities and provides analytical solutions for fluxes and metabolite concentrations when large changes are made. Published flux and metabolite concentration data are used, obtained from a reconstructed section of glycolysis converting 3-phosphoglycerate to pyruvate [Giersch, C. (1995) Eur. J. Biochem. 227, 194-201]. With the lin-log approach, all data from different experiments can be combined to give realistic elasticity and flux control coefficient estimates by linear regression. Despite the large changes, a good agreement of fluxes and metabolite concentrations is obtained between the measured and calculated values according to the lin-log model. Furthermore, it is shown that the lin-log approach allows a rigorous statistical evaluation to identify the optimal reference state and the optimal model structure assumption. In conclusion, the lin-log approach addresses practical problems encountered in the traditional metabolic control analysis-based methods by introducing suitable nonlinear kinetics, thus providing a novel framework with improved procedures for the estimation of elasticities and control parameters from large perturbation experiments.     

The determination of binding parameters when the total and free substrate concentrations are not approximately equal.

The maximal extractable activity of "malic" enzyme (EC 1.1.1.40) in rat islets of Langerhans was similar to that reported for liver. Thus "malic" enzyme may catalyse a near-equilibrium reaction in the cytosol of islets of Langerhans. Measurements of islet content of malate and pyruvate, the metabolite substrate and product of "malic" enzyme, were therefore used to calculate the cytosolic ration of [NADPH]/[NADP+]. This ratio was higher in islets incubated with 20 mM-glucose than in islets incubated with 2 mM-glucose.     

Inhibition of Drosophila melanogaster acetylcholinesterase by high concentrations of substrate.

Acetylcholine hydrolysis by acetylcholinesterase is inhibited at high substrate concentrations. To determine the residues involved in this phenomenon, we have mutated most of the residues lining the active-site gorge but mutating these did not completely eliminate hydrolysis. Thus, we analyzed the effect of a nonhydrolysable substrate analogue on substrate hydrolysis and on reactivation of an analogue of the acetylenzyme. Analyses of various models led us to propose the following sequence of events: the substrate initially binds at the rim of the active-site gorge and then slides down to the bottom of the gorge where it is hydrolyzed. Another substrate molecule can bind to the peripheral site: (a) when the choline is still inside the gorge - it will thereby hinder its exit; (b) after choline has dissociated but before deacetylation occurs - binding at the peripheral site increases deacetylation rate but (c) if a substrate molecule bound to the peripheral site slides down to the bottom of the active-site before the catalytic serine is deacetylated, its new position will prevent the approach of water, thus blocking deacetylation.     

Constitutive mineralization of low concentrations of the herbicide linuron by a Variovorax sp. strain

The mineralization of the herbicide linuron at concentrations of μg and mg L⁻¹ was studied in liquid batch experiments with Variovorax sp. strain SRS16. The strain was highly efficient at mineralizing a range of linuron concentrations (0.002–10 mg L⁻¹) with 20–60% of the added ¹⁴C-ring-labeled linuron metabolized to ¹⁴CO₂ within hours to days depending on the initial linuron concentration and incubation period. At mg L⁻¹ linuron concentrations the mineralization activity by SRS16 was inducible and a shift to constitutive mineralization activity was apparent with a reduction in the linuron concentration to μg L⁻¹ levels. This study revealed that strain SRS16 is a promising candidate for bioaugmentation of water or soil resources contaminated with low linuron concentrations.     

Formation of several bacterial c-type cytochromes requires a novel membrane-anchored protein that faces the periplasm

We report here the discovery of a novel bacterial gene (cycH) whose product is involved in the biogenesis of most of the cellular cytochromes c. The cycH gene was detected in the course of characterizing a cytochrome oxidase-deficient Bradyrhizobium japonicum Tn5 mutant (strain CO×3) in which the transposon insertion disrupted cycH. Ali of the c-type cytochromes detectable in aerobically grown B. Japonicum wild-type cells were absent in the C0X3 mutant, with the exception of cytochrome c₁. A secondary phenotypic effect was the spectroscopic absence of the aa₃-type cytochrome c oxidase. The nucleotide sequence of the cloned wild-type cycH gene predicted a membrane-bound 369-amino-acid protein with an M_r of 39727. Results from studies on its membrane topology suggested that approximately 110 N-terminal amino acids are involved in anchoring the protein in the membrane, whereas the remaining two-thirds of the protein are exposed to the periplasm. We postulate that the CycH protein plays an essential role in an as yet unidentified periplasmic step in the biogenesis of holocytochromes c, except that of cytochrome c₁.     

Cometabolism of chlorinated solvents by nitrifying bacteria: kinetics, substrate interactions, toxicity effects, and bacterial response

Pure cultures of ammonia-oxidizing bacteria, Nitrosomonas europaea, were exposed to trichloroethylene (TCE), 1,1-dichloroethylene (1,1-DCE), chloroform (CF), 1,2-dichloroethane (1,2-DCA), or carbon tetrachloride (CT), in the presence of ammonia, in a quasi-steady-state bioreactor. Estimates of enzyme kinetics constants, solvent inactivation constants, and culture recovery constants were obtained by simultaneously fitting three model curves to experimental data using nonlinear optimization techniques and an enzyme kinetics model, referred to as the inhibition, inactivation, and recovery (IIR) model, that accounts for inhibition of ammonia oxidation by the solvent, enzyme inactivation by solvent product toxicity, and respondent synthesis of new enzyme (recovery). Results showed relative enzyme affinities for ammonia monooxygenase (AMO) of 1,1-DCE approximately TCE > CT > NH(3) > CF > 1,2-DCA. Relative maximum specific substrate transformation rates were NH(3) > 1,2-DCA > CF > TCE approximately 1,1-DCE > CT (=0). The TCE, CF, and 1,1-DCE inactivated the cells, with 1,1-DCE being about three times more potent than TCE or CF. Under the conditions of these experiments, inactivating injuries caused by TCE and 1,1-DCE appeared limited primarily to the AMO enzyme, but injuries caused by CF appeared to be more generalized. The CT was not oxidized by N. europaea while 1,2-DCA was oxidized quite readily and showed no inactivation effects. Recovery capabilities were demonstrated with all solvents except CF. A method for estimating protein yield, the relationship between the transformation capacity model and the IIR model, and a condition necessary for sustainable cometabolic treatment of inactivating substrates are presented. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 520-534, 1997.