Robust and efficient design of experiments for the Monod model

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.     

Biodegradation kinetics of select polycyclic aromatic hydrocarbon (PAH) mixtures by <Emphasis Type="Italic">Sphingomonas paucimobilis</Emphasis> EPA505

Many contaminated sites commonly have complex mixtures of polycyclic aromatic hydrocarbons (PAHs) whose individual microbial biodegradation may be altered in mixtures. Biodegradation kinetics for fluorene, naphthalene, 1,5-dimethylnaphthalene and 1-methylfluorene were evaluated in sole substrate, binary and ternary systems using Sphingomonas paucimobilis EPA505. The first order rate constants for fluorene, naphthalene, 1,5-dimethylnaphthalene, and 1-methylfluorene were comparable; yet Monod parameters were significantly different for the tested PAHs. S. paucimobilis completely degraded all the components in binary and ternary mixtures; however, the initial degradation rates of individual components decreased in the presence of competitive PAHs. Results from the mixture experiments indicate competitive interactions, demonstrated mathematically. The generated model appropriately predicted the biodegradation kinetics in mixtures using parameter estimates from the sole substrate experiments, validating the hypothesis of a common rate-determining step. Biodegradation kinetics in mixtures were affected by the affinity coefficients of the co-occurring PAHs and mixture composition. Experiments with equal concentrations of substrates demonstrated the effect of concentration on competitive inhibition. Ternary experiments with naphthalene, 1,5-dimethylnaphthalene and 1-methylfluorene revealed delayed degradation, where depletion of naphthalene and 1,5-dimethylnapthalene occurred rapidly only after the complete removal of 1-methylfluorene. The substrate interactions observed in mixtures require a multisubstrate model to account for simultaneous degradation of substrates. PAH contaminated sites are far more complex than even ternary mixtures; however these studies clearly demonstrate the effect that interactions can have on individual chemical kinetics. Consequently, predicting natural or enhanced degradation of PAHs cannot be based on single compound kinetics as this assumption would likely overestimate the rate of disappearance.     

Re-interpretation of the logistic equation for batch microbial growth in relation to Monod kinetics

Aims:  To determine the underlying substrate utilization mechanism in the logistic equation for batch microbial growth by revealing the relationship between the logistic and Monod kinetics. Also, to determine the logistic rate constant in terms of Monod kinetic constants.
Methods and Results:  The logistic equation used to describe batch microbial growth was related to the Monod kinetics and found to be first-order in terms of the substrate and biomass concentrations. The logistic equation constant was also related to the Monod kinetic constants. Similarly, the substrate utilization kinetic equations were derived by using the logistic growth equation and related to the Monod kinetics.
Conclusion:  It is revaled that the logistic growth equation is a special form of the Monod growth kinetics when substrate limitation is first-order with respect to the substrate concentration. The logistic rate constant ( k ) is directly proportional to the maximum specific growth rate constant ( μ _m) and initial substrate concentration ( S ₀) and also inversely related to the saturation constant ( K _s).
Significance and Impact of the Study:  The semi-empirical logistic equation can be used instead of Monod kinetics at low substrate concentrations to describe batch microbial growth using the relationship between the logistic rate constant and the Monod kinetic constants.     

The impact of feed composition on biodegradation of benzoate under cyclic (aerobic/anoxic) conditions

The response of a mixed microbial culture to different feed compositions, that is, containing benzoate and pyruvate as sole carbon sources at different levels, was studied in a chemostat with a 48-h hydraulic residence time under cyclic aerobic and anoxic (denitrifying) conditions. The cyclic bacterial culture was well adapted to different feed compositions as evidenced by the lack of accumulation of benzoate or pyruvate in the chemostat. Both the benzoate-degrading capabilities and the in vitro catechol 2,3-dioxygenase (C23DO) activities of the cyclic bacterial cultures were in direct proportion to the flux through the chemostat of the substrate degraded by the pathway containing C23DO, with some exceptions. The quantity of C23DO showed a transient decrease during the initial portion of the aerobic period before returning to the level present during the anoxic period. That decrease was most likely caused by the production of H(2)O(2) by the cells upon being returned to aerobic conditions.     

Chronic effect of erythromycin on substrate biodegradation kinetics of activated sludge

This study evaluated the chronic impact of erythromycin, a macrolide antibiotic, on microbial activities, mainly focusing on changes in process kinetics induced on substrate biodegradation and all related biochemical processes of microbial metabolism. Experiments involved two fill/draw reactors sustained at steady state at two different sludge ages of 10 and 2.0 days, fed with peptone mixture and continuous erythromycin dosing of 50 mg/L. Oxygen uptake rate profiles were generated in a series of parallel batch reactors seeded with biomass from fill/draw systems at selected periods of steady-state operation. Experimental data were evaluated by model calibration reflecting inhibitory effect on process kinetics: continuous erythromycin dosing inhibited microbial growth, reduced the rate of hydrolysis, blocked substrate storage and accelerated endogenous respiration. Adverse impact was mainly due to changes inflicted on the composition of microbial community. Interruption of erythromycin feeding resulted in partial recovery of microbial response. Sludge age affected the nature of inhibition, indicating different process kinetics for faster growing microbial community. Kinetic evaluation additionally revealed the toxic effect of erythromycin, which inactivated a fraction of biomass. Mass balance using oxygen uptake rate data also identified a stoichiometric impact, where a fraction of available substrate, although completely removed, could not be utilized in metabolic activities.     

Effect of different non-ionic surfactants on the biodegradation of PAHs by diverse aerobic bacteria

The aim of this work was to evaluate the effect of several non-ionic surfactants (Tween-80, Triton X-100 and Tergitol NP-10) on the ability of different bacteria (Enterobacter sp., Pseudomonas sp. and Stenotrophomonas sp.) to degrade polycyclic aromatic hydrocarbons (PAHs). Bacterial cultures were performed at 25 °C in an orbital shaker under dark conditions in BHB medium containing 1% of surfactant and 500 mg l⁻¹ of each PAH. Experiments performed with Tween-80 showed the highest cell density values and maximum specific growth rate because this surfactant was used as a carbon source by all bacteria. High degree of PAHs degradation (>90%) was reached in 15 days in all experiments. Toxicity increased at early times using Tween-80 but decreased to low levels in a short time after the firsts 24 h. On the other hand, Triton X-100 and Tergitol NP-10 were not biodegraded and toxicity kept constant along time. However, PAHs-degradation rate was higher, especially by the action of Enterobacter sp. with Tween-80 or Triton X-100. Control experiments performed without surfactant showed a significant decrease in biomass growth rate with a subsequent loss of biodegradation activity likely due to a reduced solubility and bioavailability of PAHs in absence of surfactant.     

Effect of yeast extract on growth kinetics during aerobic biodegradation of chlorobenzoic acids

The Monod or Andrews kinetic parameters describing the growth of Pseudomonas sp. CPE2 strain on 2,5-dich!orobenzoic acid and 2-chlorobenzoic acid, and Al-caligenes sp. CPE3 strain on 3,4-dichlorobenzoic acid, 4-chlorobenzoic acid, and 3-chlorobenzoic acid were determined from batch and continuous growth experiments conducted in the presence or absence of yeast extract (50 mg/L). Strain CPE2 displayed inhibitory growth kinetics in the absence of yeast extract and a noninhibitory kinetics in the presence of yeast extract. Similar results were obtained for CPE3. The presence of yeast extract also resulted in a significant increase in the affinity of the strains for the chlorobenzoic acids they degraded. (c) 1995 John Wiley & Sons, Inc.     

Concentration dependent growth/non-growth linked kinetics of endosulfan biodegradation by <Emphasis Type="Italic">Pseudomonas aeruginosa</Emphasis>

The rates of biodegradation of endosulfan by P. aeruginosa were determined with different initial endosulfan concentrations (10, 50, 100, 150, 200 and 250 mg l⁻¹) and different growth linked kinetic models were fitted at these concentrations. At 10 mg endosulfan l⁻¹, Monod no growth model was well fitted. Monod with growth model described the biodegradation pattern at an initial concentration of 50, 100 and 150 mg endosulfan l⁻¹. Significant increases of P. aeruginosa MN2B14 density in broth culture during incubation further support this result. Conversely, zero order kinetic model was well fitted into the biodegradation data if initial endosulfan concentration was ≥200 mg endosulfan l⁻¹. The kinetics of endosulfan biodegradation by P. aeruginosa MN2B14 in liquid broth was highly dependent upon its initial concentration. The results of this study could be employed for predicting the persistence of endosulfan in water environment containing P. aeruginosa as an endosulfan degrading bacterium.     

Aerobic biodegradation of benzene and toluene under hypersaline conditions at the Great Salt Plains, Oklahoma

The Great Salt Plains is a 65-km(2) hypersaline habitat of geological origin located in north-central Oklahoma. Contamination of such ecosystems by petroleum compounds is expected from non-point sources and due to increased human activities. Little information exists about the ability of halophilic and halotolerant bacteria present in such ancient and uncontaminated environments to degrade aromatic hydrocarbons. An enrichment culture was established from soil samples obtained from the salt flats using benzene as the sole carbon and energy source. The enrichment degraded benzene at varied salt concentrations ranging from 0 to 4M. Studies showed that roughly 33% of the (14)C-benzene was converted to (14)CO(2), indicating the mineralization capacity of native bacteria. Bacterial community structure analysis using denaturing gradient gel electrophoresis showed that different phylotypes were dominant at different salt concentrations.     

Optimization of operating parameters for sludge process reduction under alternating aerobic/oxygen-limited conditions by response surface methodology

Batch tests were employed to estimate the optimal conditions for excess sludge reduction under an alternating aerobic/oxygen-limited environment using response surface methodology. Three key operating parameters, initial mixed liquor suspended solids (initial MLSS), HRT (hydraulic retention time) and reaction temperature (T), were selected, and their interrelationships studied by the Box–Behnken design. The experimental data and ANOVA analysis showed that the coefficient of determination (R²) was 0.9956 and the adjR² was 0.9912, which demonstrates that the modified model was significant. The optimum conditions were predicted to give a maximal ΔMLSS yield of 226 mg/L at an initial MLSS of 10,021 ± 50 mg/L, an HRT of 9.1 h and a reaction temperature of 29 °C. The prediction was tested by triplicate experiments, where a ΔMLSS yield of 233 mg/L was achieved under the chosen optimal conditions. This excellent correlation between the predicted and measured values provides confidence in the model.     

Biodegradation kinetics of 2,4,6-Trichlorophenol by an acclimated mixed microbial culture under aerobic conditions

The objective of this study was to achieve a better quantitative understanding of the kinetics of 2,4,6-trichlorophenol (TCP) biodegradation by an acclimated mixed microbial culture. An aerobic mixed microbial culture, obtained from the aeration basin of the wastewater treatment plant, was acclimated in shake flasks utilizing various combinations of 2,4,6-TCP (25–100 mg l⁻¹), phenol (300 mg l⁻¹) and glycerol (2.5 mg l⁻¹) as substrates. Complete primary TCP degradation and a corresponding stoichiometric release of chloride ion were observed by HPLC and IEC analytical techniques, respectively. The acclimated cultures were then used as an inoculum for bench scale experiments in a 4 l stirred-tank reactor (STR) with 2,4,6-TCP as the sole carbon/energy (C/E) source. The phenol acclimated mixed microbial culture consisted of primarily Gram positive and negative rods and was capable of degrading 2,4,6-TCP completely. None of the predicted intermediate compounds were detected by gas chromatography in the cell cytoplasm or supernatant. Based on the disappearance of 2,4,6-TCP, degradation was well modelled by zero-order kinetics which was also consistent with the observed oxygen consumption. Biodegradation rates were compared for four operating conditions including two different initial 2,4,6-TCP concentrations and two different initial biomass concentrations. While the specific rate constant was not dependent on the initial 2,4,6-TCP concentration, it did depend on the initial biomass concentration (X _init). A lower biomass concentration gave a much higher zero-order specific degradation rate. This behaviour was attributed to a lower average biomass age or cell retention time (θ_x) for these cultures. The implications of this investigation are important for determining and predicting the potential risks associated with TCP, its degradation in the natural environment or the engineering implications for ex situ treatment of contaminated ground water or soil.     

Microorganisms participating in the biodegradation of modified polyethylene films in different soils under laboratory conditions

The degree of biodegradation of low-density polyethylene (LDPE) films modified with Bionolle^® polyester in different soils under laboratory conditions was evaluated. Films were incubated in soils from waste coal, a forest and an extinct volcano crater. Prior to degradation studies, soils underwent chemical and microbiological analysis. Film weight loss and mechanical properties, as well as the surface of the polymeric samples determined via scanning electron microscopy, were evaluated after 75, 150 and 225 days of biodegradation. Important chemical changes in the polymeric chains were detected by Fourier Transform Infrared Spectroscopy (FTIR). Fungal and bacterial species that were able to grow on the film surfaces were monitored in order to see whether the films were easily colonised by autochthonous microorganisms (i.e., typical to each soil). Identification of microorganisms was based on their cellular fatty acid methyl ester (FAME) profiles. Biodegradation of modified polyethylene films in soils led to significant changes (i.e., elongation at brake of 98%) in their mechanical properties that were caused by biochemical modifications of both polyester and polyethylene. Compared to waste coal soil, films underwent rapid biodegradation in soils that were rich in organic matter. Bacteria belonging to the genus, Bacillus, and the fungi, Gliocladium viride, Aspergillus awamori and Mortierella subtilissima, were easily able to colonise both polyethylene and polyethylene modified with Bionolle^®.     

Stoichiometry and kinetics of acetate uptake under anaerobic conditions by an enriched culture of phosphorus-accumulating organisms at different pHs

The effect of pH on the stoichiometry and kinetics of acetate uptake by phosphorus-accumulating organisms (PAOs) was studied. The stoichiometry of glycogen consumption and poly-beta-hydroxy-alkanoates (PHA) accumulation was independent of the pH over the range 6.5 to 8.0. It was again demonstrated that the amount of phosphorus released per acetate taken up (P/Hac ratio) was linearly dependent on pH, because of additional energy requirements for acetate transport at higher pH. The slope of this relationship was similar to that in previously published work, but the absolute values were different, indicating that the P/Hac ratio is the most variable stoichiometric parameter associated with the anaerobic metabolism of PAOs. A kinetic expression for acetate-uptake rate was developed and tested. It assumes a zero-order form when the polyphosphate content of the biomass is not limiting. When the polyphosphate content becomes low, the rate is significantly decreased. The expression was tested in situations in which polyphosphate was a limiting factor in the rate of acetate uptake, in which the glycogen content of the biomass became very low, and in which both glycogen and polyphosphate were present in excess. The model was able to simulate the three situations adequately. Additionally, the rate of acetate uptake was independent of the pH for the range studied (6.5 to 8.0).     

Microbial biomass and growth kinetics of microorganisms in chernozem soils under different land use modes

The carbon content of microbial biomass and the kinetic characteristics of microbial respiration response to substrate addition have been estimated for chernozem soils under different land use: arable lands used for 10, 46, and 76 years, mowed meadow, natural forest, and forest shelter belt. Microbial biomass and the content of microbial carbon in humus (C_mic /C_org) decreased in the following order: soils under forest cenoses—mowed meadow—10-year arable land—46- and 75-year arable land. The amount of microbial carbon in the long-plowed horizon was 40% of its content in the upper horizon of natural forest. Arable soils were characterized by a lower metabolic diversity of microbial community and by the highest portion of microorganisms able to grow directly on glucose introduced into soil. The effects of different scenarios of carbon sequestration in soil on the amounts and activity of microbial biomass are discussed.     

Phosphate‐limited growth of the marine diatom Thalassiosira weissflogii (Bacillariophyceae): evidence of non‐monod growth kinetics1

The marine diatom Thalassiosira weissflogii (Grunow) G. A. Fryxell & Hasle was grown in a chemostat over a series of phosphate‐limited growth rates. Ambient substrate concentrations were determined from bioassays involving picomolar spikes of ³³P‐labeled phosphate, and maximum uptake rates were determined from analogous bioassays that included the addition of micromolar concentrations of unlabeled phosphate and tracer concentrations of ³³P. The relationship between cell phosphorus quotas and growth rates was well described by the Droop equation. Maximum uptake rates of phosphate spikes were several orders of magnitude higher than steady state uptake rates. Despite the large size of the T. weissflogii cells, diffusion of phosphate through the boundary layer around the cells had little effect on growth kinetics, in part because the cellular N:P ratios exceeded the Redfield ratio at all growth rates. Fitting the Monod equation to the experimental data produced an estimate of the nutrient‐saturated growth rate that was ~50% greater than the maximum growth rate observed in batch culture. A modified hyperbolic equation with a curvature that is a maximum in magnitude at positive growth rates gave a better fit to the data and an estimate of the maximum growth rate that was consistent with observations. The failure of the Monod equation to describe the data may reflect a transition from substrate to co‐substrate limitation and/or the presence of an inducible uptake system.     

Respirometric evaluation and modeling of glucose utilization by Escherichia coli under aerobic and mesophilic cultivation conditions

The study presents a mechanistic model for the evaluation of glucose utilization by Escherichia coli under aerobic and mesophilic growth conditions. In the first step, the experimental data was derived from batch respirometric experiments conducted at 37 degrees C, using two different initial substrate to microorganism (S(0)/X(0)) ratios of 15.0 and 1.3 mgCOD/mgSS. Acetate generation, glycogen formation and oxygen uptake rate profile were monitored together with glucose uptake and biomass increase throughout the experiments. The oxygen uptake rate (OUR) exhibited a typical profile accounting for growth on glucose, acetate and glycogen. No acetate formation (overflow) was detected at low initial S(0)/X(0) ratio. In the second step, the effect of culture history developed under long-term growth limiting conditions on the kinetics of glucose utilization by the same culture was evaluated in a sequencing batch reactor (SBR). The system was operated at cyclic steady state with a constant mean cell residence time of 5 days. The kinetic response of E.coli culture was followed by similar measurements within a complete cycle. Model calibration for the SBR system showed that E. coli culture regulated its growth metabolism by decreasing the maximum growth rate (lower microH) together with an increase of substrate affinity (lower K(S)) as compared to uncontrolled growth conditions. The continuous low rate operation of SBR system induced a significant biochemical substrate storage capability as glycogen in parallel to growth, which persisted throughout the operation. The acetate overflow was observed again as an important mechanism to be accounted for in the evaluation of process kinetics.     

Effect of propanil,linuron, and dicamba on the degradation kinetics of 2,4‐dichlorophenoxyacetic acid by Burkholderia sp. A study by differential analysis of 2,4‐dichlorophenoxyacetic acid degradation data

The successive application of distinct pesticides, or mixtures of them, is a frequent practice that could adversely affect the microbial species inhabiting soil and aquatic ecosystems. The ability of soil or aquatic microbiota to degrade a pesticide could be affected by the presence of another. If the degradation rate of the first compound is inhibited, its dissipation half‐life in the environment could be hazardously enlarged. Few studies have been made to quantify the impact on the biodegradation rate of pesticides in soils or water by the presence of other pesticides. In this work, a method for assessing the effect of a pesticide on the biodegradation rate of another, measuring its effect on the biodegradation kinetics of a single bacterial strain is presented. The mathematical analysis is a powerful tool to study the stoichiometry and kinetics of microbial processes, which was used to evaluate independently, in detail, the effect of three pesticides (propanil, linuron, and dicamba) on the biodegradation kinetics of 2,4‐dichlorophenoxyacetic acid by a strain of Burkholderia sp. It was evidenced that linuron and dicamba caused a decay of more than 40% in the top instantaneous degradation rate of 2,4‐dichlorophenoxyacetic acid, while propanil showed a minimal effect.     

Modeling of yeast <Emphasis Type="Italic">Brettanomyces bruxellensis</Emphasis> growth at different acetic acid concentrations under aerobic and anaerobic conditions

Glucose utilization by Brettanomyces bruxellensis at different acetic acid concentrations under aerobic and anaerobic conditions was investigated. The presence of the organic acid disturbs the growth and fermentative activity of the yeast when its concentration exceeds 2 g l⁻¹. A mathematical model is proposed for the kinetic behavior analysis of yeast growing in batch culture. A Matlab algorithm was used for estimation of model parameters, whose confidence intervals were also calculated at a 0.95 probability level using a t-Student distribution for f degrees of freedom. The model successfully simulated the batch kinetics observed at different concentrations of acetic acid under both oxygen conditions.