A kinetic model incorporating energy spilling for substrate removal in substrate-sufficient batch culture of activated sludge

Batch assays are currently used to study the kinetic behavior of microbial growth. However, it has been shown that the outcome of batch experiments is greatly influenced by the initial ratio of substrate concentration (S _o) to biomass concentration (X _o). Substrate-sufficient batch culture is known to have mechanisms of spilling energy that lead to significant nongrowth-associated substrate consumption, and the Monod equation is no longer appropriate. By incorporating substrate consumption associated with energy spilling into the balance of the substrate oxidation reaction, a kinetic model for the observed specific substrate consumption rate was developed for substrate-sufficient batch culture of activated sludge, and was further verified by experimental data. It was demonstrated that the specific substrate consumption rate increased with the increase of the S _o/X _o ratio, and the majority of substrate was consumed through energy spilling at high S _o/X _o ratios. It appears that the S _o/X _o ratio is a key parameter in regulating metabolic pathways of microorganisms. Received: 18 January 1999 / Received revision: 7 May 1999 / Accepted: 28 May 1999     

Kinetics study of pyridine biodegradation by a novel bacterial strain,Rhizobium sp. NJUST18

Biodegradation of pyridine by a novel bacterial strain, Rhizobium sp. NJUST18, was studied in batch experiments over a wide concentration range (from 100 to 1,000 mg l^?1). Pyridine inhibited both growth of Rhizobium sp. NJUST18 and biodegradation of pyridine. The Haldane model could be fitted to the growth kinetics data well with the kinetic constants μ* = 0.1473 h^?1, K _s = 793.97 mg l^?1, K _i = 268.60 mg l^?1 and S _m = 461.80 mg l^?1. The true μ _max, calculated from μ*, was found to be 0.0332 h^?1. Yield coefficient Y _X/S depended on S _i and reached a maximum of 0.51 g g^?1 at S _i of 600 mg l^?1. V _max was calculated by fitting the pyridine consumption data with the Gompertz model. V _max increased with initial pyridine concentration up to 14.809 mg l^?1 h^?1. The q _S values, calculated from $V_{ \hbox{max} }$ , were fitted with the Haldane equation, yielding q _Smax = 0.1212 g g^?1 h^?1 and q* = 0.3874 g g^?1 h^?1 at S _m′ = 507.83 mg l^?1, K _s′ = 558.03 mg l^?1, and K _i′ = 462.15 mg l^?1. Inhibition constants for growth and degradation rate value were in the same range. Compared with other pyridine degraders, μ _max and S _m obtained for Rhizobium sp. NJUST18 were relatively high. High K _i and K _i′ values and extremely high K _s and K _s′ values indicated that NJUST18 was able to grow on pyridine within a wide concentration range, especially at relatively high concentrations.     

Determination of intrinsic monod kinetic parameters for two heterotrophic tetrachloroethene (PCE)‐respiring strains and insight into their application

A complete set of mathematically identifiable and meaningful kinetic parameters estimates is needed to accurately describe the activity of individual populations that dehalorespire tetrachloroethene (PCE) and other chlorinated ethenes. These data may be difficult to extract from the literature because kinetic parameter estimates obtained using mixed cultures may reflect the activity of multiple dehalorespiring populations, while those obtained at low initial substrate‐to‐biomass ratios (S₀/X₀) are influenced by culture history and are generally not relevant to other systems. This study focused on estimation of electron donor and acceptor utilization kinetic parameters for the heterotrophic dehalorespirers Desulfuromonas michiganensis strain BB1 and Desulfitobacterium sp. strain PCE1. Electron acceptor utilization kinetic parameters that are identifiable and independent of culture history, i.e., intrinsic, could be estimated at S₀/X₀ ≥ 10, with both concentrations expressed as chemical oxygen demand (COD). However, the parameter estimates did not accurately describe dechlorination kinetics at lower S₀/X₀ ratios. The maximum specific substrate utilization rates (q_max) and half‐saturation constants (K_S) for PCE and trichloroethene (TCE) estimated for the two heterotrophic strains are higher than the values reported for Dehalococcoides cultures. These results suggest that the natural niche of Dehalococcoides strains that can metabolize a range of chlorinated ethenes may be to respire dichloroethene and vinyl chloride produced by Desulfuromonas and Desulfitobacterium strains or other populations that dechlorinate PCE and TCE at faster rates. Few data exist on the electron donor utilization kinetics of heterotrophic dehalorespirers. The results of this study suggest that Desulfuromonas and Desulfitobacterium strains should be able to compete for organic electron donors with other heterotrophic populations in the subsurface. Biotechnol. Bioeng. 2009; 104: 301–311 © 2009 Wiley Periodicals, Inc.     

Influence of the ratio of the initial substrate concentration to biomass concentration on the performance of a sequencing batch reactor

Biomass behaviour and COD removal in a benchscale activated sludge reactor have been studied alternating anaerobic and aerobic conditions. Particular attention has been paid to the influence of the ratio of the initial substrate concentration (S ₀) to the initial biomass concentration (X ₀) on the reactor performance. Tests at very low ratios (S ₀/X ₀<2) demonstrate the existence of a threshold below which the reactor performance is seriously affected (S ₀/X ₀=0.5). Under conditions of total suppression of cell duplication, substrate maintenance requirements have also been calculated for the microbial consortium present in the activated sludges. The results obtained show that stressed biomass can survive conditions of substrate lack better than unstressed biomass.List of Symbols b h^–1 specific death rate - COD g/l chemical oxygen demand - DO g/l dissolved oxygen concentration - K _s g/l Monod saturation constant - MLSS g/l mixed liquor suspended solid concentration - P g/l phosphorus concentration - S g/l substrate concentration - S ₀ g/l initial substrate concentration - SS g/l suspended solid concentration - t h time - X g/l biomass concentration - X ₀ g/l initial biomass concentration - Y _SX g/g yield of growth on substrate - _max h^–1 maximum specific growth rate     

Methanogenic degradation kinetics of phenolic compounds in aquifer-derived microcosms

In this segment of a larger multidisciplinary study of the movement and fate of creosote derived compounds in a sand-and-gravel aquifer, we present evidence that the methanogenic degradation of the major biodegradable phenolic compounds and concomitant microbial growth in batch microcosms derived from contaminated aquifer material can be described using Monod kinetics. Substrate depletion and bacterial growth curves were fitted to the Monod equations using nonlinear regression analysis. The method of Marquardt was used for the determination of parameter values that best fit the experimental data by minimizing the residual sum of squares. The Monod kinetic constants ( _max , K _s, Y, and k _d) that describe phenol, 2-, 3-, and 4-methylphenol degradation and concomitant microbial growth were determined under conditions that were substantially different from those previously reported for microcosms cultured from sewage sludge. The K _s values obtained in this study are approximately two orders of magnitude lower than values obtained for the anaerobic degradation of phenol in digesting sewage sludge, indicating that the aquifer microorganisms have developed enzyme systems that are adapted to low nutrient conditions. The values for k _d are much less than _max, and can be neglected in the microcosms. The extremely low Y values, approximately 3 orders of magnitude lower than for the sewage sludge derived cultures, and the very low numbers of microorganisms in the aquifer derived microcosms suggest that these organisms use some unique strategies to survive in the subsurface environment.Abbreviations GC gas chromatography - HPLC high performance liquid chromatography - LBSSB likelihood based sum of squares boundaries - MPN most probable number - NLR nonlinear regression analysis - OFAG oxygen free Argon gas - PCP pentachlorophenol - RSS residual sum of squares - SRB sulfate reducing bacteria     

Phenol degradation by a psychrotrophic strain of Pseudomonas putida

Summary Cell growth and phenol degradation kinetics were studied at 10°C for a psychrotrophic bacterium, Pseudomonas putida Q5. The batch studies were conducted for initial phenol concentrations, S_o, ranging from 14 to 1000 mg/1. The experimental data for 14<=S_o<=200 mg/1 were fitted by non-linear regression to the integrated Haldane substrate inhibition growth rate model. The values of the kinetic parameters were found to be: _m=0.119 h^–1, K _S=5.27 mg/1 and K _I=377 mg/1. The yield factor of dry biomass from substrate consumed was Y=0.55. Compared to mesophilic pseudomonads previously studied, the psychrotrophic strain grows on and degrades phenol at rates that are ca. 65–80% lower. However, use of the psychrotrophic microorganism may still be economically advantageous for waste-water treatment processes installed in cold climatic regions, and in cases where influent waste-water temperatures exhibit seasonal variation in the range 10–30°C.Nomenclature K _S saturation constant (mg/l) - K _I substrate inhibition constant (mg/l) - specific growth rate (h^–1) - _m maximum specific growth rate without substrate inhibition (h^–1) - _max maximum achievable specific growth rate with substrate inhibition (h^–1) - S substrate (phenol) concentration (mg/l) - S_o initial substrate concentration (mg/l) - S_max substrate concentration corresponding to _max (mg/l) - t time (h) - X cell concentration, dry basis (mg DW/l) - X_f final cell concentration, dry basis (mg DW/l) - X_o initial cell concentration, dry basis (mg DW/l) - Y yield factor (mg DW cell produced/mg substrate consumed)     

Ferrous iron oxidation and uranium extraction by Thiobacillus ferrooxidans

The microbiological oxidation of ferrous iron in batch and continuous systems has been investigated in relation to uranium extraction from a low-grade ore by Thiobacillus ferrooxidans. The influence of the parameters, agitation, and aeration on oxygen saturation concentration, rate of oxygen mass transfer, and rate of ferrous iron oxidation was demonstrated. The kinetic values, V_max and K were determined using an adapted Monod equation for different dilution rates and initial concentrations of ferrous iron. The power requirements for initial leaching conditions were also calculated. Uranium extraction as high as 68% has been realized during nine days of treatment. Regrinding the leach residue and its subsequent leaching yielded 87% uranium solubilization.     

Novel differential elimination method for determining kinetic coefficients under substrate self-inhibition

A differential elimination method (DEM) is developed to determine the kinetic coefficients for substrate self-inhibition. Finite differentiation of the equation eliminates either K_I or K_S, which enables the equation to be linearized so that [^(\textq)] {\hat{\text{q}}} , K_S, and K_I can be estimated without using nonlinear least square regression (NLSR). The DEM options that eliminate K_I or K_S 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, q_max. The estimates for S_max, the concentration at which the maximum specific substrate utilization rate is observed, were relatively invariant among the methods, even when K_S and K_I 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.     

Simultaneous estimation ofV max,Km, and the rate of endogenous substrate production (R) from substrate depletion data

The nonlinear and 3 linearized forms of the integrated Michaelis-Menten equation were evaluated for their ability to provide reliable estimates of uptake kinetic parameters, when the initial substrate concentration (S₀) is not error-free. Of the 3 linearized forms, the one where t/(S₀–S) is regressed against ln(S₀/S)/(S₀–S) gave estimates ofV _max and K_m closest to the true population means of these parameters. Further, this linearization was the least sensitive of the 3 to errors (±1%) in S₀. Our results illustrate the danger of relying on r² values for choosing among the 3 linearized forms of the integrated Michaelis-Menten equation. Nonlinear regression analysis of progress curve data, when S₀ is not free of error, was superior to even the best of the 3 linearized forms. The integrated Michaelis-Menten equation should not be used to estimateV _max and K_m when substrate production occurs concomitant with consumption of added substrate. We propose the use of a new equation for estimation of these parameters along with a parameter describing endogenous substrate production (R) for kinetic studies done with samples from natural habitats, in which the substrate of interest is an intermediate. The application of this new equation was illustrated for both simulated data and previously obtained H₂ depletion data. The only means by whichV _max, K_m, and R may be evaluated from progress curve data using this new equation is via nonlinear regression, since a linearized form of this equation could not be derived. Mathematical components of computer programs written for fitting data to either of the above nonlinear models using nonlinear least squares analysis are presented.     

Modeling the Biodegradation Kinetics of Perchlorate in the Presence of Oxygen and Nitrate as Competing Electron Acceptors

A mathematical model was developed to describe the biodegradation kinetics of perchlorate in the presence of nitrate and oxygen as competing electron acceptors. The rate of perchlorate degradation is described as a function of the electron donor (acetate) degradation rate, the concentration of the alternate electron acceptors, and rates of biomass growth and decay. The kinetics of biomass growth are described using a modified Monod model, and inhibition factors are incorporated to describe the influence of oxygen and nitrate on perchlorate degradation. In order to develop input parameters for the model, a series of batch biodegradation studies were performed using Azospira suillum JPLRND, a perchlorate-degrading strain isolated from groundwater. This strain is capable of utilizing oxygen, nitrate, or perchlorate as terminal electron acceptors. The maximum specific growth rate (μ_max) and half-saturation constant (K _S ^don) for the bacterium when utilizing either perchlorate or nitrate were similar; 0.16 per h and 158 mg acetate/L, respectively. However, these parameters were different when the strain was growing on oxygen. In this case, μ_max and K _S ^don were 0.22 per h and 119 mg acetate/L, respectively. The batch experiments also revealed that nitrate inhibits perchlorate biodegradation by this strain. This finding was incorporated into the model by applying an inhibition coefficient (K _i ^nit) value of 25 mg nitrate/L. Combined with appropriate groundwater transport models, this model can be used to predict perchlorate biodegradation during in situ remediation efforts.     

Kinetic manifestations of allosteric interactions in models of regulatory enzymes with "indirect" co-operativity

The shape of the plots of initial reaction rate (ν) versus initial substrate concentration ([S]₀) and versus initial concentration of allosteric effector ([F]₀) for the model of allosteric enzyme of Monod, Wyman &; Changeux (1965) and for the model of dissociating regulatory enzyme has been analysed by means of the inconstant exponent (q) for substrate or effector concentration, respectively. It has been shown that allosteric interactions in above-mentioned models with “indirect” co-operativity may be manifested not only by the sigmoidal shape of the plot of ν versus [S]₀ or ν versus [F]₀ (with one point of inflexion) but also by the increase in the magnitude of exponent q in progress of saturation process of the enzyme by the substrate or by the effector in the absence of the sigmoidal shape of these plots. It has been shown also that the plot of ν versus [S]₀ has two inflexion points when the parameters have certain definite values. One of these inflexion points (or even both at definite values of the parameters) is hardly discernible. At certain definite values of the parameters two inflexion points may be kinetically manifested by such phenomenon as “negative” co-operativity (q < 1). This is possible if one of the interconvertable enzyme forms exceeds another not only in the affinity to the substrate but also in the value of the rate constant for catalytic breakdown of the enzyme-substrate complex.     

Degradation of formaldehyde in packed-bed bioreactor by kissiris-immobilized Ralstonia eutropha

The ability of the Ralstonia eutropha cells to utilize formaldehyde (FA) as the only source of carbon and energy was studied in the kissiris-immobilized cell bioreactor (KICB) in batch-recirculation and continuous modes of operation. In batch-recirculation experiments, the test bacterium could tolerate concentrations of FA up to 1,400 mg/L at 30°C and aeration rate equal to 0.75 vvm (r _S = 7.25 mg/L/h, q S = 0.019 g_FA/g_cell/h). However, further increase of initial FA concentration resulted in degradation reaction of FA to stop at 1,600 mg/L. Results of continuous mode experiments showed that the biodegradation performance of the KICB was dependent on both feed flow rate and inlet FA concentration parameters. The optimum feed flow rate which corresponded to the highest biodegradation rate (r _S = 240.3 mg/L/h) was observed at Q = 18 mL/min when KICB did not operate under the external mass transfer limiting regime. Substrate inhibition kinetics (Edwards and Luong equations) were used to describe the experimental specific degradation rates data. According to the Luong model, the values of the maximum specific degradation rate (q _max), half-saturation coefficient (K _S), the maximum allowable FA concentration (S _m), and the shape factor (n) were 0.178 g_FA/g_cell/h, 250.9 mg/L, 1,600 mg/L, and 1.86, respectively.     

Kinetic behavior of mixed populations of activated sludge

The kinetic behavior of heterogeneous microbial populations of sewage origin was studied in a single-stage isothermal continuous flow completely mixed aeration tank. A series of experiments were carried out at various dilution rates using glucose as the growth limiting substrate. The steady-state behavior of the system was observed at each dilution rate and the results were found to fit fairly well with the steady-state equation bayed on the Monod model with an endogenous respiration term included, i.e., μ = μ_mS/(K_s + S) ? K_d. The growth kinetics of cells harvested at steady state for each dilution rate were studied using batch experiments. The multiple response data of the system as functions of time were used to estimate the parameter values in the above kinetic model. It was found that values of the growth parameters changed significantly and systematically with cell population. For example, values of μ_m were high at high dilution rates and low at low dilution rates. It was also found that only those batch growth parameters from cells obtained at fairly high dilution rates are comparable with those estimated by the results of steady-state operations. The results of this investigation suggest that (1) different cell populations pre dominated at different steady-state dilution rates, with high dilution rates resulting in predominantly fast-growing organisms and low dilution rates resulting in predominantly slow-growing cells, and (2) risk exists in any randomly picked batch experiment to predict the steady-state behavior of the system when heterogeneous microbial populations must be used.     

Cultivation of thermophilic methanogen KN-15 on H2-CO2 under pressurized conditions

Cultivation of the thermophilic methanogen KN-15 was carried out under pressurized batch and continuous conditions. In pressurized batch culture, both the turning point at which cell growth changed from exponential to linear and the growth rate during the linear growth phase increased with the rise of total pressure of the gas phase in the fermentor. The cell concentration reached 18.5 g dry cell/l after 10 h of batch cultivation under 3.0 × 10⁵ Pa pressurized conditions. Under pressurized continuous conditions, it was also observed that the cell concentration and cell productivities increased with the rise of total pressure of the gas phase. Cell and methane productivities of 3.0 g dry cell/l/h and 1.28 mol/l/h, respectively, were achieved in 3.0 × 10⁵ Pa pressurized continuous culture. According to the results from the Monod model application, the achievable cell productivities (V_max) and the Monod type saturation constant for cell productivities (K_s^′) were 12.8 g dry cell/l/h and 9.7 × 10⁵ Pa, respectively.     

Applications of modelling for bioprocess design and control in industrial production

The on-line measurement of the relevant parameters and the control conception for three production processes for fine chemicals by fermentation and biotransformation at the 15 m³ scale were developed. The models describe the bioprocesses which successfully result in fully automated manufacturing steps. Modelling also proved to be a valuable tool for a better insight into biochemical fundamentals of the processes. Moreover, proper use of data logging, modelling and process control was important for quality, since two processes were controlled on-line and quality relevant deviations were registered early. Finally, combining modelling with simulation, we could drastically reduce both development time and cost.List of Symbols F l/h flux - V l volume - U ₀ g/l nicotinonitrile concentration influx - U g/l actual nicotinonitrile concentration - q _ug/gh specific educt (=nicotinonitrile) transformation rate - x g/l biocatalyst concentration - p ₀ g/l nicotinamide concentration influx - p g/l actual nicotinamide concentration - q _pg/gh specific product (=nicotinamide) formation rate - k parameter loss of activity - q _{u, max}g/gh max. specific educt transformation rate - K _ug/l saturation constant for nicotinonitrile - K _ig/l inhibition constant for nicotinonitrile - K _iig/l inhibition constant for nicotinamide - MW _Ag/mol molecular weight for nicotinonitrile - MW _Bg/mol molecular weight for nicotinamide - NS Nicotinic acid - 6-HNS 6-Hydroxynicotinic acid - r _{NS, 6HNS} g/lh 6-HNS production rate - r _{6HNS, X} g/lh biomass production rate - r _{NS, 6HNS, max} g/lh max. 6-HNS production rate - S _NS g/l actual NS concentration - K _{S, NS} g/l saturation constant for NS - K _{i, 6HNS} g/l inhibition constant for 6-HNS - K _o2 g/l saturation constant for oxygen - r _{6HNS, X, max} g/lh max. biomass production rate - S _6HNS g/l actual 6-HNS concentration - K _{ii, NS} g/l inhibition constant for NS - RQ mol/mol respiration quotient - S _xylg/l actual xylene concentration - K _{i, xyl}g/ inhibition constant for xylene - K _{i, DMPY}g/ inhibition constant for 2,5-dimethylpyrazine - r _Xg/lh biomass production rate - r _{X, max}g/lh max. biomass production rate - K _{s, xyl}g/l saturation constant for xylene - S _DMPYg/l actual concentration of DMPY - K _{i, MPCA}g/ inhibition constant for MPCA - K _O2g/ saturation constant for oxygen - S _MPCAg/l actual MPCA concentration - S _O2g/l actual oxygen concentration - r _MPCAg/lh MPCA production rate - r _{MPCA, max}g/lh max. MPCA production rate - k _lgl inhibition constant for the intermediates - k _{s, DMPY}gl saturation constant for DMPY     

Kinetics of soluble microbial product formation in substrate-sufficient batch culture of activated sludge

The kinetics of soluble microbial product (SMP) formation under substrate-sufficient conditions appear to exhibit different patterns from substrate-limited cultures. However, energy spilling-associated SMP formation is not taken into account in the existing kinetic models and classification of SMP. Based on the concepts of growth yield and energy uncoupling, a kinetic model describing energy spilling-associated SMP formation in relation to the ratio of initial substrate concentration to initial biomass concentration (S ₀/X ₀) was developed for substrate-sufficient batch culture of activated sludge, and was verified by experimental data. The specific rate of energy spilling-associated SMP formation showed an increasing trend with the S ₀/X ₀ ratio up to its maximum value. The SMP productivity coefficient (α _p/e) was defined from the model on the basis of energy spilling-associated substrate consumption. Results revealed that less than 5% of energy spilling-associated substrate consumption was converted into SMP. Electronic Publication     

Kinetics of phenol degradation using Pseudomonas putida MTCC 1194

Pseudomonas putida (MTCC 1194) has been used to degrade phenol in water in the concentration range 100–1000?ppm. The inhibition effects of phenol as substrate have become predominant above the concentration of 500?ppm (5.31?mmoles/dm³). The optimum temperature and initial pH required for maximum phenol biodegradation were 30?°C and 7.00 respectively. From the degradation data the activation energy (E _a ) was found to be equal to 13.8?kcal/g mole substrate reacted. The most suitable inoculum age and volume for highest phenol degradation were 12?hrs and 7% v/v respectively. Surfactants had negligible effect on phenol biodegradation process for this microorganism. Monod model has been used to interpret the free cell data on phenol biodegradation. The kinetic parameters have been estimated upto initial concentration of 5.31?mmoles/dm³. μ _max and K _S gradually increased with higher concentration of phenol. However, beyond the phenol concentration of 5.31?mmoles/dm³, the inhibition became prominant. The μ _max has been to be a strong function of initial phenol concentration. The simulated and the experimental phenol degradation profiles have good correspondence with each other.     

Kinetic study of Lactococcus lactis strains (SLT6 and SLT10) growth on papain-hydrolysed whey

The effect of controlled whey hydrolysis by papain on growth of two lactic acid bacteria isolated from artisanal Leben: Lactococcus lactis var. diacetylactis (SLT6 and SLT10) was investigated. The higher biomass and maximum specific growth rate (μ _max) were obtained after 30 min of hydrolysis. HPLC analysis of peptides showed that whey hydrolysis reduced the amount of peptides of MW > 400 Da and increased those peptides of MW < 400 Da. The two studied strains exhibited different peptide requirements. The pH-controlled batch cultures in 30 min hydrolysed whey followed the Monod kinetic for growth and for lactate production. The values of the key kinetic constants were: maximum specific growth rate (μ _max), 1.08 and 0.56 h^?1; yield biomass on lactose (Y _x/s), 0.20 and 0.18 g g^?1 and saturation constant K _s, 4.2 and 2.8 g L^?1 for SLT6 and SLT10, respectively. When compared with batch experimental data, the model provided good predictions for growth, lactose utilisation and lactate production profiles.