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     

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     

A new kinetic approach to microbial storage process

In this work, a new kinetic approach was proposed to describe the microbial growth, substrate consumption, and formation and utilization of the intracellular storage products (X _STO) in activated sludge. It was found that the formation of X _STO was coupled with energy generation and respiration and that the X _STO formation rate was proportional to the substrate utilization rate. A high amount of external substrate resulted in a relatively rapid storage process with a large fraction of substrate electrons for X _STO formation. The maximum growth rate of active biomass on X _STO and the yield coefficient for growth on the storage polymers were estimated as 0.12 h⁻¹ and 0.60 g chemical oxygen demand (COD) _X g⁻¹ COD_STO, respectively. This established model was verified with the experimental results from two different case studies with pure and mixed cultures. Results showed that this kinetic model was able to accurately and mechanistically describe the microbial storage processes.     

A kinetic model for energy spilling-associated product formation in substrate-sufficient continuous culture

It has been demonstrated that excess substrate can cause uncoupling between anabolism and catabolism, which leads to energy spilling. However, the Luedeking-Piret equation for product formation does not account for the energy spilling-associated product formation due to substrate excess. Based on the growth yield and energy uncoupling models proposed earlier, a kinetic model describing energy spilling-associated product formation in relation to residual substrate concentration was developed for substrate-sufficient continuous culture and was further verified with literature data. The parameters in the proposed model are well defined and have their own physical meanings. From this model, the specific productivity of unit energy spilling-associated substrate consumption, and the maximum product yield coefficient, can be determined. Results show that the majority of energy spilling-associated substrate consumption was converted to carbon dioxide and less than 6% was fluxed into the metabolites, while it was found that the maximum product yield coefficients varied markedly under different nutrient limitations. The results from this research can be used to develop the optimized bioprocess for maximizing valuable product formation.     

Reduced Growth Yield of Activated Sludge in Organic Protonophore-Containing Batch Culture

Abstract The effects of organic protonophores 2,4-dinitrophenol (dNP) and para-nitrophenol (pNP) on the observed growth yield (Y _obs) was studied using batch cultures of activated sludge microorganisms. A growth yield model was proposed in relation to the ratio of initial protonophore concentration (C _u) to initial biomass concentration (X ₀) and was verified with experimental data. It was found that Y _obs decreased with the increase of the C _u/X ₀ ratio, while the specific rate of glucose consumption was increased. Results showed that the C _u/X ₀ ratio could more reasonably reflect the real strength of organic protonophore exerted to activated sludge than using C _u only. Based on the concept of growth yield, a model describing the uncoupling degree between energy generated via electron transport system and energy used for growth was further developed for protonophore-containing batch culture. It was shown that more than 60% of glucose was consumed through a futile cycle of energy rather than for growth at higher C _u/X ₀ ratios. This research usefully shows that the dissipation of energy via uncoupling biochemical processes can reduce excessive production of activated sludge markedly. Received: 28 April 1999; Accepted: 14 September 1999; Online Publication: 6 March 2000     

Impact of initial conditions on extant microbial kinetic parameter estimates: application to chlorinated ethene dehalorespiration

Monod kinetics are the foundation of mathematical models of many environmentally important biological processes, including the dehalorespiration of chlorinated ethene groundwater contaminants. The Monod parameters—q _max, the maximum specific substrate utilization rate, and K _S, the half-saturation constant—are typically estimated in batch assays, which are superficially simple to prepare and maintain. However, if initial conditions in batch assays are not chosen carefully, it is unlikely that the estimated parameter values will be meaningful because they do not reflect microbial activity in the environmental system of interest, and/or they are not mathematically identifiable. The estimation of q _max and K _S values that are highly correlated undoubtedly contributes significantly to the wide range in reported parameter values and may undermine efforts to use mathematical models to demonstrate the occurrence of natural attenuation or predict the performance of engineered bioremediation approaches. In this study, a series of experimental and theoretical batch kinetic assays were conducted using the tetrachloroethene-respirer Desulfuromonas michiganensis to systematically evaluate the effects of initial batch assay conditions, expressed as the initial substrate (S ₀)-to-initial biomass concentration (X ₀) ratio (S ₀/X ₀) and the S ₀/K _S ratio on parameter correlation. An iterative approach to obtain meaningful Monod parameter estimates was developed and validated using three different strains and can be broadly applied to a range of other substrates and populations. While the S ₀/X ₀ ratio is critical to obtaining kinetic parameter estimates that reflect in situ microbial activity, this study shows that optimization of the S ₀/K _S ratio is key to minimizing Monod parameter correlation.     

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)     

Kinetics of <Emphasis Type="Italic">Bacillus thuringiensis</Emphasis> var. <Emphasis Type="Italic">israelensis</Emphasis> growth on high glucose concentrations

The kinetic and general growth features of Bacillus thuringiensis var. israelensis were evaluated. Initial glucose concentration (S ₀) in fermentation media varied from 10 to 152 g/l. The results afforded to characterize four morphologically and physiologically well-defined culture phases, independent of S ₀ values: Phase I, vegetative growth; Phase II, transition to sporulation; Phase III, sporulation; and Phase IV, spores maturation and cell lysis. Important process parameters were also determined. The maximum specific growth rates (μ _X,m) were not affected with S ₀ up to 75 g/l (1.0–1.1 per hour), but higher glucose concentrations resulted in growth inhibition by substrate, revealed by a reduction in μ _X,m values. These higher S ₀ values led to longer Phases III and IV and delayed sporulation. Similar biomass concentrations (X _m = 15.2–15.9 g/l) were achieved with S ₀ over 30.8 g/l, with increasing residual substrate, suggesting a limitation in some other nutrients and the use of glucose to form other metabolites. In this case, with S ₀ from 30.8 to 152 g/l, cell yield (Y _X/S ) decreased from 0.58 to 0.41 g/g. On the other hand, with S ₀ = 10 g/l growth was limited by substrate, and Y _X/S has shown its maximum value (0.83 g/g).     

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.     

Diagnosing lactic acid fermentation based on specific rates of growth,substrate consumption and product formation

The on-line calculated specific rates of growth, substrate consumption and product formation were used to diagnose microbial activities during a lactic acid fermentation. The specific rates were calculated from on-line measured cell mass, and substrate and product concentrations. The specific rates were more sensitive indicators of slight changes in fermentation conditions than such monitored data as cell mass or product concentrations.List of Symbols 1/h specific rate of cell growth - 1/h specific rate of substrate consumption - 1/h specific rate of product formation - ^* dimensionless specific rate of cell growth - ^* dimensionless specific rate of substrate consumption - ^* dimensionless specific rate of product formation - _max 1/h maximum specific rate of cell growth - _max 1/h maximum specific rate of substrate consumption - _max 1/h maximum specific rate of product formation - X g/l cell mass concentration - S g/l substrate concentration - S ^* dimensionless substrate concentration - S ₀ g/l initial substrate concentration - P g/l product concentration     

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.     

High concentration cultivation of Bifidobacterium longum in fermenter with cross-flow filtration

Summary High concentration cultivation of Bifidobacterium longum in a fermenter with cross-flow filtration using a ceramic filter is described. Continuous cross-flow filtration allowed complete recycling of the cells to the fermenter and also continuous separation of inhibitory metabolites. The final cell concentration attained in the cultivation was 54.4 g dry wt./l; this was seven times as high as that without cross-flow filtration. The time course of the cultivation with cross-flow filtration was predicted, based on the assumption that the specific growth rate can be expressed only as a function of concentrations of metabolites (acetate and lactate) in a culture broth.Nomenclature D dilution rate (h^-1) - m maintenance coefficient (h^-1) - OD ₅₇₀ optimal density at 570 nm - P _A acetate concentration (g/l) - P _A0 initial acetate concentration (g/l) - P _L lactate concentration (g/l) - P _L0 initial lactate concentration (g/l) - S lactose (substrate) concentration (g/l) - S ₀ initial lactose (substrate) concentration (g/l) - t cultivation time (h) - Y _x/s growth yield (g/g) - X dry cell concentration (g/l) - X ₀ initial dry cell concentration (g/l) - constant - constant     

Hydrocarbon fermentation: Kinetics of microbial cell growth

Modeling of microbial growth using nonmiscible substrate is studied when kinetics of substrate dissolution is rate limiting. When the substrate concentration is low, the growth rate is described by an analytical relation that can be identified as a Contois relationship. If the substrate concentration is greater than a critical value S_crit, the potentially useful hydrocarbon S* concentration is described by S* = S_crit/(1 + S_crit/S). A relationship was found between S_crit and the biomass concentration X. When X increased, S_crit decreased. The cell growth rate is related to a relation μ = μ_m[A(X/S_crit)(1 + S_crit/S) + 1]^?1. This model describes the evolution of the growth rate when exponential or linear growth occurs, which is related to physico-chemical properties and hydrodynamic fermentation conditions. Experimental data to support the model are presented.     

Practical design equations for trickling-filter process

The concept of solid retention time (SRT) was applied in the trickling-filter process. A rational model of the trickling-filter process employing activated-sludge-process operational parameters was presented. The design equation was developed as follows; 1/SRT = [(S₀ ? S_n)/X ]·(F/V)·Y ? k_d, where SRT is the sludge retention time, S₀ is the influent substrate concentration; S_n is the effluent substrate concentration; X is the total cell mass retained per unit filter volume; V is the total volume of the filter; F is the influent flow rate; Y is the cell yield, and k_d is the cell decay rate. A laboratory-scale trickling-filter pilot plant treating synthetic sucrose waste-water was studied to verify the present design equation. The solid retention time was evaluated from the total slime mass (active and inactive) retained and the sludge wasted daily. It was found that the present design equation could be applied for designing the trickling-filter process by the application of SRT employed in the activated sludge process. Also, the SRT could be related to the hydraulic loading and influent substrate concentration for a given filter medium. The variation of SRT by the hydraulic loading at constant organic loading was observed and could be expressed by the mechanistic model. When SRT was maintained more than 12 days, it provided the highest five-day biological oxygen demand (BOD₅) removal, minimum sludge production, and lowest sludge volume index (SVI) value. The present model does include both microbial growth kinetic concepts, which can be more practical and meaningful for the design of a trickling filter.     

Der Einfluß der Prozeßparameter auf die Ethanolausbeute in Batchprozessen bei Verwendung von Saccharomyces cerevisiae

The production costs of ethanol are dependent on the efficiency of the substrate-ethanol conversion to a high degree. The more the substrate used during the fermentation is converted into alcohol the better is the economy of the process. Therefore the ethanol yield Y _S^P is an important object of the process optimization. In batch fermentation processes the most essential influence factors are the initial biomass concentration X₀, the initial substrate concentration S₀, the temperature T, and the pH-value. A model reflecting the complex relationships between these influence factors and the ethanol yield could be obtained by regression. It allows an exact valuation of these optimum process parameters which are necessary for realizing high ethanol yields in the batch fermentation. For the strain Saccharomyces cerevisiae Sc 5 used in this research was found an ethanol yield maximum Y_S^P = 0˙5384 at the parameters X₀ = 64.61 g/l S₀ = 82.91 g/l T = 36.45°C pH = 6.54.     

A kinetic model for product formation of microbial and mammalian cells

Growth of microbial and mammalian cells can be classified into substrate-limited and substrate-sufficient growth according to the relative availability of the substrate (carbon and energy source) and other nutrients. It has been observed for a number of microbial and mammalian cells that the consumption rate of substrate and energy (ATP) is generally higher under substratesufficient conditions than under substrate limitation. Accordingly, the product formation under substrate excess often exhibits different patterns from those under substrate limitation. The extent of increase or decrease in product formation may depend not only on the nature of limitation and cell growth rate but also on the residual substrate concentration in a relatively wide range. The product formation kinetic models existing in literature cannot describe these effects. In this study, the Luedeking-Piret kinetic is extended to include a term describing the effect of residual substrate concentration. The extended model has a similar structure to the kinetic model for substrate and energy consumption rate recently proposed by Zeng and Deckwer. The applicability of the extended model is demonstrated with three microbial cultures for the production of primary metabolites and three hybridoma cell cultures for the production of ammonia and lactic acid over a wide range of substrate concentration. The model describes the product formation in all these cultures satisfactorily. Using this model, the range of residual substrate concentration, in which the product formation is affected, can be quantitatively assessed. (c) 1995 John Wiley & Sons, Inc.     

Fluidized bed biomethanation of acetic acid

Summary The kinetics of acetate biomethanation was studied in a high recycle ratio biological fluidized bed reactor behaving in practice as a completely mixed reactor. The active biofilm consisted of bacteria from a methane fermenter that after spontaneous immobilization on the bed particles (sand) were adapted to acetate as the only carbon source. The effects of temperature (13°, 20°, 25° and 35°C), substrate concentration (500, 1000 and 1500 mg chemical oxygen demand (COD) l^-1) and hydraulic retention time (1 to 8 h) on substrate consumption were studied. Maximum substrate consumption (as % COD reduction) amounted from 25% (13°C, 1500 mg COD l^-1) to 93% (35°C, 500 mg COD l^-1). At 35°C the concentration of attached biomass presented a weakly increase with reactor substrate concentration (from 3.10 g VS l^-1 to 4.54 g VS l^-1 for 32 and 1150 mg COD l^-1 respectively). On the other hand when reducing , a sharp incrase in biomass loss coefficient was observed showing that excess biofilm growth was continuously removed by shearing forces. Thus in the assayed conditions the attached biomass concentration was basically determined by the bed superficial velocity. Result show that diffusional resistances are negligible. Data are fairly well correlated by a variable order kinetic model. The apparent reaction order is a function of temperature and increases from 0.27 to 0.7 when temperature decreases from 35° C to 13°C.Nomenclature b Total biomass loss coefficient (T^-1) - J Flux of substrate removal into the biofilm surface (ML^-2 T^-1) - J _d Flux of substrate removed into the biofilm surface in deep conditions (ML^-2 T^-1) - k Maximum specific rate of substrate utilization (T^-1) - K Variable order kinetic constant (T^-1 M^n-1 L^3n-3) - K _s9 Hall saturation constant (ML^-3) - n Reaction order - q Feed flow rate (L³ T^-1) - S Substrate concentration (ML^-3) - Se Effluent substrate concentration (ML^-3) - So Influent substrate concentration (ML^-3) - Se_min Minimum substrate concentration able to sustain a steady-state biofilm (ML^-3) - T Temperature - t Time(T) - V Bed volume (L³) - VS Volatile solids (M) - VSS Volatile suspended solids - X Attached biomass concentration (ML^-3) - X _c Effluent volatile suspended solids (ML^-3) - Y Yield coefficient - Hydraulic retention time (T) This work forms part of a Doctoral Thesis of senior author     

Evaluation of steady-state-biofilm kinetics

Laboratory-scale biofilm reactors were used to evaluate a model of the kinetics of steady-state biofilm and the concept that there is a minimum concentration, S_min, below which no steady-state activity can occur. With acetate as the ratelimiting substrate, the steady-state concept of S_min was verified for naturally grown biofilms. Substrate removal and biofilm thickness declined rapidly as the substrate concentration approached S_min, which was 0.66 mg/liter for acetate. Using independently derived kinetic parameters, the model of steady-state-biofilm kinetics successfully predicted substrate utilization and biofilm thickness without the need for fitting factors. The results imply that organic materials may persist in water and wastewater, in part, because they are too low in concentration to supply sufficient energy to sustain the microorganisms.     

Unstructured models for suspension cultures of Taxus media cells in a bioreactor under substrate-sufficient conditions

For a better understanding of the simulation, optimization, and process control in cell cultures, good kinetic models are necessary for large scale plant cell culture. In this paper, the systematic kinetics of taxol production by Taxus media cell suspension cultures in a stirred 15-L bioreactor under substrate-sufficient conditions and the absence of inducer intervention were studied. A kinetic model of cell growth was established by logistic equation, and kinetic unstructured models of substrate consumption, product synthesis and rheological behavior were constituted, which incorporated energy spilling. These models were verified by comparing the simulation results with those obtained experimentally. These results showed that energy spilling was a key factor that must be considered in constructing unstructured kinetic models of Taxus media cell suspension cultures in a stirred bioreactor under substrate-sufficient conditions. Besides, an optimized operation measure of decreasing energy spilling was proposed. An increase of 17.64% in cell biomass and 14.88% in taxol concentration were obtained when the strategy of limiting added carbon several times was experimentally implemented in a 15-L bioreactor. Results demonstrated that these established models should be helpful in the process prediction and operation optimization to guide the production and amplification of Taxus media cell suspension cultures in a bioreactor.     

A cybernetic model to predict the effect of freely available nitrogen substrate on rifamycin B production in complex media

It is well-known that secondary metabolite production is repressed by excess nitrogen substrate available in the fermentation media. Although the nitrogen catabolite repression has been known, quantitative process models have not been reported to represent this phenomenon in complex medium. In this paper, we present a cybernetic model for rifamycin B production via Amycolatopsis mediterranei S699 in complex medium, which is typically used in industry. Nitrogen substrate is assumed to be present in two forms in the medium; available nitrogen (S _ANS) such as free amino acids and unavailable nitrogen (S _UNS) such as peptides and proteins. The model assumes that an inducible enzyme catalyzes the conversion of S _UNS to S _ANS. Although S _ANS is required for growth and product formation, high concentrations were found to inhibit rifamycin production. To experimentally validate the model, five different organic nitrogen sources were used that differ in the ratio of S _ANS/S _UNS. The model successfully predicts higher rifamycin B productivity for nitrogen sources that contain lower initial S _ANS. The higher productivity is attributed to the sustained availability of S _ANS at low concentration via conversion of S _UNS to S _ANS, thereby minimizing the effects of nitrogen catabolite repression on rifamycin production. The model can have applications in model-based optimization of substrate feeding recipe and in monitoring and control of fed batch processes.