Monod-type Expression Research Articles

Evaluation of the interaction of temperature and light intensity on the growth of Phaeodactylum tricornutum: Kinetic modeling and optimization

In this study, the effects of two highly variable factors, temperature ranging from 10–35 °C and light intensity from 98–1289 μmol m−2s-1, on the specific growth rate, μ, of a diatom, Phaeodactylum tricornutum, at a constant aeration rate of 3000 cm3 min-1 were elucidated. The choice of the adequate kinetic models describing the growth related to temperature and light intensity resulted in rapid determination of optimum growth conditions. Ratkowsky’s square root model and Monod-type model were assessed as the most suitable expressions among the three temperature- and eight light intensity-dependent models, respectively, presenting the highest adjusted R2 and smallest average relative deviation (ARD) values by means of nonlinear least squares method. Also, among the kinetic model approaches utilized to verify the combined effects of temperature and light intensity, the temperature-dependent Ratkowsky model in conjunction with the Monod-type expression with the smallest ARD value (4.19 %) and a high adjusted R2 (0.9775) exhibited the best surface fit. The optimum cultivation temperature and light intensity conditions for the achieving maximum specific growth rate of P. tricornutum were determined as 21 °C and 496 μmol m−2s-1, respectively, by the help of the Central Composite Design (CCD) of the Response Surface Methodology (RSM).

“Untangling Hyporheic Residence time Distributions and Whole Stream” “Metabolism Using a Hydrological Process Model”

The interaction of the water residence time (RT) in hyporheic sediments with the sediment metabolic rates is believed to be a key factor controlling whole stream metabolism. However, due to the methodological difficulties, there is little data that investigates this fundamental theory of aquatic ecology. Here, we report on progress made to combine numerical modelling with a series of modification to laboratory flumes overcoming methodological difficulties e.g. by creating steady flow paths for assessment of metabolic rates. To model the biogeochemical performance and to validate the model results, sediment structures were introduced in both, the model and the flumes, leading to differing RT distributions. Furthermore, the DOC supply in the flumes was manipulated to test the whole stream metabolic response with regard to RT distributions. In the flumes, hydraulic conditions were assessed using conservative tracer and heat as tracer. Metabolic activity was assessed using oxygen dynamics as a proxy of community respiration (CR). Residence time and metabolic processes were modelled using a multicomponent reactive transport code called MIN3P and calibrated with regard to the hydraulic conditions using the results obtained from the flume experiments. Monod type expressions were used to implement metabolic activity terms in the model. Using the results of the hydrological process model, a sensitivity analysis of the impact of RT distributions on the metabolic activity could yield supporting proof of an existing link between the two.

Modelling the metabolic shift of polyphosphate-accumulating organisms

Enhanced biological phosphorus removal (EBPR) is one of the most important methods of phosphorus removal in municipal wastewater treatment plants, having been described by different modelling approaches. In this process, the PAOs (polyphosphate accumulating organisms) and GAOs (glycogen accumulating organisms) compete for volatile fatty acids uptake under anaerobic conditions. Recent studies have revealed that the metabolic pathways used by PAOs in order to obtain the energy and the reducing power needed for polyhydroxyalkanoates synthesis could change depending on the amount of polyphosphate stored in the cells. The model presented in this paper extends beyond previously developed metabolic models by including the ability of PAO to change their metabolic pathways according to the content of poly-P available. The processes of the PAO metabolic model were adapted to new formulations enabling the change from P-driven VFA uptake to glycogen-driven VFA uptake using the same process equations. The stoichiometric parameters were changed from a typical PAO coefficient to a typical GAO coefficient depending on the internal poly-P with Monod-type expressions. The model was calibrated and validated with seven experiments under different internal poly-P concentrations, showing the ability to correctly represent the PAO metabolic shift at low poly-P concentrations. The sensitivity and error analysis showed that the model is robust and has the ability to describe satisfactorily the change from one metabolic pathway to the other one, thereby encompassing a wider range of process conditions found in EBPR plants.

Effect of substrate and IPTG concentrations on the burden to growth of Escherichia coli on glycerol due to the expression of Lac proteins

Expression of proteins unneeded for growth diverts cellular resources from making necessary protein and leads to a reduction in the growth rate of an organism. This reduction in growth rate is termed as cost. Cost plays an important role in determining the selected expression of a protein in a particular environment. Characterization of cost is important in biotechnology industries where microorganisms are used to produce foreign proteins. We have used the lactose system in Escherichia coli to quantify the cost of growth on glycerol in the presence of isopropyl-β-D-thiogalactopyranoside (IPTG), an inducer of the lactose system. The effect of the concentration of the carbon source, glycerol, and the inducer of Lac enzymes, IPTG, is studied. The results show that the cost is dependent on the glycerol concentration with a decreasing trend with increasing concentration of glycerol. Also as expected, the cost increases and saturates at a higher concentration of IPTG. The studies also demonstrate that the cost is higher in early exponential phase relative to late exponential phase during the growth as has been reported in the literature. Hill equation fit yielded a typical Monod-type expression for growth on glycerol with and without IPTG. An apparent half-saturation constant was defined which was used to characterize the burden on growth due to protein expression.

Combining Computational Fluid Dynamics with a Biokinetic Model for Predicting Ammonia and Phosphate Behavior in Aeration Tanks

The aim of this study was to use computational fluid dynamics for predicting the behavior of reactive pollutants (ammonia and phosphate) in the aerobic zone of the bioreactor located at the Wschod wastewater treatment plant in Gdansk, Poland. The one-dimensional advection-dispersion equation was combined with simple biokinetic models incorporating the Monod-type expressions as source terms for the two pollutants. The problem was solved numerically by a multi-step splitting technique algorithm. The dispersion coefficient, E(L), was estimated using a statistical method and numerical optimization based on experimental data from three tracer studies. With the first method, the values of EL varied within the range 1082 to 1860 m2/h and 695 to 1355 m2/h, respectively, in sections 1 and 2 of the aerobic zone. Except for one case, deviations of the corresponding numerically optimized values of E(L) did not exceed 14%. The maximum specific rates of nitrification [r(n,max,20) = 4.6 g N/(kg VSS h)] and phosphate uptake [r(Pupt,max,20) = 13.5 g P/(kg VSS h)] at T = 20 degrees C were determined based on laboratory batch experiments. With minor adjustments of the kinetic parameters, the model was capable of accurately predicting the longitudinal profiles of ammonia and phosphate in the aerobic zone, and the simulation results were presented using the actual horizontal geometry of the bioreactor as a background.

Mathematical modelling of the composting process: A review

In this paper mathematical models of the composting process are examined and their performance evaluated. Mathematical models of the composting process have been derived from both energy and mass balance considerations, with solutions typically derived in time, and in some cases, spatially. Both lumped and distributed parameter models have been reported, with lumped parameter models presently predominating in the literature. Biological energy production functions within the models included first-order, Monod-type or empirical expressions, and these have predicted volatile solids degradation, oxygen consumption or carbon dioxide production, with heat generation derived using heat quotient factors. Rate coefficient correction functions for temperature, moisture, oxygen and/or free air space have been incorporated in a number of the first-order and Monod-type expressions. The most successful models in predicting temperature profiles were those which incorporated either empirical kinetic expressions for volatile solids degradation or CO 2 production, or which utilised a first-order model for volatile solids degradation, with empirical corrections for temperature and moisture variations. Models incorporating Monod-type kinetic expressions were less successful. No models were able to predict maximum, average and peak temperatures to within criteria of 5, 2 and 2 °C, respectively, or to predict the times to reach peak temperatures to within 8 h. Limitations included the modelling of forced aeration systems only and the generation of temperature validation data for relatively short time periods in relation to those used in full-scale composting practice. Moisture and solids profiles were well predicted by two models, but oxygen and carbon dioxide profiles were generally poorly modelled. Further research to obtain more extensive substrate degradation data, develop improved first-order biological heat production models, investigate mechanistically-based moisture correction factors, explore the role of moisture tension, investigate model performance over thermophilic composting time periods, provide more information on model sensitivity and incorporate natural ventilation aeration expressions into composting process models, is suggested.

Periodic operation of biofilters. A concise model and experimental validation

Concise model of biofiltration based on a linear driving force concept, that takes into account adsorption of pollutant in the support phase and its biodegradation therein with the rate governed by a modified three-parameter Monod-type expression, was shown to be suitable to portray the transient behavior of biofilters arising from the periodic operation. Good agreement between simulations and experiments was obtained for the biodegradation of methyl-ethyl-ketone or n-butanol on a pre-selected bark bed in a broad range of operating conditions.

An error estimation of Michaelis-Menten (Monod)-type kinetics

Due to research on biochemistry and genetic engineering, mathematical models of microbial growth have become more complicated but Michaelis-Menten or Monod type expressions have still been used for conversion rates, uptake rates, etc. It is worth examining the error that can be caused by these quasi-steady-state-hypotheses. This paper presents a simple but very effective rationale function that describes the error of the quasi-steady-state hypothesis in enzyme kinetics. A simplified fermentation kinetic model was used for comparison of microbial growth but no analytical error function has been found for batch cultivation. In the case of continuous fermentation the error can be given in an analytical form. Many simulations, based on real SCP experiments, show a significant effect of the quasi-steady-state hypothesis. Since the rate constants of intracellular events are not really known, we have to be very careful when taking into account Michaelis-Menten type expressions in the building of complicated models.

An evaluation of a simple kinetic model for the treatment of domestic sewage by means of an anaerobic rotating biological contactor

Abstract In this study, the application of the mathematical model proposed by Andreadakis and Cailas to experimental data obtained in the treatment of domestic sewage is examined. A single-stage laboratory scale unit of an anaerobic rotating biological contactor (AnRBC) was used in the studies to produce kinetic parameters for the Andreadakis and Cailas model. The results demonstrated that a simple Monod-type expression can satisfactorily simulate the performance of an anaerobic rotating biological contactor and the model maintains its validity even with high-strength domestic wastewater.

Kinetics and mathematical modeling of homoacetic fermentation of lactate by Clostridium formicoaceticum

Fermentation kinetics of Clostridium formicoaceticum grown on lactate at pH 7.0 and 35 degrees C was studied. Acetate was the only fermentation product and its production was growth associated. The growth of this bacterium was insensitive to the lactate concentrations studied, but was inhibited by acetic acid. A Monod-type expression with product inhibition similar to the noncompetitive inhibition of enzyme kinetics was used to model the batch fermentation. An integrated equation was developed and used to help estimating the kinetic parameters in the model. This mathematical model can be used to simulate the homoacetic fermentation of lactate by C. formicoaceticum at pH 7.0 and 35 degrees C.

Effect of hydrogen and carbon dioxide partial pressures on growth and sulfide production of the extremely thermophilic archaebacterium Pyrodictium brockii

The effect of hydrogen and carbon dioxide partial pressure on the growth of the extremely thermophilic archaebacterium Pyrodictium brockii at 98 degrees C was investigated. Previous work with this bacterium has been done using an 80:20 hydrogen-carbon dioxide gas phase with a total pressure of 4 atm; no attempt has been made to determine if this mixture is optimal. It was found in this study that reduced hydrogen partial pressures affected cell yield, growth rate, and sulfide production. The effect of hydrogen partial pressure on cell yield and growth rate was less dramatic when compared to the effect on sulfide production, which was not found to be growth-associated. Carbon dioxide was also found to affect growth but only at very low partial pressures. The relationship between growth rate and substrate concentration could be correlated with a Monod-type expression for either carbon dioxide or hydrogen as the limiting substrate. The results from this study indicate that a balance must be struck between cell yields and sulfide production in choosing an optimal hydrogen partial pressure for the growth of P. brockii.

Steady state phenol degradation in a draft‐tube, gas‐liquid‐solid fluidized‐bed bioreactor

AbstractExperiments on phenol biodegradation by a mixed culture in a draft‐tube, three‐phase fluidized‐bed biofilm reactor (DTFBR) at the steady state were performed. The characteristics of biofilms developed in the DTFBR were identified. A steady state biofilm model was proposed that considers the simultaneous diffusion and reaction of oxygen and phenol within the biofilm and the external mass transfer resistance between the biofilm and the completely mixed bulk liquid phase. The proposed model assumes a double‐substrate limiting mechanism for microbial growth kinetics, and Haldane and Monod type expressions were used to characterize the dependence of microbial specific growth rate on phenol and oxygen, respectively. The experimental results were used to test the validity of the proposed model.

Modeling Toxicity in Methane Fermentation Systems

Wastewater treatment using anaerobic methane fermentation offers several significant advantages over aerobic methods, but is considered unreliable when treating wastewaters containing toxicants. Three models describing toxicity phenomena are given to help engineers develop more rational design and operational strategies. The first model describes the recovery pattern of methane fermentation systems from slug addition of toxicants as a function of toxicant type and concentration, and time. This model allows for prediction of periods of zero gas production and threshold toxicant concentrations. The second two models incorporate the effect of toxicity on the fundamental Monod-type expressions. Unsteady-state behavior is effectively described by both models and the importance of providing proper biological solids retention time is emphasized. The primary effect of toxicant addition is to alter process kinetics by temporarily or permanently increasing bacterial washout time. Therefore, to minimize the severity of both transient and chronic toxicity, a sufficiently large solids retention time is required.