Dynamic analysis of a microbial process: A systems engineering approach

A general mathematical model of the chemostat system is developed in order to define an experimental program of dynamic testing. A glucose-limited culture ofSaccharomyces cerevisiae was grown in a chemostat using chemically defined medium. The chemostat was perturbed from an initial steady state by changes in input glucose concentration, dilution rate, pH, and temperature. Dynamic responses of cell mass, glucose, cell number, RNA, and protein concentrations were measured. A number of simulation techniques were used in developing a dynamic mathematical model and in comparing the developed model with experimental data as well as the Monod model. The resulting model was found to be quantitatively accurate and superior to the Monod model. The developed model was interpreted in the light of cell physiology. Adjustment of intracellular RNA fraction was found to be rate limiting in acceleration of cell specific growth rate.     

Correcting for the inner filter effect in measurements of fluorescent proteins in high-cell-density cultures

Fluorescent proteins (FPs), such as green fluorescent protein (GFP) and its variants, are well-developed visible markers for analyzing bioprocesses. Accurate measurement of fluorescence emitted from FPs in whole cells is complicated by the inner filter effect (IFE), which is caused by intracellular light absorption and scattering by cell particles. The IFE causes nonlinearity between fluorescence intensity and fluorophore concentrations in FP-harboring cells and can significantly influence the accuracy of FP-based analysis, especially at high cell densities. A mathematical model based on detection of fluorescence intensity using a fluorescence spectrophotometer was developed to provide a simple correction for the IFE in fluorescence intensity detection in high-density cultures. The parameters of this model were determined in three different FP-harboring bacterial strains to give the “real fluorescence” intensity without the IFE. Using these parameters, accurate analysis of FP-labeled Escherichia coli at high cell density in pure culture and in mixed cultures with fluorescent and nonfluorescent strains was easily and successfully achieved.     

Coiled tube membrane bioreactor for cultivation of hybridoma cells producing monoclonal antibodies.

A coiled tube membrane reactor was developed for the cultivation of mouse-mouse hybridoma cells producing monoclonal antibodies. The cell and antibody concentrations obtained in the membrane reactor were higher than that obtained in a batch spinner flask without a membrane. A mathematical model has been developed to describe the membrane transport coupled growth and product formation, and the physical and kinetic constants of the system were determined.     

Mathematical Modelling of the MAP Kinase Pathway Using Proteomic Datasets

The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.     

Continuous cell suspension processing using magnetically stabilized fluidized beds

The behavior of a cell suspension in a continuous magnetically stabilized fluidized bed (MSFB) was investigated both experimentally and theoretically. The low, constant pressure drop and fluidity of the solids phase in the MSFB allowed a continuous countercurrent separator to be constructed. The magnetic field eliminated all motion of the solids phase (nickel spheres) and produced a device similar to a packed-bed depth filter. Yeast cells were used as the suspended solids and the performance of the MSFB filter was assessed as a function of the bed height, solids velocity, cell concentration, and liquid composition. Removal rates could be adjusted by controlling the cell/support interaction and were found to be as high as 99%. A mathematical model was used to aid in understanding this filtration and was found to agree qualitatively with all experimental observations. Comparison of the model with the data suggests that both cell/cell binding and cell shadowing are occurring.     

Metabolic flux-based modeling of mAb production during batch and fed-batch operations

This paper proposes mathematical models that predict the physiology, growth behavior and productivity of hybridoma cells in both batch and fed-batch systems. Murine hybridoma 130-8F producing anti-F-glycoprotein monoclonal antibody was employed as a model system. A systematic approach based on metabolic flux analysis (MFA) was utilized to yield a dynamic model for predicting the concentration of significant metabolites over time. Correlation analysis was performed to formulate a Biomass Model for predicting cell concentration and viability as a function of the extracellular metabolite concentrations. The coefficients of the model equation were estimated by employing the Metropolis–Hastings algorithm. The Metabolites Model was combined with the Biomass Model to get an Integrated Model capable of predicting concentration values for substrates, extracellular metabolites, and viable and dead cell concentration by utilizing only starting concentrations as input. The prediction accuracy of the model was tested by using experimental data.     

Ethanol fermentation with cell recycling: Computer simulation

A mathematical model for glucose-to-ethanol fermentation at high yeast cell concentrations was developed. The feasibility of improving fermenter productivity over that of a conventional continuous-stirred-tank fermenter by using multiple stage reactors and yeast cell recycling was predicted by computer simulation. The optimum size distribution for multistage fermentors was obtained for different glucose feedstream concentrations and different glucose conversion levels. Productivity increases over a single-stage reactor ranged from 1.2-2.0 times. The use of yeast cell recycling to increase cell concentration and productivity increases of over 4.0 times that of a system without recycling.     

Application of an extended kalman filter method for monitoring high density cultivation of Escherichia coli

A real-time, on-line extended Kalman filter was used to describe and monitor the growth of Escherichia coli on glycerol. The growth of E. coli showed an inhibition kinetics with μ_max=0.806/h, K_S=0.68 g/l and K_i=87.4 g/l. As a feeding strategy, the conventional DO-stat with a DDC-PID control method, in which the dissolved oxygen concentration is maintained at a desired level by varying the substrate feedrate, was employed. The Kalman filter was based on an unstructured mathematical model and on-line measured data. The mathematical model comprised of mass balances of the biomass and substrate as well as kinetic and stoichiometric data which were measured prior to the process. For biomass concentration up to 50 g dry weight/l, the estimation of the process was rather accurate. At higher biomass concentration, product formation, indicated by an intense brown coloring of the fermentation broth, occured. Since the effect of this product on biomass production was not included in the mathematical model, the estimated data diverged from the experimental data at biomass concentrations greater than 50 g dry weight/l.     

A mathematical model for the batch reactor kinetics of algae growth

A mathematical model based on the Einstein law of photochemical equivalence is proposed to describe the batch growth of unicellular algae. The model was applied in an integrated form to cell concentration versus growth time data taken over an extended range of cell concentrations which include both the regions of “exponential” and “linear” growth. It is shown that a certain function of cell concentration contained in the integrated form of the model is linearly dependent on the growth time over both the “exponential” and “linear” growth regions.     

Double Cell Bulk Acoustic Wave Sensor for Ion Chromatographic Study of the Relation Between Magnesium and Growth of Organisms

An ion chromatography (IC) method with a double cell bulk acoustic wave (DCBAW) detector was used for the detection of magnesium concentration decrease during the culture of whole cells. The detector parameters were optimized according to its theoretical equation, including the cell constants and the background conductance of the adjusting cell. A low temperature coefficient and thus high sensitivity were obtained by this method. The detection limit is 0.01 ppm, and the linear range is 0.05–50 ppm. A new mathematical model was developed to describe the growth of the cell. The baseline for this model is the concept that a noninteractive growth process occurs among perfectly substitutable nutrients if the locus of points of the substrate concentrations producing equal growth rate is linear. The monitoring results agreed well with the calculated results. Received: 17 July 1999 / Accepted: 23 August 1999     

Continuous alcoholic fermentation withSaccharomyces cerevisiae recycle by tangential filtration: Key points for process modelling

Summary A mathematical model, taking in count ethanol inhibition and limitation effects with emphasis to phenomena linked to biomass is proposed. Notions of critical cell concentrations, corresponding to the appearance of inhibition or limitation effects and transfer limitations are introduced. Available space for yeast growth is also considered. The agreement between simulation and experimental results demonstrates that this model is sufficiently reliable for predictive performance of bioreactors with high cell concentrations.     

Metabolic regulation of ion-osmotic homeostasis in the non-electrostimulated cell

A mathematical model is proposed which in the limits of a cell unifield self-consistent scheme enables to interpret quantitatively the results of electrophysiological, morphological and bioenergetic measurements. Using the model one can calculate the membrane potential, ionic fluxes, intracellular ionic concentrations, cell volume, as well as the rate of ATP hydrolysis by ionic pump.     

Modelling and optimization of environmental conditions for kefiran production by Lactobacillus kefiranofaciens

A mathematical model for kefiran production by Lactobacillus kefiranofaciens was established, in which the effects of pH, substrate and product on cell growth, exopolysaccharide formation and substrate assimilation were considered. The model gave a good representation both of the formation of exopolysaccharides (which are not only attached to cells but also released into the medium) and of the time courses of the production of galactose and glucose in the medium (which are produced and consumed by the cells). Since pH and both lactose and lactic acid concentrations differently affected production and growth activity, the model included the effects of pH and the concentrations of lactose and lactic acid. Based on the mathematical model, an optimal pH profile for the maximum production of kefiran in batch culture was obtained. In this study, a simplified optimization method was developed, in which the optimal pH profile was determined at a particular final fermentation time. This was based on the principle that, at a certain time, switching from the maximum specific growth rate to the critical one (which yields the maximum specific production rate) results in maximum production. Maximum kefiran production was obtained, which was 20% higher than that obtained in the constant-pH control fermentation. A genetic algorithm (GA) was also applied to obtain the optimal pH profile; and it was found that practically the same solution was obtained using the GA.     

An experimental and modeling study on the removal of mono-chlorobenzene vapor in biotrickling filters

Removal of mono-chlorobenzene (m-CB) vapor from airstreams was studied in a biotrickling filter (BTF) operating under counter-current flow of the air and liquid streams. Experiments were performed under various values of inlet m-CB concentration, air and/or liquid volumetric flow rates, and pH of the recirculating liquid. Conversion of m-CB was never below 70% and at low concentrations exceeded 90%. A maximum removal rate of about 60 gm-3-reactor h-1 was observed. Conversion of m-CB was found to increase as the values of liquid and air flow rate increase and decrease, respectively. The effects of pH and frequency of medium replenishment on BTF performance were also investigated. The process was successfully described with a detailed mathematical model, which accounts for mass transfer and kinetic effects based on m-CB and oxygen availability. Solution of the model equations yielded m-CB and oxygen concentration profiles in all three phases (airstream, liquid, biofilm). It is predicted that oxygen has a controling effect on the process at high inlet m-CB concentrations. From independent, suspended culture, experiments it was found that m-CB biodegradation follows Andrews inhibitory kinetics. The kinetic constants were found to remain practically unchanged after the culture was used in BTF experiments for 8 months. Copyright 1998 John Wiley & Sons, Inc.     

The Boyle-Conway model including the effect of an electrogenic pump for nonexcitable cells

A mathematical model which enables a quantitative interpretation of the results of electrophysiological, morphometric, and bioenergetic measurements within the framework of a homogeneous cell is proposed. Using the model one can calculate the membrane potential, ionic fluxes, intracellular ionic concentrations, cell volume, and the rate of ATP hydrolysis with an ionic pump. Comparison between model predictions and experimental results is carried out. It is shown that the model allows correlation of the results of numerous independent experiments.     

Kinetics of substrate removal in a completely mixed anaerobic filter

A completely mixed anaerobic filter, in which the influent organic matter concentration is diluted with recirculated effluent, was found to effectively remove organic matter concentrations in high strength acidic wastewater, at a range of organic loadings and shock loads. Increases in organic loading had a substantial effect on the relative organic matter composition of the effluent and the magnitude of the fatty acid fraction showed a pattern inverse to that of the nitrogenous organics. A fixed film model was formulated which indicated that at high substrate concentrations the substrate removal rate is proportional to the square root of the substrate concentration and the specific area of the filter medium. A comparison of the biofilm model and the measured effluent concentrations tended to indicate that the substrate removal rate is primarily affected by substrate concentration, specific surface area, flow rate, and temperature of the unit.     

High hydrogen peroxide concentration in the feed-zone affects bioreactor cell productivity with liquid phase oxygen supply strategy

Liquid phase oxygen supply strategy (LPOS), in which hydrogen peroxide (H(2)O(2)) is used to supply oxygen to the bioreactor, leads to low cell productivity despite high specific productivities of relevant metabolites. We hypothesized that high H(2)O(2) concentrations in the feed-zone led to local cell death, which in turn, lead to lower cell productivity. To test the hypothesis, a mathematical model was developed. Bacillus subtilis 168 was used as the model system in this study. The model simulations of cell concentrations in the bioreactor-zone were verified with the experimental results. The feed-zone H(2)O(2) concentrations remained 12-14 times higher than bulk bioreactor concentrations. The high local concentrations are expected to cause local cell killing, which explains the decrease in overall cell production by 50% at 300 rpm compared to conventional cultivation. Further, among the four different feed strategies studied using the model, dissolved oxygen (DO) controlled H(2)O(2) feed strategy caused least local cell killing and improved overall cell production by 34%.     

Structured modeling of recombinant protein production in batch and fed-batch culture of baculovirus-infected insect cells

The infection of insect cells with baculovirus was described in a mathematical model as a part of the structured dynamic model describing whole animal cell metabolism. The model presented here is capable of simulating cell population dynamics, the concentrations of extracellular and intracellularviral components, and the heterologous product titers. The model describes the whole processes of viral infection and theeffect of the infection on the host cell metabolism. Dynamic simulation of the model in batch and fed-batch mode gave goodagreement between model predictions and experimental data. Optimum conditions for insect cell culture and viral infectionin batch and fed-batch culture were studied using the model.     

Synthetic polymers improve vitrification outcomes of macaque ovarian tissue as assessed by histological integrity and the in vitro development of secondary follicles

Long-term storage of natural tissues or tissue-engineered constructs is critical to allow off-the-shelf availability. Vitrification is a method of cryopreservation that eliminates ice formation, as ice may be detrimental to the function of natural or bioartificial tissues. In order to achieve the vitreous state, high concentrations of CPAs must be added and later removed. The high concentrations may be deleterious to cells as the CPAs are cytotoxic and single-step addition or removal will result in excessive osmotic excursions and cell death. A previously described mathematical model accounting for the mass transfer of CPAs through the sample matrix and cell membrane was expanded to incorporate heat transfer and CPA cytotoxicity. Simulations were performed for two systems, an encapsulated system of insulin-secreting cells and articular cartilage, each with different transport properties, geometry and size. Cytotoxicity and mass transfer are dependent on temperature, with a higher temperature allowing more rapid mass transfer but also causing increased cytotoxicity. The effects of temperature are exacerbated for articular cartilage, which has larger dimensions and slower mass transport through the matrix. Simulations indicate that addition and removal at 4°C is preferable to 25°C, as cell death is higher at 25°C due to increased cytotoxicity in spite of the faster mass transport. Additionally, the model indicates that less cytotoxic CPAs, especially at high temperature, would significantly improve the cryopreservation outcome. Overall, the mathematical model allows the design of addition and removal protocols that insure CPA equilibration throughout the sample while still minimizing CPA exposure and maximizing cell survival.