Growth behavior of number distributed adherent MDCK cells for optimization in microcarrier cultures

An assay for measuring the number of adherent cells on microcarriers that is independent from dilution errors in sample preparation was used to investigate attachment dynamics and cell growth. It could be shown that the recovery of seeded cells is a function of the specific rates of cell attachment and cell death, and finally a function of the initial cell‐to‐bead ratio. An unstructured, segregated population balance model was developed that considers individual classes of microcarriers covered by 1–220 cells/bead. The model describes the distribution of initially attached cells and their growth in a microcarrier system. The model distinguishes between subpopulations of dividing and nondividing cells and describes in a detailed way cell attachment, cell growth, density‐dependent growth inhibition, and basic metabolism of Madin‐Darby canine kidney cells used in influenza vaccine manufacturing. To obtain a model approach that is suitable for process control applications, a reduced growth model without cell subpopulations, but with a formulation of the specific cell growth rate as a function of the initial cell distribution on microcarriers after seeding was developed. With both model approaches, the fraction of growth‐inhibited cells could be predicted. Simulation results of two cultivations with a different number of initially seeded cells showed that the growth kinetics of adherent cells at the given cultivation conditions is mainly determined by the range of disparity in the initial distribution of cells on microcarriers after attachment. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Kinetics of growth and substrate consumption of Escherichia coli ML 30 on two carbon sources.

When E. coli ML 30 is grown in batch culture on a mineral salt medium containing a mixed carbon source of glucose and pyruvate, there is no sequential utilization of the carbon sources. The consumption of glucose and pyruvate takes place simultaneously with reciprocal influence (inhibition) on rates of substrate uptake. The specific growth rate is greater than mupmax for pyruvate but smaller than musmax for glucose. In the paper three cases of kinetics of growth and of substrate consumption at several combinations of initial substrate concentrations are considered. A mathematical model is proposed and investigated. The model allows to describe the growth on glucose or on pyruvate not only as singular carbon sources, but also as a mixed carbon source with reciprocal inhibition on rates of substrate uptake. By data fitting parameters of growth and substrate consumption were found.     

Modeling kinetics of a large‐scale fed‐batch CHO cell culture by Markov chain Monte Carlo method

Markov chain Monte Carlo (MCMC) method was applied to model kinetics of a fed‐batch Chinese hamster ovary cell culture process in 5,000‐L bioreactors. The kinetic model consists of six differential equations, which describe dynamics of viable cell density and concentrations of glucose, glutamine, ammonia, lactate, and the antibody fusion protein B1 (B1). The kinetic model has 18 parameters, six of which were calculated from the cell culture data, whereas the other 12 were estimated from a training data set that comprised of seven cell culture runs using a MCMC method. The model was confirmed in two validation data sets that represented a perturbation of the cell culture condition. The agreement between the predicted and measured values of both validation data sets may indicate high reliability of the model estimates. The kinetic model uniquely incorporated the ammonia removal and the exponential function of B1 protein concentration. The model indicated that ammonia and lactate play critical roles in cell growth and that low concentrations of glucose (0.17 mM) and glutamine (0.09 mM) in the cell culture medium may help reduce ammonia and lactate production. The model demonstrated that 83% of the glucose consumed was used for cell maintenance during the late phase of the cell cultures, whereas the maintenance coefficient for glutamine was negligible. Finally, the kinetic model suggests that it is critical for B1 production to sustain a high number of viable cells. The MCMC methodology may be a useful tool for modeling kinetics of a fed‐batch mammalian cell culture process. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Cell volume distributions reveal cell growth rates and division times

A population of cells in culture displays a range of phenotypic responses even when those cells are derived from a single cell and are exposed to a homogeneous environment. Phenotypic variability can have a number of sources including the variable rates at which individual cells within the population grow and divide. We have examined how such variations contribute to population responses by measuring cell volumes within genetically identical populations of cells where individual members of the population are continuously growing and dividing, and we have derived a function describing the stationary distribution of cell volumes that arises from these dynamics. The model includes stochastic parameters for the variability in cell cycle times and growth rates for individual cells in a proliferating cell line. We used the model to analyze the volume distributions obtained for two different cell lines and one cell line in the absence and presence of aphidicolin, a DNA polymerase inhibitor. The derivation and application of the model allows one to relate the stationary population distribution of cell volumes to extrinsic biological noise present in growing and dividing cell cultures.     

Growth and product inhibition kinetics of T-cell hybridomas producing lymphokines in batch and continuous culture.

The kinetics of growth and lymphokine formation by T-cell hybridomas were investigated in batch and continuous culture. Product inhibitions by ammonia and lactic acid were considered in the proposed model and experimental data were used to determine the kinetic and inhibition constants. The effect of dilution rate on specific substrate consumption and product formation rates was investigated.     

Modeling of <Emphasis Type="Italic">Fusarium redolens</Emphasis> Dzf2 mycelial growth kinetics and optimal fed-batch fermentation for beauvericin production

Beauvericin (BEA) is a cyclic hexadepsipeptide mycotoxin with notable phytotoxic and insecticidal activities. Fusarium redolens Dzf2 is a highly BEA-producing fungus isolated from a medicinal plant. The aim of the current study was to develop a simple and valid kinetic model for F. redolens Dzf2 mycelial growth and the optimal fed-batch operation for efficient BEA production. A modified Monod model with substrate (glucose) and product (BEA) inhibition was constructed based on the culture characteristics of F. redolens Dzf2 mycelia in a liquid medium. Model parameters were derived by simulation of the experimental data from batch culture. The model fitted closely with the experimental data over 20–50 g l⁻¹ glucose concentration range in batch fermentation. The kinetic model together with the stoichiometric relationships for biomass, substrate and product was applied to predict the optimal feeding scheme for fed-batch fermentation, leading to 54% higher BEA yield (299 mg l⁻¹) than in the batch culture (194 mg l⁻¹). The modified Monod model incorporating substrate and product inhibition was proven adequate for describing the growth kinetics of F. redolens Dzf2 mycelial culture at suitable but not excessive initial glucose levels in batch and fed-batch cultures.     

Fed-batch sorbitol to sorbose fermentation by A. suboxydans

Batch kinetics for sorbitol to sorbose bioconversion was studied at 20% sorbitol concentration. The culture featured 90% conversion of sorbitol to sorbose in 20 hours. Increasing the initial substrate concentration in the bioreactor decreased the culture specific growth rate. At 40% initial sorbitol concentration no culture growth was observed. The batch kinetics and substrate inhibition studies were used to develop the Mathematical Model of the system. The model parameters were identified using the original batch kinetic data (S _o =20%). The developed mathematical model was adopted to fed-batch cultivation with the exponential nutrient feeding. The fed-batch model was simulated and implemented experimentally. No substrate inhibition was observed in the fed-batch mode and it provided an overall productivity of 12.6?g/l-h. The fed-batch model suitably described the experimentally observed results. The model is ready for further optimization studies.     

Which future for the French Pyrenean brown bear (Ursus arctos) population? An approach using stage-structured deterministic and stochastic models

The Pyrenean brown bear (Ursus arctos) population is considered as one of the most seriously threatened with extinction in Western Europe. To assess its viability and possible needs of augmentation, we develop deterministic and stochastic stage-structured demographic models. The deterministic model reveals that a bear population cannot have a high annual growth rate and is particularly sensitive to breeder survival. High demographic parameters appear to be crucial to population persistence, especially for a small population that remains vulnerable to demographic and environmental stochasticities. The Pyrenean population cannot therefore be considered as viable. Successful conservation strategies for this population would require releasing more bears in both sub-populations in the near future.     

Microbial growth dynamics on the basis of individual budgets

The popular theories for microbial dynamics by Monod, Pirt and Droop are shown to be special cases of a model for individual budgets, in which growth and maintenance are on the expense of reserve materials. The dynamics of reserve materials is a first order process with a relaxation time proportional to cell length; maintenance is proportional to cell volume, and uptake, which depends hyperbolically on substrate density, is proportional to cell volume as well. Because of the latter, population dynamics depends on the behaviour of the individuals in a simple way, such that the cell volume distribution has no quantitative effect.When uptake is proportional to the surface area of the cell, which is realistic from a physical point of view, the relation between the individual level and the population one becomes more complicated and the cell size and shape distribution affects population dynamics. It is shown how the changing shape of rods modifies uptake and, consequently, growth.The concept of energy conductance, defined as the ratio, of the maximum surface area specific uptake and the volume specific energy reserve has been introduced in the analysis of microbial dynamics. The first tentative results indicate that the value for E. coli is close to the mean value for a wide variety of animals.Properties of the model for cell suspension at constant substrate densities are analyzed and tested against a variety of experimental data from the literature on both the individual and the population level.     

Substrate inhibition kinetics of <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> in fed-batch cultures operated at constant glucose and maltose concentration levels

Fed-batch culture is the mode of operation of choice in industrial baker’s yeast fermentation. The particular mode of culture, operated at stable glucose and maltose concentration levels, was employed in this work in order to estimate important kinetic parameters in a process mostly described in the literature as batch or continuous culture. This way, the effects of a continuously falling sugar level during a batch process were avoided and therefore the effects of various (stable) sugar levels on growth kinetics were evaluated. Comparing the kinetics of growth and the inhibition by the substrate in cultures grown on glucose, which is the preferential sugar source for Saccharomyces cerevisiae, and maltose, the most common sugar source in industrial media for baker’s yeast production, a milder inhibition effect by the substrate in maltose-grown cells was observed, as well as a higher yield coefficient. The observed sugar inhibition effect in glucostat cultures was taken into account in modeling substrate inhibition kinetics. The inhibition coefficient K _i increased with increasing sugar concentration levels, but it appeared to be unaffected by the type of substrate and almost equal for both substrates at elevated concentration levels.     

Descriptive parameter evaluation in mammalian cell culture

Several methods exist for assessing population growth and protein productivity in mammalian cell culture. These methods were critically examined here, based on experiments with two hybridoma cell lines. It is shown that mammalian cell culture parameters must be evaluated on the same basis. In batch culture mode most data is obtained on a cumulative basis (protein product titre, substrate concentration, metabolic byproduct concentration). A simple numerical integration technique can be employed to convert cell concentration data to a cumulative basis (cell-hours). The hybridoma lines used in this study included a nutritionally non-fastidious line producing low levels of MAb and a nutritionally fastidious hybridoma with high productivity. In both cases the cell-hour approach was the most appropriate means of expressing the relationship between protein productivity and cell population dynamics. The cell-hour approach could be used as the basis for all metabolic population parameter evaluations. This method has the potential to be used successfully for both prediction and optimization purposes. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.     

The kinetics of cometabolism

Experimental observations indicate that the rates of cometabolic transformation are linked to the consumption of growth substrate during growth and to the consumption of cell mass and/or energy substrate in the absence of growth substrate. Three previously proposed models (models 1 through 3) describing the kinetics of cometabolism by resting cells are compared, and the interrelationships and underlying assumptions for these models are explored. Models 1 to 3 are shown to converge at high concentrations of the nongrowth substrate. An expression describing nongrowth substrate transformation in the presence of growth substrate is proposed, and this expression is integrated with an expression for cell growth to give a single unstructured model (model 4) that encompasses models 1 to 3 and describes cometabolism by both resting and growing cells. Model 4 couples transformation of nongrowth substrate to consumption of growth substrate and biomass, and predicts that cometabolism will result, and decreased specific growth rates for a cometabolizing population. Competitive inhibition can also be incorporated in the model. Experimental aspects of model calibration and verification are discussed. The need for models that distinguish between the exhaustion of cell activity and cell death is emphasized. (c) 1993 Wiley & Sons, Inc.     

Kinetic analysis of high-concentration isopropanol biodegradation by a solvent-tolerant mixed microbial culture

The ability of a previously enriched microbial population to utilize isopropanol (IPA) as the sole carbon source within a minimal salts medium is studied. The advantage of prior enrichment procedures for the improvement of IPA biodegradation performance is demonstrated for an IPA concentration of up to 24 g L(-1). Results showing the interrelationship between temperature and substrate utilization and inhibition levels at temperatures of between 2 degrees C and 45 degrees C are examined. Models of inhibition based on enzyme kinetics are assessed via nonlinear analysis, in order to accurately represent the growth kinetics of this solvent-tolerant mixed culture. The model that best describes the data is the Levenspiel substrate inhibition model, which can predict the maximum substrate level above which growth is completely limited. This is the first report of IPA treatment of up to 24 g L(-1) by an aerobic solvent-tolerant population.     

Hidden hysteresis – population dynamics can obscure gene network dynamics

Background

Positive feedback is a common motif in gene regulatory networks. It can be used in synthetic networks as an amplifier to increase the level of gene expression, as well as a nonlinear module to create bistable gene networks that display hysteresis in response to a given stimulus. Using a synthetic positive feedback-based tetracycline sensor in E. coli, we show that the population dynamics of a cell culture has a profound effect on the observed hysteretic response of a population of cells with this synthetic gene circuit.

Results

The amount of observable hysteresis in a cell culture harboring the gene circuit depended on the initial concentration of cells within the culture. The magnitude of the hysteresis observed was inversely related to the dilution procedure used to inoculate the subcultures; the higher the dilution of the cell culture, lower was the observed hysteresis of that culture at steady state. Although the behavior of the gene circuit in individual cells did not change significantly in the different subcultures, the proportion of cells exhibiting high levels of steady-state gene expression did change.Although the interrelated kinetics of gene expression and cell growth are unpredictable at first sight, we were able to resolve the surprising dilution-dependent hysteresis as a result of two interrelated phenomena - the stochastic switching between the ON and OFF phenotypes that led to the cumulative failure of the gene circuit over time, and the nonlinear, logistic growth of the cell in the batch culture.

Conclusions

These findings reinforce the fact that population dynamics cannot be ignored in analyzing the dynamics of gene networks. Indeed population dynamics may play a significant role in the manifestation of bistability and hysteresis, and is an important consideration when designing synthetic gene circuits intended for long-term application.

     

Birth, growth and death as structuring operators in bacterial population dynamics

A new model is presented that describes microbial population dynamics that emerge from complex interactions among birth, growth and death as oriented, discrete events. Specifically, birth and death act as structuring operators for individual organisms within the population, which become synchronised as age clusters (called cell generations that are structured in age classes) that are born at the same time and die in concert; a pattern very consistent with recent experimental data that show bacterial group death correlates with temporal population dynamics in chemostats operating at carrying capacity. Although the model only assumes “natural death” (i.e., no death from predation or antimicrobial exposure), it indicates that short-term non-linear dynamic behaviour can exist in a bacterial population growing under longer term pseudo-steady-state conditions (a confined dynamic equilibrium). After summarizing traditional assumptions about bacterial aging, simulations of batch, continuous-flow, and bioreactors with recycle are used to show how population dynamics vary as function of hydraulic retention time, microbial kinetics, substrate level, and other factors that cause differential changes in the distribution of living and dead cells within the system. In summary, we show that population structures induced by birth and death (as discrete and delayed events) intrinsically create a non-linear dynamic system, implying that a true steady state can never exist in growing bacterial populations. This conclusion is discussed within the context of process stability in biotechnology.     

Individual-based modeling of phytoplankton: evaluating approaches for applying the cell quota model

Present phytoplankton models typically use a population-level (lumped) modeling (PLM) approach that assumes average properties of a population within a control volume. For modern biogeochemical models that formulate growth as a nonlinear function of the internal nutrient (e.g. Droop kinetics), this averaging assumption can introduce a significant error. Individual-based (agent-based) modeling (IBM) does not make the assumption of average properties and therefore constitutes a promising alternative for biogeochemical modeling. This paper explores the hypothesis that the cell quota (Droop) model, which predicts the population-average specific growth or cell division rate, based on the population-average nutrient cell quota, can be applied to individual algal cells and produce the same population-level results. Three models that translate the growth rate calculated using the cell quota model into discrete cell division events are evaluated, including a stochastic model based on the probability of cell division, a deterministic model based on the maturation velocity and fraction of the cell cycle completed (maturity fraction), and a deterministic model based on biomass (carbon) growth and cell size. The division models are integrated into an IBM framework (iAlgae), which combines a lumped system representation of a nutrient with an individual representation of algae. The IBM models are evaluated against a conventional PLM (because that is the traditional approach) and data from a number of steady and unsteady continuous (chemostat) and batch culture laboratory experiments. The stochastic IBM model fails the steady chemostat culture test, because it produces excessive numerical randomness. The deterministic cell cycle IBM model fails the batch culture test, because it has an abrupt drop in cell quota at division, which allows the cell quota to fall below the subsistence quota. The deterministic cell size IBM model reproduces the data and PLM results for all experiments and the model parameters (e.g. maximum specific growth rate, subsistence quota) are the same as those for the PLM. In addition, the model-predicted cell age, size (carbon) and volume distributions are consistent with those derived analytically and compare well to observations. The paper discusses and illustrates scenarios where intra-population variability in natural systems leads to differences between the IBM and PLM models.