The impulse response of Chlamydomonas reinhardii in nitrite-limited chemostat culture

This article presents a clear experimental determination of the behavior of nutrient uptake rate, mean cell nutrient content, and specific growth rate following the injection of pulses of additional limiting nutrient into a chemostat culture of Chlamydomonas reinhardii. The uptake rate per cell is a hyperbolic function of external nutrient concentration. The specific growth rate is related to the mean cell nutrient content by a hysteresis loop. The data obtained is used to test the performance of the Caperon-Droop mean cell quota model. It is demonstrated that this model cannot be used under severe transient conditions, even when modified by the introduction of a discrete time delay, a simple memory function, or time-dependent intracellular nutrient processing.     

A mathematical model for fluid shear-sensitive 3D tissue construct development

This research studies dynamic culture for 3D tissue construct development with computational fluid dynamics. It proposes a mathematical model to evaluate the impact of flow rates and flow shear stress on cell growth in 3D constructs under perfusion. The modeling results show that dynamic flow, even at flow rate as low as 0.002 cm/s, can support much better mass exchange, higher cell number, and more even cell and nutrient distribution compared to static culture. Higher flow rate can further improve nutrient supply and mass exchange in the construct, promoting better nutritious environment and cell proliferation compared to lower flow rate. In addition, consideration of flow shear stress predicts much higher cell number in the construct compared to that without shear consideration. While the nutrient can dominate shear stress in influencing cell proliferation, the shear effect increases with flow rate. The proposed model helps tissue engineers better understand the cell-flow relationship at the molecular level during dynamic culture.     

Transient response simulations of recombinant microbial populations

An asynchronous bacterial population has been approximated using a finite number of "computer" cells, each based on a complex single-cell model for Escherichia coli. This formulation correctly simulates the transient responses of protein and total cell mass synthesis rate to the sudden increase in the concentration of limiting energy source in the growth medium. Experimentally observed responses of rRNA and mRNA synthesis rates to growth rate shifts are qualitatively mirrored by the model. Simulation trends following those of a rel(-) mutant suggest that model modifications are needed to describe the dynamics of the stringent response. Simulations of the responses of recombinant populations to plasmid amplification or plasmid promoter induction also result in behavior similar to that determined experimentally. The calculated responses for recombinant populations subjected to constant promoter induction or cyclic induction-noninduction lead to the conclusion that inducible systems give greater productivity than those with fixed promoter strength. This formulation may be utilized as a basis for exploring other aspects of recombinant population dynamics.     

A kinetic analysis of hybridoma growth and metabolism in batch and continuous suspension culture: effect of nutrient concentration, dilution rate, and pH

Hybridomas are finding increased use for the production of a wide variety of monoclonal antibodies. Understanding the roles of physiological and environmental factors on the growth and metabolism of mammalian cells is a prerequisite for the development of rational scale-up procedures. An SP2/0-derived mouse hybridoma has been employed in the present work as a model system for hybridoma suspension culture. In preliminary shake flask studies to determine the effect of glucose and glutamine, it was found that the specific growth rate, the glucose and glutamine metabolic quotients, and the cumulative specific antibody production rate were independent of glucose concentration over the range commonly employed in cell cultures. Only the specific rate of glutamine uptake was found to depend on glutamine concentration. The cells were grown in continuous culture at constant pH and oxygen concentration at a variety of dilution rates. Specific substrate consumption rates and product formation rates were determined from the steady state concentrations. The specific glucose uptake rate deviated from the maintenance energy model(1) at low specific growth rates, probably due to changes in the metabolic pathways of the cells. Antibody production was not growth-associated; and higher specific antibody production rates were obtained at lower specific growth rates. The effect of pH on the metabolic quotients was also determined. An optimum in viable cell concentration was obtained between pH 7.1 and 7.4. The viable cell number and viability decreased dramatically at pH 6.8. At pH 7.7 the viable cell concentration initially decreased, but then recovered to values typical of pH 7.1-7.4. Higher specific nutrient consumption rates were found at the extreme pH values; however, glucose consumption was inhibited at low pH. The pH history also influenced the behavior at a given pH. Higher antibody metabolic quotients were obtained at the extreme pH values. Together with the effect of specific growth rate, this suggests higher antibody production under environmental or nutritional stress.     

A kinetic analysis of hybridoma growth and metabolism in batch and continuous suspension culture: effect of nutrient concentration, dilution rate, and pH. Reprinted from Biotechnology and Bioengineering, Vol. 32, Pp 947-965 (1988)

Hybridomas are finding increased use for the production of a wide variety of monoclonal antibodies. Understanding the roles of physiological and environmental factors on the growth and metabolism of mammalian cells is a prerequisite for the development of rational scale-up procedures. An SP2/0-derived mouse hybridoma has been employed in the present work as a model system for hybridoma suspension culture. In preliminary shake flask studies to determine the effect of glucose and glutaminE, it was found that the specific growth rate, the glucose and glutamine metabolic quotients, and the cumulative specific antibody production rate were independent of glucose concentration over the range commonly employed in cell cultures. Only the specific rate of glutamine uptake was found to depend on glutamine concentration. The cells were grown in continuous culture at constant pH and oxygen concentration at a variety of dilution rates. Specific substrate consumption rates and product formation rates were determined from the steady state concentrations. The specific glucose uptake rate deviated from the maintenance energy model(1) at low specific growth rates, probably due to changes in the metabolic pathways of the cells. Antibody production was not growth-associated; and higher specific antibody production rates were obtained at lower specific growth rates. The effect of pH on the metabolic quotients was also determined. An optimum in viable cell concentration was obtained between pH 7.1 and 7.4. The viable cell number and viability decreased dramatically at pH 6.8. At pH 7.7 the viable cell concentration initially decreased, but then recovered to values typical of pH 7.1-7.4. Higher specific nutrient consumption rates were found at the extreme pH values; however, glucose consumption was inhibited at low pH. The pH history also influenced the behavior at a given pH. Higher antibody metabolic quotients were obtained at the extreme pH values. Together with the effect of specific growth rate, this suggests higher antibody production under environmental or nutritional stress.     

A theoretical and empirical investigation of delayed growth response in the continuous culture of bacteria

When the growth of bacteria in a chemostat is controlled by limiting the supply of a single essential nutrient, the growth rate is affected both by the concentration of this nutrient in the culture medium and by the amount of time that it takes for the chemical and physiological processes that result in the production of new biomass. Thus, although the uptake of nutrient by cells is an essentially instantaneous process, the addition of new biomass is delayed by the amount of time that it takes to metabolize the nutrient. Mathematical models that incorporate this "delayed growth response" (DGR) phenomenon have been developed and analysed. However, because they are formulated in terms of parameters that are difficult to measure directly, these models are of limited value to experimentalists. In this paper, we introduce a DGR model that is formulated in terms of measurable parameters. In addition, we provide for this model a complete set of criteria for determining persistence versus extinction of the bacterial culture in the chemostat. Specifically, we show that DGR plays a role in determining persistence versus extinction only under certain ranges of chemostat operating parameters. It is also shown, however, that DGR plays a role in determining the steady-state nutrient and bacteria concentrations in all instances of persistence. The steady state and transient behavior of solutions of our model is found to be in agreement with data that we obtained in growing Escherichia coli 23716 in a chemostat with glucose as a limiting nutrient. One of the theoretical predictions of our model that does not occur in other DGR models is that under certain conditions a large delay in growth response might actually have a positive effect on the bacteria's ability to persist.     

Some effects of growth conditions on steady state and heat shock induced htpG gene expression in continuous cultures of Escherichia coli

Most of the data concerning heat shock gene expression reported in the literature are derived from batch culture experiments under substrate and nutrient sufficient conditions. Here, the effects of dilution rate and medium composition on the steady state and heat shock induced htpG gene expression have been investigated in continuous cultures of Escherichia coli, using a chromosomal htpG-lacZ gene fusion. During steady state growth temperature dependent patterns of the relative htpG expression were found to be largely similar, irrespective of the growth condition. However, nitrogen-limited growth resulted in a markedly reduced specific steady state htpG expression as compared to growth under carbon limitation or in complex medium, correlating qualitatively with the total cellular protein content. During heat shock, tight temperature controlled expression was evident. While the relative heat shock induced expression was largely identical at various dilution rates in a given growth medium, significantly different response patterns were observed in the three growth media at any give dilution rate. From these results a clearly temperature regulated htpG expression during both, steady and transient state growth in continuous culture is evident, which is further significantly affected by the growth condition used.     

Kinetic study of hybridoma cell growth in continuous culture: II. Behavior of producers and comparison to nonproducers

A hybridoma cell line, AFP-27-P, was cultivated in continuous culture under glucose-limited conditions. The viable cell concentration, dead-cell concentration, and cell volume all varied with the dilution rate. A model previously developed for a nonproducing clone of the same cell line, AFP-27-NP, was extended to describe the behavior of the cells. The relationship between the specific growth rate and glucose concentration is described by a function similar to the Monod model. A threshold glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentration and a minimum specific growth rate are incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. The relationship between the death rate and the glucose concentration is described by an inverted Monod-type function. Furthermore, the yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper range of specific growth rates. No maintenance term for glucose consumption is used; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepts the specific growth rate at a value close to the minimum growth rate. The productivity of antibody as a function of the specific growth rate is described by a mixed type model with a noon-growth-associated term and a negative-growth-associated term. The values for the model parameters were determined from regression analysis of the steady state data.     

The unsteady continuous culture of phosphate-limited Monochrysis lutheri droop: Experimental and theoretical analysis

A three-state variable model for phosphate-limited phytoplankton growth in a continuously lit continuous culture is proposed. In the model, the phosphate uptake rate per cell is a Michaelis-Mententype hyperbolic function of ambient nutrient concentration and the growth rate is a Droop-type hyperbolic function of cell quota. Steady-state and short-term uptake experiments with unialgal cultures of Monochrysis lutheri Droop, a marine chrysophyte, were used to calibrate the proposed model. For the long-term unsteady experiments, the model predicts well the culture's dynamic response in terms of cell density to steps down and up in influent concentration of limiting nutrient. For step changes in dilution rate, the model predicts well the culture's response to a step down but predicts poorly the culture's response to a step up. The long-term responses of the cultures to impulses in influent concentration show that the model fails to predict, even qualitatively, the behavior of the phytoplankton. Not unexpectedly, the model fails most dramatically in those experiments involving a rapid increase in cell quota, thereby demonstrating both the inherent flaws in the concept of the instantaneous growth rate as a function of instantaneous cell quota and the need for further dynamic characterization of phytoplankton behavior.     

Overexpression of cloned genes using recombinant Escherichia coli regulated by a T7 promoter: II. Two-stage continuous cultures and model simulations

A two-stage culture strategy was studied for continuous high-level production of a foreign protein in the chemically inducible T7 expression system. The first stage is dedicated to the maintenance of plasmid-bearing cells and the second stage to the target protein synthesis by induction of cells coming from the first stage. On entering the second stage, recombinant cells undergo a gradual induction of the target gene expression. These plasmid-bearing cells experience dynamic changes in intracellular compositions and specific growth rates with their individual residence times. Therefore, the overall cultural characteristics in the production stage are really averages of the contributions from the various cells with different residence times. The behavior of the two-stage culture is described by a model, which accounts for dynamic variations of cell growth and protein synthesis rates with cell residence times. Model simulations were compared with experimental results at a variety of operating conditions such as inducer concentration and dilution rate. This model is useful for understanding the behavior of two-stage continuous cultures. (c) 1993 John Wiley & Sons, Inc.     

An investigation of non-steady-state algal growth. I. An experimental model ecosystem

In order to test rigorously the transient behaviour of mathematical models of algal growth, detailed laboratory data sets with good temporal resolution are required. A series of algal growth experiments was conducted in transient conditions. Monoculture growth of, and competition for nutrients between, three contrasting species of phytoplankton (the diatom Thalassiosira pseudonana, the harmful flagellate Heterosigma carterae and the toxic dinoflagellate Alexandrium minutum) were investigated in different temperature, light and nutrient regimes. Although growth dynamics were qualitatively similar in batch culture, quantitative differences were evident in the growth response of the different species when grown in single yield-limiting nutrient conditions in identical physical conditions. Quantities such as the carbon:nitrogen (C:N) ratio and C and N per cell varied between species and within species under different growth conditions. Such results have particular significance to the development of mathematical models, which commonly represent algal populations as a single homogeneous group using a single currency such as numbers, C or N. Changes in light and temperature regime influenced algal growth: Alexandrium failed to grow at low temperatures, while specific growth rates of Thalassiosira were more sensitive to changes in temperature than those of Heterosigma. Changes in the dominant organism(s) and/or its size or nutrient status may influence the transfer of nutrients within the food web. Commonly, mathematical models make cell growth a function of a single yield-limiting nutrient. Decreased growth rates and high residual nutrient concentrations in competition experiments indicate that this approach is unlikely to be successful in conditions of limited supply of more than one nutrient, where multiple nutrient stresses will be significant.      

Experimental investigation and modeling of oscillatory behavior in the continuous culture of Zymomonas mobilis

The mechanism causing oscillation in continuous ethanol fermentation by Zymomonas mobilis under certain operating conditions has been examined. A new term, "dynamic specific growth rate," which considers inhibitory culture conditions in the recent past affecting subsequent cell behavior, is proposed in this article. Based on this concept, a model was formulated to simulate the oscillatory behavior in continuous fermentation of Zymomonas mobilis. Forced oscillation fermentation experiments, in which exogenous ethanol was added at a controlled rate to generate oscillatory behavior, were performed in order to obtain estimates for the model parameters and to validate the proposed model. In addition, data from a literature example of a sustained oscillation were analyzed by means of the model, and excellent agreement between the model simulation and experimental results was obtained. The lag in the cells' response to a changing environment, i.e., ethanol concentration change rate experienced by the cells, was shown to be the major factor contributing to the oscillatory behavior in continuous fermentation of Zymomonas mobilis under certain operating conditions. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 99-105, 1997.     

Segmented linear modeling of CHO fed‐batch culture and its application to large scale production

We describe a systematic approach to model CHO metabolism during biopharmaceutical production across a wide range of cell culture conditions. To this end, we applied the metabolic steady state concept. We analyzed and modeled the production rates of metabolites as a function of the specific growth rate. First, the total number of metabolic steady state phases and the location of the breakpoints were determined by recursive partitioning. For this, the smoothed derivative of the metabolic rates with respect to the growth rate were used followed by hierarchical clustering of the obtained partition. We then applied a piecewise regression to the metabolic rates with the previously determined number of phases. This allowed identifying the growth rates at which the cells underwent a metabolic shift. The resulting model with piecewise linear relationships between metabolic rates and the growth rate did well describe cellular metabolism in the fed‐batch cultures. Using the model structure and parameter values from a small‐scale cell culture (2 L) training dataset, it was possible to predict metabolic rates of new fed‐batch cultures just using the experimental specific growth rates. Such prediction was successful both at the laboratory scale with 2 L bioreactors but also at the production scale of 2000 L. This type of modeling provides a flexible framework to set a solid foundation for metabolic flux analysis and mechanistic type of modeling. Biotechnol. Bioeng. 2017;114: 785–797. © 2016 The Authors. Biotechnology and Bioengineering Published by Wiley Periodicals, Inc.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

Model-based analysis and design of a microchannel reactor for tissue engineering

Recently developed perfusion micro-bioreactors offer the promise of more physiologic in vitro systems for tissue engineering. Successful application of such bioreactors will require a method to characterize the bioreactor environment required to elicit desired cell function. We present a mathematical model to describe nutrient/growth factor transport and cell growth inside a microchannel bioreactor. Using the model, we first show that the nature of spatial gradients in nutrient concentration can be controlled by both design and operating conditions and are a strong function of cell uptake rates. Next, we extend our model to investigate the spatial distributions of cell-secreted soluble autocrine/paracrine growth factors in the bioreactor. We show that the convective transport associated with the continuous cell culture and possible media recirculation can significantly alter the concentration distribution of the soluble signaling molecules as compared to static culture experiments and hence needs special attention when adapting static culture protocols for the bioreactor. Further, using an unsteady state model, we find that spatial gradients in nutrient/growth factor concentrations can bring about spatial variations in the cell density distribution inside the bioreactor, which can result in lowered working volume of the bioreactor. Finally, we show that the nutrient and spatial limitations can dramatically affect the composition of a co-cultured cell population. Our results are significant for the development, design, and optimization of novel micro-channel systems for tissue engineering.     

A semicontinuous culture model that links cell growth to extracellular nutrient concentration

During semicontinuous culture, a sample of fixed volume is removed at regular time intervals to make measurements and/or harvest culture components, and an equal volume of fresh medium is immediately added to the culture, thereby instantaneously enhancing nutrient concentrations and diluting cell concentration. The resulting cell concentration versus time curve (i.e., the actual cell growth curve) has a saw-toothed appearance because of the periodic dilution of cell concentration. The observed cell concentrations correspond to the peaks of the saw-toothed curve. Cell growth rates are estimated from the locus of observed cell concentrations (i.e., from the apparent growth curve obtained by connecting the peaks of the saw-toothed curve). The sole preexisting model (Fencl's mode) for estimating cell growth rate is valid only when the cells are growing exponentially at a constant rate between samplings. This model has limited validity: despite the periodic enhancement of nutrient concentration, cell growth between samplings eventually causes nutrient depletion, and the cells cease to grow exponentially. Failure to recognize the limits of validity for Fencl' model has resulted in many erroneous applications of the model and, consequently, many incorrect estimates of cell growth rates. To provide a means for correctly estimating cell growth rates, Fencl's exponential model was extended, and a new model that describes the effects of nutrient depletion on cell growth in semi-continuous culture was obtained. The new model shows that exhaustion of a single growth-limiting nutrient in semicontinuous culture causes the locus of cell concentrations observed at time intervals of Deltat to follow a logistic growth curve. The actual cell growth rate was shown to equal the apparent logistic growth rate plus the effective dilution rate -Deltat(-1) In (1 - f), where f is the ratio of sample volume to total culture volume. Moreover, the model predicts that both the apparent logistic growth rate and the apparent steady-state cell concentration should rise linearly with the concentration of growth-limiting nutrient in the input medium, but fall linearly with increases in the effective dilution rate. The new logistic model for nutrient-limited cell growth in semicontinuous culture was successfully tested using published data for Asterionella formosa, Cyclotella meneghiniana, Daucus carota, and strain L mouse cells.     

An assessment of the role of physiological adaptation in the transient response of bacterial cultures

The RNA-limiting theory of transient response states that the primary physiological adaptation which occurs when microbial cultures are grown at specific rates less than their maximum is a decrease in the cellular level of RNA. It predicts that, as a result of this decrease, the response of the culture to a shift-up in growth rate will be limited by its RNA level. In order to test the RNA-limiting theory and to investigate the role physiological adaptation in transient response, experiments were performed in which steady-state chemostat cultures of Pseudomonasputida grown at various specific rates were transferred to batch reactors containing sufficient carbon source (L-lysine) and nutrients to remove all external growth restrictions. Samples were collected during the subsequent transient period for determination of the macromolecular composition and the maximum instantaneous oxygen uptake rate. The results indicated that, while decreases in the RNA level did significantly affect the nature of the transient response, other unidentified components varied with the steady-state specific growth rate at which the culture had been grown prior to the shift-up and that the levels of those components affected the nature of the subsequent transient response. This implies that the RNA-limiting theory is inadequate for describing the transient responses of cultures grown over a wide range of specific growth rates.     

A 3D Hybrid Model for Tissue Growth: The Interplay between Cell Population and Mass Transport Dynamics

To provide theoretical guidance for the design and in vitro cultivation of bioartificial tissues, we have developed a multiscale computational model that can describe the complex interplay between cell population and mass transport dynamics that governs the growth of tissues in three-dimensional scaffolds. The model has three components: a transient partial differential equation for the simultaneous diffusion and consumption of a limiting nutrient; a cellular automaton describing cell migration, proliferation, and collision; and equations that quantify how the varying nutrient concentration modulates cell division and migration. The hybrid discrete-continuous model was parallelized and solved on a distributed-memory multicomputer to study how transport limitations affect tissue regeneration rates under conditions encountered in typical bioreactors. Simulation results show that the severity of transport limitations can be estimated by the magnitude of two dimensionless groups: the Thiele modulus and the Biot number. Key parameters including the initial seeding mode, cell migration speed, and the hydrodynamic conditions in the bioreactor are shown to affect not only the overall rate, but also the pattern of tissue growth. This study lays the groundwork for more comprehensive models that can handle mixed cell cultures, multiple nutrients and growth factors, and other cellular processes, such as cell death.     

Continuous cultivation of fission yeast: Analysis of single-cell protein synthesis kinetics

A fundamental problem in microbial reactor analysis is identification of the relationship between environment and individual cell metabolic activity. Population balance equations provide a link between experimental measurements of composition frequency functions in microbial populations on the one hand and macromolecular synthesis kinetics and cell division control parameters for single cells on the other. Flow microfluorometry measurements of frequency functions for single-cell protein content in Schizosaccharomyces pombe in balanced exponential growth have been analyzed by two different methods. One approach utilizes the integrated form of the population balance equation known as the Collins-Richmond equation, and the other method involves optimization of parameters in assumed kinetic and cell division functional forms in order to best fit measured frequency functions with corresponding model solutions. Both data interpretation techniques indicate that rates of protein synthesis increase most in small protein content cells as the population specific growth rate increases, leading to parabolic single-cell protein synthesis kinetics at large specific growth rates. Utilization of frequency function data for an asynchronous population is shown in this case to be a far more sensitive method for determination of single-cell kinetics than is monitoring the metabolic dynamics of a single cell or, equivalently, synchronous culture analyses.