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.     

螺旋藻批式与连续培养及其生长动力学

在内循环气升式光生物反应器中,分别研究了螺旋藻细胞在批式和连续培养条件下的生长特性,结果表明：Richards模型和指数衰减模型可较好地描述批式培养时细胞和碳源底物浓度与培养时间的关系;批式培养时最大细胞生长速率为0371g/d/L,细胞对碳的得率系数为3.439g/gC;连续培养时随着稀释率的增大,细胞和底物浓度分别呈下降和上升趋势;连续培养时最大细胞产率为0.362g/L/d,最佳稀释率为0.45/d,细胞对碳的得率系数为2.050g/gC;所提出的连续培养动力学模型可较好地拟合实验数据。     

Predictive macroscopic modeling of cell growth,metabolism and monoclonal antibody production: Case study of a CHO fed-batch production

We describe a systematic approach to establish predictive models of CHO cell growth, cell metabolism and monoclonal antibody (mAb) formation during biopharmaceutical production. The prediction is based on a combination of an empirical metabolic model connecting extracellular metabolic fluxes with cellular growth and product formation with mixed Monod-inhibition type kinetics that we generalized to every possible external metabolite. We describe the maximum specific growth rate as a function of the integral viable cell density (IVCD). Moreover, we also take into account the accumulation of metabolites in intracellular pools that can influence cell growth. This is possible even without identification and quantification of these metabolites as illustrated with fed-batch cultures of Chinese Hamster Ovary (CHO) cells producing a mAb. The impact of cysteine and tryptophan on cell growth and cell productivity was assessed, and the resulting macroscopic model was successfully used to predict the impact of new, untested feeding strategies on cell growth and mAb production. This model combining piecewise linear relationships between metabolic rates, growth rate and production rate together with Monod-inhibition type models for cell growth did well in predicting cell culture performance in fed-batch cultures even outside the range of experimental data used for establishing the model. It could therefore also successfully be applied for in silico prediction of optimal operating conditions.     

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.     

Kinetic analysis of the effect of cell density on hybridoma cell growth in batch culture

The effect of cell density on cell growth was investigated in a suspension batch culture of hybridoma cells. The specific growth rate was found to increase with increasing initial cell density and then to decrease with further increases in initial cell density. In order to quantitatively describe the dependence of specific growth rate on cell density, a kinetic model is proposed, which satisfactorily represents the experimental data.     

Model for the feedback control system of bacterial growth. II. Growth in continuous culture

A mathematical model is developed that describes substrate limited bacterial growth in a continuous culture and that is based upon the conceptual framework elaborated in a previous paper for describing the feedback control system of cell growth [S. Bleecken, (1988). J. theor. Biol. 133, 37.] Central to the theory are the ideas that the limiting substrate is converted into low molecular weight building blocks of macromolecular synthesis which again are converted into biomass (RNA and protein) and that the rates of RNA and protein synthesis are controlled by the intracellular concentration of building blocks. It is shown that a continuous culture can be simulated by two interconnected feedback control systems the actuating signals of which are limiting substrate concentration and the intracellular concentration of building blocks, respectively. Three types of steady-states are found to appear in a continuous culture, besides the well-known stable steady-state of the whole culture there exist two batchlike steady-states of the biotic part of the culture which are metastable. The model is used to analyse the steady-states and their stability properties as well as the dynamic responses of biomass, RNA, protein, building block and substrate concentrations to changes in environmental conditions. Especially the inoculation of a continuous culture and the effects of step changes in dilution rate, inlet substrate concentration and growth temperature are studied in detail. Relations between the growth behaviour of a single cell and that of a continuous culture are derived. The RNA to protein ratio is introduced as a rough measure of the physiological state of cells and it is shown that a cell reacts to environmental changes with a simple pattern of basic responses in growth rate and physiological state. There are reasons to assume that the model presented is the minimal version of a structured model of bacterial growth and represents an optimum compromise between biological relevance and mathematical practicability.     

Identification of Growth Phases and Influencing Factors in Cultivations with AGE1.HN Cells Using Set-Based Methods

Production of bio-pharmaceuticals in cell culture, such as mammalian cells, is challenging. Mathematical models can provide support to the analysis, optimization, and the operation of production processes. In particular, unstructured models are suited for these purposes, since they can be tailored to particular process conditions. To this end, growth phases and the most relevant factors influencing cell growth and product formation have to be identified. Due to noisy and erroneous experimental data, unknown kinetic parameters, and the large number of combinations of influencing factors, currently there are only limited structured approaches to tackle these issues. We outline a structured set-based approach to identify different growth phases and the factors influencing cell growth and metabolism. To this end, measurement uncertainties are taken explicitly into account to bound the time-dependent specific growth rate based on the observed increase of the cell concentration. Based on the bounds on the specific growth rate, we can identify qualitatively different growth phases and (in-)validate hypotheses on the factors influencing cell growth and metabolism. We apply the approach to a mammalian suspension cell line (AGE1.HN). We show that growth in batch culture can be divided into two main growth phases. The initial phase is characterized by exponential growth dynamics, which can be described consistently by a relatively simple unstructured and segregated model. The subsequent phase is characterized by a decrease in the specific growth rate, which, as shown, results from substrate limitation and the pH of the medium. An extended model is provided which describes the observed dynamics of cell growth and main metabolites, and the corresponding kinetic parameters as well as their confidence intervals are estimated. The study is complemented by an uncertainty and outlier analysis. Overall, we demonstrate utility of set-based methods for analyzing cell growth and metabolism under conditions of uncertainty.     

Improved vitality of experimental random dorsal skin flaps in rats treated with enriched cell culture medium

A defined, serum-free cell culture medium supplemented with nonsteroidal anabolic hormones, insulin, thyroxin, and growth hormone was found to accelerate wound healing by stimulating vascularized granulation tissue formation, epithelialization, and angiogenesis. The aim of this work was to study the effect of cell culture medium on the survival rate of cephalically based random dorsal skin flaps in an animal model. A total of 77 Sprague-Dawley rats were randomized into five treatment groups: pharmacologic delay with cell culture medium, flap enhancement with cell culture medium, surgical delay, biological delay with saline, and control. Statistically significant differences in distal flap necrosis were found among all groups (p<0.003). The rats treated with cell culture medium before flap elevation showed a significant increase in flap viability: a survival rate of 83 percent, compared with the control group, which demonstrated a survival rate of only 58 percent (p<0.0001). The surgical delay and the groups treated with cell culture medium yielded similar results with no significant difference between them. This study indicates that preoperative injection of cell culture medium may play a role in decreasing skin flap necrosis.     

Kinetic model of cell growth and secondary metabolite synthesis in plant cell culture ofThalictrum rugosum

A structured kinetic model was proposed to describe cell growth and synthesis of a secondary metabolite, berberine, in batch suspension culture ofThalictrum rugosum. The model was developed by representing the physiological state of the cell in terms of the activity and the viability, which can be estimated using the culture fluorescence measurement. In the proposed model, the cells were divided into three types; active-viable, nonactive-viable, and dead cells. The model was formulated in terms of cell growth (dry/fresh weight, activity, and viability), carbon source utilization (sucrose, glucose and fructose), and product formation (intracellular and extracellular berberine). The concept of cell expansion and the death phase were also included in this model to describe the sugar accumulation and the release of intracellular berberine into medium by cell lysis, respectively. The parameters used in this model were estimated based on the experimental results in conjunction with numerical optimization techniques. Satisfactory agreement between the model and experimental data was obtained. The proposed model could accurately predict cell growth and product synthesis as well as the distribution of the secondary metabolite between the cell and the medium. It is suggested that the proposed model could be extended as a useful framework for quantitative analysis of physiological characteristics in the other plant cell culture systems.     

Modeling suppression of cell death by Bcl-2 over-expression in myeloma NS0 6A1 cells

A novel population-balance model was employed to evaluate the suppression of cell death in myeloma NS0 6A1 cells metabolically engineered to over-express the apoptotic suppressor Bcl-2. The model is robust in its ability to simulate cell population dynamics in batch suspension culture and in response to thymidine-induced growth inhibition: 89% of simulated cell concentrations are within two standard deviations of experimental data. Kinetic rate constants in model equations suggest that Bcl-2 over-expression extends culture longevity from 6 days to at least 15 days by suppressing the specific rate of early apoptotic cell formation by more than 6-fold and necrotic cell formation by at least 3-fold, despite nearly a 3-fold decrease in initial cell growth rate and no significant change in the specific rate of late apoptotic cell formation. This computational analysis supports a mechanism in which Bcl-2 is a common mediator of early apoptotic and necrotic events occurring at rates that are dependent on cellular factors accumulating over time. The model has current application to the rational design of cell cultures through metabolic engineering for the industrial production of biopharmaceuticals.     

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.     

A novel model for studying Baculovirus infection process

In this paper, a new Ansatz for modelling the Baculovirus infection cycle is presented. The base of this model is the cell cycle distribution at the time of infection. It is possible to calculate the growth of the culture and the initiation of virus processing by considering cell cycle distribution. By taking into account the length of the viral genome and the polymerase activity, it is possible to calculate the virus production rate, which underlies a logistic growth. In the present work, a new hypothesis explaining the accelerated death rates of infected cells has been introduced. This assumption provides the possibilities of performing calculation without any fixed time intervals. The simulation was tested by comparing experimental data with the model prediction. Therefore, cell cycle distributions over the culture time and the growth behaviour of infected and non-infected insect cells were measured. A model, Baculovirus coding for GFP was employed for the present investigation, as it allows tracking the infection and determining the effectiveness of the infection, which is highly dependent on the cell density at the time of infection (TOI). Furthermore, the new model is is taken to simulate data gained from literature about virus release and adsorption. The new assumptions make the model more independent to fit into different cultivation systems.     

A general model for aerobic yeast growth: batch growth

A general model for aerobic yeast growth in batch culture is presented. It is based on the concept that the aerobic metabolism of all yeasts is determined by the relative sizes of the transport rate of sugar into the cell and the transport rate of respiratory intermediates into the mitochondrion. If the rate of sugar uptake rate exceeds the rate of transport of respiratory intermediates into the mitochondrion (as in Saccharomyces cerevisiae, S. uvarum, and S. pombe), the metabolism exhibits the features of ethanol excretion and limited specific oxygen uptake rate. If the rate of transport of respiratory intermediates into the mitochondrion is of the same order as the transport of sugar into the cell (as in Candida utilis), the metabolism is characterized by little or no ethanol excretion and a much higher specific oxygen uptake rate. Batch data from an extensive range of yeast and carbon sources is used to illustrate the use of this model. The ability of this model to fit such an extensive range of experimental data suggests that it can be used as a generalized model for aerobic yeast growth.     

A 3D in situ cell counter reveals that breast tumor cell (MDA‐MB‐231) proliferation rate is reduced by the collagen matrix density

Many cell types require the biophysical and biochemical cues within the 3D extracellular matrix (ECM) to exhibit their true physiologically relevant behavior. As a result, cell culture platforms have been evolving from traditional 2D petridish plates into 3D biomatrices, and there is a need for developing analytic tools to characterize 3D cell culture. The existing cell counting method, using a hemocytometer or coulter counter, requires that cells are suspended in fluids prior to counting. This poses a challenge for 3D cell culture as cells are embedded in a 3D biomatrix. We use a facile 3D cell counting method that overcomes this limitation and allows for in situ cell counting in a 3D cell culture using equipment that is commonly available in a biology lab. Using a breast tumor cell line, MDA‐MB‐231, as a model system, we demonstrated that MDA‐MB‐231 cells (1) grow slower within a 3D collagen matrix than on a 2D substrate for an extended growth time (a week) with a comparable, initial cell‐to‐cell distance, (2) their cell growth rate decreases with the increase of collagen concentration, showing a linear growth rate rather than an exponential growth rate. Further work using flow cytometry showed that the observed growth rate reduction was consistent with the retardation of the transition to S (synthesis) phase in the cell cycle. This work demonstrates the validity of the 3D cell counting method and the importance of cell–ECM interactions in cell proliferation. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:990–996, 2015     

Analysis of cell cycle activity and population dynamics in heterogeneous plant cell suspensions using flow cytometry

Flow cytometry was used to measure cell cycle parameters in Solanum aviculare plant cell suspensions. Methods for bromodeoxyuridine (BrdU) labeling of plant nuclei were developed so that cell cycle times and the proportion of cells participating in growth could be determined as a function of culture time and conditions. The percentage of cells active in the cell cycle at 25 degrees C decreased from 52% to 19% within 7.6 d of culture; presence of a relatively large proportion of non-active cells was reflected in the results for culture growth. While the maximum specific growth rate of the suspensions at 25 degrees C was 0.34 d-1 (doubling time: 2.0 d), the specific growth rate of active cells was significantly greater at 0.67 d-1, corresponding to a cell cycle time of 1.0 d. A simple model of culture growth based on exponential and linear growth kinetics and the assumption of constant cell cycle time was found to predict with reasonable accuracy the proportion of active cells in the population as a function of time. Reducing the temperature to 17 degrees C lowered the culture growth rate but prolonged the exponential growth phase compared with 25 degrees C; the percentage of cells participating in the cell cycle was also higher. Exposure of plant cells to different agitation intensities in shake flasks had a pronounced effect on the distribution of cells within the cell cycle. The proportion of cells in S phase was 1.8 times higher at a shaker speed of 160 rpm than at 100 rpm, while the frequency of G0 + G1 cells decreased by up to 27%. Because of the significant levels of intraculture heterogeneity in suspended plant cell systems, flow cytometry is of particular value in characterizing culture properties and behavior.     

A simple model to describe transient differences between cell number and biomass growth rates of Escherichia coli

Information on the response of a microbial culture to dynamic environmental conditions is necessary for the design of transient operation processes. However, most attempts at modelling culture response have been directed at describing the steady-state behavior. Thus, there is a need for adequate dynamic models for process design. Simulations of nutrient shifts were completed using a "single-cell" model for Escherichia coli. It was discovered that the specific mass growth rate and the specific number of cells growth rate were different under transient conditions, whereas at steady state (balanced growth) these rates are equivalent. Using these observations, a simple delay model to describe the transient behavior of the two growth rates is formulated and tested. The model contains as state variables only the readily measurable macroscopic quantities (biomass, cell number, and limiting nutrient). This model agreed well with the predictions of the single-cell model.     

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.     

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.     

Application of a simple unstructured kinetic and cost of goods models to support T-cell therapy manufacture

Manufacturing of cell therapy products requires sufficient understanding of the cell culture variables and associated mechanisms for adequate control and risk analysis. The aim of this study was to apply an unstructured ordinary differential equation-based model for prediction of T-cell bioprocess outcomes as a function of process input parameters. A series of models were developed to represent the growth of T-cells as a function of time, culture volumes, cell densities, and glucose concentration using data from the Ambr®15 stirred bioreactor system. The models were sufficiently representative of the process to predict the glucose and volume provision required to maintain cell growth rate and quantitatively defined the relationship between glucose concentration, cell growth rate, and glucose utilization rate. The models demonstrated that although glucose is a limiting factor in batch supplied medium, a delivery rate of glucose at significantly less than the maximal specific consumption rate (0.05 mg 1 × 10⁶ cell h⁻¹) will adequately sustain cell growth due to a lower glucose Monod constant determining glucose consumption rate relative to the glucose Monod constant determining cell growth rate. The resultant volume and exchange requirements were used as inputs to an operational BioSolve cost model to suggest a cost-effective T-cell manufacturing process with minimum cost of goods per million cells produced and optimal volumetric productivity in a manufacturing settings. These findings highlight the potential of a simple unstructured model of T-cell growth in a stirred tank system to provide a framework for control and optimization of bioprocesses for manufacture.     

Exponential growth kinetics for Polyporus versicolor and Pleurotus ostreatus in submerged culture.

Simple mathematical models for a batch culture of pellet-forming fungi in submerged culture were tested on growth data for Polyporus versicolor (ATCC 12679) and Pleurotus ostreatus (ATCC 9415). A kinetic model based on a growth rate proportional to the two-thirds power of the cell mass was shown to be satisfactory. A model based on a growth rate directly proportional to the cell mass fitted the data equally well, however, and may be preferable because of mathematical simplicity.