Analysis of the kinetic growth patterns of cultured cells. III. The effect of inoculation density, of a geroprotector-antioxidant and of stationary-phase aging

With the help of a previously devised model of cultured cell growth kinetics it was shown that the "plateau" level on the growth curve of human embryo diploid fibroblasts increased, if the cells were grown with Epigid geroprotector-antioxidant (equal results with two drug concentrations: 10(-5) and 10(-7) M, resp.). It was also found that the "plateau" level on the growth curve of cultured "3 days aged" Chinese hamster cells (subcultivated to a fresh medium 3 days after a 1:6 subcultivation) lays higher than the "plateau" level of "14 days aged" cells but lower than that of "7 day aged" cells. Furthermore it was shown that an increase in inoculation density of Chinese hamster cells increased proportionately the rate of cell population growth but had a little effect on the "plateau" level of the growth curve. The data obtained are discussed in terms of some "proliferative" theories of cellular ageing.     

Analysis of DNA synthesis rate of cultured cells from flow cytometric data

The rate of DNA synthesis along S phase is estimated from flow cytometric histograms on the basis of a mathematical model of a cell population. In the absence of loss, the model expresses the population kinetics in terms of DNA synthesis rate, S-phase influx, and population size. A single histogram is sufficient to determine the DNA synthesis rate when the population is in balanced exponential growth. Two suitably chosen histograms are necessary if the S-phase influx is exponential in a time interval longer than the S-phase duration. The analysis procedure was tested on published autoradiographic data and applied to three cultured cell lines (CM-S, 3LL, and M14 cells) that show various patterns of DNA distribution. In each case the cell-cycle fractions, the DNA synthesis rate, and the S-phase duration were obtained.     

Different growth patterns of a cancer cell population as a function of its starting growth characteristics: analysis by mathematical modelling

The growth kinetics of a cancer cell population as a function of the total number of cells and the proportion of proliferating and resting cells at the beginning of the growth has been analysed by a mathematical model. The model takes into account the processes of cell division, death and transition from proliferation to rest and backwards. It is shown that a single cell population growing under the same environmental conditions has an extremely broad spectrum of growth patterns. The whole multiplicity of possible growth patterns has been determined by the inherent cellular growth characteristics of the population, while the growth pattern actually realized of the variety of growth curves depends on the total number of cells and the proportion of proliferating and resting cells at the initial moment of growth. The model is shown to provide a good prediction of experimentally measured kinetics of regrowth of tumour cells subcultured after various times of the growth in unfed cultures, and the kinetics of tumour cell growth after severe hypoxia. The role of cell transitions between proliferating and resting stages in the problem of growth control is discussed.     

Individual‐based and stochastic modeling of cell population dynamics considering substrate dependency

In this article, we propose an individual‐based and stochastic modeling approach that is capable of describing the bacterial cell population dynamics during a batch culture. All stochastic nature inherent in intracellular molecular level reactions and cell division processes were considered in a single model framework by embedding a sub‐model describing individual cell's growth kinetics in a discrete event simulation algorithm. The resultant unique feature of the model is that the effects of the stochasticities on the cell population dynamics can be investigated for different substrate‐dependent cell growth kinetics. When Monod kinetics was used as the sub‐model, the stochasticities only slightly affected the cell mass increase and substrate consumption profiles during the batch culture although they were still important in describing the changes of cell population distributions. When Andrews substrate inhibition kinetics was used, however, it was revealed that the overall cell population dynamics could be seriously influenced by the stochasticities. Under a critical initial substrate level, the cell population could proliferate against the substrate inhibition only when the stochasticities were considered. Biotechnol. Bioeng. 2009;103: 891–899. © 2009 Wiley Periodicals, Inc.     

Proliferation kinetics of MCF-7 cell cultures. I. Relative influence of estrogens and antiestrogens on the growth of the cell population

The cellular hormone dependent cell line MCF-7 is a tumoral model of mammary cancer the growth kinetics of which operating under the influence of varied and opposed hormonal factors (estrogens and antiestrogens at precise concentration levels) has provided the means of knowing the action mechanisms of such agents. In this study, carried out with cultured MCF-7 cells under well defined experimental conditions, it has been shown that: 1) antiestrogens (OH-TAM) seem to be opposed to the growing process of the cellular population the elements of which, under the influence of OH-TAM, double the value of the parameter TD (Doubling Time); 2) estrogens (17-beta-E2) cancel out this effect and promote the growth of MCF-7 cells whether OH-TAM is previously or simultaneously added to the culture medium; 3) the observation of this estrogenic action needs accurate experimental conditions without which the effect may not be seen.     

Population dynamics of human activated natural killer cells in culture

The growth kinetics and population dynamics of recombinent interleukin-2 (rlL-2) stimulated human natural killer (NK) cell-enriched populations were studied in vitro. The NK-enriched populations was obtained from normal peripheral blood mononuclear cells (PBMNC) by immunomagnetic bead depletion of CD3(+) and CD5(+) T cells. The growth kinetics of NK cells, T cells, monocytes, and total cells are shown. In the absence of PBMNC accessory cells, the NK-enriched population showed limited expansion. In the presence of PBMNC accessory cells, the NK-enriched population expanded threefold more than in the absence of accessory cells due to increased NK cell growth rate and increased duration of exponential growth. Using a Transwell system, which separates two cell population by a polycarbonate membrane, the accessory cells were shown to act on the NK-enriched population via a diffusible factor. Accessory cell conditioned media was able to replace the accessory cell population to stimulate NK cell expansion. A monocyte-enriched population prepared by sheep red blood cell rosetting of T cells was extensively phenotyped and compared with the NK-enriched populations. Although the final cultured cells were phenotypically homogeneous for CD56(+)/CD3(-) NK cells, the initial NK precusor populations appear to be different. Namely, the NK cell precursors in the monocyte-enriched population were predominantly CD56(+)/CD2(-). Kinetic equations were formulated for this culture system and the effects of major culture variables are investigated.     

Stathmokinetic Analysis of Human Epidermal Cells in vitro

Proliferation kinetics of cultured human epidermal cells is characterized in quantitative terms. Three distinct subpopulations of keratinocytes, two of which are cycling have been discriminated by two parameter DNA/RNA flow cytometry. Based on mathematical modelling, the cell cycle parameters of the cycling subpopulations have been assessed from stathmokinetic data collected at different time points after initiation of cultures (7–15 days). the first subpopulation is composed of low-RNA cells which resemble basal keratinocytes of epidermis and which show some characteristics of stem cells; these cells have a mean generation time of approximately 100 hr. the second subpopulation consists of high-RNA cells, resembling stratum spinosum cells of epidermis, which have an average generation time of approximately 40 hr. the third subpopulation consists of non-cycling cells with G_o/G₁ DNA content, with cytochemical features similar to those of cells in granular layer of epidermis. The results based on modelling can reproduce with acceptable accuracy the actual growth curve of the cultured cell population. Analysis of kinetics and differentiation of human keratinocytes is of interest in view of the recent application of cultured epidermal cell sheets for transplantation onto burn wounds. the results of this study also reveal the existence of regulatory mechanisms associated with proliferation and differentiation in the cultured epidermal cell population.     

Analysis of the kinetic growth patterns of cultured cells. II. The action of ionizing radiation, an alkylating agent and a low-frequency electromagnetic field

With the help of the earlier devised model of cultured cell growth kinetics it is shown that the "plateau" level on the growth curve of Chinese hamster cells decreased proportionally to a dose of the agent applied after a short-term treatment by gamma-radiation or by alkylating agent thiophosphamide. The analysis of our own and literature data enabled us to propose that the lowering of the growth curve may testify to the geropromoter character (i.e. manifesting in ageing promoting) of the investigated factor action. As the low-frequency electromagnetic field induces similar changes in the growth curve, it is related (together with both the above factors investigated) to geropromoters.     

A cellular automaton model for microcarrier cultures

In order to achieve high cell densities anchoragedependent cells are commonly cultured on microcarriers, where spatial restrictions to cell growth complicates the determination of the growth kinetics. To design and operate large-scale bioreactors for microcarrier cultures, the effect of this spatial restriction to growth, referred to as contact inhibition, must be decoupled from the growth kinetics. In this article, a cellular automaton approach is recommended to model the growth of anchorage-dependent cells on microcarriers. The proposed model is simple to apply yet provides an accurate representation of contact-inhibited cell growth on microcarriers. The distribution of the number of neighboring cells per cell, microcarrier surface areas, and inoculation densities are taken into account with this model. When compared with experimental data for Vero and MRC-5 microcarrier cultures, the cellular automaton predictions were very good. Furthermore, the model can be used to generate contact-inhibition growth curves to decouple the effect of contact-inhibition from growth kinetics. With this information, the accurate determination of kinetic parameters, such as nutrient uptake rates, and the effects of other environmental factors, such as toxin levels, may be determined. (c) 1994 John Wiley & Sons, Inc.     

Monte Carlo simulation of malignant growth. Examples of the behavior of chloroleukemia after specific perturbations

This paper describes a stochastic model of cell population growth constructed to simulate biological reality in different experimental conditions. Using the computer program developed, the behavior of the cell population and of several experimentally measurable kinetic parameters was studied after specific perturbations, especially those involving sudden changes in the duration of the G₁ phase of the cell cycle (chalone action). It was demonstrated that mere prolongation of the G₁ phase can lead to tumor regression. The results also showed that it is sometimes difficult, if not impossible, intuitively to reach a correct interpretation of seemingly unequivocal biological data and, hence, that conclusions regarding cell population kinetics are hazardous without the aid of a rigorous model.     

A novel population balance model to investigate the kinetics of in vitro cell proliferation: part II. Numerical solution, parameters' determination, and model outcomes

Based on the general theoretical model developed in Part I of this work, a series of numerical simulations related to the in vitro proliferation kinetics of adherent cells is here presented. First the complex task of assigning a specific value to all the parameters of the proposed population balance (PB) model is addressed, by also highlighting the difficulties arising when performing proper comparisons with experimental data. Then, a parametric sensitivity analysis is performed, thus identifying the more relevant parameters from a kinetics perspective. The proposed PB model can be adapted to describe cell growth under various conditions, by properly changing the value of the adjustable parameters. For this reason, model parameters able to mimic cell culture behavior under microgravity conditions are identified by means of a suitable parametric sensitivity analysis. Specifically, it is found that, as the volume growth parameter is reduced, proliferation slows down while cells arrest in G0/G1 or G2/M depending on the initial distribution of cell population. On the basis of this result, model capabilities have been tested by means of a proper comparison with literature experimental data related to the behavior of synchronized and not-synchronized cells under micro- and standard gravity levels.     

Individual-based and continuum models of growing cell populations: a comparison

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.     

Effects of spatial variation of cells and nutrient and product concentrations coupled with product inhibition on cell growth in a polymer scaffold.

The effects of spatial variation of cells and nutrient and product concentration, in combination with product inhibition in cell growth kinetics on chondrocyte generation in a polymer scaffold, are analyzed. Experimental studies reported previously have demonstrated spatial dependence in the cultivation of chondrocytes. In the present study, the cell-polymer system is assumed to consist of two distinct phases. The cells, fluid, polymer matrix, and extracellular matrix comprise one phase, and the other phase consists of a fluid and polymer matrix. The only two species in the fluid considered to affect cell growth are the nutrient and product. The multiphase transport process of these two species in the cell-polymer system is described by the species continuity equations and corresponding boundary conditions for each individual phase. A volume-averaging approach is utilized for this system to derive averaged species continuity equations for the nutrient and product concentrations. The volume-averaging approach allows for a single species in a two-phase system to be represented by a single averaged continuity equation. Competitive product inhibition, saturation kinetics of substrate, and cell population control are assumed to affect the cell growth kinetics. A modified Contois growth kinetic model is used to represent the three factors that affect cell growth. A parameter analysis is performed and the results are compared qualitatively with experimental data found in the literature.     

Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro

We present a three-dimensional individual cell-based, biophysical model to study the effect of normal and malfunctioning growth regulation and control on the spatial-temporal organization of growing cell populations in vitro. The model includes explicit representations of typical epithelial cell growth regulation and control mechanisms, namely 1), a cell-cell contact-mediated form of growth inhibition; 2), a cell-substrate contact-dependent cell-cycle arrest; and 3), a cell-substrate contact-dependent programmed cell death (anoikis). The model cells are characterized by experimentally accessible biomechanical and cell-biological parameters. First, we study by variation of these cell-specific parameters which of them affect the macroscopic morphology and growth kinetics of a cell population within the initial expanding phase. Second, we apply selective knockouts of growth regulation and control mechanisms to investigate how the different mechanisms collectively act together. Thereby our simulation studies cover the growth behavior of epithelial cell populations ranging from undifferentiated stem cell populations via transformed variants up to tumor cell lines in vitro. We find that the cell-specific parameters, and in particular the strength of the cell-substrate anchorage, have a significant impact on the population morphology. Furthermore, they control the efficacy of the growth regulation and control mechanisms, and consequently tune the transition from controlled to uncontrolled growth that is induced by the failures of these mechanisms. Interestingly, however, we find the qualitative and quantitative growth kinetics to be remarkably robust against variations of cell-specific parameters. We compare our simulation results with experimental findings on a number of epithelial and tumor cell populations and suggest in vitro experiments to test our model predictions.     

Stathmokinetic analysis of human epidermal cells in vitro

Proliferation kinetics of cultured human epidermal cells is characterized in quantitative terms. Three distinct subpopulations of keratinocytes, two of which are cycling, have been discriminated by two parameter DNA/RNA flow cytometry. Based on mathematical modelling, the cell cycle parameters of the cycling subpopulations have been assessed from stathmokinetic data collected at different time points after initiation of cultures (7-15 days). The first subpopulation is composed of low-RNA cells which resemble basal keratinocytes of epidermis and which show some characteristics of stem cells; these cells have a mean generation time of approximately 100 hr. The second subpopulation consists of high-RNA cells, resembling stratum spinosum cells of epidermis, which have an average generation time of approximately 40 hr. The third subpopulation consists of non-cycling cells with G0/G1 DNA content, with cytochemical features similar to those of cells in granular layer of epidermis. The results based on modelling can reproduce with acceptable accuracy the actual growth curve of the cultured cell population. Analysis of kinetics and differentiation of human keratinocytes is of interest in view of the recent application of cultured epidermal cell sheets for transplantation onto burn wounds. The results of this study also reveal the existence of regulatory mechanisms associated with proliferation and differentiation in the cultured epidermal cell population.     

波动温度下罗非鱼特定腐败菌生长动力学模型和货架期预测

研究了0℃~15℃范围的波动温度条件下,有氧贮藏养殖罗非鱼的特定腐败菌-假单胞菌的生长动力学模型及其对剩余货架期预测的适用性。由Belehradek方程建立了温度对假单胞菌生长动力学影响的数学模型,在设计的两种波动温度条件下假单胞菌生长动力学模型的预测值,与波动温度贮藏罗非鱼中假单胞菌生长的实测值比较,偏差度在0.906~0.942之间,准确度在1.13~1.19之间。以假单胞菌生长动力学模型预测的剩余货架期,与波动温度贮藏罗非鱼的感官、VBN和假单胞菌数评价获得的实测剩余货架期相比较,相对误差分别为5.9%和-9.1%。显示在贮藏温度波动的情况下,假单胞菌生长动力学模型同样可以快速可靠地实时预测0℃~15℃贮藏的罗非鱼剩余货架期。     

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.     

Generality of the growth kinetics of the average individual cell in different bacterial populations.

The kinetics of growth of all the cells in a population is reflected in the shape of the size distribution of the population. To ascertain whether the kinetics of growth of the average individual cell is similar for different strains or growth conditions, we compared the shape of normalized size distributions obtained from steady-state populations. Significant differences in the size distributions were found, but these could be ascribed either to the precision achieved at division or to a constriction period which is long relative to the total cell cycle time. The remaining difference is quite small. Thus, without establishing the pattern itself, it is concluded that the basic course of growth is very similar for the various Escherichia coli strains examined and probably also for other rod-shaped bacteria. The effects of differences in culture technique (batch or chemostat culture), growth rate, and differences among strains were not found to influence the shape of the size distributions and hence the growth kinetics in a direct manner; small differences were found, but only when the precision at division or the fraction of constricted cells (long constriction period) were different as well.     

Global analysis of endothelial cell line proliferation patterns based on nutrient-depletion models: implications for a standardization of cell proliferation assays

It is known that cell populations growing in different environmental conditions may exhibit different proliferation patterns. However, it is not clear if, despite the diversity of the so-observed patterns, inherent cellular growth characteristics of the population can nevertheless be determined. This study quantifies the proliferative behaviour of the permanent endothelial human cell line, Eahy926, and establishes to which extent the estimation of the cell proliferation rate depends on variations of the experimental protocols. Cell proliferation curves were obtained for cells cultured over 16 days and the influences of cell seeding densities, foetal bovine serum content and frequency of culture medium changes were investigated. Quantitative dynamic modelling was conducted to evaluate the kinetic characteristics of this cell population. We proposed successive models and retained a nutrient-depletion toxicity dependant model, which takes into account the progressive depletion of nutrients, as well as the increase of toxicity in the cell culture medium. This model is shown to provide a very good and robust prediction of the experimental proliferation curves, whatever are the considered frequency of culture medium changes and serum concentrations. Thus, the model enables an intrinsic quantification of the parameters driving in vitro EAhy926 proliferation, including proliferation, nutrient consumption and toxicity increase rates, rather independently of the experiments design. We therefore propose that such models could provide a basis for a standardized quantification of intrinsic cell proliferation kinetics.     

Dissociation between early loss of actin fibres and subsequent cell death in serum-deprived quiescent Balb/c-3T3 cells

Serum withdrawal from either growing or quiescent Balb/c-3T3 murine fibroblasts causes a loss of F-actin fibres and focal adhesions within 30 min. Cells that are growing survive serum deprivation, whereas the great majority of density-arrested quiescent cells die during a period of up to 5 h from serum withdrawal. During this time an approximately constant fraction of the quiescent cell population dies per unit time. The population half-life is 60–70 min during this time. Addition of an appropriate cell growth factor or second messenger agonist at the time of serum withdrawal or within 2 h after serum withdawal protects a similar fraction of viable cells. These findings suggest a model according to which withdrawal of serum (i.e. growth factors) initiates the death process in cells of the population with kinetics that approximate first-order kinetics. We postulate that appropriate growth factors or second messenger agonists block the initiating event that starts the cell death process.