A cellular automaton model for the proliferation of migrating contact-inhibited cells.

A cellular automaton is used to develop a model describing the proliferation dynamics of populations of migrating, contact-inhibited cells. Simulations are carried out on two-dimensional networks of computational sites that are finite-state automata. The discrete model incorporates all the essential features of the cell locomotion and division processes, including the complicated dynamic phenomena occurring when cells collide. In addition, model parameters can be evaluated by using data from long-term tracking and analysis of cell locomotion. Simulation results are analyzed to determine how the competing processes of contact inhibition and cell migration affect the proliferation rates. The relation between cell density and contact inhibition is probed by following the temporal evolution of the population-average speed of locomotion. Our results show that the seeding cell density, the population-average speed of locomotion, and the spatial distribution of the seed cells are crucial parameters in determining the temporal evolution of cell proliferation rates. The model successfully predicts the effect of cell motility on the growth of isolated megacolonies of keratinocytes, and simulation results agree very well with experimental data. Model predictions also agree well with experimentally measured proliferation rates of bovine pulmonary artery endothelial cells (BPAE) cultured in the presence of a growth factor (bFGF) that up-regulates cell motility.     

Evidence for ERK1/2 phosphorylation controlling contact inhibition of proliferation in Madin-Darby canine kidney epithelial cells

Increasing cell density arrests epithelial cell proliferation by a process termed contact inhibition. We investigated mechanisms of contact inhibition using a model of contact-inhibited epithelial cells. Hepatocyte growth factor (HGF) treatment of contact-inhibited Madin-Darby canine kidney (MDCK) cells stimulated cell proliferation and increased levels of phosphorylated ERK1/2 (phospho-ERK1/2) and cyclin D1. MEK inhibitors PD-98059 and U0126 inhibited these HGF-dependent changes, indicating the dependence on phosphorylation of ERK1/2 during HGF-induced loss of contact inhibition. In relation to contact-inhibited high-density cells, low-density MDCK cells proliferated and had higher levels of phospho-ERK1/2 and cyclin D1. PD-98059 and U0126 inhibited low-density MDCK cell proliferation. Trypsinization of high-density MDCK cells immediately increased phospho-ERK1/2 and was followed by a transient increase in cyclin D1 levels. Reformation of cell junctions after trypsinization led to decreases in phospho-ERK1/2 and cyclin D1 levels. High-density MDCK cells express low levels of both cyclin D1 and phospho-ERK1/2, and treatment of these cells with fresh medium containing HGF but not fresh medium alone for 6 h increased phospho-ERK1/2 and cyclin D1 levels compared with cells without medium change. These data provide evidence that HGF abrogates MDCK cell contact inhibition by increasing ERK1/2 phosphorylation and levels of cyclin D1. These results suggest that in MDCK cells, contact inhibition of cell proliferation in the presence of serum occurs by cell density-dependent regulation of ERK1/2 phosphorylation. cell density; cyclin D1; hepatocyte growth factor; cell cycle; extracellular signal-regulated kinases     

Cell population dynamics modulate the rates of tissue growth processes

The development and testing of a discrete model describing the dynamic process of tissue growth in three-dimensional scaffolds is presented. The model considers populations of cells that execute persistent random walks on the computational grid, collide, and proliferate until they reach confluence. To isolate the effect of population dynamics on tissue growth, the model assumes that nutrient and growth factor concentrations remain constant in space and time. Simulations start either by distributing the seed cells uniformly and randomly throughout the scaffold, or from an initial condition designed to simulate the migration and cell proliferation phase of wound healing. Simulations with uniform seeding show that cell migration enhances tissue growth by counterbalancing the adverse effects of contact inhibition. This beneficial effect, however, diminishes and disappears completely for large migration speeds. By contrast, simulations with the "wound" seeding mode show a continual enhancement of tissue regeneration rates with increasing cell migration speeds. We conclude that cell locomotory parameters and the spatial distribution of seed cells can have profound effects on the dynamics of the process and, consequently, on the pattern and rates of tissue growth. These results can guide the design of experiments for testing the effectiveness of biomimetic modifications for stimulating tissue growth.     

Proliferation of anchorage-dependent contact-inhibited cells. II: experimental results and validation of the theoretical models

This study establishes that the cellular automata models developed in an earlier article capture the essential features of the proliferation process for anchorage-dependent contact-inhibited cells. Model predictions are in excellent agreement with experimental data obtained with bovine pulmonary artery endothelial cells. The models are particularly suitable for predictive purposes since they have no adjustable parameters. All model parameters can be easily obtained from a priori measurements. Our studies also show that proliferation rates are very sensitive to the spatial distributions of seed cells. The adverse effects of seeding heterogeneities become more pronounced as a cell population approaches confluency and they should be accounted for in experimental studies attempting to assess the response of cells to external stimuli.     

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.     

Modeling of contact-inhibited animal cell growth on flat surfaces and spheres

A model of contact-inhibited growth of cells on flat and spherical surfaces is presented. It shows that contact inhibition does not significantly affect the calculated growth rate of cells unless they are allowed to multiply a large amount from the original seeding density. Microcarriers seeded at low densities require long times to reach confluence because contact inhibition becomes important. In systems with both growth and separate cell death, the equilibrium fraction of holes in the confluent monolayer is below 8% if the death rate is less than half the growth rate, but increases rapidly as the death rate increases from that value.     

Reentry into the cell cycle of contact-inhibited vascular endothelial cells by a phosphatase inhibitor. Possible involvement of extracellular signal-regulated kinase and phosphatidylinositol 3-kinase

Vascular endothelial cells are unique in that they exit from the cell cycle when they come into contact with each other. Although the phenomenon is called "contact inhibition," little is known about the cellular mechanisms involved. Here we show that the phosphatase inhibitor sodium orthovanadate (SOV) induced the reentry of contact-inhibited human umbilical vascular endothelial cells (HUVECs) into the cell cycle and that reentry was associated with activation of the extracellular signal-regulated kinase (ERK) and phosphatidylinositol 3-kinase (PI 3-K)/Akt pathways. SOV stimulated [(3)H]thymidine uptake of contact-inhibited HUVECs in a time- and dose-dependent manner. SOV-induced increase in [(3)H]thymidine uptake was significantly inhibited by the mitogen-activated protein kinase kinase inhibitor PD98059 and by the PI 3-K inhibitor LY294002. SOV also stimulated the expression of cyclin D1, cyclin E, and cyclin A, and the activity of CDK2 kinase, whereas it decreased the expression of p27(kip1). In marked contrast, growth media alone did not induce these changes. Furthermore, these SOV-induced changes were abolished by pretreatment with PD98059 and LY294002. SOV stimulated phosphorylation of ERK and Akt in contact-inhibited HUVECs, while growth media alone did not. This phosphorylation was associated with inhibition of phosphatase activity in the cells. Finally, overexpression of high cell density-enhanced protein tyrosine phosphatase 1 inhibited c-fos and cyclin A promoter activity. Taken together, our results suggest that in contact-inhibited HUVECs, increased phosphatase activity suppressed the ERK and PI 3-K/Akt pathways, resulting in exit from the cell cycle by down-regulation of cyclin D1, cyclin E, and cyclin A and by up-regulation of p27(kip1).     

Anchorage-dependent chick embryo fibroblasts synthesise DNA and proliferate when cultured in multilayered sheets suspended among glass fibres.

Chick embryo fibroblasts (CEFs) spontaneously form multicellular and multilayered sheets suspended on the network of glass fibres which are stabilized by fibronectin containing protein deposits located at cell-to-cell contacts. The cells situated within the sheets are surrounded by the neighbouring cells and their mechanical equilibrium is stabilised by intercellular "parabaric" effects. It was found that CEFs in the sheets retain relatively high mitotic activity corresponding to that observed in sparse monolayer cultures. These cells grew up to much higher local density than in confluent and contact-inhibited monolayer cultures and developed an abundance of microfilament bundles that terminated at vinculin-containing protein complexes. The results presented demonstrate that direct contact with solid substratum, cell-to-cell contacts, local cell density, and intercellular exchange of humoral factors are not directly involved in the density-dependent inhibition of growth observed in monolayer cultures. They also support the concepts concerning the role of mechanical equilibrium of cell membrane and sub-membranous cytoskeleton in the regulation of proliferation of non-transformed cells.     

Segregated mathematical model for growth of anchorage-dependent MDCK cells in microcarrier culture

To describe the growth behavior of anchorage-dependent mammalian cells in microcarrier systems, various approaches comprising deterministic and stochastic single cell models as well as automaton-based models have been presented in the past. The growth restriction of these often contact-inhibited cells by spatial effects is described at levels with different complexity but for the most part not taking into account their metabolic background. Compared to suspension cell lines these cells have a comparatively long lag phase required for attachment and start of proliferation on the microcarrier. After an initial phase of exponential growth only a moderate specific growth rate is achieved due to restrictions in space available for cell growth, limiting medium components, and accumulation of growth inhibitors. Here, a basic deterministic unstructured segregated cell model for growth of Madin Darby Canine Kidney (MDCK) cells used in influenza vaccine production is described. Four classes of cells are considered: cells on microcarriers, cells in suspension, dead cells, and lysed cells. Based on experimental data, cell attachment and detachment is taken explicitly into account. The model allows simulation of the overall growth behavior in microcarrier culture, including the lag phase. In addition, it describes the time course of uptake and release of key metabolites and the identification of parameters relevant for the design and optimization of vaccine manufacturing processes.     

A novel population balance model to investigate the kinetics of in vitro cell proliferation: part I. Model development

In biotechnology and biomedicine reliable models of cell proliferation kinetics need to capture the relevant phenomena taking place during the mitotic cycle. To this aim, a novel mathematical model helpful to investigate the intrinsic kinetics of in vitro culture of adherent cells up to confluence is proposed in this work. Specifically, the attention is focused on the simulation of proliferation (increase of cell number) and maturation (increase of cell size and DNA content) till contact inhibition eventually takes place inside a Petri dish. Accordingly, the proposed model is based on a population balance (PB) approach that allows one to quantitatively describe cell cycle progression through the different phases the cells of the entire population experienced during their own life. In particular, the proposed model has been developed as a 2D, multi-staged, and unstructured PB, by considering a different sub-population of cells for any single phase of the cell cycle. These sub-populations are discriminated through cellular volume and DNA content, that both increase during the mitotic cycle. The adopted mathematical expressions of the transition rates between two subsequent phases and the temporal increase of cell volume and DNA content are thoroughly analyzed and discussed with respect to those ones available in the literature. Specifically, the corresponding uncertainties and pitfalls are pointed out, by also taking into account the difficulties and the limitations involved in the quantitative measurements currently practicable for these biological systems. A novel mathematical expression for contact inhibition in line with the PB model developed is also formulated, along with a proper comparison between modeled and measurable DNA distributions. The strategy for a reliable, independent tuning of the adjustable parameters involved in the proposed model along with its numerical solution is outlined in Part II of this work, where it is also shown how it can be profitably used to gain a deeper insight into the phenomena involved during cell cultivation under microgravity conditions.     

CELL—CELL CONTACTS ACCELERATE CELL COLONY GROWTH IN SPARSE CULTURES OF CHICK EMBRYO FIBROBLASTS

There is no cell proliferation in very sparcely plated chick embryo cell cultures. Substituting conditioned medium or adding of ethanol-fixed homologous cells to the cultures accelerates cell colony growth. The mechanism for the mitogenic action of fixed cells is considered to be the contact stimulation of cell proliferation, and addition of extra cells to sparse culture is believed to mimic the cell micro-environment existing in subconfluent cultures. The role of diverse cell—cell contacts in cultured cell growth regulation is discussed. The procedure used (addition of ethanol-fixed cells) may improve normal cell cloning techniques.     

Macrophage-mediated cytostasis of neoplastic hemopoietic cells: cytofluorometric analysis of the reversible cell cycle block

Nonactivated mouse peritoneal macrophages inhibit the proliferation of neoplastic hemopoietic cells in vitro. This effect is dependent upon the number of adherent macrophages present in cultures of hemopoietic tumor cells and can be documented by various parameters used as indices of cell proliferation. The two-layer soft agar culture system permits analysis of the regulatory functions of macrophage-derived diffusible substances under conditions of extremely low cell density and where macrophage-tumor cell contact is prevented by the gel matrix. The ability of the underlayers of macrophages to inhibit colony formation by hemopoietic tumor cells indicates that such an effect can be mediated by factor(s) elaborated by macrophages. Evidence that the mode of action of macrophages on tumor cell proliferation is cytostatic rather than cytotoxic is the capability of the macrophages to retard tumor cell growth in a particular phase of the cell cycle with retention of cell viability. Growth inhibition could be demonstrated to be reversible, with tumor cells entering normal cell cycle distributions shortly after being removed from macrophages or macrophage-derived factors. Cytofluorometric analysis of cell cycle inhibition correlated with viable cell counts and mitotic indices and confirms the suitability of this method for studying tumor cell proliferation.     

EFFECT OF ADENOSINE 3''-5''-CYCLIC MONOPHOSPHATE ON CELL PROLIFERATION

Secondary cultures of human diploid fibroblasts, which demonstrate density-dependent inhibition of cell growth, were used to study the effect of adenosine 3'-5'-cyclic monophosphate (cAMP) on cell proliferation. DNA synthesis in nonconfluent cultures and in contact-inhibited cultures stimulated to grow by refeeding with fresh medium was found to be inhibited by exogenous cAMP. The properties of this inhibition of DNA synthesis, together with the alterations in cAMP metabolism observed in confluent cultures of cells stimulated with fresh medium to resume growth, strongly suggest that cAMP is involved in contact-inhibition of cell proliferation.     

Establishment and characterization of two cell lines derived from primary cultures of Gekko japonicus cerebral cortex

Adult Gekko japonicus is one of those vertebrates that are able to regenerate their missing or amputated tail. The most interesting feature of this animal lies in the ability of its spinal cord to regrow a functional tail. A fundamental question is whether the neuroglial cells play a different role compared with high vertebrates. Since in vitro studies using primary neuroglial cells are hampered by the limited lifespan and miscellaneous genetic background of these cells, we generated neuroglial cell lines from primary cell cultures of cerebral cortex of G. japonicus. The SV40 (simian‐virus‐40) T antigen gene was introduced into primary cell cultures. Cell cycle analysis, cell growth and proliferation, cell colony formation and contact inhibition, as well as karyotype assays were investigated. Two cell colonies, Gsn‐1 and Gsn‐3, were immunochemically characterized as glial fibrillary acidic protein and galactocerebroside‐positive respectively. Compared with parental primary cells, the Gsn cells displayed shorter population doubling time, decreased percentage of cells in the G0/G1 phase, higher cell proliferation index, and increased cell activity. In assays of colony characteristics, Gsn cells showed increased cell activity at the lower cell densities or FBS (fetal bovine serum) supplement. The karyotype of immortalized Gsn cells exhibited transformational characteristics with hyperdiploid and polyploid chromosomes. The cell lines will provide a useful in vitro model for gecko neuroglial cells and facilitate systematic studies investigating the biological functions of specific gene products related to regeneration of the central nervous system.     

Logistic Proliferation of Cells in Scratch Assays is Delayed

Scratch assays are used to study how a population of cells re-colonises a vacant region on a two-dimensional substrate after a cell monolayer is scratched. These experiments are used in many applications including drug design for the treatment of cancer and chronic wounds. To provide insights into the mechanisms that drive scratch assays, solutions of continuum reaction–diffusion models have been calibrated to data from scratch assays. These models typically include a logistic source term to describe carrying capacity-limited proliferation; however, the choice of using a logistic source term is often made without examining whether it is valid. Here we study the proliferation of PC-3 prostate cancer cells in a scratch assay. All experimental results for the scratch assay are compared with equivalent results from a proliferation assay where the cell monolayer is not scratched. Visual inspection of the time evolution of the cell density away from the location of the scratch reveals a series of sigmoid curves that could be naively calibrated to the solution of the logistic growth model. However, careful analysis of the per capita growth rate as a function of density reveals several key differences between the proliferation of cells in scratch and proliferation assays. Our findings suggest that the logistic growth model is valid for the entire duration of the proliferation assay. On the other hand, guided by data, we suggest that there are two phases of proliferation in a scratch assay; at short time, we have a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. These two phases are observed across a large number of experiments performed at different initial cell densities. Overall our study shows that simply calibrating the solution of a continuum model to a scratch assay might produce misleading parameter estimates, and this issue can be resolved by making a distinction between the disturbance and growth phases. Repeating our procedure for other scratch assays will provide insight into the roles of the disturbance and growth phases for different cell lines and scratch assays performed on different substrates.     

Unequal cell division, growth regulation and colony size of mammalian cells: a mathematical model and analysis of experimental data.

This work describes mathematically the dynamics of expansion of cell populations from the initial division of single cells to colonies of several hundred cells. This stage of population growth is strongly influenced by stochastic (random) elements including, among others, cell death and quiescence. This results in a wide distribution of colony sizes. Experimental observations of the NIH3T3 cell line as well as for the NIH3T3 cell line transformed with the ras oncogene were obtained for this study. They include the number of cells in 4-day-old colonies initiated from single cells and measurements of sizes of sister cells after division, recorded in the 4-day-old colonies. The sister cell sizes were recorded in a way which enabled investigation of their interdependence. We developed a mathematical model which includes cell growth and unequal cell division, with three possible outcomes of each cell division: continued cell growth and division, quiescence, and cell death. The model is successful in reproducing experimental observations. It provides good fits to colony size distributions for both NIH3T3 mouse fibroblast cells and the same cells transformed with the rasEJ human cancer gene. The difference in colony size distributions could be fitted by assuming similar cell lifetimes (12-13 hr) and similar probabilities of cell death (q = 0.15), but using different probabilities of quiescence, r = 0 for the ras oncogene transformed cells and r = 0.1 for the non-transformed cells. The model also reproduces the evolution of distributions of sizes of cells in colonies, from a single founder cell of any specified size to the stable limit distribution after eight to ten cell divisions. Application of the model explains in what way both random events and deterministic control mechanisms strongly influence cell proliferation at early stages in the expansion of colonies.