Analysis of endothelial cell locomotion: Differential effects of motility and contact inhibition

Video microscopy and digital time-lapse recording were used to monitor locomotion and proliferation of bovine pulmonary artery endothelial (BPAE) cells cultured with varying concentrations of basic fibroblast growth factor (bFGF). Cell trajectories were reconstructed using a generalized nearest-neighbor algorithm and analyzed to determine how cell motility is affected by cell-cell collisions, cell divisions, and increasing cell density. The temporal evolution patterns of the average speed of locomotion for all cells in a culture were computed and the effects of varying bFGF concentrations were analyzed. Intermediate concentrations of bFGF (30 and 50 ng/mL) significantly increased the speed of locomotion above the levels we observed with 0 and 100 ng/mL concentrations of bFGF. Increases in cell density due to proliferation were immediately accompanied by a decrease in the average speed of locomotion of the cell population. Finally, the effect of bFGF concentration on the overall cell proliferation rates was assessed. With the addition of 30 or 50 ng/mL of bFGF to the culture media, the observed cell proliferation rates increased significantly. The proliferation rates decreased when the bFGF concentration increased to 100 ng/mL. These results show that bFGF concentrations that increase the motility of BPAE cells also increase the observed cell proliferation rates. (c) 1994 John Wiley & Sons, Inc.     

Multi-scale modeling of a wound-healing cell migration assay

A continuum model and a discrete model are developed to capture the population-scale and cell-scale behavior in a wound-healing cell migration assay created from a scrape wound in a confluent cell monolayer. During wound closure, the cell population forms a sustained traveling wave, with close contact between cells behind the wavefront. Cells exhibit contact inhibition of migration and contact-limited proliferation. The continuum model includes the two dominant mechanisms and characteristics of cell migration and proliferation, using a cell diffusivity function that decreases with cell density and a logistic proliferative growth term. The discrete model arises naturally from the continuum model. Individual cells are simulated as continuous-time random walkers with nearest-neighbor transitions, together with a birth/death process. The migration and proliferation parameters are determined by analysing individual mice 3T3 fibroblast cell trajectories obtained during the development of a confluent cell monolayer and in a wound healing assay. The population-scale model successfully predicts the shape and speed of the traveling wave, while the discrete model is also successful in capturing the contact inhibition of migration effects.     

Proliferation of anchorage-dependent contact-inhibited cells: I. Development of theoretical models based on cellular automata

We report the development of new class of discrete models that can accurately describe the contact-inhibited proliferation of anchorage-dependent cells. The models are based on cellular automata, and they quantitatively account for contact inhibition phenomena occurring during all stages of the proliferation process: (a) the initial stage of "exponential" growth of cells without contact inhibition; (b) the second stage where cell colonies form and grow with few colony mergings; and (c) the final stage where proliferation rates are dominated by colony merging events. Model prediction are presented and analyzed to study the complicated dynamics of large cell populations and determine how the initial spatial cell distribution, the seeding density, and the geometry of the growth surface affect the observed proliferation rates. Finally, we present a model variant that can simulate contact-inhibited proliferation of asynchronous cell populations with arbitrary cell cycle-time distribution. The latter model can also compute the percentage of cells that are in a specific phase of their division cycle at a given time.     

Hybrid cellular automaton modeling of nutrient modulated cell growth in tissue engineering constructs

Mathematic models help interpret experimental results and accelerate tissue engineering developments. We develop in this paper a hybrid cellular automata model that combines the differential nutrient transport equation to investigate the nutrient limited cell construct development for cartilage tissue engineering. Individual cell behaviors of migration, contact inhibition and cell collision, coupled with the cell proliferation regulated by oxygen concentration were carefully studied. Simplified two-dimensional simulations were performed. Using this model, we investigated the influence of cell migration speed on the overall cell growth within in vitro cell scaffolds. It was found that intense cell motility can enhance initial cell growth rates. However, since cell growth is also significantly modulated by the nutrient contents, intense cell motility with conventional uniform cell seeding method may lead to declined cell growth in the final time because concentrated cell population has been growing around the scaffold periphery to block the nutrient transport from outside culture media. Therefore, homogeneous cell seeding may not be a good way of gaining large and uniform cell densities for the final results. We then compared cell growth in scaffolds with various seeding modes, and proposed a seeding mode with cells initially residing in the middle area of the scaffold that may efficiently reduce the nutrient blockage and result in a better cell amount and uniform cell distribution for tissue engineering construct developments.     

Computational model for cell migration in three-dimensional matrices

Although computational models for cell migration on two-dimensional (2D) substrata have described how various molecular and cellular properties and physiochemical processes are integrated to accomplish cell locomotion, the same issues, along with certain new ones, might contribute differently to a model for migration within three-dimensional (3D) matrices. To address this more complicated situation, we have developed a computational model for cell migration in 3D matrices using a force-based dynamics approach. This model determines an overall locomotion velocity vector, comprising speed and direction, for individual cells based on internally generated forces transmitted into external traction forces and considering a timescale during which multiple attachment and detachment events are integrated. Key parameters characterize cell and matrix properties, including cell/matrix adhesion and mechanical and steric properties of the matrix; critical underlying molecular properties are incorporated explicitly or implicitly. Model predictions agree well with experimental results for the limiting case of migration on 2D substrata as well as with recent experiments in 3D natural tissues and synthetic gels. Certain predicted features such as biphasic behavior of speed with density of matrix ligands for 3D migration are qualitatively similar to their 2D counterparts, but new effects generally absent in 2D systems, such as effects due to matrix sterics and mechanics, are now predicted to arise in many 3D situations. As one particular sample manifestation of these effects, the optimal levels of cell receptor expression and matrix ligand density yielding maximal migration are dependent on matrix mechanical compliance.     

Dependence of intracellular alkali-ion concentrations of 3T3 and SV 40-3T3 cells on growth density.

Intracellular contents of potassium and of sodium are determined for 3T3 and SV 40-3T3 cells in dependence of growth density. In parallel, total cell volume and volume of intracellular water is determined for these cells suspended in physiological buffer. Intracellular potassium concentration thus evaluated for suspended 3T3 cells exhibits a sharp decrease at cellular growth densities which lead to density dependent inhibition of cell proliferation. In the case of SV 40-3T3 cells, this drop of potassium concentration with increasing cellular growth density is not observed, which correlates well with the absence of cell density dependent inhibition of cell growth in the transformed cell line. These results support the notion that processes of stimulation of quiescent 3T3 cells or of cell density dependent inhibition of their proliferation are mediated by processes including changes of potassium transport characteristics leading to increase or decrease respectively of their intracellular potassium concentration. Furthermore, these and other results suggest, that a difference between normal and transformed cells most relevant to their different proliferation behaviour might reside in different transport characteristics for potassium of the plasma membranes of these cells.     

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     

Growth Regulation In Multilayered Cultures of Human Diploid Fibroblasts: the Roles of Contact, Movement and Matrix Production

Abstract. Early subcultures of human embryonic lung fibroblasts are exceptional, as they grow far beyond confluence before growth ceases: the stationary dish may well contain 3-10 monolayer equivalents. Maximal growth rates, however, occur at about one-sixth confluence when doubling times are 15-20 hr; a density at which cell contacts begin to become frequent. the fact that a slowing down of growth is first apparent at such low densities argues against this regulation being due to diffusion effects. Confirmation of the role of short-range or contact interactions in growth regulation comes from an experiment using mixed cultures of fibroblasts: this shows that growth inhibition is not carried by medium-borne influences but depends on short-range (<1 mm) interactions. Evidence that cells can escape the effects of such contact interactions and so divide comes from time-lapse studies of dense cultures: there is a burst of motility soon after a fresh-medium change, which is followed by a burst of mitosis × 20 hr later. A medium change to conditioned medium supplemented with 10% foetal calf serum leads to neither the burst of motility nor the subsequent burst of mitosis, although this medium is better able to support the growth of sparse cells than is fresh medium. Data are also presented to show that the amount of collagen deposited in superconfluent cultures affects their growth: the stimulation of collagen production with ascorbic acid leads to an unexpectedly low stationary cell density and rather less movement in the culture. This result suggests that the collagen stabilizes cell contacts that are responsible for growth inhibition. the question of why these cells grow more slowly as density increases cannot be answered directly by these experiments; nevertheless, the results suggest that cell contact affects the permeability of the cell membrane to medium.     

Growth regulation in multilayered cultures of human diploid fibroblasts: the roles of contact, movement and matrix production

Early subcultures of human embryonic lung fibroblasts are exceptional, as they grow far beyond confluence before growth ceases: the stationary dish may well contain 3-10 monolayer equivalents. Maximal growth rates, however, occur at about one-sixth confluence when doubling times are 15-20 hr; a density at which cell contacts begin to become frequent. The fact that a slowing down of growth is first apparent at such low densities argues against this regulation being due to diffusion effects. Confirmation of the role of short-range or contact interactions in growth regulation comes from an experiment using mixed cultures of fibroblasts: this shows that growth inhibition is not carried by medium-borne influences but depends on short-range (less than 1 mm) interactions. Evidence that cells can escape the effects of such contact interactions and so divide comes from time-lapse studies of dense cultures: there is a burst of motility soon after a fresh-medium change, which is followed by a burst of mitosis approximately 20 hr later. A medium change to conditioned medium supplemented with 10% foetal calf serum leads to neither the burst of motility nor the subsequent burst of mitosis, although this medium is better able to support the growth of sparse cells than is fresh medium. Data are also presented to show that the amount of collagen deposited in superconfluent cultures affects their growth: the stimulation of collagen production with ascorbic acid leads to an unexpectedly low stationary cell density and rather less movement in the culture. This result suggests that the collagen stabilizes cell contacts that are responsible for growth inhibition. The question of why these cells grow more slowly as density increases cannot be answered directly by these experiments; nevertheless, the results suggest that cell contact affects the permeability of the cell membrane to medium.     

Analysis of cell locomotion on ligand gradient substrates

Directional cell motility plays a key role in many biological processes like morphogenesis, inflammation, wound repair, angiogenesis, immune response, and tumor metastasis. Cells respond to the gradient in surface ligand density by directed locomotion towards the direction of higher ligand density. Theoretical models which address the physical basis underlying the regulatory effect of ligand gradient on cell motility are highly desirable. Predictive models not only contribute to a better understanding of biological processes, but they also provide a quantitative interconnection between cell motility and biophysical properties of the extracellular matrix (ECM) for rational design of biomaterials as scaffolds in tissue engineering. In this work, we consider a one‐dimensional (1D) continuum viscoelastic model to predict the cell velocity in response to linearly increasing density of surface ligands on a substrate. The cell is considered as a 1D linear viscoelastic object with position dependent elasticity due to the variation in actin network density. The cell–substrate interaction is characterized by a frictional force, controlled by the density of ligand–receptor pairs. The generation of contractile stresses is described in terms of kinetic equations for the reactions between actins, myosins, and guanine nucleotide regulatory proteins. The model predictions show a reasonable agreement with experimentally measured cell speeds, considering biologically relevant values for the model parameters. The model predicts a biphasic relationship between cell speed and slope of gradient as well as a maximum limiting speed after a finite migration time. For a given slope of ligand gradient, the onset of the limiting speed appears at longer times for substrates with lower ligand gradients. The model can be applied to the design of biomaterials as scaffolds for guided tissue regeneration as it predicts an optimum range for the slope of ligand gradient. Biotechnol. Bioeng. 2009;103: 424–429. © 2009 Wiley Periodicals, Inc.     

Biophysical integration of effects of epidermal growth factor and fibronectin on fibroblast migration

Cell migration is regulated simultaneously by growth factors and extracellular matrix molecules. Although information is continually increasing regarding the relevant signaling pathways, there exists little understanding concerning how these pathways integrate to produce the biophysical processes that govern locomotion. Herein, we report the effects of epidermal growth factor (EGF) and fibronectin (Fn) on multiple facets of fibroblast motility: locomotion speed, membrane extension and retraction activity, and adhesion. A surprising finding is that EGF can either decrease or increase locomotion speed depending on the surface Fn concentration, despite EGF diminishing global cell adhesion at all Fn concentrations. At the same time, the effect of EGF on membrane activity varies from negative to positive to no-effect as Fn concentration and adhesion range from low to high. Taking these effects together, we find that EGF and Fn regulate fibroblast migration speed through integration of the processes of membrane extension, attachment, and detachment, with each of these processes being rate-limiting for locomotion in sequential regimes of increasing adhesivity. Thus, distinct biophysical processes are shown to integrate for overall cell migration responses to growth factor and extracellular matrix stimuli.     

Autowaves in a model of invasive tumor growth

A mathematical model for invasive tumor growth is proposed, which takes into account cell division, death, and motility. The model includes local cell density and the distribution of nutrient (oxygen) concentration. Cancer cells die in the absence of nutrients; therefore, the distribution of oxygen in tissue substantially affects both the tumor proliferation rate and its structure. The model adequately describes the experimentally measured rate of tumor proliferation. The existence of autowave solutions is demonstrated, and their properties are investigated. The results are compared with the properties of the Kolmogorov-Petrovskii-Piskunov and Fisher equations. It is shown that the nutrient distribution influences the selection of speed and the convergence of the initial conditions to the automodel solution.     

Density inhibition of motility in 3T3 fibroblasts and their SV40 transformants

A dramatic decrease in cellular motility (measured by means of the augmented diffusion constant, D^∗) was observed with increasing cell area densities of 3T3 fibroblasts. This phenomenon was named density inhibition of motility, and a quantitative measure of this effect, the coefficient of density inhibition of motility, was proposed. Control experiments precluded depletion of a nutritional “locomotion factor(s)” as an explanation for the observed decrease in 3T3 motility. By contrast, SV40 transformants exhibited negligible density inhibition of motility. Data and arguments were presented in support of the hypothesis that the strong density inhibition of motility observed for 3T3 reflected a strong mutual adhesivity of these cells, and that the weak density inhibition of motility observed for SV3T3 reflected a correspondingly weak mutual adhesivity.     

A model for cell motility on soft bio-adhesive substrates

Mechanical stiffness of bio-adhesive substrates has been recognized as a major regulator of cell motility. We present a simple physical model to study the crawling locomotion of a contractile cell on a soft elastic substrate. The mechanism of rigidity sensing is accounted for using Schwarz's two-spring model Schwarz et al. (2006). The predicted dependency between the speed of motility and substrate stiffness is qualitatively consistent with experimental observations. The model demonstrates that the rigidity dependent motility of cells is rooted in the regulation of actomyosin contractile forces by substrate deformation at each anchorage point. On stiffer substrates, the traction forces required for cell translocation acquire larger magnitude but show weaker asymmetry which leads to slower cell motility. On very soft substrates, the model predicts a biphasic relationship between the substrate rigidity and the speed of locomotion, over a narrow stiffness range, which has been observed experimentally for some cell types.     

Competition amongst Eph receptors regulates contact inhibition of locomotion and invasiveness in prostate cancer cells

Metastatic cancer cells typically fail to halt migration on contact with non-cancer cells. This invasiveness is in contrast to normal mesenchymal cells that retract on contact with another cell. Why cancer cells are defective in contact inhibition of locomotion is not understood. Here, we analyse the dynamics of prostate cancer cell lines co-cultured with fibroblasts, and demonstrate that a combinatorial code of Eph receptor activation dictates whether cell migration will be contact inhibited. The unimpeded migration of metastatic PC-3 cells towards fibroblasts is dependent on activation of EphB3 and EphB4 by ephrin-B2, which we show activates Cdc42 and cell migration. Knockdown of EphB3 and EphB4 restores contact inhibition of locomotion to PC-3 cells. Conversely, homotypic collisions between two cancer cells results in contact inhibition of locomotion, mediated by EphA-Rho-Rho kinase (ROCK) signalling. Thus, the migration of cancer cells can switch from restrained to invasive, depending on the Eph-receptor profile of the cancer cell and the reciprocal ephrin ligands expressed by neighbouring cells.     

Space-Limited Mitosis in the Glazier–Graner–Hogeweg Model

The Glazier–Graner–Hogeweg (GGH) model is a cellular automata framework for representing the time evolution of cellular systems, appealing because unlike many other individual-cell-based models it dynamically simulates changes in cell shape and size. Proliferation has seen some implementation into this modelling framework, but without consensus in the literature as to how this behaviour is best represented. Additionally, the majority of published GGH model implementations which feature proliferation do so in order to simulate a certain biological situation where mitosis is important, but without analysis of how these proliferation routines operate on a fundamental level. Here, a method of proliferation for the GGH model which uses separate cell phenotypes to differentiate cells which have entered or just left the mitotic phase of the cell cycle is presented and demonstrated to correctly predict logistic growth on a macroscopic scale (in accordance with experimental evidence). Comparisons between model simulations and the generalised logistic growth model provide an interpretation of the latter’s ‘shape parameter’, and the proliferation routine used here is shown to offer the modeller somewhat predictable control over the proliferation rate, important for ensuring temporal consistency between different cellular behaviours in the model. All results are found to be insensitive to the inclusion of active cell motility. The implications of these simulated proliferation assays towards problems in cell biology are also discussed.     

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.     

Stimulating the proliferation of quiescent 3T3 fibroblasts by peptide growth factors or by agents which elevate cellular cyclic AMP level has opposite effects on motility

The effects of some chemically defined growth factors on the locomotion of quiescent Swiss 3T3 fibroblasts have been studied. A computer digitiser has been used to facilitate recording the paths followed by cells in time-lapse films; this method allows 500 cell-hours to be recorded in 1 h of real time. Individual cells in the same culture vary widely in speed. This variation is not associated with the positions of the cells in the cell cycle; a small deceleration which seems to occur in G2 cannot account for any significant part of the variation seen. Nor is it related to the time elapsing before the cell divides, although this is equally variable; the speed and age at division of particular cells appear to be entirely independent of one another. Nevertheless, good reproducibility is seen between the mean speeds of large numbers of cells from the same type of culture. The mean speed of quiescent cells is less than 2 microns/h. A mixture of epidermal growth factor (EGF) and vasopressin, in the presence of insulin, is known to be a potent promoter of proliferation in this system. We have found it to increase speed to 30 microns/h. Agents which stimulate the cellular level of cAMP are also known to be potent promoters of proliferation in the presence of insulin. We have found these agents to be inhibitors of locomotion; several cycles of cell division take place while the cells move at a speed no greater than that seen in the presence of cytochalasin B (CB) or colchicine. These findings therefore give further support to the idea that there may be two different classes of growth-promoting factors, with major differences in their mode of action. They show that some members of these two different classes have opposite effects on motility.     

A generalized transport model for biased cell migration in an anisotropic environment

 A generalized transport model is derived for cell migration in an anisotropic environment and is applied to the specific cases of biased cell migration in a gradient of a stimulus (taxis; e.g., chemotaxis or haptotaxis) or along an axis of anisotropy (e.g., contact guidance). The model accounts for spatial or directional dependence of cell speed and cell turning behavior to predict a constitutive cell flux equation with drift velocity and diffusivity tensor (termed random motility tensor) that are explicit functions of the parameters of the underlying random walk model. This model provides the connection between cell locomotion and the resulting persistent random walk behavior to the observed cell migration on longer time scales, thus it provides a framework for interpreting cell migration data in terms of underlying motility mechanisms. Received: 8 April 1999