Modeling cell migration in 3D: Status and challenges

Cell migration is a multi-scale process that integrates signaling, mechanics and biochemical reaction kinetics. Various mathematical models accurately predict cell migration on 2D surfaces, but are unable to capture the complexities of 3D migration. Additionally, quantitative 3D cell migration models have been few and far between. In this review we look and characterize various mathematical models available in literature to predict cell migration in 3D matrices and analyze their strengths and possible changes to these models that could improve their predictive capabilities.Key words: cell migration, 3D motility, mathematical models, cancer, multi-scale     

3D culture model and computer-assisted videomicroscopy to analyze migratory behavior of noninvasive and invasive bronchial epithelial cells

To date, most of the studies in the field of cell migration have been applied to two-dimensional (2D) models. To mimic the three-dimensional (3D) conditions similar to those observed in vivo during tumor invasion, we developed a 3D model of cell migration in which cells were embedded in a collagen I matrix placed in a double-compartment chamber. Using time-lapse videomicroscopy and interactive cell tracking in a four-dimensional data set, we determined the cell trajectories and their migration kinetics. We compared the 2D and 3D migratory behavior of a noninvasive cell line (16HBE) with the migratory behavior of an invasive cell line (BZR). Our results show that the 3D migration kinetics of the noninvasive cell line were lower than the migration kinetics of the invasive cell line. In contrast, in 2D models, no significant difference was observed between the two cell lines. To validate our 3D model, we further investigated the effect of epidermal growth factor (EGF), a promoter of tumor cell motility and invasion on the noninvasive cell line (16HBE). EGF increased significantly the migration kinetics of the noninvasive cell line. Our results show that the 3D model of cell migration allowed us to differentiate the migratory behavior of invasive and noninvasive cells and that such a model can help in the development of molecular targeted therapy as it approaches the in vivo conditions. tumor invasion; metastasis; image analysis; kinetic migration; epidermal growth factor     

Occupy tissue: The movement in cancer metastasis

The critical role of migration and invasion in cancer metastasis warrants new therapeutic approaches targeting the machinery regulating cell migration and invasion. While 2-dimensional (2D) models have helped identify a range of adhesion molecules, cytoskeletal components and regulators that are potentially important for cell migration, the use of models that better mimic the 3-dimensional (3D) environment has yielded new insights into the physiology of cell movement. For example, studying cells in 3D models has revealed that invading cancer cells may switch between heterogeneous invasion modes and thus evade pharmacological inhibition of invasion. Here we summarize published data in which the role of cell adhesion molecules in 2D vs. 3D migration have been directly compared and discuss mechanisms that regulate migration speed and persistence in 2D and 3D. Finally we discuss limits of 3D culture models to recapitulate the in vivo �situation.     

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.     

Life ins't flat: Taking cancer biology to the next dimension

Classically, most cell culture experiments have been performed under adherent 2D conditions. Cells in the human body grow within an organized 3D matrix, surrounded by other cells. The behavior of individual cells is controlled through their interactions with their immediate neighbors and the extracellular matrix. The complex summation of these multiple signals determines whether a given cell undergoes differentiation, apoptosis, proliferation, or invasion. In 2D culture many of these complex interactions are lost. As a result, there are a growing number of studies which report differences in phenotype, cellular signaling, cell migration, and drug responses when the same cells are grown under 2D or 3D culture conditions. One potential application of these techniques is to anticancer drug discovery, which has long been hampered by the lack of good preclinical models. Compounds with good antitumor activity in 2D cell culture models often fail to translate into the clinic. Here we suggest that the response of cancer cells to drugs is determined in part by the 3D tumor microenvironment and discuss models to re-create the 3D tumor microenvironment in vitro. It is likely that the adoption of these and other 3D models will allow us to more closely re-create the behavior of the tumor in vivo which may lead to identifying better anticancer drug candidates at an earlier stage of development.     

Epigallocatechin-3-gallate (EGCG) inhibits the migratory behavior of tumor bronchial epithelial cells

Background

Many studies associated the main polyphenolic constituent of green tea, (-)-Epigallocatechin-3-gallate (EGCG), with inhibition of cancers, invasion and metastasis. To date, most of the studies have focused on the effect of EGCG on cell proliferation or death. Since cell migration is an important mechanism involved in tumor invasion, the aim of the present work was to target another approach of the therapeutic effect of EGCG, by investigating its effect on the cell migratory behavior.

Methods

The effect of EGCG (at concentrations lower than 10 μg/ml) on the migration speed of invasive cells was assessed by using 2D and 3D models of cell culture. We also studied the effects of EGCG on proteinases expression by RT-PCR analysis. By immunocytochemistry, we analyzed alterations of vimentin organization in presence of different concentrations of EGCG.

Results

We observed that EGCG had an inhibitory effect of cell migration in 2D and 3D cell culture models. EGCG also inhibited MMP-2 mRNA and protein expression and altered the intermediate filaments of vimentin.

Conclusion

Taken together, our results demonstrate that EGCG is able to inhibit the migration of bronchial tumor cells and could therefore be an attractive candidate to treat tumor invasion and cell migration.     

Acute lung inflammation and ventilator-induced lung injury caused by ATP via the P2Y receptors: an experimental study

Background

Many studies associated the main polyphenolic constituent of green tea, (-)-Epigallocatechin-3-gallate (EGCG), with inhibition of cancers, invasion and metastasis. To date, most of the studies have focused on the effect of EGCG on cell proliferation or death. Since cell migration is an important mechanism involved in tumor invasion, the aim of the present work was to target another approach of the therapeutic effect of EGCG, by investigating its effect on the cell migratory behavior.

Methods

The effect of EGCG (at concentrations lower than 10 μg/ml) on the migration speed of invasive cells was assessed by using 2D and 3D models of cell culture. We also studied the effects of EGCG on proteinases expression by RT-PCR analysis. By immunocytochemistry, we analyzed alterations of vimentin organization in presence of different concentrations of EGCG.

Results

We observed that EGCG had an inhibitory effect of cell migration in 2D and 3D cell culture models. EGCG also inhibited MMP-2 mRNA and protein expression and altered the intermediate filaments of vimentin.

Conclusion

Taken together, our results demonstrate that EGCG is able to inhibit the migration of bronchial tumor cells and could therefore be an attractive candidate to treat tumor invasion and cell migration.     

3D printing to construct in vitro multicellular models of melanoma

Currently, there is a lack of suitable models for in-vitro studies of malignant melanoma and traditional single cell culture models no longer reproduce tumor structure and physiological complexity well. The tumor microenvironment is closely related to carcinogenesis and it is particularly important to understand how tumor cells interact and communicate with surrounding nonmalignant cells. Three-dimensional (3D) in vitro multicellular culture models can better simulate the tumor microenvironment due to their excellent physicochemical properties. In this study, 3D composite hydrogel scaffolds were prepared from gelatin methacrylate and polyethylene glycol diacrylate hydrogels by 3D printing and light curing techniques, and 3D multicellular in vitro tumor culture models were established by inoculating human melanoma cells (A375) and human fibroblasts cells on them. The cell proliferation, migration, invasion, and drug resistance of the 3D multicellular in vitro model was evaluated. Compared with the single-cell model, the cells in the multicellular model had higher proliferation activity and migration ability, and were easy to form dense structures. Several tumor cell markers, such as matrix metalloproteinase-9 (MMP-9), MMP-2, and vascular endothelial growth factor, were highly expressed in the multicellular culture model, which were more favorable for tumor development. In addition, higher cell survival rate was observed after exposure to luteolin. The anticancer drug resistance result of the malignant melanoma cells in the 3D bioprinted construct demonstrated physiological properties, suggesting the promising potential of current 3D printed tumor model in the development of personalized therapy, especially for discovery of more conducive targeted drugs.     

Micron-scale positioning of features influences the rate of polymorphonuclear leukocyte migration

Microfabrication technology was used to create regular arrays of micron-size holes (2 microm x 2 microm x 210 nm) on fused quartz and photosensitive polyimide surfaces. The patterned surfaces, which possessed a basic structural element of a three-dimensional (3-D) network (i.e., spatially separated mechanical edges), were used as a model system for studying the effect of substrate microgeometry on neutrophil migration. The edge-to-edge spacing between features was systematically varied from 6 microm to 14 microm with an increment of 2 microm. In addition, collagen was used to coat the patterned quartz surfaces in an attempt to change the adhesive properties of the surfaces. A radial flow detachment assay revealed that cell adhesion was the strongest on the quartz surface (approximately 50% cell attached), whereas it was relatively weaker on polyimide and collagen-coated quartz (approximately 25% cell attached). Cell adhesion to each substrate was not affected either by the presence of holes or by the spacing between holes. A direct visualization assay showed that neutrophil migration on each patterned surface could be characterized as a persistent random walk; the dependence of the random motility coefficient (mu) as a function of spacing was biphasic with the optimal spacing at approximately 10 microm on each substrate. The presence of evenly distributed holes at the optimal spacing of 10 microm enhanced mu by a factor of 2 on polyimide, a factor of 2.5 on collagen-coated quartz, and a factor of 10 on uncoated quartz. The biphasic dependence on the mechanical edges of neutrophil migration on 2-D patterned substrate was strikingly similar to that previously observed during neutrophil migration within 3-D networks, suggesting that microfabricated materials provide relevant models of 3-D structures with precisely defined physical characteristics. In addition, our results demonstrate that the microgeometry of a substrate, when considered separately from adhesion, can play a significant role in cell migration.     

The third dimension bridges the gap between cell culture and live tissue

Moving from cell monolayers to three-dimensional (3D) cultures is motivated by the need to work with cellular models that mimic the functions of living tissues. Essential cellular functions that are present in tissues are missed by 'petri dish'-based cell cultures. This limits their potential to predict the cellular responses of real organisms. However, establishing 3D cultures as a mainstream approach requires the development of standard protocols, new cell lines and quantitative analysis methods, which include well-suited three-dimensional imaging techniques. We believe that 3D cultures will have a strong impact on drug screening and will also decrease the use of laboratory animals, for example, in the context of toxicity assays.     

Analysis of Cell Migration within a Three-dimensional Collagen Matrix

The ability to migrate is a hallmark of various cell types and plays a crucial role in several physiological processes, including embryonic development, wound healing, and immune responses. However, cell migration is also a key mechanism in cancer enabling these cancer cells to detach from the primary tumor to start metastatic spreading. Within the past years various cell migration assays have been developed to analyze the migratory behavior of different cell types. Because the locomotory behavior of cells markedly differs between a two-dimensional (2D) and three-dimensional (3D) environment it can be assumed that the analysis of the migration of cells that are embedded within a 3D environment would yield in more significant cell migration data. The advantage of the described 3D collagen matrix migration assay is that cells are embedded within a physiological 3D network of collagen fibers representing the major component of the extracellular matrix. Due to time-lapse video microscopy real cell migration is measured allowing the determination of several migration parameters as well as their alterations in response to pro-migratory factors or inhibitors. Various cell types could be analyzed using this technique, including lymphocytes/leukocytes, stem cells, and tumor cells. Likewise, also cell clusters or spheroids could be embedded within the collagen matrix concomitant with analysis of the emigration of single cells from the cell cluster/ spheroid into the collagen lattice. We conclude that the 3D collagen matrix migration assay is a versatile method to analyze the migration of cells within a physiological-like 3D environment.     

Guidance of Cell Migration by Substrate Dimension

There is increasing evidence to suggest that physical parameters, including substrate rigidity, topography, and cell geometry, play an important role in cell migration. As there are significant differences in cell behavior when cultured in 1D, 2D, or 3D environments, we hypothesize that migrating cells are also able to sense the dimension of the environment as a guidance cue. NIH 3T3 fibroblasts were cultured on micropatterned substrates where the path of migration alternates between 1D lines and 2D rectangles. We found that 3T3 cells had a clear preference to stay on 2D rather than 1D substrates. Cells on 2D surfaces generated stronger traction stress than did those on 1D surfaces, but inhibition of myosin II caused cells to lose their sensitivity to substrate dimension, suggesting that myosin-II-dependent traction forces are the determining factor for dimension sensing. Furthermore, oncogene-transformed fibroblasts are defective in mechanosensing while generating similar traction forces on 1D and 2D surfaces. Dimension sensing may be involved in guiding cell migration for both physiological functions and tissue engineering, and for maintaining normal cells in their home tissue.     

Computational modelling and analysis of mechanical conditions on cell locomotion and cell–cell interaction

Between other parameters, cell migration is partially guided by the mechanical properties of its substrate. Although many experimental works have been developed to understand the effect of substrate mechanical properties on cell migration, accurate 3D cell locomotion models have not been presented yet. In this paper, we present a novel 3D model for cells migration. In the presented model, we assume that a cell follows two main processes: in the first process, it senses its interface with the substrate to determine the migration direction and in the second process, it exerts subsequent forces to move. In the presented model, cell traction forces are considered to depend on cell internal deformation during the sensing step. A random protrusion force is also considered which may change cell migration direction and/or speed. The presented model was applied for many cases of migration of the cells. The obtained results show high agreement with the available experimental and numerical data.     

Modeling cell gradient sensing and migration in competing chemoattractant fields

Directed cell migration mediates physiological and pathological processes. In particular, immune cell trafficking in tissues is crucial for inducing immune responses and is coordinated by multiple environmental cues such as chemoattractant gradients. Although the chemotaxis mechanism has been extensively studied, how cells integrate multiple chemotactic signals for effective trafficking and positioning in tissues is not clearly defined. Results from previous neutrophil chemotaxis experiments and modeling studies suggested that ligand-induced homologous receptor desensitization may provide an important mechanism for cell migration in competing chemoattractant gradients. However, the previous mathematical model is oversimplified to cell gradient sensing in one-dimensional (1-D) environment. To better understand the receptor desensitization mechanism for chemotactic navigation, we further developed the model to test the role of homologous receptor desensitization in regulating both cell gradient sensing and migration in different configurations of chemoattractant fields in two-dimension (2-D). Our results show that cells expressing normal desensitizable receptors preferentially orient and migrate toward the distant gradient in the presence of a second local competing gradient, which are consistent with the experimentally observed preferential migration of cells toward the distant attractant source and confirm the requirement of receptor desensitization for such migratory behaviors. Furthermore, our results are in qualitative agreement with the experimentally observed cell migration patterns in different configurations of competing chemoattractant fields.     

Motogenic and biosynthetic response of adult skin fibroblasts to TGF-beta isoforms (-1, -2 and -3) determined by 'tissue response unit': role of cell density and substratum

We have recently demonstrated that the three principal mammalian isoforms of transforming growth factor beta (TGF-beta) exert distinct effects upon: (1) the migration of confluent adult fibroblasts into 3D gels of native type I collagen fibres (i.e. TGF-beta-1 and -2 had no apparent motogenic activity, whilst TGF-beta-3 induced a dose-dependent stimulation of cell migration); and (2) the synthesis of hyaluronan (HA) by these cells is also affected by the TGF-beta isoforms in a manner which parallels their effect on cell migration. The objective of the present study is to elucidate the manner in which this differential activity of the TGF-beta-1, -2 and -3 may be modulated by experimental parameters. Data presented in this communication indicate that cytokine bioactivity is determined by a combination of cell density and the nature of the macromolecular substratum. Thus, we now report that all three TGF-beta isoforms inhibit the migration of subconfluent cells in the collagen gel assay. Our data confirm that the migration of confluent cells is stimulated by TGF-beta-3 and further indicate that this motogenic activity is completely abrogated by either TGF-beta-1 or -2 when these are co-incubated with TGF-beta-3. In contrast to these results obtained using a native type I collagen substratum, all three isoforms stimulated adult fibroblast migration in the transmembrane assay (in which cells are adherent to a 2-D porous polycarbonate substratum). The precise effect of TGF-beta isoforms on HA synthesis was also affected by cell density and the nature of the substratum in a manner which paralleled their diverse effects on cell migration (i.e. stimulation, inhibition or no effect). Streptomyces hyaluronidase completely neutralized the TGF-beta-3-induced stimulation of confluent fibroblast migration, thus suggesting a mechanistic link between the cytokine-induced cell migration and HA synthesis under these conditions. Taken together, these data indicate that: (1) the bioactivity of TGF-beta-1, -2 and -3 are determined by cell density, the macromolecular substratum and the presence of other cytokines; and (2) it is therefore necessary to define cytokine bioactivity within the context of a larger 'tissue response unit' which more fully defines the activity state of the target cell and its microenvironment.     

Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells

Brain extracellular space (ECS) constitutes a porous medium in which diffusion is subject to hindrance, described by tortuosity, lambda = (D/D*)1/2, where D is the free diffusion coefficient and D* is the effective diffusion coefficient in brain. Experiments show that lambda is typically 1.6 in normal brain tissue although variations occur in specialized brain regions. In contrast, different theoretical models of cellular assemblies give ambiguous results: they either predict lambda-values similar to experimental data or indicate values of about 1.2. Here we constructed three different ECS geometries involving tens of thousands of cells and performed Monte Carlo simulation of 3-D diffusion. We conclude that the geometrical hindrance in the ECS surrounding uniformly spaced convex cells is independent of the cell shape and only depends on the volume fraction alpha (the ratio of the ECS volume to the whole tissue volume). This dependence can be described by the relation lambda = ((3-alpha)/2)1/2, indicating that the geometrical hindrance in such ECS cannot account for lambda > 1.225. Reasons for the discrepancy between the theoretical and experimental tortuosity values are discussed.     

Validation of a mathematical approach to estimate dynamic scapular orientation

The goal of this study was to develop and validate a non-invasive approach to estimate scapular kinematics in individual patients. We hypothesized that individualized mathematical algorithms can be developed using motion capture data to accurately estimate dynamic scapula orientation based on measured humeral orientations and acromion process positions. The accuracy of the mathematical algorithms was evaluated against a gold standard of biplane fluoroscopy using a 2D to 3D fluoroscopy/model matching process. Individualized linear models were developed for nine healthy adult shoulders. These models were used to predict scapulothoracic kinematics, and the predicted kinematics were compared to kinematics obtained using biplane fluoroscopy to determine the accuracy of the algorithms. Results showed strong correlations between mathematically predicted kinematics and validation kinematics. Estimated kinematics were within 8° of validation kinematics. We concluded that individualized linear models show promise for providing accurate, non-invasive measurements of scapulothoracic kinematics in a clinical environment.