Mathematical model for the effects of adhesion and mechanics on cell migration speed

Actin cytoskeleton regulates functional anchorage-migration switch during T-cadherin-induced phenotype modulation of vascular smooth muscle cells

Vascular smooth muscle cell (SMC) switching between differentiated and dedifferentiated phenotypes is reversible and accompanied by morphological and functional alterations that require reconfiguration of cell-cell and cell-matrix adhesion networks. Studies attempting to explore changes in overall composition of the adhesion nexus during SMC phenotype transition are lacking. We have previously demonstrated that T-cadherin knockdown enforces SMC differentiation, whereas T-cadherin upregulation promotes SMC dedifferentiation. This study used human aortic SMCs ectopically modified with respect to T-cadherin expression to characterize phenotype-associated cell-matrix adhesion molecule expression, focal adhesions configuration and migration modes. Compared with dedifferentiated/migratory SMCs (expressing T-cadherin), the differentiated/contractile SMCs (T-cadherin-deficient) exhibited increased adhesion to several extracellular matrix substrata, decreased expression of several integrins, matrix metalloproteinases and collagens, and also distinct focal adhesion, adherens junction and intracellular tension network configurations. Differentiated and dedifferentiated phenotypes displayed distinct migrational velocity and directional persistence. The restricted migration efficiency of the differentiated phenotype was fully overcome by reducing actin polymerization with ROCK inhibitor Y-27632 whereas myosin II inhibitor blebbistatin was less effective. Migration efficiency of the dedifferentiated phenotype was diminished by promoting actin polymerization with lysophosphatidic acid. These findings held true in both 2D-monolayer and 3D-spheroid migration models. Thus, our data suggest that despite global differences in the cell adhesion nexus of the differentiated and dedifferentiated phenotypes, structural actin cytoskeleton characteristics per se play a crucial role in permissive regulation of cell-matrix adhesive interactions and cell migration behavior during T-cadherin-induced SMC phenotype transition.

Shifting the optimal stiffness for cell migration

Cell migration, which is central to many biological processes including wound healing and cancer progression, is sensitive to environmental stiffness, and many cell types exhibit a stiffness optimum, at which migration is maximal. Here we present a cell migration simulator that predicts a stiffness optimum that can be shifted by altering the number of active molecular motors and clutches. This prediction is verified experimentally by comparing cell traction and F-actin retrograde flow for two cell types with differing amounts of active motors and clutches: embryonic chick forebrain neurons (ECFNs; optimum ∼1 kPa) and U251 glioma cells (optimum ∼100 kPa). In addition, the model predicts, and experiments confirm, that the stiffness optimum of U251 glioma cell migration, morphology and F-actin retrograde flow rate can be shifted to lower stiffness by simultaneous drug inhibition of myosin II motors and integrin-mediated adhesions.

Cell migration is sensitive to environmental stiffness, but how cells sense optimal stiffness is not known. Here the authors develop a model that predicts that the optimum can be shifted by altering the number of active molecular motors and clutches, and verify their model in two cell types.

The Upregulation of Integrin αDβ2 (CD11d/CD18) on Inflammatory Macrophages Promotes Macrophage Retention in Vascular Lesions and Development of Atherosclerosis

Macrophage accumulation is a critical step during development of chronic inflammation, initiating progression of many devastating diseases. Leukocyte-specific integrin α_Dβ₂ (CD11d/CD18) is dramatically upregulated on macrophages at inflammatory sites. Previously we found that CD11d overexpression on cell surfaces inhibits in vitro cell migration due to excessive adhesion. In this study, we have investigated how inflammation-mediated CD11d upregulation contributes to macrophage retention at inflammatory sites during atherogenesis. Atherosclerosis was evaluated in CD11d^-/-/ApoE^-/- mice after 16 wk on a Western diet. CD11d deficiency led to a marked reduction in lipid deposition in aortas and isolated macrophages. Macrophage numbers in aortic sinuses of CD11d^-/- mice were reduced without affecting their apoptosis and proliferation. Adoptive transfer of fluorescently labeled wild-type and CD11d^-/- monocytes into ApoE^-/- mice demonstrated similar recruitment from circulation, but reduced accumulation of CD11d^-/- macrophages within the aortas. Furthermore, CD11d expression was significantly upregulated on macrophages in atherosclerotic lesions and M1 macrophages in vitro. Interestingly, expression of the related ligand-sharing integrin CD11b was not altered. This difference defines their distinct roles in the regulation of macrophage migration. CD11d-deficient M1 macrophages demonstrated improved migration in a three-dimensional fibrin matrix and during resolution of peritoneal inflammation, whereas migration of CD11b^-/- M1 macrophages was not affected. These results prove the contribution of high densities of CD11d to macrophage arrest during atherogenesis. Because high expression of CD11d was detected in several inflammation-dependent diseases, we suggest that CD11d/CD18 upregulation on proinflammatory macrophages may represent a common mechanism for macrophage retention at inflammatory sites, thereby promoting chronic inflammation and disease development.

The size-speed-force relationship governs migratory cell response to tumorigenic factors

Normal and transformed motile cells follow a common trend in which size and contractile forces are negatively correlated with cell speed. However, tumorigenic factors amplify the preexisting population heterogeneity and lead some cells to exhibit biomechanical properties that are more extreme than those observed with normal cells.

Tumor development progresses through a complex path of biomechanical changes leading first to cell growth and contraction and then cell deadhesion, scattering, and invasion. Tumorigenic factors may act specifically on one of these steps or have a wider spectrum of actions, leading to a variety of effects and thus sometimes to apparent contradictory outcomes. Here we used micropatterned lines of collagen type I/fibronectin on deformable surfaces to standardize cell behavior and measure simultaneously cell size, speed of motion and magnitude of the associated traction forces at the level of a single cell. We analyzed and compared the normal human breast cell line MCF10A in control conditions and in response to various tumorigenic factors. In all conditions, a wide range of biomechanical properties was identified. Despite this heterogeneity, normal and transformed motile cells followed a common trend whereby size and contractile forces were negatively correlated with cell speed. Some tumorigenic factors, such as activation of ErbB2 or loss of the βsubunit of casein kinase 2, shifted the whole population toward a faster speed and lower contractility state. Treatment with transforming growth factor β induced some cells to adopt opposing behaviors such as extremely high versus extremely low contractility. Thus tumor transformation amplified preexisting population heterogeneity and led some cells to exhibit biomechanical properties that were more extreme than those observed with normal cells.

A poroelastic mixture model of mechanobiological processes in biomass growth: theory and application to tissue engineering

In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular "force isotropy" as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection-diffusion-reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations.

Biphasic Dependence of Glioma Survival and Cell Migration on CD44 Expression Level

While several studies link the cell-surface marker CD44 to cancer progression, conflicting results show both positive and negative correlations with increased CD44 levels. Here, we demonstrate that the survival outcomes of genetically induced glioma-bearing mice and of high-grade human glioma patients are biphasically correlated with CD44 level, with the poorest outcomes occurring at intermediate levels. Furthermore, the high-CD44-expressing mesenchymal subtype exhibited a positive trend of survival with increased CD44 level. Mouse cell migration rates in ex vivo brain slice cultures were also biphasically associated with CD44 level, with maximal migration corresponding to minimal survival. Cell simulations suggest that cell-substrate adhesiveness is sufficient to explain this biphasic migration. More generally, these results highlight the potential importance of non-monotonic relationships between survival and biomarkers associated with cancer progression.

The influence of biomechanical properties and cannabinoids on tumor invasion

BACKGROUND

Cannabinoids are known to have an anti-tumorous effect, but the underlying mechanisms are only sparsely understood. Mechanical characteristics of tumor cells represent a promising marker to distinguish between tumor cells and the healthy tissue. We tested the hypothesis whether cannabinoids influence the tumor cell specific mechanical and migratory properties and if these factors are a prognostic marker for the invasiveness of tumor cells.

METHODS

3 different glioblastoma cell lines were treated with cannabinoids and changes of mechanical and migratory properties of single cells were measured using atomic force microscopy and time lapse imaging. The invasiveness of cell lines was determined using a co-culture model with organotypic hippocampal slice cultures.

RESULTS

We found that cannabinoids are capable of influencing migratory and mechanical properties in a cell line specific manner. A network analysis revealed a correlation between a "generalized stiffness" and the invasiveness for all tumor cell lines after 3 and 4 d of invasion time: r3d = -0.88 [-0.52;-0.97]; r4d = -0.90 [-0.59;-0.98].

CONCLUSIONS

Here we could show that a "generalized stiffness" is a profound marker for the invasiveness of a tumor cell population in our model and thus might be of high clinical relevance for drug testing. Additionally cannabinoids were shown to be of potential use for therapeutic approaches of glioblastoma.

Spatial and temporal coordination of traction forces in one-dimensional cell migration

Migration of a fibroblast along a collagen fiber can be regarded as cell locomotion in one-dimension (1D). In this process, a cell protrudes forward, forms a new adhesion, produces traction forces, and releases its rear adhesion in order to advance itself along a path. However, how a cell coordinates its adhesion formation, traction forces, and rear release in 1D migration is unclear. Here, we studied fibroblasts migrating along a line of microposts. We found that when the front of a cell protruded onto a new micropost, the traction force produced at its front increased steadily, but did so without a temporal correlation in the force at its rear. Instead, the force at the front coordinated with a decrease in force at the micropost behind the front. A similar correlation in traction forces also occurred at the rear of a cell, where a decrease in force due to adhesion detachment corresponded to an increase in force at the micropost ahead of the rear. Analysis with a bio-chemo-mechanical model for traction forces and adhesion dynamics indicated that the observed relationship between traction forces at the front and back of a cell is possible only when cellular elasticity is lower than the elasticity of the cellular environment.

Cell polarity signaling in the plasticity of cancer cell invasiveness

Apico-basal polarity is typical of cells present in differentiated epithelium while front-rear polarity develops in motile cells. In cancer development, the transition from epithelial to migratory polarity may be seen as the hallmark of cancer progression to an invasive and metastatic disease. Despite the morphological and functional dissimilarity, both epithelial and migratory polarity are controlled by a common set of polarity complexes Par, Scribble and Crumbs, phosphoinositides, and small Rho GTPases Rac, Rho and Cdc42. In epithelial tissues, their mutual interplay ensures apico-basal and planar cell polarity. Accordingly, altered functions of these polarity determinants lead to disrupted cell-cell adhesions, cytoskeleton rearrangements and overall loss of epithelial homeostasis. Polarity proteins are further engaged in diverse interactions that promote the establishment of front-rear polarity, and they help cancer cells to adopt different invasion modes. Invading cancer cells can employ either the collective, mesenchymal or amoeboid invasion modes or actively switch between them and gain intermediate phenotypes. Elucidation of the role of polarity proteins during these invasion modes and the associated transitions is a necessary step towards understanding the complex problem of metastasis. In this review we summarize the current knowledge of the role of cell polarity signaling in the plasticity of cancer cell invasiveness.

NBR1 enables autophagy-dependent focal adhesion turnover

The selective autophagy cargo receptor NBR1 enhances the disassembly of cell-matrix focal adhesions during cell migration.

Autophagy is a catabolic pathway involving the sequestration of cellular contents into a double-membrane vesicle, the autophagosome. Although recent studies have demonstrated that autophagy supports cell migration, the underlying mechanisms remain unknown. Using live-cell imaging, we uncover that autophagy promotes optimal migratory rate and facilitates the dynamic assembly and disassembly of cell-matrix focal adhesions (FAs), which is essential for efficient motility. Additionally, our studies reveal that autophagosomes associate with FAs primarily during disassembly, suggesting autophagy locally facilitates the destabilization of cell-matrix contact sites. Furthermore, we identify the selective autophagy cargo receptor neighbor of BRCA1 (NBR1) as a key mediator of autophagy-dependent FA remodeling. NBR1 depletion impairs FA turnover and decreases targeting of autophagosomes to FAs, whereas ectopic expression of autophagy-competent, but not autophagy-defective, NBR1 enhances FA disassembly and reduces FA lifetime during migration. Our findings provide mechanistic insight into how autophagy promotes migration by revealing a requirement for NBR1-mediated selective autophagy in enabling FA disassembly in motile cells.

T cell migration, search strategies and mechanisms

T cell migration is essential for T cell responses; it allows for the detection of cognate antigen at the surface of antigen-presenting cells and for interactions with other cells involved in the immune response. Although appearing random, growing evidence suggests that T cell motility patterns are strategic and governed by mechanisms that are optimized for both the activation stage of the cell and for environment-specific cues. In this Opinion article, we discuss how the combined effects of T cell-intrinsic and -extrinsic forces influence T cell motility patterns in the context of highly complex tissues that are filled with other cells involved in parallel motility. In particular, we examine how insights from 'search theory' can be used to describe T cell movement across an 'exploitation-exploration trade-off' in the context of activation versus effector function and lymph nodes versus peripheral tissues.

Computational Tension Mapping of Adherent Cells Based on Actin Imaging

Forces transiting through the cytoskeleton are known to play a role in adherent cell activity. Up to now few approaches haves been able to determine theses intracellular forces. We thus developed a computational mechanical model based on a reconstruction of the cytoskeleton of an adherent cell from fluorescence staining of the actin network and focal adhesions (FA). Our custom made algorithm converted the 2D image of an actin network into a map of contractile interactions inside a 2D node grid, each node representing a group of pixels. We assumed that actin filaments observed under fluorescence microscopy, appear brighter when thicker, we thus presumed that nodes corresponding to pixels with higher actin density were linked by stiffer interactions. This enabled us to create a system of heterogeneous interactions which represent the spatial organization of the contractile actin network. The contractility of this interaction system was then adapted to match the level of force the cell truly exerted on focal adhesions; forces on focal adhesions were estimated from their vinculin expressed size. This enabled the model to compute consistent mechanical forces transiting throughout the cell. After computation, we applied a graphical approach on the original actin image, which enabled us to calculate tension forces throughout the cell, or in a particular region or even in single stress fibers. It also enabled us to study different scenarios which may indicate the mechanical role of other cytoskeletal components such as microtubules. For instance, our results stated that the ratio between intra and extra cellular compression is inversely proportional to intracellular tension.

3D NUMERICAL STUDY OF CELL DEFORMATION AND MIGRATION IN A FLOW CHAMBER

In recent years, the physiological phenomena of cell displacement and deformation in blood vessels have gradually become an important topic in the field of biomechanics, and also have important theoretical significance and application value in clinical medicine. To study the migration and deformation of blood cell, the influence of elastic modulus on its behavior, and the effect of deformation on its migration. A numerical simulation of a single cell displacement and deformation in a flow chamber was conducted in the present study using a computer program based on the fluid–solid coupling. The displacement and deformation of the cells with different elastic modulus as well as the influence of deformation on the movement of the cell were investigated. The results showed that the cell with greater elastic modulus had a smaller deformation in the direction of gravity and fluid velocity. The deformation of the cell had obvious effect on the displacement in the direction of gravity. The smaller the deformation of the cell in the direction of gravity was, the higher the cell could jump. The three-dimensional numerical calculation method adopted in this paper and the results obtained can provide a reference for the study of the cell mechanic behavior in the vessels.

Stochastic model explains formation of cell arrays on H/O-diamond patterns

Cell migration plays an important role in many biological systems. A relatively simple stochastic model is developed and used to describe cell behavior on chemically patterned substrates. The model is based on three parameters: the speed of cell movement (own and external), the probability of cell adhesion, and the probability of cell division on the substrate. The model is calibrated and validated by experimental data obtained on hydrogen- and oxygen-terminated patterns on diamond. Thereby, the simulations reveal that: (1) the difference in the cell movement speed on these surfaces (about 1.5×) is the key factor behind the formation of cell arrays on the patterns, (2) this difference is provided by the presence of fetal bovine serum (validated by experiments), and (3) the directional cell flow promotes the array formation. The model also predicts that the array formation requires mean distance of cell travel at least 10% of intended stripe width. The model is generally applicable for biosensors using diverse cells, materials, and structures.

Three-dimensional matrix fiber alignment modulates cell migration and MT1-MMP utility by spatially and temporally directing protrusions

Multiple attributes of the three-dimensional (3D) extracellular matrix (ECM) have been independently implicated as regulators of cell motility, including pore size, crosslink density, structural organization, and stiffness. However, these parameters cannot be independently varied within a complex 3D ECM protein network. We present an integrated, quantitative study of these parameters across a broad range of complex matrix configurations using self-assembling 3D collagen and show how each parameter relates to the others and to cell motility. Increasing collagen density resulted in a decrease and then an increase in both pore size and fiber alignment, which both correlated significantly with cell motility but not bulk matrix stiffness within the range tested. However, using the crosslinking enzyme Transglutaminase II to alter microstructure independently of density revealed that motility is most significantly predicted by fiber alignment. Cellular protrusion rate, protrusion orientation, speed of migration, and invasion distance showed coupled biphasic responses to increasing collagen density not predicted by 2D models or by stiffness, but instead by fiber alignment. The requirement of matrix metalloproteinase (MMP) activity was also observed to depend on microstructure, and a threshold of MMP utility was identified. Our results suggest that fiber topography guides protrusions and thereby MMP activity and motility.

A Review of Cell Adhesion Studies for Biomedical and Biological Applications

Cell adhesion is essential in cell communication and regulation, and is of fundamental importance in the development and maintenance of tissues. The mechanical interactions between a cell and its extracellular matrix (ECM) can influence and control cell behavior and function. The essential function of cell adhesion has created tremendous interests in developing methods for measuring and studying cell adhesion properties. The study of cell adhesion could be categorized into cell adhesion attachment and detachment events. The study of cell adhesion has been widely explored via both events for many important purposes in cellular biology, biomedical, and engineering fields. Cell adhesion attachment and detachment events could be further grouped into the cell population and single cell approach. Various techniques to measure cell adhesion have been applied to many fields of study in order to gain understanding of cell signaling pathways, biomaterial studies for implantable sensors, artificial bone and tooth replacement, the development of tissue-on-a-chip and organ-on-a-chip in tissue engineering, the effects of biochemical treatments and environmental stimuli to the cell adhesion, the potential of drug treatments, cancer metastasis study, and the determination of the adhesion properties of normal and cancerous cells. This review discussed the overview of the available methods to study cell adhesion through attachment and detachment events.

From Single Cells to Engineered and Explanted Tissues: New Perspectives in Bacterial Infection Biology

Cell culture techniques are essential for studying host-pathogen interactions. In addition to the broad range of single cell type-based two-dimensional cell culture models, an enormous amount of coculture systems, combining two or more different cell types, has been developed. These systems enable microscopic visualization and molecular analyses of bacterial adherence and internalization mechanisms and also provide a suitable setup for various biochemical, immunological, and pharmacological applications. The implementation of natural or synthetical scaffolds elevated the model complexity to the level of three-dimensional cell culture. Additionally, several transwell-based cell culture techniques are applied to study bacterial interaction with physiological tissue barriers. For keeping highly differentiated phenotype of eukaryotic cells in ex vivo culture conditions, different kinds of microgravity-simulating rotary-wall vessel systems are employed. Furthermore, the implementation of microfluidic pumps enables constant nutrient and gas exchange during cell cultivation and allows the investigation of long-term infection processes. The highest level of cell culture complexity is reached by engineered and explanted tissues which currently pave the way for a more comprehensive view on microbial pathogenicity mechanisms.

Epithelia migration: a spatiotemporal interplay between contraction and adhesion

Epithelial tissues represent 60% of the cells that form the human body and where more than 90% of all cancers derived. Epithelia transformation and migration involve altered cell contractile mechanics powered by an actomyosin-based cytoskeleton and influenced by cell-cell and cell-extracellular matrix interactions. A balance between contractile and adhesive forces regulates a large number of cellular and tissue properties crucial for epithelia migration and tumorigenesis. In this review, the forces driving normal epithelia transformation into highly motile and invasive cells and tissues will be discussed.

Combinative in vitro studies and computational model to predict 3D cell migration response to drug insult

The development of drugs to counter diseases related to cell migration has resulted in a multi-billion dollar endeavor. Unfortunately, few drugs have emerged from this effort highlighting the need for new methods to enhance assays to study, analyze and control cell migration. In response to this complex process, computational models have emerged as potent tools to describe migration providing a high throughput and low cost method. However, most models are unable to predict migration response to drug with direct application to in vitro experiments. In addition to this, no model to date has attempted to describe migration in response to drugs while incorporating simultaneously protein signaling, proteolytic activity, and 3D culture. In this paper, we describe an integrated computational approach, in conjunction with in vitro observations, to serve as a platform to accurately predict migration in 3D matrices incorporating the function of matrix metalloproteinases (MMPs) and their interaction with the Extracellular signal-related kinase (ERK) signaling pathway. Our results provide biological insight into how matrix density, MMP activity, integrin adhesions, and p-ERK expression all affect speed and persistence in 3D. Predictions from the model provide insight toward improving drug combinations to more effectively reduce both speed and persistence during migration and the role of integrin adhesions in motility. In this way our integrated platform provides future potential to streamline and improve throughput toward the testing and development of migration targeting drugs with tangible application to current in vitro assays.

A guide to mechanobiology: Where biology and physics meet

Cells actively sense and process mechanical information that is provided by the extracellular environment to make decisions about growth, motility and differentiation. It is important to understand the underlying mechanisms given that deregulation of the mechanical properties of the extracellular matrix (ECM) is implicated in various diseases, such as cancer and fibrosis. Moreover, matrix mechanics can be exploited to program stem cell differentiation for organ-on-chip and regenerative medicine applications. Mechanobiology is an emerging multidisciplinary field that encompasses cell and developmental biology, bioengineering and biophysics. Here we provide an introductory overview of the key players important to cellular mechanobiology, taking a biophysical perspective and focusing on a comparison between flat versus three dimensional substrates. This article is part of a Special Issue entitled: Mechanobiology.

Effect of adhesion and chemokine presentation on T-lymphocyte haptokinesis

Motility is critical for the function of T-lymphocytes. Motility in T-lymphocytes is driven by the occupancy of chemokine receptors by chemokines, and modulated by adhesive interactions. However, it is not well understood how the combination of adhesion and chemokine binding affects T-lymphocyte migration. We used microcontact printing on polymeric substrates to measure how lymphocyte migration is quantitatively controlled by adhesion and chemokine ligation. Focusing only on random motion, we found that T-lymphocytes exhibit biphasic motility in response to the substrate concentration of either ICAM-1 or VCAM-1, and generally display more active motion on ICAM-1 surfaces. Furthermore, we examined how the combination of the homeostatic chemokines CCL19 and CCL21 contribute to motility. By themselves, CCL19 and CCL21, ligands for CCR7, elicit biphasic motility, but their combination synergistically increases CCR7 mediated chemokinesis on ICAM-1. By presenting CCL21 with ICAM-1 on the surface with soluble CCL19, we observed random motion that is greater than what is observed with soluble chemokines alone. These data suggest that ICAM-1 has a greater contribution to motility than VCAM-1 and that both adhesive interactions and chemokine ligation work in concert to control T-lymphocyte motility.

Three-dimensional numerical model of cell morphology during migration in multi-signaling substrates

Cell Migration associated with cell shape changes are of central importance in many biological processes ranging from morphogenesis to metastatic cancer cells. Cell movement is a result of cyclic changes of cell morphology due to effective forces on cell body, leading to periodic fluctuations of the cell length and cell membrane area. It is well-known that the cell can be guided by different effective stimuli such as mechanotaxis, thermotaxis, chemotaxis and/or electrotaxis. Regulation of intracellular mechanics and cell's physical interaction with its substrate rely on control of cell shape during cell migration. In this notion, it is essential to understand how each natural or external stimulus may affect the cell behavior. Therefore, a three-dimensional (3D) computational model is here developed to analyze a free mode of cell shape changes during migration in a multi-signaling micro-environment. This model is based on previous models that are presented by the same authors to study cell migration with a constant spherical cell shape in a multi-signaling substrates and mechanotaxis effect on cell morphology. Using the finite element discrete methodology, the cell is represented by a group of finite elements. The cell motion is modeled by equilibrium of effective forces on cell body such as traction, protrusion, electrostatic and drag forces, where the cell traction force is a function of the cell internal deformations. To study cell behavior in the presence of different stimuli, the model has been employed in different numerical cases. Our findings, which are qualitatively consistent with well-known related experimental observations, indicate that adding a new stimulus to the cell substrate pushes the cell to migrate more directionally in more elongated form towards the more effective stimuli. For instance, the presence of thermotaxis, chemotaxis and electrotaxis can further move the cell centroid towards the corresponding stimulus, respectively, diminishing the mechanotaxis effect. Besides, the stronger stimulus imposes a greater cell elongation and more cell membrane area. The present model not only provides new insights into cell morphology in a multi-signaling micro-environment but also enables us to investigate in more precise way the cell migration in the presence of different stimuli.

Nanotopography enhanced mobility determines mesenchymal stem cell distribution on micropatterned semiconductors bearing nanorough areas

Surface micropatterns are relevant instruments for the in vitro analysis of cell cultures in non-conventional planar conditions. In this work, two semiconductors (Si and TiO2) have been micropatterned by combined ion-beam/chemical-etching processes leading to selective areas bearing nanorough features. A preferential affinity of human mesenchymal stem cells (hMSCs) for planar areas versus nanotopographic ones is observed. Fluorescence microscopy after β-catenin staining suggests that hMSCs adhesion is inhibited on nanostructured porous silicon areas. This has a direct impact in the development of actin fibers and suggests different cell migration mechanisms on the materials of a micropattern. hMSCs organization on nanotopographic micropatterns has been modeled by using a simplified random walk approach. The model attributes preferential cell mobilities on the nanotopographic areas with respect to the planar and considers purely stochastic movement with no inertial term. Simulations of the cell distribution have been run on 1D and 2D micropatterns and compared with the real hMSC cultures. The simulations allow defining two regimes for cell organization as a function of cell density. hMSCs ordering on planar areas is diffusion-induced in most micropatterns but constriction forced disorder appears for high cell densities. The relative mobility on the planar versus nanotopographic areas can be used as a quality indicator of the nanotopography contrasts in the diffusion induced ordering regime. It is shown that the relative mobility is favorable for the TiO2 versus the Si based system, and allows envisaging its use for the calibrated design of nanotopography based micropatterned materials.

A zebrafish embryo behaves both as a "cortical shell-liquid core" structure and a homogeneous solid when experiencing mechanical forces

Mechanical properties are vital for living cells, and various models have been developed to study the mechanical behavior of cells. However, there is debate regarding whether a cell behaves more similarly to a "cortical shell-liquid core" structure (membrane-like) or a homogeneous solid (cytoskeleton-like) when experiencing stress by mechanical forces. Unlike most experimental methods, which concern the small-strain deformation of a cell, we focused on the mechanical behavior of a cell undergoing small to large strain by conducting microinjection experiments on zebrafish embryo cells. The power law with order of 1.5 between the injection force and the injection distance indicates that the cell behaves as a homogenous solid at small-strain deformation. The linear relation between the rupture force and the microinjector radius suggests that the embryo behaves as membrane-like when subjected to large-strain deformation. We also discuss the possible reasons causing the debate by analyzing the mechanical properties of F-actin filaments.

Physical influences of the extracellular environment on cell migration

The way in which a cell migrates is influenced by the physical properties of its surroundings, in particular the properties of the extracellular matrix. How the physical aspects of the cell's environment affect cell migration poses a considerable challenge when trying to understand migration in complex tissue environments and hinders the extrapolation of in vitro analyses to in vivo situations. A comprehensive understanding of these problems requires an integrated biochemical and biophysical approach. In this Review, we outline the findings that have emerged from approaches that span these disciplines, with a focus on actin-based cell migration in environments with different stiffness, dimensionality and geometry.

Neuronal differentiation of human placenta–derived multi-potent stem cells enhanced by cell body oscillation on gelatin hydrogel

Gelatin is a biocompatible material commonly employed in biomaterial design and tissue engineering. However, there is currently a lack of research into the development of gelatin hydrogels for facilitating specific lineage development of stem cells. In this study, the neuronal differentiation of human placenta–derived multi-potent (stem) cells was systematically optimized through the engineering of the gelatin hydrogel properties. The swelling ratio of Type A or Type B gelatin hydrogel changes during hydrogel formation in the gelatin concentration ranges from 16 to 6 wt%. In general, placenta-derived multi-potent (stem) cells effectively adhere on both, acidic and basic gelatin hydrogels with different swelling ratios as shown by the high attachment ratio of around 80%. Interestingly, adhered placenta-derived multi-potent (stem) cells had significant cell body oscillations on either 6 or 10 wt% gelatin hydrogels during the first 3 h of cell seeding. For placenta-derived multi-potent (stem) cells pre-cultured on 6 and 10 wt% gelatin hydrogel for either 2 or 12 h and subjected to 3-isobutyl-1-methylxanthine to induce neuronal differentiation, the periodic contraction and extension of placenta-derived multi-potent (stem) cells pre-cultured for 2 h successfully directed the cells into neuron-like lineages. In contrast, the lack of cell body oscillation restrained the placenta-derived multi-potent (stem) cells pre-cultured for 12 h from differentiating into neuronal cells on the same gelatin hydrogels in response to 3-isobutyl-1-methylxanthine stimulation. Overall, the possibility of engineering the properties of gelatin hydrogel to trigger stem cell development into a neuronal lineage through cell body oscillations was clearly demonstrated.

High-throughput 3D cell invasion chip enables accurate cancer metastatic assays

Chemotaxis is the phenomenon by which the migration and invasion of cells is directed in response to an extracellular chemical gradient. Chemotaxis of tumor cells and tumor-associated inflammatory and stromal cells is mediated by chemokines, chemokine receptors, growth factors, and growth factor receptors. Current techniques used to study chemotactic driven cell invasion and metastasis utilize two-dimensional migration assays involving imaging and analyzing tumor cells on glass slides or plastic surfaces, which requires large numbers of cells and often lacks real-time monitoring of vertical cell movement and systematically controlled chemotactic gradients, leading to contradictory results compared to those from clinical investigations and animal models. We addressed such challenges by developing a high-throughput microdevice with 4000 ultraminiaturized wells to monitor real-time, three-dimensional cell invasion over a wide range of cell densities and also screen drugs that inhibit cell invasion and potentially prevent metastatic malignancy. Additionally, this microdevice generates opposing gradients for two types of cells on the same chip, which builds a controlled system with sequentially changing components to study environmental effects from basal and immune cells.

Modes and mechanisms of T cell motility: roles for confinement and Myosin-IIA

T cells are charged with surveying tissues for evidence of their cognate foreign antigens. Subsequently, they must navigate to effector sites, which they enter through the process of trans-endothelial migration (TEM). During interstitial migration, T cells migrate according to one of two modes that are distinguished by the strength and sequence of adhesions and the requirement for Myosin-IIA. In contrast during TEM, T cells require Myosin-IIA for the final process of pushing their nucleus through the endothelium. A generalized model emerges with dual roles for Myosin-IIA: This motor protein acts like a tensioning or expansion spring, transmitting force across the cell cortex to sites of surface contact and also optimizing the frictional coupling with substrata by modulating the surface area of the contact. The phosphorylation and deactivation of this motor following TCR engagement can allow T cells to rapidly alter the degree to which they adhere to surfaces and to switch to a mode of interaction with surfaces that is more conducive to forming a synapse with an antigen-presenting cell.

A simple force-motion relation for migrating cells revealed by multipole analysis of traction stress

For biophysical understanding of cell motility, the relationship between mechanical force and cell migration must be uncovered, but it remains elusive. Since cells migrate at small scale in dissipative circumstances, the inertia force is negligible and all forces should cancel out. This implies that one must quantify the spatial pattern of the force instead of just the summation to elucidate the force-motion relation. Here, we introduced multipole analysis to quantify the traction stress dynamics of migrating cells. We measured the traction stress of Dictyostelium discoideum cells and investigated the lowest two moments, the force dipole and quadrupole moments, which reflect rotational and front-rear asymmetries of the stress field. We derived a simple force-motion relation in which cells migrate along the force dipole axis with a direction determined by the force quadrupole. Furthermore, as a complementary approach, we also investigated fine structures in the stress field that show front-rear asymmetric kinetics consistent with the multipole analysis. The tight force-motion relation enables us to predict cell migration only from the traction stress patterns.

Cell migration on planar and three-dimensional matrices: a hydrogel-based perspective

The migration of cells is a complex process that is dependent on the properties of the surrounding environment. In vivo, the extracellular environment is complex with a wide range of physical features, topographies, and protein compositions. There have been a number of approaches to design substrates that can recapitulate the complex architecture in vivo. Two-dimensional (2D) substrates have been widely used to study the effect of material properties on cell migration. However, such substrates do not capture the intricate structure of the extracellular environment. Recent advances in hydrogel assembly and patterning techniques have enabled the design of new three-dimensional (3D) scaffolds and microenvironments. Investigations conducted on these matrices provide growing evidence that several established migratory trends obtained from studies on 2D substrates could be significantly different when conducted in a 3D environment. Since cell migration is closely linked to a wide range of physiological functions, there is a critical need to examine migratory trends on 3D matrices. In this review, our goal is to highlight recent experimental studies on cell migration within engineered 3D hydrogel environments and how they differ from planar substrates. We provide a detailed examination of the changes in cellular characteristics such as morphology, speed, directionality, and protein expression in 3D hydrogel environments. This growing field of research will have a significant impact on tissue engineering, regenerative medicine, and in the design of biomaterials.

A conservative algorithm for parabolic problems in domains with moving boundaries

We describe a novel conservative algorithm for parabolic problems in domains with moving boundaries developed for modeling in cell biology. The spatial discretization is accomplished by applying Voronoi decomposition to a fixed rectangular grid. In the vicinity of the boundary, the procedure generates irregular Voronoi cells that conform to the domain shape and merge seamlessly with regular control volumes in the domain interior. Consequently, our algorithm is free of the CFL stability issue due to moving interfaces and does not involve cell-merging or mass redistribution. Local mass conservation is ensured by finite-volume discretization and natural-neighbor interpolation. Numerical experiments with two-dimensional geometries demonstrate exact mass conservation and indicate an order of convergence in space between one and two. The use of standard meshing techniques makes extension of the method to three dimensions conceptually straightforward.

Collective cell migration of primary zebrafish keratocytes

Fish keratocytes are an established model in single cell motility but little is known about their collective migration. Initially, sheets migrate from the scale at ~145 μm/h but over the course of 24h the rate of leading edge advance decreases to ~23 μm/h. During this period, leader cells retain their ability to migrate rapidly when released from the sheet and follower cell area increases. After the addition of RGD peptide, leader cell lamellae are lost, altering migratory forces within the sheet, resulting in rapid retraction. Leader and follower cell states interconvert within minutes with changes in cell-cell adhesions. Leader cells migrate as single cells when they detach from the leading edge and single cells appear to become leader cells if they rejoin the sheet. Follower cells rapidly establish leader cell morphology during closing of holes formed during sheet expansion and revert to follower cell morphology after hole-closure. Inhibition of Rho associated kinase releases leader cells and halts advancement of the leading edge suggesting an important role for the intercellular actomyosin cable at the leading edge. In addition, the presence of the stationary scale orients direction of sheet migration which is characterized by a more uniform advance of the leading edge than in some cell line systems. These data establish fish keratocyte explant cultures as a collective cell migration system and suggest that cell-cell interactions determine the role of keratocytes within the migrating sheet.

Biomaterial arrays with defined adhesion ligand densities and matrix stiffness identify distinct phenotypes for tumorigenic and nontumorigenic human mesenchymal cell types

Here, we aimed to investigate migration of a model tumor cell line (HT-1080 fibrosarcoma cells, HT-1080s) using synthetic biomaterials to systematically vary peptide ligand density and substrate stiffness. A range of substrate elastic moduli were investigated by using poly(ethylene glycol) (PEG) hydrogel arrays (0.34 - 17 kPa) and self-assembled monolayer (SAM) arrays (~0.1-1 GPa), while cell adhesion was tuned by varying the presentation of Arg-Gly-Asp (RGD)-containing peptides. HT-1080 motility was insensitive to cell adhesion ligand density on RGD-SAMs, as they migrated with similar speed and directionality for a wide range of RGD densities (0.2-5% mol fraction RGD). Similarly, HT-1080 migration speed was weakly dependent on adhesion on 0.34 kPa PEG surfaces. On 13 kPa surfaces, a sharp initial increase in cell speed was observed at low RGD concentration, with no further changes observed as RGD concentration was increased further. An increase in cell speed ~ two-fold for the 13 kPa relative to the 0.34 kPa PEG surface suggested an important role for substrate stiffness in mediating motility, which was confirmed for HT-1080s migrating on variable modulus PEG hydrogels with constant RGD concentration. Notably, despite ~ two-fold changes in cell speed over a wide range of moduli, HT-1080s adopted rounded morphologies on all surfaces investigated, which contrasted with well spread primary human mesenchymal stem cells (hMSCs). Taken together, our results demonstrate that HT-1080s are morphologically distinct from primary mesenchymal cells (hMSCs) and migrate with minimal dependence on cell adhesion for surfaces within a wide range of moduli, whereas motility is strongly influenced by matrix mechanical properties.

ONE-DIMENSIONAL MODELING AND SIMULATIONS OF MIGRATION OF CULTURED FIBROBLASTS

Cell migration is crucial for many physiological functions such as wound healing, immuno-response and carcinogenesis. In this study an one-dimensional model of migration of fibroblasts was developed by modeling and integrating five subcellular processes, namely, actin protrusion, focal adhesion formation, stress fiber formation, polarization and retraction. The direction of migration was determined by polarization, which was related to direction of the stiffness gradient of the substrate. By controlling intensity of ultraviolet exposure on type-I collagen, a substrate with a stiffness gradient could be fabricated. Kinematic analyses of positions of the cell front, the nucleus and the cell rear, were utilized as inputs to the model. Simulation results of five live NIH 3T3 fibroblasts showed that the model was capable of simulating fast moving, slow moving and back-and-forth moving of the cells on the substrate.

Molecular mechanisms underlying the divergent roles of SPARC in human carcinogenesis

Communication between the cell and its surrounding environment, consisting of proteinaceous (non-living material) and extracellular matrix (ECM), is important for biophysiological and chemical signaling. This signaling results in a range of cellular activities, including cell division, adhesion, differentiation, invasion, migration and angiogenesis. The ECM non-structural secretory glycoprotein called secreted protein, acidic and rich in cysteine (SPARC), plays a significant role in altering cancer cell activity and the tumor's microenvironment (TME). However, the role of SPARC in cancer research has been the subject of controversy. This review mainly focuses on recent advances in understanding the contradictory nature of SPARC in relation to ECM assembly, cancer cell proliferation, adhesion, migration, apoptosis and tumor growth.

Stringent requirement for spatial arrangement of extracellular matrix in supporting cell morphogenesis and differentiation

Background

In vitro experiments on the functional roles of extracellular matrix (ECM) components usually involve the culture of cells on surfaces coated with purified ECM components. These experiments can seldom recuperate the spatial arrangement of ECM found in vivo. In this study, we have overcome this obstacle by using histological sections of bovine Achilles tendon as cell culture substrates.

Results

We found that tendon sections can be viewed as a pre-formed block of ECM in which the collagen fibrils exhibited a spatial regularity unraveled in any artificially constructed scaffold. By carving the tendon at different angles relative to its main axis, we created different surfaces with distinct spatial arrangements of collagen fibrils. To assess the cellular responses to these surfaces, human mesenchymal stem cells (MSCs) were directly cultured on these sections, hence exposed to the collagen with different spatial orientations. Cells seeded on longitudinal tendon sections adopted a highly elongated and aligned morphology, and expressed an increased level of tenomodulin, suggesting that the collagen fibrils present in this section provide a microenvironment that facilitates cell morphogenesis and differentiation. However, MSC elongation, alignment and induction of tenomodulin diminished dramatically even as the sectioned angle changed slightly.

Conclusion

Our results suggest that cell functions are influenced not only by the type or concentration of ECM components, but also by the precise spatial arrangements of these molecules. The method developed in this study offers a simple and robust way for the studying of cell-ECM interactions, and opens many research avenues in the field of matrix biology.

A mathematical model of the coupled mechanisms of cell adhesion, contraction and spreading

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell's cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell's boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.

Matrikine and matricellular regulators of EGF receptor signaling on cancer cell migration and invasion

Cancer invasion is a complex process requiring, among other events, extensive remodeling of the extracellular matrix including deposition of pro-migratory and pro-proliferative moieties. In recent years, it has been described that while invading through matrices cancer cells can change shape and adapt their migration strategies depending on the microenvironmental context. Although intracellular signaling pathways governing the mesenchymal to amoeboid migration shift and vice versa have been mostly elucidated, the extracellular signals promoting these shifts are largely unknown. In this review, we summarize findings that point to matrikines that bind specifically to the EGF receptor as matricellular molecules that enable cancer cell migrational plasticity and promote invasion.

Motility efficiency and spatiotemporal synchronization in non-metastatic vs. metastatic breast cancer cells

Metastatic breast cancer cells move not only more rapidly and persistently than their non-metastatic variants but in doing so use the mechanical work of the cytoskeleton more efficiently. The efficiency of the cell motions is defined for entire cells (rather than parts of the cell membrane) and is related to the work expended in forming membrane protrusions and retractions. This work, in turn, is estimated by integrating the protruded and retracted areas along the entire cell perimeter and is standardized with respect to the net translocation of the cell. A combination of cross-correlation, Granger causality, and morphodynamic profiling analyses is then used to relate the efficiency to the cell membrane dynamics. In metastatic cells, the protrusions and retractions are highly "synchronized" both in space and in time and these cells move efficiently. In contrast, protrusions and retractions formed by non-metastatic cells are not "synchronized" corresponding to low motility efficiencies. Our work provides a link between the kinematics of cell motions and their energetics. It also suggests that spatiotemporal synchronization might be one of the hallmarks of invasiveness of cancerous cells.

Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility

A physicochemical model is used to describe the coupling of adhesion, cytoskeletal, and signaling dynamics during cell migration. Analysis of stochastic simulations predicts relationships between measurable quantities that reflect partitioning of stress between F-actin–bound adhesions, which act as a molecular clutch, and retrograde F-actin flow.

Animal cell migration is a complex process characterized by the coupling of adhesion, cytoskeletal, and signaling dynamics. Here we model local protrusion of the cell edge as a function of the load-bearing properties of integrin-based adhesions, actin polymerization fostered by adhesion-mediated signaling, and mechanosensitive activation of RhoA that promotes myosin II–generated stress on the lamellipodial F-actin network. Analysis of stochastic model simulations illustrates how these pleiotropic functions of nascent adhesions may be integrated to govern temporal persistence and frequency of protrusions. The simulations give mechanistic insight into the documented effects of extracellular matrix density and myosin abundance, and they show characteristic, nonnormal distributions of protrusion duration times that are similar to those extracted from live-cell imaging experiments. Analysis of the model further predicts relationships between measurable quantities that reflect the partitioning of stress between tension on F-actin–bound adhesions, which act as a molecular clutch, and dissipation by retrograde F-actin flow.

Geometric control of cell migration

Morphological polarization involving changes in cell shape and redistribution of cellular signaling machinery, initiate the migration of mammalian cells. Golgi complex typically localizes in front of the nucleus, and this frontwards polarization has been proposed to be involved in directional migration. However, the sequence of events remains unresolved. Does Golgi polarization precede directional migration or vice-versa? We address this question by constraining cells to specific areas and shapes then tracking their motile behavior and the spatio-temporal distribution of Golgi apparatus upon release. Results show that while the position of the Golgi complex depends on the cell geometry, the subcellular localization of the Golgi complex does not define the cell's leading edge. Cells constrained within elongated geometries exhibit polarized extension of lamellipodia and upon release, migrate preferentially along the long axis of the cell. Minimally constrained cells released from larger areas however, exhibit retarded migration regardless of lamellipodia protrusion activity.

Extracellular acidic pH inhibits oligodendrocyte precursor viability, migration, and differentiation

Axon remyelination in the central nervous system requires oligodendrocytes that produce myelin. Failure of this repair process is characteristic of neurodegeneration in demyelinating diseases such as multiple sclerosis, and it remains unclear how the lesion microenvironment contributes to decreased remyelination potential of oligodendrocytes. Here, we show that acidic extracellular pH, which is characteristic of demyelinating lesions, decreases the migration, proliferation, and survival of oligodendrocyte precursor cells (OPCs), and reduces their differentiation into oligodendrocytes. Further, OPCs exhibit directional migration along pH gradients toward acidic pH. These in vitro findings support a possible in vivo scenario whereby pH gradients attract OPCs toward acidic lesions, but resulting reduction in OPC survival and motility in acid decreases progress toward demyelinated axons and is further compounded by decreased differentiation into myelin-producing oligodendrocytes. As these processes are integral to OPC response to nerve demyelination, our results suggest that lesion acidity could contribute to decreased remyelination.

Dosage of amyloid precursor protein affects axonal contact guidance in Down syndrome

Amyloid precursor protein (APP), encoded on Hsa21, functions as a cell adhesion molecule (CAM) in axonal growth cones (GCs) of the developing brain. We show here that axonal GCs of human fetal Down syndrome (DS) neurons (and of a DS mouse model) overexpress APP protein relative to euploid controls. We investigated whether DS neurons generate an abnormal, APP-dependent GC phenotype in vitro. On laminin, which binds APP and β1 integrins (Itgb1), DS neurons formed enlarged and faster-advancing GCs compared to controls. On peptide matrices that bind APP only, but not on those binding exclusively Itgb1 or L1CAM, DS GCs were significantly enlarged (2.0-fold), formed increased close adhesions (1.8-fold), and advanced faster (1.4-fold). In assays involving alternating stripes of monospecific matrices, human control GCs exhibited no preference for any of the substrates, whereas DS GCs preferred the APP-binding matrix (cross-over decreased significantly from 48.2 to 27.2%). Reducing APP expression in DS GCs with siRNA normalized most measures of the phenotype, including substrate choice. These experiments show that human DS neurons exhibit an APP-dependent, abnormal GC phenotype characterized by increased adhesion and altered contact guidance. The results suggest that APP overexpression may perturb axonal pathfinding and circuit formation in developing DS brain.

The role of engineering approaches in analysing cancer invasion and metastasis

In the past decade, novel materials, probes and tools have enabled fundamental and applied cancer researchers to take a fresh look at the complex problem of tumour invasion and metastasis. These new tools, which include imaging modalities, controlled but complex in vitro culture conditions, and the ability to model and predict complex processes in vivo, represent an integration of traditional with novel engineering approaches; and their potential effect on quantitatively understanding tumour progression and invasion looks promising.