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

Nanoscale tissue engineering: spatial control over cell-materials interactions

Cells interact with the surrounding environment by making tens to hundreds of thousands of nanoscale interactions with extracellular signals and features. The goal of nanoscale tissue engineering is to harness these interactions through nanoscale biomaterials engineering in order to study and direct cellular behavior. Here, we review two- and three-dimensional (2- and 3D) nanoscale tissue engineering technologies, and provide a holistic overview of the field. Techniques that can control the average spacing and clustering of cell adhesion ligands are well established and have been highly successful in describing cell adhesion and migration in 2D. Extension of these engineering tools to 3D biomaterials has created many new hydrogel and nanofiber scaffold technologies that are being used to design in vitro experiments with more physiologically relevant conditions. Researchers are beginning to study complex cell functions in 3D. However, there is a need for biomaterials systems that provide fine control over the nanoscale presentation of bioactive ligands in 3D. Additionally, there is a need for 2- and 3D techniques that can control the nanoscale presentation of multiple bioactive ligands and that can control the temporal changes in the cellular microenvironment.

An adhesion-dependent switch between mechanisms that determine motile cell shape

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes.

Cell migration is important for many biological processes: white blood cells chase down and kill bacteria to guard against infection, epithelial cells crawl across open wounds to promote healing, and embryonic cells move collectively to form organs and tissues during embryogenesis. In all of these cases, migration depends on the spatial and temporal organization of multiple forces, including actin-driven protrusion of the cell membrane, membrane tension, cell-substrate adhesion, and myosin-mediated contraction of the actin network. In this work, we have used a simple cell type, the fish epithelial keratocyte, as a model system to investigate the manner in which these forces are integrated to give rise to large-scale emergent properties such as cell shape and movement. Keratocytes are normally fan-shaped and fast-moving, but we have found that keratocytes migrate more slowly and assume round or asymmetric shapes when cell-substrate adhesion strength is too high or too low. By correlating measurements of adhesion-dependent changes in cell shape and speed with measurements of adhesion and myosin localization patterns and actin network organization, we have developed a mechanical model in which keratocyte shape and movement emerge from adhesion and myosin-dependent regulation of the dynamic actin cytoskeleton.

A numerical model for durotaxis

Cell migration is a phenomenon that is involved in several physiological processes. In the absence of external guiding factors it shares analogies with Brownian motion. The presence of biochemical or biophysical cues, on the other hand, can influence cell migration transforming it in a biased random movement. Recent studies have shown that different cell types are able to recognise the mechanical properties of the substratum over which they move and that these properties direct the motion through a process called durotaxis. In this work a 2D mathematical model for the description of this phenomenon is presented. The model is based on the Langevin equation that has been modified to take into account the local mechanical properties of the substratum perceived by the cells. Numerical simulations of the model provide individual cell tracks, whose characteristics can be compared with experimental observations directly. The present model is solved for two important cases: an isotropic substratum, to check that random motility is recovered as a subcase, and a biphasic substratum, to investigate durotaxis. The degree of agreement is satisfactory in both cases. The model can be a useful tool for quantifying relevant parameters of cell migration as a function of the substratum mechanical properties.

From molecular signal activation to locomotion: an integrated, multiscale analysis of cell motility on defined matrices

The adhesion, mechanics, and motility of eukaryotic cells are highly sensitive to the ligand density and stiffness of the extracellular matrix (ECM). This relationship bears profound implications for stem cell engineering, tumor invasion and metastasis. Yet, our quantitative understanding of how ECM biophysical properties, mechanotransductive signals, and assembly of contractile and adhesive structures collude to control these cell behaviors remains extremely limited. Here we present a novel multiscale model of cell migration on ECMs of defined biophysical properties that integrates local activation of biochemical signals with adhesion and force generation at the cell-ECM interface. We capture the mechanosensitivity of individual cellular components by dynamically coupling ECM properties to the activation of Rho and Rac GTPases in specific portions of the cell with actomyosin contractility, cell-ECM adhesion bond formation and rupture, and process extension and retraction. We show that our framework is capable of recreating key experimentally-observed features of the relationship between cell migration and ECM biophysical properties. In particular, our model predicts for the first time recently reported transitions from filopodial to “stick-slip” to gliding motility on ECMs of increasing stiffness, previously observed dependences of migration speed on ECM stiffness and ligand density, and high-resolution measurements of mechanosensitive protrusion dynamics during cell motility we newly obtained for this study. It also relates the biphasic dependence of cell migration speed on ECM stiffness to the tendency of the cell to polarize. By enabling the investigation of experimentally-inaccessible microscale relationships between mechanotransductive signaling, adhesion, and motility, our model offers new insight into how these factors interact with one another to produce complex migration patterns across a variety of ECM conditions.

A mathematical model for mesenchymal and chemosensitive cell dynamics

The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared.

Cortactin: a multifunctional regulator of cellular invasiveness

Branched actin assembly is critical for a variety of cellular processes that underlie cell motility and invasion, including cellular protrusion formation and membrane trafficking. Activation of branched actin assembly occurs at various subcellular locations via site-specific activation of distinct WASp family proteins and the Arp2/3 complex. A key branched actin regulator that promotes cell motility and links signaling, cytoskeletal and membrane trafficking proteins is the Src kinase substrate and Arp2/3 binding protein cortactin. Due to its frequent overexpression in advanced, invasive cancers and its general role in regulating branched actin assembly at multiple cellular locations, cortactin has been the subject of intense study. Recent studies suggest that cortactin has a complex role in cellular migration and invasion, promoting both on-site actin polymerization and modulation of autocrine secretion. Diverse cellular activities may derive from the interaction of cortactin with site-specific binding partners.

Measurement of Cell Adhesion and Migration on Protein-Coated Surfaces

The performance of biomaterials forin vivoandin vitroapplications can depend critically on tissue cell adhesion and migration. We have been investigating the role that specific reversible interactions between cell adhesion receptors and complementary substratum-bound ligands play in the regulation of cell adhesion and migration. With an axisymmetric radial flow detachment assay (RFDA) [1] we measured cell-substratum adhesive strength for human smooth muscle cells (HSMCs) on surfaces coated with type IV collagen (CIV). We found that the critical shear stress for detachment increased linearly with increasing CIV coating concentration. Using time-lapse videomicroscopy and image analysis we tracked the movement of individual HSMCs over similar CIV-coated surfaces. Cell speed and persistence were determined for variations in CIV coating concentration by applying a persistent random walk model for individual cell movement. Cell speed reached a maximum at an intermediate concentration of CIV, supporting the hypothesis that an optimal cell-substratum adhesiveness exists for HSMC movement. This combination of techniques for measuring adhesion and motility provides a valuable tool to examine the role of cell-biomaterial interactions on cell behavior.

Acidic extracellular pH promotes activation of integrin α(v)β(3)

Acidic extracellular pH is characteristic of the cell microenvironment in several important physiological and pathological contexts. Although it is well established that acidic extracellular pH can have profound effects on processes such as cell adhesion and migration, the underlying molecular mechanisms are largely unknown. Integrin receptors physically connect cells to the extracellular matrix, and are thus likely to modulate cell responses to extracellular conditions. Here, we examine the role of acidic extracellular pH in regulating activation of integrin α_vβ₃. Through computational molecular dynamics simulations, we find that acidic extracellular pH promotes opening of the α_vβ₃ headpiece, indicating that acidic pH can thereby facilitate integrin activation. This prediction is consistent with our flow cytometry and atomic force microscope-mediated force spectroscopy assays of integrin α_vβ₃ on live cells, which both demonstrate that acidic pH promotes activation at the intact cell surface. Finally, quantification of cell morphology and migration measurements shows that acidic extracellular pH affects cell behavior in a manner that is consistent with increased integrin activation. Taken together, these computational and experimental results suggest a new and complementary mechanism of integrin activation regulation, with associated implications for cell adhesion and migration in regions of altered pH that are relevant to wound healing and cancer.

Changes in astrocyte shape induced by sublytic concentrations of the cholesterol-dependent cytolysin pneumolysin still require pore-forming capacity

Streptococcus pneumoniae is a common pathogen that causes various infections, such as sepsis and meningitis. A major pathogenic factor of S. pneumoniae is the cholesterol-dependent cytolysin, pneumolysin. It produces cell lysis at high concentrations and apoptosis at lower concentrations. We have shown that sublytic amounts of pneumolysin induce small GTPase-dependent actin cytoskeleton reorganization and microtubule stabilization in human neuroblastoma cells that are manifested by cell retraction and changes in cell shape. In this study, we utilized a live imaging approach to analyze the role of pneumolysin’s pore-forming capacity in the actin-dependent cell shape changes in primary astrocytes. After the initial challenge with the wild-type toxin, a permeabilized cell population was rapidly established within 20-40 minutes. After the initial rapid permeabilization, the size of the permeabilized population remained unchanged and reached a plateau. Thus, we analyzed the non-permeabilized (non-lytic) population, which demonstrated retraction and shape changes that were inhibited by actin depolymerization. Despite the non-lytic nature of pneumolysin treatment, the toxin’s lytic capacity remained critical for the initiation of cell shape changes. The non-lytic pneumolysin mutants W433F-pneumolysin and delta6-pneumolysin, which bind the cell membrane with affinities similar to that of the wild-type toxin, were not able to induce shape changes. The initiation of cell shape changes and cell retraction by the wild-type toxin were independent of calcium and sodium influx and membrane depolarization, which are known to occur following cellular challenge and suggested to result from the ion channel-like properties of the pneumolysin pores. Excluding the major pore-related phenomena as the initiation mechanism of cell shape changes, the existence of a more complex relationship between the pore-forming capacity of pneumolysin and the actin cytoskeleton reorganization is suggested.

Mechanics and regulation of cell shape during the cell cycle

Many cell types undergo dramatic changes in shape throughout the cell cycle. For individual cells, a tight control of cell shape is crucial during cell division, but also in interphase, for example during cell migration. Moreover, cell cycle-related cell shape changes have been shown to be important for tissue morphogenesis in a number of developmental contexts. Cell shape is the physical result of cellular mechanical properties and of the forces exerted on the cell. An understanding of the causes and repercussions of cell shape changes thus requires knowledge of both the molecular regulation of cellular mechanics and how specific changes in cell mechanics in turn effect global shape changes. In this chapter, we provide an overview of the current knowledge on the control of cell morphology, both in terms of general cell mechanics and specifically during the cell cycle.

A POROELASTIC MODEL FOR CELL CRAWLING INCLUDING MECHANICAL COUPLING BETWEEN CYTOSKELETAL CONTRACTION AND ACTIN POLYMERIZATION

Much is known about the biophysical mechanisms involved in cell crawling, but how these processes are coordinated to produce directed motion is not well understood. Here, we propose a new hypothesis whereby local cytoskeletal contraction generates fluid flow through the lamellipodium, with the pressure at the front of the cell facilitating actin polymerization which pushes the leading edge forward. The contraction, in turn, is regulated by stress in the cytoskeleton. To test this hypothesis, finite element models for a crawling cell are presented. These models are based on nonlinear poroelasticity theory, modified to include the effects of active contraction and growth, which are regulated by mechanical feedback laws. Results from the models agree reasonably well with published experimental data for cell speed, actin flow, and cytoskeletal deformation in migrating fish epidermal keratocytes. The models also suggest that oscillations can occur for certain ranges of parameter values.

Eukaryotic chemotaxis

During eukaryotic chemotaxis, external chemical gradients guide the crawling motion of cells. This process plays an important role in a large variety of biological systems and has wide ranging medical implications. New experimental techniques including confocal microscopy and microfluidics have advanced our understanding of chemotaxis while numerical modeling efforts are beginning to offer critical insights. In this short review, we survey the current experimental status of the field by dividing chemotaxis into three distinct "modules": directional sensing, polarity and motility. For each module, we attempt to point out potential new directions of research and discuss how modeling studies interact with experimental investigations.

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.

Effects of RGDS sequence genetically interfused in the silk fibroin light chain protein on chondrocyte adhesion and cartilage synthesis

Initial chondrocyte-silk fibroin interactions are implicated in chondrogenesis when using fibroin as a scaffold for chondrocytes. Here, we focused on integrin-mediated cell-scaffold adhesion and prepared cell adhesive fibroin in which a tandem repeat of the Arg-Gly-Asp-Ser (RGDS) sequence was genetically interfused in the fibroin light chain (L-chain) (L-RGDSx2 fibroin). We investigated the effects of the sequence on chondrocyte adhesion and cartilage synthesis, in comparison to the effects of fibronectin. As the physicochemical surface properties (e.g., wettability and zeta potential) of the fibroin substrate were not affected by the modification, specific cell adhesion to the RGDS predominately changed the chondrocyte adhesive state. This suggestion was also supported by the competitive inhibition of chondrocyte attachment to the L-RGDSx2 fibroin substrate with soluble RGD peptides in the medium. Unlike fibronectin, the expression of RGDS in the fibroin L-chain had no effect on chondrocyte spreading area but enhanced mRNA expression levels of integrins alpha5 and beta1, and aggrecan at 12 h after seeding. Although both the sequence and fibronectin increased cell adhesive force, chondrocytes grown on the fibroin substrate exhibited a peak in the force with time in culture. These results suggested that moderate chondrocyte adhesion to fibroin induced by the RGDS sequence was able to maintain the chondrogenic phenotype and, from the histology findings, the sequence could facilitate chondrogenesis.

The role of cell contraction and adhesion in dictyostelium motility

The crawling motion of Dictyostelium discoideum on substrata involves a number of coordinated events including cell contractions and cell protrusions. The mechanical forces exerted on the substratum during these contractions have recently been quantified using traction force experiments. Based on the results from these experiments, we present a biomechanical model of the contraction phase of Dictyostelium discoideum motility with an emphasis on the adhesive properties of the cell-substratum contact. Our model assumes that the cell contracts at a constant rate and is bound to the substratum by adhesive bridges that are modeled as elastic springs. These bridges are established at a spatially uniform rate while detachment occurs at a spatially varying, load-dependent rate. Using Monte Carlo simulations and assuming a rigid substratum, we find that the cell speed depends only weakly on the detachment kinetics of the cell-substratum interface, in agreement with experimental data. By varying the parameters that control the adhesive and contractile properties of the cell, we are able to make testable predictions. We also extend our model to include a flexible substrate and show that our model is able to produce substratum deformations and force patterns that are quantitatively and qualitatively in agreement with experimental data.

An optical method to quantify the density of ligands for cell adhesion receptors in three-dimensional matrices

The three-dimensional matrix that surrounds cells is an important insoluble regulator of cell phenotypes. Examples of such insoluble surfaces are the extracellular matrix (ECM), ECM analogues and synthetic polymeric biomaterials. Cell-matrix interactions are mediated by cell adhesion receptors that bind to chemical entities (adhesion ligands) on the surface of the matrix. There are currently no established methods to obtain quantitative estimates of the density of adhesion ligands recognized by specific cell adhesion receptors. This article presents a new optical-based methodology for measuring ligands of adhesion receptors on three-dimensional matrices. The study also provides preliminary quantitative results for the density of adhesion ligands of integrins alpha(1)beta(1) and alpha(2)beta(1) on the surface of collagen-based scaffolds, similar to biomaterials that are used clinically to induce regeneration in injured skin and peripheral nerves. Preliminary estimates of the surface density of the ligands of these two major collagen-binding receptors are 5775 +/- 2064 ligands microm(-2) for ligands of alpha(1)beta(1) and 17 084 +/- 5353 ligands microm(-2) for ligands of alpha(2)beta(1). The proposed methodology can be used to quantify the surface chemistry of insoluble surfaces that possess biological activity, such as native tissue ECM and biomaterials, and therefore can be used in cell biology, biomaterials science and regenerative medical studies for quantitative description of a matrix and its effects on cells.

Improving bacterial cellulose for blood vessel replacement: Functionalization with a chimeric protein containing a cellulose-binding module and an adhesion peptide

Chimeric proteins containing a cellulose-binding module (CBM) and an adhesion peptide (RGD or GRGDY) were produced and used to improve the adhesion of human microvascular endothelial cells (HMEC) to bacterial cellulose (BC). The effect of these proteins on the HMEC-BC interaction was studied. The results obtained demonstrated that recombinant proteins containing adhesion sequences were able to significantly increase the attachment of HMEC to BC surfaces, especially the RGD sequence. The images obtained by scanning electron microscopy showed that the cells on the RGD-treated BC present a more elongated morphology 48h after cell seeding. The results also showed that RGD decreased the in-growth of HMEC cells through the BC and stimulated the early formation of cord-like structures by these endothelial cells. Thus, the use of recombinant proteins containing a CBM domain, with high affinity and specificity for cellulose surfaces allows control of the interaction of this material with cells. CBM may be combined with virtually any biologically active protein for the modification of cellulose-based materials, for in vitro or in vivo applications.

Cell physician: reading cell motion: a mathematical diagnostic technique through analysis of single cell motion

Cell motility is an essential phenomenon in almost all living organisms. It is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading cell motion, namely, understanding the underlying biophysical and mechanochemical processes, is of paramount importance. The mathematical model developed in this paper determines some physical features and material properties of the cells locally through analysis of live cell image sequences and uses this information to make further inferences about the molecular structures, dynamics, and processes within the cells, such as the actin network, microdomains, chemotaxis, adhesion, and retrograde flow. The generality of the principals used in formation of the model ensures its wide applicability to different phenomena at various levels. Based on the model outcomes, we hypothesize a novel biological model for collective biomechanical and molecular mechanism of cell motion.

Confinement-optimized three-dimensional T cell amoeboid motility is modulated via myosin IIA-regulated adhesions

During trafficking through tissues, T cells fine-tune their motility to balance the extent and duration of cell-surface contacts with the need to traverse an entire organ. In vivo, Myosin-IIA-deficient T cells exhibited a triad of defects including over-adherence to high-endothelial venules, reduced interstitial migration, and inefficient completion of recirculation through lymph nodes. Spatiotemporal analysis of 3-dimensional motility in microchannels revealed that the degree of confinement and Myosin-IIA function, rather than integrin adhesion as proposed by the haptokinetic model, optimize motility rate. This occurs via a Myosin-IIA-dependent rapid ‘walking’ motility mode using multiple small and simultaneous adhesions to the substrate, which prevent spurious and prolonged adhesions. Adhesion discrimination provided by Myosin-IIA is thus necessary for optimizing motility through complex tissues.

Enzyme mediated site-specific surface modification

Stable tethering of bioactive peptides like RGD to surfaces can be achieved via chemical bonding, biotin streptavidin interaction, or photocross-linking. More challenging is the immobilization of proteins, since methods applied to immobilize peptides are either not specific or versatile enough or might even compromise the protein's bioactivity. To overcome this limitation, we have employed a scheme that by enzymatic (transglutaminase) reaction allows the site-directed and site-specific coupling of growth factors and other molecules to nonfouling poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g-PEG) coated surfaces under physiological conditions. By our modular and flexible design principle, we are able to functionalize these surfaces directly with peptides and growth factors or precisely position poly(ethylene glycol) (PEG)-like hydrogels for the presentation of growth factors as exemplified with vascular endothelial growth factor (VEGF).

Covalently immobilized RGD gradient on PEG hydrogel scaffold influences cell migration parameters

Understanding the influence of a controlled spatial distribution of biological cues on cell activities can be useful to design "cell instructive" materials, able to control and guide the formation of engineered tissues in vivo and in vitro. To this purpose, biochemical and mechanical properties of the resulting biomaterial must be carefully designed and controlled. In this work, the effect of covalently immobilized RGD peptide gradients on poly(ethylene glycol) diacrylate hydrogels on cell behaviour was studied. We set up a mechanical device generating gradients based on a fluidic chamber. Cell response to RGD gradients with different slope (0.7, 1 and 2 mM cm(-1)) was qualitatively and quantitatively assessed by evaluating cell adhesion and, in particular, cell migration, compared to cells seeded on hydrogels with uniform distribution of RGD peptides. To evaluate the influence of RGD gradient and to exclude any concentration effect on cell response, all analyses were carried out in a specific region of the gradients which displayed the same average concentration of RGD (1.5 mM). Results suggest that cells recognize the RGD gradient and adhere onto it assuming a stretched shape. Moreover, cells tend to migrate in the direction of the gradient, as their speed is higher than that of cells migrating on hydrogels with a uniform distribution of RGD and increases by increasing RGD gradient steepness. This increment is due to an augmentation of bias speed component of the mean squared speed, that is, the drift of the cell population migrating on the anisotropic surface provided by the RGD gradient.

Bipedal locomotion in crawling cells

Many complex cellular processes from mitosis to cell motility depend on the ability of the cytoskeleton to generate force. Force-generating systems that act on elastic cytoskeletal elements are prone to oscillating instabilities. In this work, we have measured spontaneous shape and movement oscillations in motile fish epithelial keratocytes. In persistently polarized, fan-shaped cells, retraction of the trailing edge on one side of the cell body is out of phase with retraction on the other side, resulting in periodic lateral oscillation of the cell body. We present a physical description of keratocyte oscillation in which periodic retraction of the trailing edge is the result of elastic coupling with the leading edge. Consistent with the predictions of this model, the observed frequency of oscillation correlates with cell speed. In addition, decreasing the strength of adhesion to the substrate reduces the elastic force required for retraction, causing cells to oscillate with higher frequency at relatively lower speeds. These results demonstrate that simple elastic coupling between movement at the front of the cell and movement at the rear can generate large-scale mechanical integration of cell behavior.

A model of fibroblast motility on substrates with different rigidities

To function efficiently in the body, the biological cells must have the ability to sense the external environment. Mechanosensitivity toward the extracellular matrix was identified as one of the sensing mechanisms affecting cell behavior. It was shown experimentally that a fibroblast cell prefers locomoting over the stiffer substrate when given a choice between a softer and a stiffer substrate. In this article, we develop a discrete model of fibroblast motility with substrate-rigidity sensing. Our model allows us to understand the interplay between the cell-substrate sensing and the cell biomechanics. The model cell exhibits experimentally observed substrate rigidity sensing, which allows us to gain additional insights into the cell mechanosensitivity.

A mathematical model of intercellular signaling during epithelial wound healing

Recent experiments monitoring the healing process of wounded epithelial monolayers have demonstrated the necessity of MAPK activation for coordinated cell movement after damage. This MAPK activity is characterized by two wave-like phenomena. One MAPK "wave" that originates immediately after injury, propagates deep into the cell sheet, away from the edge, and then rebounds back to the wound interface. After this initial MAPK activity has largely disappeared, a second MAPK front propagates slowly from the wound interface and also continues into the cell sheet, maintaining a sustained level of MAPK activity throughout the cell sheet. It has been suggested that the first wave is initiated by Reactive Oxygen Species (ROS) generated at the time of injury. In this work, we develop a minimal mathematical model that reproduces the observed behavior. The main ingredients of our model are a competition between ligand (e.g., Epithelial Growth Factor) and ROS for the activation of Epithelial Growth Factor Receptor, and a feedback loop between receptor occupancy and MAPK activation. We explore the mathematical properties of the model and look for traveling wave solutions consistent with the experimentally observed MAPK activity patterns.

Adhesive dynamics of lubricated films

Membrane waves have been observed near the leading edge of a motile cell. Such phenomenon is the result of the interplay between hydrodynamics and adhesive dynamics. Here we consider membrane dynamics on a thin fluid gap supported by adhesive bonds. Using coupled lubrication theory and adhesive dynamics, we derive an evolution equation to account for membrane tension, bending, adhesion, and viscous lubrication. Four adhesion scenarios are examined: no adhesion, uniform adhesion, clustered adhesion, and focal adhesion. Two contrasting traveling wave types are found, namely, tension and adhesion waves. Tension waves disperse with time and space, whereas adhesion waves show increased amplitudes and are highly persistent. We show that the transition from tension to adhesion waves depends on a necessary, but insufficient, criterion that the wave amplitude must exceed a critical gap height, which is dependent on adhesion binding probability. We also show that strong adhesion results in sharp tension-to-adhesion wave transitions. The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.

Stochastic model of integrin-mediated signaling and adhesion dynamics at the leading edges of migrating cells

Productive cell migration requires the spatiotemporal coordination of cell adhesion, membrane protrusion, and actomyosin-mediated contraction. Integrins, engaged by the extracellular matrix (ECM), nucleate the formation of adhesive contacts at the cell's leading edge(s), and maturation of nascent adhesions to form stable focal adhesions constitutes a functional switch between protrusive and contractile activities. To shed additional light on the coupling between integrin-mediated adhesion and membrane protrusion, we have formulated a quantitative model of leading edge dynamics combining mechanistic and phenomenological elements and studied its features through classical bifurcation analysis and stochastic simulation. The model describes in mathematical terms the feedback loops driving, on the one hand, Rac-mediated membrane protrusion and rapid turnover of nascent adhesions, and on the other, myosin-dependent maturation of adhesions that inhibit protrusion at high ECM density. Our results show that the qualitative behavior of the model is most sensitive to parameters characterizing the influence of stable adhesions and myosin. The major predictions of the model, which we subsequently confirmed, are that persistent leading edge protrusion is optimal at an intermediate ECM density, whereas depletion of myosin IIA relieves the repression of protrusion at higher ECM density.

Stochastic Dynamics of Membrane Protrusion Mediated by the DOCK180/Rac Pathway in Migrating Cells

Cell migration is regulated by processes that control adhesion to extracellular matrix (ECM) and force generation. While our fundamental understanding of how these control mechanisms are actuated at the molecular level (signal transduction) has been refined over many years, appreciation of their dynamics has grown more recently. Here, we formulate and analyze by stochastic simulation a quantitative model of signaling mediated by the integrin family of adhesion receptors. Nascent adhesions foster the activation of the small GTPase Rac by at least two distinct signaling pathways, one of which involves tyrosine phosphorylation of the scaffold protein paxillin and formation of multiprotein complexes containing the guanine nucleotide exchange factor DOCK180. Active Rac promotes protrusion of the cell's leading edge, which in turn enhances the rate of nascent adhesion nucleation; we call this feedback mechanism the core protrusion cycle. Protrusion is antagonized by stable adhesions, which form by myosin-dependent maturation of nascent adhesions, and we propose here a feedforward mechanism mediated by the tyrosine kinase c-Src by which this antagonism is regulated so as to allow transient protrusion at higher densities of ECM. We show that this "buffering of inhibition" mechanism, coupled with the core protrusion cycle, is capable of tuning the frequencies of protrusion and adhesion maturation events.

What makes cells move: requirements and obstacles for spontaneous cell motility

Movement of individual cells and of cellular cohorts, chains or sheets requires physical forces that are established through interactions of cells with their environment. In vivo, migration occurs extensively during embryonic development and in adults during wound healing and tumorigenesis. In order to identify the molecular events involved in cell movement, in vitro systems have been developed. These have contributed to the definition of a number of molecular pathways put into play in the course of migratory behaviours, such as mesenchymal and amoeboid movement. More recently, our knowledge of migratory modes has been enriched by analyses of cells exploring and moving through three-dimensional (3D) matrices. While the cells' morphologies differ in 2D and 3D environments, the basic mechanisms that put a cellular body into motion are remarkably similar. Thus, in both 2D and 3D, the polarity of the migrating cell is initially defined by a specific subcellular localization of signalling molecules and components of molecular machines required for motion. While the polarization can be initiated either in response to extracellular signalling or be a chance occurrence, it is reinforced and sustained by positive feedback loops of signalling molecules. Second, adhesion to a substratum is necessary to generate forces that will propel the cell engaged in either mesenchymal or ameboid migration. For collective cell movement, intercellular coordination constitutes an additional requirement: a cell cohort remains stationary if individual cells pull in opposite directions. Finally, the availability of space to move into is a general requirement to set cells into motion. Lack of free space is probably the main obstacle for migration of most healthy cells in an adult multicellular organism. Thus, the requirements for cell movement are both intrinsic to the cell, involving coordinated signalling and interactions with molecular machines, and extrinsic, imposed by the physicochemical nature of the environment. In particular, the geometry and stiffness of the support act on a range of signalling pathways that induce specific cell migratory responses. These issues are discussed in the present review in the context of published work and our own data on collective migration of hepatocyte cohorts.

Development of a three dimensional multiscale computational model of the human epidermis

Transforming Growth Factor (TGF-β1) is a member of the TGF-beta superfamily ligand-receptor network. and plays a crucial role in tissue regeneration. The extensive in vitro and in vivo experimental literature describing its actions nevertheless describe an apparent paradox in that during re-epithelialisation it acts as proliferation inhibitor for keratinocytes. The majority of biological models focus on certain aspects of TGF-β1 behaviour and no one model provides a comprehensive story of this regulatory factor's action. Accordingly our aim was to develop a computational model to act as a complementary approach to improve our understanding of TGF-β1. In our previous study, an agent-based model of keratinocyte colony formation in 2D culture was developed. In this study this model was extensively developed into a three dimensional multiscale model of the human epidermis which is comprised of three interacting and integrated layers: (1) an agent-based model which captures the biological rules governing the cells in the human epidermis at the cellular level and includes the rules for injury induced emergent behaviours, (2) a COmplex PAthway SImulator (COPASI) model which simulates the expression and signalling of TGF-β1 at the sub-cellular level and (3) a mechanical layer embodied by a numerical physical solver responsible for resolving the forces exerted between cells at the multi-cellular level. The integrated model was initially validated by using it to grow a piece of virtual epidermis in 3D and comparing the in virtuo simulations of keratinocyte behaviour and of TGF-β1 signalling with the extensive research literature describing this key regulatory protein. This research reinforces the idea that computational modelling can be an effective additional tool to aid our understanding of complex systems. In the accompanying paper the model is used to explore hypotheses of the functions of TGF-β1 at the cellular and subcellular level on different keratinocyte populations during epidermal wound healing.

Interstitial cell migration: integrin-dependent and alternative adhesion mechanisms

Adhesion and migration are integrated cell functions that build, maintain and remodel the multicellular organism. In migrating cells, integrins are the main transmembrane receptors that provide dynamic interactions between extracellular ligands and actin cytoskeleton and signalling machineries. In parallel to integrins, other adhesion systems mediate adhesion and cytoskeletal coupling to the extracellular matrix (ECM). These include multifunctional cell surface receptors (syndecans and CD44) and discoidin domain receptors, which together coordinate ligand binding with direct or indirect cytoskeletal coupling and intracellular signalling. We review the way that the different adhesion systems for ECM components impact cell migration in two- and three-dimensional migration models. We further discuss the hierarchy of these concurrent adhesion systems, their specific tasks in cell migration and their contribution to migration in three-dimensional multi-ligand tissue environments.

Exploring hypotheses of the actions of TGF-beta1 in epidermal wound healing using a 3D computational multiscale model of the human epidermis

In vivo and in vitro studies give a paradoxical picture of the actions of the key regulatory factor TGF-beta1 in epidermal wound healing with it stimulating migration of keratinocytes but also inhibiting their proliferation. To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-beta1 literature-derived rule sets and equations embedded within it. At the cellular level, an agent-based bottom-up model that focuses on individual interacting units (keratinocytes) was used. This was based on literature-derived rules governing keratinocyte behavior and keratinocyte/ECM interactions. The selection of these rule sets is described in detail in this paper. The agent-based model was then linked with a subcellular model of TGF-beta1 production and its action on keratinocytes simulated with a complex pathway simulator. This multiscale model can be run at a cellular level only or at a combined cellular/subcellular level. It was then initially challenged (by wounding) to investigate the behavior of keratinocytes in wound healing at the cellular level. To investigate the possible actions of TGF-beta1, several hypotheses were then explored by deliberately manipulating some of these rule sets at subcellular levels. This exercise readily eliminated some hypotheses and identified a sequence of spatial-temporal actions of TGF-beta1 for normal successful wound healing in an easy-to-follow 3D model. We suggest this multiscale model offers a valuable, easy-to-visualize aid to our understanding of the actions of this key regulator in wound healing, and provides a model that can now be used to explore pathologies of wound healing.

Blebbistatin inhibits contraction and accelerates migration in mouse hepatic stellate cells

BACKGROUND AND PURPOSE

Blebbistatin, an inhibitor of myosin-II-specific ATPase, has been used to inhibit contraction of invertebrate and mammalian muscle preparations containing non-muscle myosin. Activated hepatic stellate cells have contractile properties and play an important role in the pathophysiology of liver fibrosis and portal hypertension. Therefore, hepatic stellate cells are considered as therapeutic target cells. In the present study, we studied the effect of blebbistatin during the transition of mouse hepatic stellate cells into contractile myofibroblasts.

EXPERIMENTAL APPROACH

Effects of blebbistatin on cell morphology were evaluated by phase contrast microscopy. Cell stress fibres and focal adhesions were investigated by dual immunofluorescence staining and visualized using fluorescence microscopy. Contractile force generation was examined by silicone wrinkle formation assays and collagen gel contraction assays. Intracellular Ca(2+) release in response to endothelin-1 was measured by using Fluo-4. Cell migration was measured by wound healing experiments.

KEY RESULTS

In culture-activated hepatic stellate cells, blebbistatin was found to change both cell morphology and function. In the presence of blebbistatin, stellate cells became smaller, acquired a dendritic morphology and had less myosin IIA-containing stress fibres and vinculin-containing focal adhesions. Moreover, blebbistatin impaired silicone wrinkle formation, reduced collagen gel contraction and blocked endothelin-1-induced intracellular Ca(2+) release. Finally, it promoted wound-induced cell migration.

CONCLUSIONS AND IMPLICATIONS

By inhibiting myosin II ATPase, blebbistatin has profound effects on the morphology and function of activated hepatic stellate cells. Our data suggest that myosin II could be a therapeutic target in the treatment of liver fibrosis and portal hypertension.

Actin-myosin viscoelastic flow in the keratocyte lamellipod

The lamellipod, the locomotory region of migratory cells, is shaped by the balance of protrusion and contraction. The latter is the result of myosin-generated centripetal flow of the viscoelastic actin network. Recently, quantitative flow data was obtained, yet there is no detailed theory explaining the flow in a realistic geometry. We introduce models of viscoelastic actin mechanics and myosin transport and solve the model equations numerically for the flat, fan-shaped lamellipodial domain of keratocytes. The solutions demonstrate that in the rapidly crawling cell, myosin concentrates at the rear boundary and pulls the actin network inward, so the centripetal actin flow is very slow at the front, and faster at the rear and at the sides. The computed flow and respective traction forces compare well with the experimental data. We also calculate the graded protrusion at the cell boundary necessary to maintain the cell shape and make a number of other testable predictions. We discuss model implications for the cell shape, speed, and bi-stability.

Expression of estrogen receptor beta increases integrin alpha1 and integrin beta1 levels and enhances adhesion of breast cancer cells

Estrogen effects on mammary gland development and differentiation are mediated by two receptors (ERalpha and ERbeta). Estrogen-bound ERalpha induces proliferation of mammary epithelial and cancer cells, while ERbeta is important for maintenance of the differentiated epithelium and inhibits proliferation in different cell systems. In addition, the normal breast contains higher ERbeta levels compared to the early stage breast cancers, suggesting that loss of ERbeta could be important in cancer development. Analysis of ERbeta-/- mice has consistently revealed reduced expression of cell adhesion proteins. As such, ERbeta is a candidate modulator of epithelial homeostasis and metastasis. Consequently, the aim of this study was to analyze estrogenic effects on adhesion of breast cancer cells expressing ERalpha and ERbeta. As ERbeta is widely found in breast cancer but not in cell lines, we used ERalpha positive T47-D and MCF-7 human breast cancer cells to generate cells with inducible ERbeta expression. Furthermore, the colon cancer cell lines SW480 and HT-29 were also used. Integrin alpha1 mRNA and protein levels increased following ERbeta expression. Integrin beta1-the unique partner for integrin alpha1-increased only at the protein level. ERbeta expression enhanced the formation of vinculin containing focal complexes and actin filaments, indicating a more adhesive potential. This was confirmed by adhesion assays where ERbeta increased adhesion to different extracellular matrix proteins, mostly laminin. In addition, ERbeta expression was associated to less cell migration. These results indicate that ERbeta affects integrin expression and clustering and consequently modulates adhesion and migration of breast cancer cells.

MMP7 shedding of syndecan-1 facilitates re-epithelialization by affecting alpha(2)beta(1) integrin activation

Background

Lung injury promotes the expression of matrix metalloproteinase-7 (MMP7, matrilysin), which is required for neutrophil recruitment and re-epithelialization. MMP7 governs the lung inflammatory response through the shedding of syndecan-1. Because inflammation and repair are related events, we evaluated the role of syndecan-1 shedding in lung re-epithelialization.

Methodology/Principal Finding

Epithelial injury induced syndecan-1 shedding from wild-type epithelium but not from Mmp7^−/− mice in vitro and in vivo. Moreover, cell migration and wound closure was enhanced by MMP7 shedding of syndecan-1. Additionally, we found that syndecan-1 augmented cell adhesion to collagen by controlling the affinity state of the α₂β₁ integrin.

Conclusion/Significance

MMP7 shedding of syndecan-1 facilitates wound closure by causing the α₂β₁ integrin to assume a less active conformation thereby removing restrictions to migration. MMP7 acts in the lungs to regulate inflammation and repair, and our data now show that both these functions are controlled through the shedding of syndecan-1.

Experimental-computational evaluation of human bone marrow stromal cell spreading on trabecular bone structures

The clinical application of macro-porous scaffolds for bone regeneration is significantly affected by the problem of insufficient cell colonization. Given the wide variety of different scaffold structures used for tissue engineering it is essential to derive relationships for cell colonization independent of scaffold architecture. To study cell population spreading on 3D structures decoupled from nutrient limitations, an in vitro culture system was developed consisting of thin slices of human trabecular bone seeded with Human Bone Marrow Stromal Cells, combined with dedicated microCT imaging and computational modeling of cell population spreading. Only the first phase of in vitro scaffold colonization was addressed, in which cells migrate and proliferate up to the stage when the surface of the bone is covered as a monolayer, a critical prerequisite for further tissue formation. The results confirm the model's ability to represent experimentally observed cell population spreading. The key advantage of the computational model was that by incorporating complex 3D structure, cell behavior can be characterized quantitatively in terms of intrinsic migration parameters, which could potentially be used for predictions on different macro-porous scaffolds subject to additional experimental validation. This type of modeling will prove useful in predicting cell colonization and improving strategies for skeletal tissue engineering.

A mathematical approach to bone tissue engineering

Tissue engineering is becoming consolidated in the biomedical field as one of the most promising strategies in tissue repair and regenerative medicine. Within this discipline, bone tissue engineering involves the use of cell-loaded porous biomaterials, i.e. bioscaffolds, to promote bone tissue regeneration in bone defects or diseases such as osteoporosis, although it has not yet been incorporated into daily clinical practice. The overall success of a particular bone tissue engineering application depends strongly on scaffold design parameters, which do away with long and expensive clinical protocols. Computer simulation is a useful tool that may reduce animal experiments and help to identify optimal patient-specific designs after concise model validation. In this paper, we present a novel mathematical approach to bone regeneration within scaffolds, based on a multiscale framework. Results are presented over an actual scaffold microstructure, showing the potential of computer simulation, and how it can aid in the task of making bone tissue engineering a reality in clinical practice.

Multiscale modelling and nonlinear simulation of vascular tumour growth

In this article, we present a new multiscale mathematical model for solid tumour growth which couples an improved model of tumour invasion with a model of tumour-induced angiogenesis. We perform nonlinear simulations of the multi-scale model that demonstrate the importance of the coupling between the development and remodeling of the vascular network, the blood flow through the network and the tumour progression. Consistent with clinical observations, the hydrostatic stress generated by tumour cell proliferation shuts down large portions of the vascular network dramatically affecting the flow, the subsequent network remodeling, the delivery of nutrients to the tumour and the subsequent tumour progression. In addition, extracellular matrix degradation by tumour cells is seen to have a dramatic affect on both the development of the vascular network and the growth response of the tumour. In particular, the newly developing vessels tend to encapsulate, rather than penetrate, the tumour and are thus less effective in delivering nutrients.

Myosin-IIA and ICAM-1 regulate the interchange between two distinct modes of T cell migration

How T cells achieve rapid chemotactic motility under certain circumstances and efficient cell surface surveillance in others is not fully understood. We show that T lymphocytes are motile in two distinct modes: a fast "amoeboid-like" mode, which uses sequential discontinuous contacts to the substrate; and a slower mode using a single continuously translating adhesion, similar to mesenchymal motility. Myosin-IIA is necessary for fast amoeboid motility, and our data suggests that this occurs via cyclical rear-mediated compressions that eliminate existing adhesions while licensing subsequent ones at the front of the cell. Regulation of Myosin-IIA function in T cells is thus a key mechanism to regulate surface contact area and crawling velocity within different environments. This can provide T lymphocytes with motile and adhesive properties that are uniquely suited toward alternative requirements for immune surveillance and response.