Cell Migration and Cell-Cell Interaction in the Presence of Mechano-Chemo-Thermotaxis

Although there are several computational models that explain the trajectory that cells take during migration, till now little attention has been paid to the integration of the cell migration in a multi-signaling system. With that aim, a generalized model of cell migration and cell-cell interaction under multisignal environments is presented herein. In this work we investigate the spatio-temporal cell-cell interaction problem induced by mechano-chemo-thermotactic cues. It is assumed that formation of a new focal adhesion generates traction forces proportional to the stresses transmitted by the cell to the extracellular matrix. The cell velocity and polarization direction are calculated based on the equilibrium of the effective forces associated to cell motility. It is also assumed that, in addition to mechanotaxis signals, chemotactic and thermotactic cues control the direction of the resultant traction force. This model enables predicting the trajectory of migrating cells as well as the spatial and temporal distributions of the net traction force and cell velocity. Results indicate that the tendency of the cells is firstly to reach each other and then migrate towards an imaginary equilibrium plane located near the source of the signal. The position of this plane is sensitive to the gradient slope and the corresponding efficient factors. The cells come into contact and separate several times during migration. Adding other cues to the substrate (such as chemotaxis and/or thermotaxis) delays that primary contact. Moreover, in all states, the average local velocity and the net traction force of the cells decrease while the cells approach the cues source. Our findings are qualitatively consistent with experimental observations reported in the related literature.     

E-Cadherin-Dependent Stimulation of Traction Force at Focal Adhesions via the Src and PI3K Signaling Pathways

The interplay between cadherin- and integrin-dependent signals controls cell behavior, but the precise mechanisms that regulate the strength of adhesion to the extracellular matrix remains poorly understood. We deposited cells expressing a defined repertoire of cadherins and integrins on fibronectin (FN)-coated polyacrylamide gels (FN-PAG) and on FN-coated pillars used as a micro-force sensor array (μFSA), and analyzed the functional relationship between these adhesion receptors to determine how it regulates cell traction force. We found that cadherin-mediated adhesion stimulated cell spreading on FN-PAG, and this was modulated by the substrate stiffness. We compared S180 cells with cells stably expressing different cadherins on μFSA and found that traction forces were stronger in cells expressing cadherins than in parental cells. E-cadherin-mediated contact and mechanical coupling between cells are required for this increase in cell-FN traction force, which was not observed in isolated cells, and required Src and PI3K activities. Traction forces were stronger in cells expressing type I cadherins than in cells expressing type II cadherins, which correlates with our previous observation of a higher intercellular adhesion strength developed by type I compared with type II cadherins. Our results reveal one of the mechanisms whereby molecular cross talk between cadherins and integrins upregulates traction forces at cell-FN adhesion sites, and thus provide additional insight into the molecular control of cell behavior.     

Both contractile axial and lateral traction force dynamics drive amoeboid cell motility

Chemotaxing Dictyostelium discoideum cells adapt their morphology and migration speed in response to intrinsic and extrinsic cues. Using Fourier traction force microscopy, we measured the spatiotemporal evolution of shape and traction stresses and constructed traction tension kymographs to analyze cell motility as a function of the dynamics of the cell’s mechanically active traction adhesions. We show that wild-type cells migrate in a step-wise fashion, mainly forming stationary traction adhesions along their anterior–posterior axes and exerting strong contractile axial forces. We demonstrate that lateral forces are also important for motility, especially for migration on highly adhesive substrates. Analysis of two mutant strains lacking distinct actin cross-linkers (mhcA⁻ and abp120⁻ cells) on normal and highly adhesive substrates supports a key role for lateral contractions in amoeboid cell motility, whereas the differences in their traction adhesion dynamics suggest that these two strains use distinct mechanisms to achieve migration. Finally, we provide evidence that the above patterns of migration may be conserved in mammalian amoeboid cells.     

Biochemical and mechanical extracellular matrix properties dictate mammary epithelial cell motility and assembly

Biochemical and mechanical cues of the extracellular matrix have been shown to play important roles in cell-matrix and cell-cell interactions. We have experimentally tested the combined influence of these cues to better understand cell motility, force generation, cell-cell interaction, and assembly in an in vitro breast cancer model. MCF-10A non-tumorigenic mammary epithelial cells were observed on surfaces with varying fibronectin ligand concentration and polyacrylamide gel rigidity. Our data show that cell velocity is biphasic in both matrix rigidity and adhesiveness. The maximum cell migration velocity occurs only at specific combination of substrate stiffness and ligand density. We found cell-cell interactions reduce migration velocity. However, the traction forces cells exert onto the substrate increase linearly with both cues, with cells in pairs exerting higher maximum tractions observed over single cells. A relationship between force and motility shows a maximum in single cell velocity not observed in cell pairs. Cell-cell adhesion becomes strongly favored on softer gels with elasticity ≤ 1250 Pascals (Pa), implying the existence of a compliance threshold that promotes cell-cell over cell-matrix adhesion. Finally on gels with stiffness similar to pre-malignant breast tissue, 400 Pa, cells undergo multicellular assembly and division into 3D spherical aggregates on a 2D surface.     

Cell Adhesion Strength Is Controlled by Intermolecular Spacing of Adhesion Receptors

Spatial patterning of biochemical cues on the micro- and nanometer scale controls numerous cellular processes such as spreading, adhesion, migration, and proliferation. Using force microscopy we show that the lateral spacing of individual integrin receptor-ligand bonds determines the strength of cell adhesion. For spacings ≥90 nm, focal contact formation was inhibited and the detachment forces as well as the stiffness of the cell body were significantly decreased compared to spacings ≤50 nm. Analyzing cell detachment at the subcellular level revealed that rupture forces of focal contacts increase with loading rate as predicted by a theoretical model for adhesion clusters. Furthermore, we show that the weak link between the intra- and extracellular space is at the intracellular side of a focal contact. Our results show that cells can amplify small differences in adhesive cues to large differences in cell adhesion strength.     

The dynamics and mechanics of endothelial cell spreading

Cell adhesion to extracellular matrix is mediated by receptor-ligand interactions. When a cell first contacts a surface, it spreads, exerting traction forces against the surface and forming new bonds as its contact area expands. Here, we examined the changes in shape, actin polymerization, focal adhesion formation, and traction stress generation that accompany spreading of endothelial cells over a period of several hours. Bovine aortic endothelial cells were plated on polyacrylamide gels derivatized with a peptide containing the integrin binding sequence RGD, and changes in shape and traction force generation were measured. Notably, both the rate and extent of spreading increase with the density of substrate ligand. There are two prominent modes of spreading: at higher surface ligand densities cells tend to spread isotropically, whereas at lower densities of ligand the cells tend to spread anisotropically, by extending pseudopodia randomly distributed along the cell membrane. The extension of pseudopodia is followed by periods of growth in the cell body to interconnect these extensions. These cycles occur at very regular intervals and, furthermore, the extent of pseudopodial extension can be diminished by increasing the ligand density. Measurement of the traction forces exerted by the cell reveals that a cell is capable of exerting significant forces before either notable focal adhesion or stress fiber formation. Moreover, the total magnitude of force exerted by the cell is linearly related to the area of the cell during spreading. This study is the first to monitor the dynamic changes in the cell shape, spreading rate, and forces exerted during the early stages (first several hours) of endothelial cell adhesion.     

An array of microfabricated pillars to study cell migration

Mechanical forces play an important role in various cellular functions, such as tumor metastasis, embryonic development or tissue formation. Cell migration involves dynamics of adhesive processes and cytoskeleton remodelling, leading to traction forces between the cells and their surrounding extracellular medium. To study these mechanical forces, a number of methods have been developed to calculate tractions at the interface between the cell and the substrate by tracking the displacements of beads or microfabricated markers embedded in continuous deformable gels. These studies have provided the first reliable estimation of the traction forces under individual migrating cells. We have developed a new force sensor made of a dense array of soft micron-size pillars microfabricated using microelectronics techniques. This approach uses elastomeric substrates that are micropatterned by using a combination of hard and soft lithography. Traction forces are determined in real time by analyzing the deflections of each micropillar with an optical microscope. Indeed, the deflection is directly proportional to the force in the linear regime of small deformations. Epithelial cells are cultured on our substrates coated with extracellular matrix protein. First, we have characterized temporal and spatial distributions of traction forces of a cellular assembly. Forces are found to depend on their relative position in the monolayer : the strongest deformations are always localized at the edge of the islands of cells in the active areas of cell protrusions. Consequently, these forces are quantified and correlated with the adhesion/scattering processes of the cells.     

Simulations of the contractile cycle in cell migration using a bio-chemical-mechanical model

Cell migration relies on traction forces in order to propel a cell. Several computational models have been developed that help explain the trajectory that cells take during migration, but little attention has been placed on traction forces during this process. Here, we investigated the spatiotemporal dynamics of cell migration by using a bio-chemical-mechanical contractility model that incorporates the first steps of cell migration on an array of posts. In the model, formation of a new adhesion causes a reactivation of stress fibre assembly within a cell. The model was able to predict the spatial distribution of traction forces observed with previous experiments. Moreover, the model found that the strain energy exerted by the traction forces of a migrating cell underwent a cyclic relationship that rose with the formation of a new adhesion and fell with the release of an adhesion at its rear.     

Role of the extracellular matrix in morphogenesis

The extracellular matrix is a complex, dynamic and critical component of all tissues. It functions as a scaffold for tissue morphogenesis, provides cues for cell proliferation and differentiation, promotes the maintenance of differentiated tissues and enhances the repair response after injury. Various amounts and types of collagens, adhesion molecules, proteoglycans, growth factors and cytokines or chemokines are present in the tissue- and temporal-specific extracellular matrices. Tissue morphogenesis is mediated by multiple extracellular matrix components and by multiple active sites on some of these components. Biologically active extracellular matrix components may have use in tissue repair, regeneration and engineering, and in programming stem cells for tissue replacement.     

Modelling Biological Gel Contraction by Cells: Mechanocellular Formulation and Cell Traction Force Quantification

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. This revised version was published online in June 2006 with corrections to the Cover Date.     

How Nucleus Mechanics and ECM Microstructure Influence the Invasion of Single Cells and Multicellular Aggregates

In order to move in a three-dimensional extracellular matrix, the nucleus of a cell must squeeze through the narrow spacing among the fibers and, by adhering to them, the cell needs to exert sufficiently strong traction forces. If the nucleus is too stiff, the spacing too narrow, or traction forces too weak, the cell is not able to penetrate the network. In this article, we formulate a mathematical model based on an energetic approach, for cells entering cylindrical channels composed of extracellular matrix fibers. Treating the nucleus as an elastic body covered by an elastic membrane, the energetic balance leads to the definition of a necessary criterion for cells to pass through the regular network of fibers, depending on the traction forces exerted by the cells (or possibly passive stresses), the stretchability of the nuclear membrane, the stiffness of the nucleus, and the ratio of the pore size within the extracellular matrix with respect to the nucleus diameter. The results obtained highlight the importance of the interplay between mechanical properties of the cell and microscopic geometric characteristics of the extracellular matrix and give an estimate for a critical value of the pore size that represents the physical limit of migration and can be used in tumor growth models to predict their invasive potential in thick regions of ECM.     

Cell shape and cell division

The correlation between cell shape elongation and the orientation of the division axis described by early cell biologists is still used as a paradigm in developmental studies. However, analysis of early embryo development and tissue morphogenesis has highlighted the role of the spatial distribution of cortical cues able to guide spindle orientation. In vitro studies of cell division have revealed similar mechanisms. Recent data support the possibility that the orientation of cell division in mammalian cells is dominated by cell adhesion and the associated traction forces developed in interphase. Cell shape is a manifestation of these adhesive and tensional patterns. These patterns control the spatial distribution of cortical signals and thereby guide spindle orientation and daughter cell positioning. From these data, cell division appears to be a continuous transformation ensuring the maintenance of tissue mechanical integrity.     

A time-dependent phenomenological model for cell mechano-sensing

Adherent cells normally apply forces as a generic means of sensing and responding to the mechanical nature of their surrounding environment. How these forces vary as a function of the extracellular rigidity is critical to understanding the regulatory functions that drive important phenomena such as wound healing or muscle contraction. In recognition of this fact, experiments have been conducted to understand cell rigidity-sensing properties under known conditions of the extracellular environment, opening new possibilities for modeling this active behavior. In this work, we provide a physics-based constitutive model taking into account the main structural components of the cell to reproduce its most significant contractile properties such as the traction forces exerted as a function of time and the extracellular stiffness. This model shows how the interplay between the time-dependent response of the acto-myosin contractile system and the elastic response of the cell components determines the mechano-sensing behavior of single cells.     

Single cell rigidity sensing: A complex relationship between focal adhesion dynamics and large-scale actin cytoskeleton remodeling

ABSTRACT

Many physiological and pathological processes involve tissue cells sensing the rigidity of their environment. In general, tissue cells have been shown to react to the stiffness of their environment by regulating their level of contractility, and in turn applying traction forces on their environment to probe it. This mechanosensitive process can direct early cell adhesion, cell migration and even cell differentiation. These processes require the integration of signals over time and multiple length scales. Multiple strategies have been developed to understand force- and rigidity-sensing mechanisms and much effort has been concentrated on the study of cell adhesion complexes, such as focal adhesions, and cell cytoskeletons. Here, we review the major biophysical methods used for measuring cell-traction forces as well as the mechanosensitive processes that drive cellular responses to matrix rigidity on 2-dimensional substrates.     

Aligned forces: Origins and mechanisms of cancer dissemination guided by extracellular matrix architecture

Organized extracellular matrix (ECM), in the form of aligned architectures, is a critical mediator of directed cancer cell migration by contact guidance, leading to metastasis in solid tumors. Current models suggest anisotropic force generation through the engagement of key adhesion and cytoskeletal complexes drives contact-guided migration. Likewise, disrupting the balance between cell–cell and cell–ECM forces, driven by ECM engagement for cells at the tumor–stromal interface, initiates and drives local invasion. Furthermore, processes such as traction forces exerted by cancer and stromal cells, spontaneous reorientation of matrix-producing fibroblasts, and direct binding of ECM modifying proteins lead to the emergence of collagen alignment in tumors. Thus, as we obtain a deeper understanding of the origins of ECM alignment and the mechanisms by which it is maintained to direct invasion, we are poised to use the new paradigm of stroma-targeted therapies to disrupt this vital axis of disease progression in solid tumors.     

A helping hand: How vinculin contributes to cell-matrix and cell-cell force transfer

Vinculin helps cells regulate and respond to mechanical forces. It is a scaffolding protein that tightly regulates its interactions with potential binding partners within adhesive structures—including focal adhesions that link the cell to the extracellular matrix and adherens junctions that link cells to each other—that physically connect the force-generating actin cytoskeleton (CSK) with the extracellular environment. This tight control of binding partner interaction—mediated by vinculin's autoinhibitory head–tail interaction—allows vinculin to rapidly interact and detach in response to changes in the dynamic forces applied through the cell. In doing so, vinculin modulates the structural composition of focal adhesions and the cell's ability to generate traction forces and adhesion strength. Recent evidence suggests that vinculin plays a similar role in regulating the fate and function of cell–cell junctions, further underscoring the importance of this protein. Using our lab's recent work as a starting point, this commentary explores several outstanding questions regarding the nature of vinculin activation and its function within focal adhesions and adherens junctions.     

Stabilizing to disruptive transition of focal adhesion response to mechanical forces

Strong mechanical forces can, obviously, disrupt cell–cell and cell–matrix adhesions, e.g., cyclic uniaxial stretch induces instability of cell adhesion, which then causes the reorientation of cells away from the stretching direction. However, recent experiments also demonstrated the existence of force dependent adhesion growth (rather than dissociation). To provide a quantitative explanation for the two seemingly contradictory phenomena, a microscopic model that includes both integrin–integrin interaction and integrin–ligand interaction is developed at molecular level by treating the focal adhesion as an adhesion cluster. The integrin clustering dynamics and integrin–ligand binding dynamics are then simulated within one unified theoretical frame with Monte Carlo simulation. We find that the focal adhesion will grow when the traction force is higher than a relative small threshold value, and the growth is dominated by the reduction of local chemical potential energy by the traction force. In contrast, the focal adhesion will rupture when the traction force exceeds a second threshold value, and the rupture is dominated by the breaking of integrin–ligand bonds. Consistent with the experiments, these results suggest a force map for various responses of cell adhesion to different scales of mechanical force.     

Integrin-dependent actomyosin contraction regulates epithelial cell scattering

The scattering of Madin-Darby canine kidney cells in vitro mimics key aspects of epithelial-mesenchymal transitions during development, carcinoma cell invasion, and metastasis. Scattering is induced by hepatocyte growth factor (HGF) and is thought to involve disruption of cadherin-dependent cell-cell junctions. Scattering is enhanced on collagen and fibronectin, as compared with laminin1, suggesting possible cross talk between integrins and cell-cell junctions. We show that HGF does not trigger any detectable decrease in E-cadherin function, but increases integrin-mediated adhesion. Time-lapse imaging suggests that tension on cell-cell junctions may disrupt cell-cell adhesion. Varying the density and type of extracellular matrix proteins shows that scattering correlates with stronger integrin adhesion and increased phosphorylation of the myosin regulatory light chain. To directly test the role of integrin-dependent traction forces, substrate compliance was varied. Rigid substrates that produce high traction forces promoted scattering, in comparison to more compliant substrates. We conclude that integrin-dependent actomyosin traction force mediates the disruption of cell-cell adhesion during epithelial cell scattering.