A phenomenological cohesive model for the macroscopic simulation of cell–matrix adhesions

Cell adhesion is crucial for cells to not only physically interact with each other but also sense their microenvironment and respond accordingly. In fact, adherent cells can generate physical forces that are transmitted to the surrounding matrix, regulating the formation of cell–matrix adhesions. The main purpose of this work is to develop a computational model to simulate the dynamics of cell–matrix adhesions through a cohesive formulation within the framework of the finite element method and based on the principles of continuum damage mechanics. This model enables the simulation of the mechanical adhesion between cell and extracellular matrix (ECM) as regulated by local multidirectional forces and thus predicts the onset and growth of the adhesion. In addition, this numerical approach allows the simulation of the cell as a whole, as it models the complete mechanical interaction between cell and ECM. As a result, we can investigate and quantify how different mechanical conditions in the cell (e.g., contractile forces, actin cytoskeletal properties) or in the ECM (e.g., stiffness, external forces) can regulate the dynamics of cell–matrix adhesions.     

The effects of mechanical forces on intestinal physiology and pathology

The epithelial and non-epithelial cells of the intestinal wall experience a myriad of physical forces including strain, shear, and villous motility during normal gut function. Pathologic conditions alter these forces, leading to changes in the biology of these cells. The responses of intestinal epithelial cells to forces vary with both the applied force and the extracellular matrix proteins with which the cells interact, with differing effects on proliferation, differentiation, and motility, and the regulation of these effects involves similar but distinctly different signal transduction mechanisms. Although normal epithelial cells respond to mechanical forces, malignant gastrointestinal epithelial cells also respond to forces, most notably by increased cell adhesion, a critical step in tumor metastasis. This review will focus on the phenomenon of mechanical forces influencing cell biology and the mechanisms by which the gut responds these forces in both the normal as well as pathophysiologic states when forces are altered. Although more is known about epithelial responses to force, information regarding mechanosensitivity of vascular, neural, and endocrine cells within the gut wall will also be discussed, as will, the mechanism by which forces can regulate epithelial tumor cell adhesion.     

The Role of Vinculin in the Regulation of the Mechanical Properties of Cells

Vinculin couples as a focal adhesion protein the extracellular matrix (ECM) through integrins to the actomyosin cytoskeleton. During the last years vinculin has become the focus of cell mechanical measurements and a key protein regulating the transmission of contractile forces. In earlier reports vinculin has been described as an inhibitor of cell migration on planar substrates, because knock-out of vinculin in F9 mouse embryonic carcinoma cells and mouse embryonic fibroblasts showed increased cell motility on 2D substrates. The role of vinculin in cell invasion through a 3D extracellular matrix is still fragmentarily investigated. This review presents vinculin in its role as a regulator of cellular mechanical functions. Contractile force generation is reduced when vinculin is absent, or enhanced when vinculin is present. Moreover, the generation of contractile forces is a prerequisite for cell invasion through a dense 3D ECM, where the pore-size is smaller than the diameter of the cell nucleus (<2 μm). Measurements of cell’s biophysical properties will be presented. In summary, vinculin’s leading role among focal adhesion proteins in regulating the mechanical properties of cells will be discussed.     

Fibroblast biology. Signals targeting the synovial fibroblast in arthritis

Fibroblast-like cells in the synovial lining (type B lining cells), stroma and pannus tissue are targeted by many signals, such as the following: ligands binding to cell surface receptors; lipid soluble, small molecular weight mediators (eg nitric oxide [NO], prostaglandins, carbon monoxide); extracellular matrix (ECM)-cell interactions; and direct cell-cell contacts, including gap junctional intercellular communication. Joints are subjected to cyclic mechanical loading and shear forces. Adherence and mechanical forces affect fibroblasts via the ECM (including the hyaluronan fluid phase matrix) and the pericellular matrix (eg extracellular matrix metalloproteinase inducer [EMMPRIN]) matrices, thus modulating fibroblast migration, adherence, proliferation, programmed cell death (including anoikis), synthesis or degradation of ECM, and production of various cytokines and other mediators [1]. Aggressive, transformed or transfected mesenchymal cells containing proto-oncogenes can act in the absence of lymphocytes, but whether these cells represent regressed fibroblasts, chondrocytes or bone marrow stem cells is unclear.     

Integrins and extracellular matrix in mechanotransduction

Integrins bind extracellular matrix fibrils and associate with intracellular actin filaments through a variety of cytoskeletal linker proteins to mechanically connect intracellular and extracellular structures. Each component of the linkage from the cytoskeleton through the integrin-mediated adhesions to the extracellular matrix therefore transmits forces that may derive from both intracellular, myosin-generated contractile forces and forces from outside the cell. These forces activate a wide range of signaling pathways and genetic programs to control cell survival, fate, and behavior. Additionally, cells sense the physical properties of their surrounding environment through forces exerted on integrin-mediated adhesions. This article first summarizes current knowledge about regulation of cell function by mechanical forces acting through integrin-mediated adhesions and then discusses models for mechanotransduction and sensing of environmental forces.     

Contractile forces regulate cell division in three-dimensional environments

Physical forces direct the orientation of the cell division axis for cells cultured on rigid, two-dimensional (2D) substrates. The extent to which physical forces regulate cell division in three-dimensional (3D) environments is not known. Here, we combine live-cell imaging with digital volume correlation to map 3D matrix displacements and identify sites at which cells apply contractile force to the matrix as they divide. Dividing cells embedded in fibrous matrices remained anchored to the matrix by long, thin protrusions. During cell rounding, the cells released adhesive contacts near the cell body while applying tensile forces at the tips of the protrusions to direct the orientation of the cell division axis. After cytokinesis, the daughter cells respread into matrix voids and invaded the matrix while maintaining traction forces at the tips of persistent and newly formed protrusions. Mechanical interactions between cells and the extracellular matrix constitute an important mechanism for regulation of cell division in 3D environments.     

Influence of mechanical stress on cell viability

The cartilage is a hydrated connective tissue in joints that withstands and distributes mechanical forces. The chondrocytes utilize mechanical signals to regulate their metabolic activity through complex biological and biophysical interactions with the extracellular matrix (ECM). The aim of this work was to study the influence of mechanical stress on cells behavior cultured in 3D biosystems (alginate and alginate supplemented with hyaluronate). After mechanical stimulation, cell viability and cell death process were the main studied parameters. Our results indicated that viability and cell cycle progression were inhibited under mechanical stimulation, as far as the extracellular matrix was not yet synthesized. In contrast, on day 21, the mechanical stimulation had positive effect on these parameters.     

Fibroblast biology: Signals targeting the synovial fibroblast in arthritis

Fibroblast-like cells in the synovial lining (type B lining cells), stroma and pannus tissue are targeted by many signals, such as the following: ligands binding to cell surface receptors; lipid soluble, small molecular weight mediators (eg nitric oxide [NO], prostaglandins, carbon monoxide); extracellular matrix (ECM)-cell interactions; and direct cell-cell contacts, including gap junctional intercellular communication. Joints are subjected to cyclic mechanical loading and shear forces. Adherence and mechanical forces affect fibroblasts via the ECM (including the hyaluronan fluid phase matrix) and the pericellular matrix (eg extracellular matrix metalloproteinase inducer [EMMPRIN]) matrices, thus modulating fibroblast migration, adherence, proliferation, programmed cell death (including anoikis), synthesis or degradation of ECM, and production of various cytokines and other mediators [1]. Aggressive, transformed or transfected mesenchymal cells containing proto-oncogenes can act in the absence of lymphocytes, but whether these cells represent regressed fibroblasts, chondrocytes or bone marrow stem cells is unclear.     

Traction forces exerted through N-cadherin contacts

BACKGROUND INFORMATION: Mechanical forces play an important role in the organization, growth and function of living tissues. The ability of cells to transduce mechanical signals is governed by two types of microscale structures: focal adhesions, which link cells to the extracellular matrix, and adherens junctions, which link adjacent cells through cadherins. Although many studies have examined forces induced by focal adhesions, there is little known about the role of adherens junctions in force-regulation processes. The present study focuses on the determination of force transduction through cadherins at a single cell level. RESULTS: We characterized for the first time the distribution of forces developed by the cell through cadherin contacts. A N-cadherin (neural cadherin)-Fc chimaera, which mimicks the cell adhesion molecule N-cadherin, was immobilized on a muFSA (micro-force sensor array), comprising a dense array of vertical elastomer pillars, which were used both as a cell culture support for N-cadherin-expressing C2 myogenic cells and as detectors for force mapping. We coated the top of the pillars on which cells adhere and recruit adhesion complexes and F-actin. Individual pillar bending allowed the measurement of forces that mainly developed at the cell edge and directed toward their centre. Similar force distribution and amplitude were detected with an unrelated cell line of neuronal origin. Further comparison with forces applied by cells on pillars coated with fibronectin indicates that mechanical stresses transduced through both types of adhesions were comparable in distribution, orientation and amplitude. CONCLUSIONS: These results present a versatile method to measure and map forces exerted by cell-cell adhesion complexes. They show that cells transduce mechanical stress through cadherin contacts which are of the same order as magnitude of those previously characterized for focal adhesions. Altogether, they emphasize the mechanotransduction role of cytoskeleton-linked adhesion receptors of the cadherin family in tissue cohesion and reshaping.     

Breast Cancer Cells Adapt Contractile Forces to Overcome Steric Hindrance

Cell migration through the extracellular matrix is governed by the interplay between cell-generated propulsion forces, adhesion forces, and resisting forces arising from the steric hindrance of the matrix. Steric hindrance in turn depends on matrix porosity, matrix deformability, cell size, and cell deformability. In this study, we investigate how cells respond to changes in steric hindrance that arise from altered cell mechanical properties. Specifically, we measure traction forces, cell morphology, and invasiveness of MDA-MB 231 breast cancer cells in three-dimensional collagen gels. To modulate cell mechanical properties, we either decrease nuclear deformability by twofold overexpression of the nuclear protein lamin A or we introduce into the cells stiff polystyrene beads with a diameter larger than the average matrix pore size. Despite this increase of steric hindrance, we find that cell invasion is only marginally inhibited, as measured by the fraction of motile cells and the mean invasion depth. To compensate for increased steric hindrance, cells employ two alternative strategies. Cells with higher nuclear stiffness increase their force polarity, whereas cells with large beads increase their net contractility. Under both conditions, the collagen matrix surrounding the cells stiffens dramatically and carries increased strain energy, suggesting that increased force polarity and increased net contractility are functionally equivalent strategies for overcoming an increased steric hindrance.     

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.     

Shear Force at the Cell-Matrix Interface: Enhanced Analysis for Microfabricated Post Array Detectors

The interplay of mechanical forces between the extracellular environment and the cytoskeleton drives development, repair, and senescence in many tissues. Quantitative definition of these forces is a vital step in understanding cellular mechanosensing. Microfabricated post array detectors (mPADs) provide direct measurements of cell-generated forces during cell adhesion to extracellular matrix. A new approach to mPAD post labeling, volumetric imaging, and an analysis of post bending mechanics determined that cells apply shear forces and not point moments at the matrix interface. In addition, these forces could be accurately resolved from post deflections by using images of post tops and bases. Image analysis tools were then developed to increase the precision and throughput of post centroid location. These studies resulted in an improved method of force measurement with broad applicability and concise execution using a fully automated force analysis system. The new method measures cell-generated forces with less than 5% error and less than 90 seconds of computational time. Using this approach, we demonstrated direct and distinct relationships between cellular traction force and spread cell surface area for fibroblasts, endothelial cells, epithelial cells and smooth muscle cells.     

On the mechanochemical theory of biological pattern formation with application to vasculogenesis

We first describe the Murray-Oster mechanical theory of pattern formation, the biological basis of which is experimentally well documented. The model quantifies the interaction of cells and the extracellular matrix via the cell-generated forces. The model framework is described in quantitative detail. Vascular endothelial cells, when cultured on gelled basement membrane matrix, rapidly aggregate into clusters while deforming the matrix into a network of cord-like structures tessellating the planar culture. We apply the mechanical theory of pattern formation to this culture system and show that neither strain-biased anisotropic cell traction nor cell migration are necessary for pattern formation: isotropic, strain-stimulated cell traction is sufficient to form the observed patterns. Predictions from the model were confirmed experimentally.     

Brushes,cables, and anchors: Recent insights into multiscale assembly and mechanics of cellular structural networks

The remarkable ability of living cells to sense, process, and respond to mechanical stimuli in their environment depends on the rapid and efficient interconversion of mechanical and chemical energy at specific times and places within the cell. For example, application of force to cells leads to conformational changes in specific mechanosensitive molecules which then trigger cellular signaling cascades that may alter cellular structure, mechanics, and migration and profoundly influence gene expression. Similarly, the sensitivity of cells to mechanical stresses is governed by the composition, architecture, and mechanics of the cellular cytoskeleton and extracellular matrix (ECM), which are in turn driven by molecular-scale forces between the constituent biopolymers. Understanding how these mechanochemical systems coordinate over multiple length and time scales to produce orchestrated cell behaviors represents a fundamental challenge in cell biology. Here, we review recent advances in our understanding of these complex processes in three experimental systems: the assembly of axonal neurofilaments, generation of tensile forces by actomyosin stress fiber bundles, and mechanical control of adhesion assembly.     

The role of focal adhesion complexes in fibroblast mechanotransduction during scar formation

Historically, great efforts have been made to elucidate the biochemical pathways that direct the complex process of wound healing; however only recently has there been recognition of the importance that mechanical signals play in the process of tissue repair and scar formation. The body's physiologic response to injury involves a dynamic interplay between mechanical forces and biochemical cues which directs a cascade of signals leading ultimately to the formation of fibrotic scar. Fibroblasts are a highly mechanosensitive cell type and are also largely responsible for the generation of the fibrotic matrix during scar formation and are thus a critical player in the process of mechanotransduction during tissue repair. Mechanotransduction is initiated at the interface between the cell membrane and the extracellular matrix where mechanical signals are first translated into a biochemical response. Focal adhesions are dynamic multi-protein complexes through which the extracellular matrix links to the intracellular cytoskeleton. These focal adhesion complexes play an integral role in the propagation of this initial mechanical cue into an extensive network of biochemical signals leading to widespread downstream effects including the influx of inflammatory cells, stimulation of angiogenesis, keratinocyte migration, fibroblast proliferation and collagen synthesis. Increasing evidence has demonstrated the importance of the biomechanical milieu in healing wounds and suggests that an integrated approach to the discovery of targets to decrease scar formation may prove more clinically efficacious than previous purely biochemical strategies.     

Intercellular mechanotransduction: cellular circuits that coordinate tissue responses to mechanical loading

Physical forces play an important role in modulating cell function and shaping tissue structure. Mechanotransduction, the process by which cells transduce physical force-induced signals into biochemical responses, is critical for mediating adaptations to mechanical loading in connective tissues. While much is known about mechanotransduction in cells involving forces delivered through extracellular matrix proteins and integrins, there is limited understanding of how mechanical signals are propagated through the interconnected cellular networks found in tissues and organs. We propose that intercellular mechanotransduction is a critical component for achieving coordinated remodeling responses to force application in connective tissues. We examine here recent evidence on different pathways of intercellular mechanotransduction and suggest a general model for how multicellular structures respond to mechanical loading as an integrated unit.     

Paracrine cellular and extracellular matrix interactions with mesenchymal progenitors during pulmonary alveolar septation

Alveolar development in humans primarily occurs postnatally and requires a carefully orchestrated expansion of distal epithelial and mesenchymal progenitor populations and coordinated differentiation, to create a highly segmented gas‐exchange surface. The regulation of alveolarization normally assimilates cues from paracrine cell–cell, cell–extracellular matrix, and mechanical interactions which are superimposed on cells and the extracellular matrix through phasic respiratory movement. In bronchopulmonary dysplasia, the entire process is precociously initiated when cellular and extracellular components are adapted to the saccular stage where movement and circulation are much more limited. This review focuses on mesenchymal cells (fibroblasts, endothelial cells, and pericytes), and epithelial cells are primarily discussed as sources of growth factor ligands or recipients of ligands produced by mesenchymal cells. Some interstitial fibroblasts differentiate to contractile myofibroblasts, containing a smooth muscle‐actin rich cytoskeleton, which connects with tensile and elastic elements in the extracellular matrix, and together comprise a load‐bearing network that diffuses mechanical forces during respiration. Other interstitial fibroblasts assimilate neutral lipid droplets, which regulate the differentiation of distal epithelial progenitors and surfactant production by alveolar type 2 cells. Pericytes organize and reinforce the capillary network as it expands to match the coverage of type 1 epithelial cells. Hyperoxia and the mechanical load imposed by positive pressure mechanical ventilation disrupt these paracrine interactions, leaving thickened alveolar walls, airways and arterioles, thereby diminishing gas‐exchange surface area. Better understanding of these mechanisms of alveolar septation will lead to more effective treatments to preserve and perhaps augment the surface usual sequence of events that drive alveolarization. Birth Defects Research (Part A) 100:227–239, 2014. © 2014 Wiley Periodicals, Inc.     

Myosin II and mechanotransduction: a balancing act

Adherent cells respond to mechanical properties of the surrounding extracellular matrix. Mechanical forces, sensed at specialized cell-matrix adhesion sites, promote actomyosin-based contraction within the cell. By manipulating matrix rigidity and adhesion strength, new roles for actomyosin contractility in the regulation of basic cellular functions, including cell proliferation, migration and stem cell differentiation, have recently been discovered. These investigations demonstrate that a balance of forces between cell adhesion on the outside and myosin II-based contractility on the inside of the cell controls many aspects of cell behavior. Disturbing this balance contributes to the pathogenesis of various human diseases. Therefore, elaborate signaling networks have evolved that modulate myosin II activity to maintain tensional homeostasis. These include signaling pathways that regulate myosin light chain phosphorylation as well as myosin II heavy chain interactions.     

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.