Computational Tension Mapping of Adherent Cells Based on Actin Imaging

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

Dynamic and structural signatures of lamellar actomyosin force generation

The regulation of cellular traction forces on the extracellular matrix is critical to cell adhesion, migration, proliferation, and differentiation. Diverse lamellar actin organizations ranging from contractile lamellar networks to stress fibers are observed in adherent cells. Although lamellar organization is thought to reflect the extent of cellular force generation, understanding of the physical behaviors of the lamellar actin cytoskeleton is lacking. To elucidate these properties, we visualized the actomyosin dynamics and organization in U2OS cells over a broad range of forces. At low forces, contractile lamellar networks predominate and force generation is strongly correlated to actomyosin retrograde flow dynamics with nominal change in organization. Lamellar networks build ～60% of cellular tension over rapid time scales. At high forces, reorganization of the lamellar network into stress fibers results in moderate changes in cellular tension over slower time scales. As stress fibers build and tension increases, myosin band spacing decreases and α-actinin bands form. On soft matrices, force generation by lamellar networks is unaffected, whereas tension-dependent stress fiber assembly is abrogated. These data elucidate the dynamic and structural signatures of the actomyosin cytoskeleton at different levels of tension and set a foundation for quantitative models of cell and tissue mechanics.     

Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.     

Mechanisms of Plastic Deformation in Collagen Networks Induced by Cellular Forces

Contractile cells can reorganize fibrous extracellular matrices and form dense tracts of fibers between neighboring cells. These tracts guide the development of tubular tissue structures and provide paths for the invasion of cancer cells. Here, we studied the mechanisms of the mechanical plasticity of collagen tracts formed by contractile premalignant acinar cells and fibroblasts. Using fluorescence microscopy and second harmonic generation, we quantified the collagen densification, fiber alignment, and strains that remain within the tracts after cellular forces are abolished. We explained these observations using a theoretical fiber network model that accounts for the stretch-dependent formation of weak cross-links between nearby fibers. We tested the predictions of our model using shear rheology experiments. Both our model and rheological experiments demonstrated that increasing collagen concentration leads to substantial increases in plasticity. We also considered the effect of permanent elongation of fibers on network plasticity and derived a phase diagram that classifies the dominant mechanisms of plasticity based on the rate and magnitude of deformation and the mechanical properties of individual fibers. Plasticity is caused by the formation of new cross-links if moderate strains are applied at small rates or due to permanent fiber elongation if large strains are applied over short periods. Finally, we developed a coarse-grained model for plastic deformation of collagen networks that can be employed to simulate multicellular interactions in processes such as morphogenesis, cancer invasion, and fibrosis.     

Traction force microscopy by deep learning

Cells interact mechanically with their surroundings by exerting and sensing forces. Traction force microscopy (TFM), purported to map cell-generated forces or stresses, represents an important tool that has powered the rapid advances in mechanobiology. However, to solve the ill-posed mathematical problem, conventional TFM involved compromises in accuracy and/or resolution. Here, we applied neural network-based deep learning as an alternative approach for TFM. We modified a neural network designed for image processing to predict the vector field of stress from displacements. Furthermore, we adapted a mathematical model for cell migration to generate large sets of simulated stresses and displacements for training and testing the neural network. We found that deep learning-based TFM yielded results that resemble those using conventional TFM but at a higher accuracy than several conventional implementations tested. In addition, a trained neural network is appliable to a wide range of conditions, including cell size, shape, substrate stiffness, and traction output. The performance of deep learning-based TFM makes it an appealing alternative to conventional methods for characterizing mechanical interactions between adherent cells and the environment.     

Soft tissue mechanotransduction in wound healing and fibrosis

Recent evidence suggests that mechanical forces can significantly impact the biologic response to injury. Integrated mechanical and chemical signaling networks have been discovered that enable physical cues to regulate disease processes such as pathologic scar formation. Distinct molecular mechanisms control how tensional forces influence wound healing and fibrosis. Conceptual frameworks to understand cutaneous repair have expanded beyond traditional cell-cytokine models to include dynamic interactions driven by mechanical force and the extracellular matrix. Strategies to manipulate these biomechanical signaling networks have tremendous therapeutic potential to reduce scar formation and promote skin regeneration.     

Collagen gel contraction assays: From modelling wound healing to quantifying cellular interactions with three-dimensional extracellular matrices

Cells respond to and actively remodel the extracellular matrix (ECM). The dynamic and bidirectional interaction between cells and ECM, especially their mechanical interactions, has been found to play an essential role in triggering a series of complex biochemical and biomechanical signal pathways and in regulating cellular functions and behaviours. The collagen gel contraction assay (CGCA) is a widely used method to investigate cell–ECM interactions in 3D environments and provides a mechanically associated readout reflecting 3D cellular contractility. In this review, we summarize various versions of CGCA, with an emphasis on recent high-throughput and low-consumption CGCA techniques. More importantly, we focus on the technique of force monitoring during the contraction of collagen gel, which provides a quantitative characterization of the overall forces generated by all the resident cells in the collagen hydrogel. Accordingly, we present recent biological applications of the CGCA, which have expanded from the initial wound healing model to other studies concerning cell–ECM interactions, including fibrosis, cancer, tissue repair and the preparation of biomimetic microtissues.     

Cell mechanics studied by a reconstituted model tissue

Tissue models reconstituted from cells and extracellular matrix (ECM) simulate natural tissues. Cytoskeletal and matrix proteins govern the force exerted by a tissue and its stiffness. Cells regulate cytoskeletal structure and remodel ECM to produce mechanical changes during tissue development and wound healing. Characterization and control of mechanical properties of reconstituted tissues are essential for tissue engineering applications. We have quantitatively characterized mechanical properties of connective tissue models, fibroblast-populated matrices (FPMs), via uniaxial stretch measurements. FPMs resemble natural tissues in their exponential dependence of stress on strain and linear dependence of stiffness on force at a given strain. Activating cellular contractile forces by calf serum and disrupting F-actin by cytochalasin D yield "active" and "passive" components, which respectively emphasize cellular and matrix mechanical contributions. The strain-dependent stress and elastic modulus of the active component were independent of cell density above a threshold density. The same quantities for the passive component increased with cell number due to compression and reorganization of the matrix by the cells.     

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.     

Computational model for cell migration in three-dimensional matrices

Although computational models for cell migration on two-dimensional (2D) substrata have described how various molecular and cellular properties and physiochemical processes are integrated to accomplish cell locomotion, the same issues, along with certain new ones, might contribute differently to a model for migration within three-dimensional (3D) matrices. To address this more complicated situation, we have developed a computational model for cell migration in 3D matrices using a force-based dynamics approach. This model determines an overall locomotion velocity vector, comprising speed and direction, for individual cells based on internally generated forces transmitted into external traction forces and considering a timescale during which multiple attachment and detachment events are integrated. Key parameters characterize cell and matrix properties, including cell/matrix adhesion and mechanical and steric properties of the matrix; critical underlying molecular properties are incorporated explicitly or implicitly. Model predictions agree well with experimental results for the limiting case of migration on 2D substrata as well as with recent experiments in 3D natural tissues and synthetic gels. Certain predicted features such as biphasic behavior of speed with density of matrix ligands for 3D migration are qualitatively similar to their 2D counterparts, but new effects generally absent in 2D systems, such as effects due to matrix sterics and mechanics, are now predicted to arise in many 3D situations. As one particular sample manifestation of these effects, the optimal levels of cell receptor expression and matrix ligand density yielding maximal migration are dependent on matrix mechanical compliance.     

The role of the cytoskeleton in cellular force generation in 2D and 3D environments

To adhere and migrate, cells generate forces through the cytoskeleton that are transmitted to the surrounding matrix. While cellular force generation has been studied on 2D substrates, less is known about cytoskeletal-mediated traction forces of cells embedded in more in vivo-like 3D matrices. Recent studies have revealed important differences between the cytoskeletal structure, adhesion, and migration of cells in 2D and 3D. Because the cytoskeleton mediates force, we sought to directly compare the role of the cytoskeleton in modulating cell force in 2D and 3D. MDA-MB-231 cells were treated with agents that perturbed actin, microtubules, or myosin, and analyzed for changes in cytoskeletal organization and force generation in both 2D and 3D. To quantify traction stresses in 2D, traction force microscopy was used; in 3D, force was assessed based on single cell-mediated collagen fibril reorganization imaged using confocal reflectance microscopy. Interestingly, even though previous studies have observed differences in cell behaviors like migration in 2D and 3D, our data indicate that forces generated on 2D substrates correlate with forces within 3D matrices. Disruption of actin, myosin or microtubules in either 2D or 3D microenvironments disrupts cell-generated force. These data suggest that despite differences in cytoskeletal organization in 2D and 3D, actin, microtubules and myosin contribute to contractility and matrix reorganization similarly in both microenvironments.     

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.     

Structural insights into the mechanical regulation of molecular recognition sites

Intriguing experimental and computational data are emerging to suggest that mechanical forces regulate the functional states of some proteins by stretching them into nonequilibrium states. Using the extracellular matrix protein fibronectin as an example, we discuss molecular design principles that might control the exposure of a protein's recognition sites, and/or their relative distances, in a force-dependent manner. Fibronectin regulates many cellular functions by binding directly to integrins. Although integrins have a key role in the transduction of force across the cell membrane by coupling the extracellular matrix to the cytoskeleton, the studies reviewed here suggest that fibronectin might be one of the molecules responsible for the initial transformation of mechanical force into a biochemical signal.     

Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions

The interactions between biochemical processes and mechanical signaling play important roles during various cellular processes such as wound healing, embryogenesis, metastasis, and cell migration. While traditional traction force measurements have provided quantitative information about cell matrix interactions in two dimensions, recent studies have shown significant differences in the behavior and morphology of cells when placed in three-dimensional environments. Hence new quantitative experimental techniques are needed to accurately determine cell traction forces in three dimensions. Recently, two approaches both based on laser scanning confocal microscopy have emerged to address this need. This study highlights the details, implementation and advantages of such a three-dimensional imaging methodology with the capability to compute cellular traction forces dynamically during cell migration and locomotion. An application of this newly developed three-dimensional traction force microscopy (3D TFM) technique to single cell migration studies of 3T3 fibroblasts is presented to show that this methodology offers a new quantitative vantage point to investigate the three-dimensional nature of cell-ECM interactions.     

Musculoskeletal mechanobiology: Interpretation by external force and engineered substratum

Mechanobiology aims to discover how the mechanical environment affects the biological activity of cells and how cells’ ability to sense these mechanical cues is converted into elicited cellular responses. Musculoskeletal mechanobiology is of particular interest given the high mechanical loads that musculoskeletal tissues experience on a daily basis. How do cells within these mechanically active tissues interpret external loads imposed on their extracellular environment, and, how are cell–substrate interactions converted into biochemical signals? This review outlines many of the main mechanotransduction mechanisms known to date, and describes recent literature examining effects of both external forces and cell–substrate interactions on musculoskeletal cells. Whether via application of external forces and/or cell–substrate interactions, our understanding and regulation of musculoskeletal mechanobiology can benefit by expanding upon traditional models, and shedding new light through novel investigative approaches. Current and future work in this field is focused on identifying specific forces, stresses, and strains at the cellular and tissue level through both experimental and computational approaches, and analyzing the role of specific proteins through fluorescence-based investigations and knockdown models.     

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.     

Transition from Actin-Driven to Water-Driven Cell Migration Depends on External Hydraulic Resistance

Cells in vivo can reside in diverse physical and biochemical environments. For example, epithelial cells typically live in a two-dimensional (2D) environment, whereas metastatic cancer cells can move through dense three-dimensional matrices. These distinct environments impose different kinds of mechanical forces on cells and thus potentially can influence the mechanism of cell migration. For example, cell movement on 2D flat surfaces is mostly driven by forces from focal adhesion and actin polymerization, whereas in confined geometries, it can be driven by water permeation. In this work, we utilize a two-phase model of the cellular cytoplasm in which the mechanics of the cytosol and the F-actin network are treated on an equal footing. Using conservation laws and simple force balance considerations, we are able to describe the contributions of water flux, actin polymerization and flow, and focal adhesions to cell migration both on 2D surfaces and in confined spaces. The theory shows how cell migration can seamlessly transition from a focal adhesion- and actin-based mechanism on 2D surfaces to a water-based mechanism in confined geometries.     

Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields

In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.     

Invited Review: Role of mechanophysiology in aging of ECM: effects of changes in mechanochemical transduction.

Mechanical forces play a role in the development and evolution of extracellular matrices (ECMs) found in connective tissue. Gravitational forces acting on mammalian tissues increase the net muscle forces required for movement of vertebrates. As body mass increases during development, musculoskeletal tissues and other ECMs are able to adapt their size to meet the increased mechanical requirements. However, the control mechanisms that allow for rapid growth in tissue size during development are altered during maturation and aging. The purpose of this mini-review is to examine the relationship between mechanical loading and cellular events that are associated with downregulation of mechanochemical transduction, which appears to contribute to aging of connective tissue. These changes result from decreases in growth factor and hormone levels, as well as decreased activation of the phosphorelay system that controls cell division, gene expression, and protein synthesis. Studies pertaining to the interactions among mechanical forces, growth factors, hormones, and their receptors will better define the relationship between mechanochemical transduction processes and cellular behavior in aging tissues.     

Remodeling of Fibrous Extracellular Matrices by Contractile Cells: Predictions from Discrete Fiber Network Simulations

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element–based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.