Nucleation and decay initiation are the stiffness-sensitive phases of focal adhesion maturation

From stress fiber to focal adhesion: a role of actin crosslinkers in force transmission

The contractile apparatus, stress fiber (SF), is connected to the cell adhesion machinery, focal adhesion (FA), at the termini of SF. The SF-FA complex is essential for various mechanical activities of cells, including cell adhesion to the extracellular matrix (ECM), ECM rigidity sensing, and cell migration. This mini-review highlights the importance of SF mechanics in these cellular activities. Actin-crosslinking proteins solidify SFs by attenuating myosin-driven flows of actin and myosin filaments within the SF. In the solidified SFs, viscous slippage between actin filaments in SFs and between the filaments and the surrounding cytosol is reduced, leading to efficient transmission of myosin-generated contractile force along the SFs. Hence, SF solidification via actin crosslinking ensures exertion of a large force to FAs, enabling FA maturation, ECM rigidity sensing and cell migration. We further discuss intracellular mechanisms for tuning crosslinker-modulated SF mechanics and the potential relationship between the aberrance of SF mechanics and pathology including cancer.

Force-dependent focal adhesion assembly and disassembly: A computational study

Cells interact with the extracellular matrix (ECM) via cell-ECM adhesions. These physical interactions are transduced into biochemical signals inside the cell which influence cell behaviour. Although cell-ECM interactions have been studied extensively, it is not completely understood how immature (nascent) adhesions develop into mature (focal) adhesions and how mechanical forces influence this process. Given the small size, dynamic nature and short lifetimes of nascent adhesions, studying them using conventional microscopic and experimental techniques is challenging. Computational modelling provides a valuable resource for simulating and exploring various "what if?" scenarios in silico and identifying key molecular components and mechanisms for further investigation. Here, we present a simplified mechano-chemical model based on ordinary differential equations with three major proteins involved in adhesions: integrins, talin and vinculin. Additionally, we incorporate a hypothetical signal molecule that influences adhesion (dis)assembly rates. We find that assembly and disassembly rates need to vary dynamically to limit maturation of nascent adhesions. The model predicts biphasic variation of actin retrograde velocity and maturation fraction with substrate stiffness, with maturation fractions between 18-35%, optimal stiffness of ∼1 pN/nm, and a mechanosensitive range of 1-100 pN/nm, all corresponding to key experimental findings. Sensitivity analyses show robustness of outcomes to small changes in parameter values, allowing model tuning to reflect specific cell types and signaling cascades. The model proposes that signal-dependent disassembly rate variations play an underappreciated role in maturation fraction regulation, which should be investigated further. We also provide predictions on the changes in traction force generation under increased/decreased vinculin concentrations, complementing previous vinculin overexpression/knockout experiments in different cell types. In summary, this work proposes a model framework to robustly simulate the mechanochemical processes underlying adhesion maturation and maintenance, thereby enhancing our fundamental knowledge of cell-ECM interactions.

Multiscale models of integrins and cellular adhesions

Computational models of integrin-based adhesion complexes have revealed important insights into the mechanisms by which cells establish connections with their external environment. However, how changes in conformation and function of individual adhesion proteins regulate the dynamics of whole adhesion complexes remains largely elusive. This is because of the large separation in time and length scales between the dynamics of individual adhesion proteins (nanoseconds and nanometers) and the emergent dynamics of the whole adhesion complex (seconds and micrometers), and the limitations of molecular simulation approaches in extracting accurate free energies, conformational transitions, reaction mechanisms, and kinetic rates, that can inform mechanisms at the larger scales. In this review, we discuss models of integrin-based adhesion complexes and highlight their main findings regarding: (i) the conformational transitions of integrins at the molecular and macromolecular scales and (ii) the molecular clutch mechanism at the mesoscale. Lastly, we present unanswered questions in the field of modeling adhesions and propose new ideas for future exciting modeling opportunities.

On the significance of membrane unfolding in mechanosensitive cell spreading: Its individual and synergistic effects

Mechanosensitivity of cell spread area to substrate stiffness has been established both through experiments and different types of mathematical models of varying complexity including both the mechanics and biochemical reactions in the cell. What has not been addressed in previous mathematical models is the role of cell membrane dynamics on cell spreading, and an investigation of this issue is the goal of this work. We start with a simple mechanical model of cell spreading on a deformable substrate and progressively layer mechanisms to account for the traction dependent growth of focal adhesions, focal adhesion induced actin polymerization, membrane unfolding/exocytosis and contractility. This layering approach is intended to progressively help in understanding the role each mechanism plays in reproducing experimentally observed cell spread areas. To model membrane unfolding we introduce a novel approach based on defining an active rate of membrane deformation that is dependent on membrane tension. Our modeling approach allows us to show that tension-dependent membrane unfolding plays a critical role in achieving the large cell spread areas experimentally observed on stiff substrates. We also demonstrate that coupling between membrane unfolding and focal adhesion induced polymerization works synergistically to further enhance cell spread area sensitivity to substrate stiffness. This enhancement has to do with the fact that the peripheral velocity of spreading cells is associated with contributions from the different mechanisms by either enhancing the polymerization velocity at the leading edge or slowing down of the retrograde flow of actin within the cell. The temporal evolution of this balance in the model corresponds to the three-phase behavior observed experimentally during spreading. In the initial phase membrane unfolding is found to be particularly important.

The interplay between physical cues and mechanosensitive ion channels in cancer metastasis

Physical cues have emerged as critical influencers of cell function during physiological processes, like development and organogenesis, and throughout pathological abnormalities, including cancer progression and fibrosis. While ion channels have been implicated in maintaining cellular homeostasis, their cell surface localization often places them among the first few molecules to sense external cues. Mechanosensitive ion channels (MICs) are especially important transducers of physical stimuli into biochemical signals. In this review, we describe how physical cues in the tumor microenvironment are sensed by MICs and contribute to cancer metastasis. First, we highlight mechanical perturbations, by both solid and fluid surroundings typically found in the tumor microenvironment and during critical stages of cancer cell dissemination from the primary tumor. Next, we describe how Piezo1/2 and transient receptor potential (TRP) channels respond to these physical cues to regulate cancer cell behavior during different stages of metastasis. We conclude by proposing alternative mechanisms of MIC activation that work in tandem with cytoskeletal components and other ion channels to bestow cells with the capacity to sense, respond and navigate through the surrounding microenvironment. Collectively, this review provides a perspective for devising treatment strategies against cancer by targeting MICs that sense aberrant physical characteristics during metastasis, the most lethal aspect of cancer.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

Multiscale mechanobiology: Coupling models of adhesion kinetics and nonlinear tissue mechanics

The mechanical behavior of tissues at the macroscale is tightly coupled to cellular activity at the microscale. Dermal wound healing is a prominent example of a complex system in which multiscale mechanics regulate restoration of tissue form and function. In cutaneous wound healing, a fibrin matrix is populated by fibroblasts migrating in from a surrounding tissue made mostly out of collagen. Fibroblasts both respond to mechanical cues, such as fiber alignment and stiffness, as well as exert active stresses needed for wound closure. Here, we develop a multiscale model with a two-way coupling between a microscale cell adhesion model and a macroscale tissue mechanics model. Starting from the well-known model of adhesion kinetics proposed by Bell, we extend the formulation to account for nonlinear mechanics of fibrin and collagen and show how this nonlinear response naturally captures stretch-driven mechanosensing. We then embed the new nonlinear adhesion model into a custom finite element implementation of tissue mechanical equilibrium. Strains and stresses at the tissue level are coupled with the solution of the microscale adhesion model at each integration point of the finite element mesh. In addition, solution of the adhesion model is coupled with the active contractile stress of the cell population. The multiscale model successfully captures the mechanical response of biopolymer fibers and gels, contractile stresses generated by fibroblasts, and stress-strain contours observed during wound healing. We anticipate that this framework will not only increase our understanding of how mechanical cues guide cellular behavior in cutaneous wound healing, but will also be helpful in the study of mechanobiology, growth, and remodeling in other tissues.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

Switching behaviour in vascular smooth muscle cell-matrix adhesion during oscillatory loading

Integrins regulate mechanotransduction between smooth muscle cells (SMCs) and the extracellular matrix (ECM). SMCs resident in the walls of airways or blood vessels are continuously exposed to dynamic mechanical forces due to breathing or pulsatile blood flow. However, the resulting effects of these forces on integrin dynamics and associated cell-matrix adhesion are not well understood. Here we present experimental results from atomic force microscopy (AFM) experiments, designed to study the integrin response to external oscillatory loading of varying amplitudes applied to live aortic SMCs, together with theoretical results from a mathematical model. In the AFM experiments, a fibronectin-coated probe was used cyclically to indent and retract from the surface of the cell. We observed a transition between states of firm adhesion and of complete detachment as the amplitude of oscillatory loading increased, revealed by qualitative changes in the force timecourses. Interestingly, for some of the SMCs in the experiments, switching behaviour between the two adhesion states is observed during single timecourses at intermediate amplitudes. We obtain two qualitatively similar adhesion states in the mathematical model, where we simulate the cell, integrins and ECM as an evolving system of springs, incorporating local integrin binding dynamics. In the mathematical model, we observe a region of bistability where both the firm adhesion and detachment states can occur depending on the initial adhesion state. The differences are seen to be a result of mechanical cooperativity of integrins and cell deformation. Switching behaviour is a phenomenon associated with bistability in a stochastic system, and bistability in our deterministic mathematical model provides a potential physical explanation for the experimental results. Physiologically, bistability provides a means for transient mechanical stimuli to induce long-term changes in adhesion dynamics-and thereby the cells' ability to transmit force-and we propose further experiments for testing this hypothesis.

Nanoscale integrin cluster dynamics controls cellular mechanosensing via FAKY397 phosphorylation

Transduction of extracellular matrix mechanics affects cell migration, proliferation, and differentiation. While this mechanotransduction is known to depend on the regulation of focal adhesion kinase phosphorylation on Y397 (FAKpY397), the mechanism remains elusive. To address this, we developed a mathematical model to test the hypothesis that FAKpY397-based mechanosensing arises from the dynamics of nanoscale integrin clustering, stiffness-dependent disassembly of integrin clusters, and FAKY397 phosphorylation within integrin clusters. Modeling results predicted that integrin clustering dynamics governs how cells convert substrate stiffness to FAKpY397, and hence governs how different cell types transduce mechanical signals. Existing experiments on MDCK cells and HT1080 cells, as well as our new experiments on 3T3 fibroblasts, confirmed our predictions and supported our model. Our results suggest a new pathway by which integrin clusters enable cells to calibrate responses to their mechanical microenvironment.

The bioenergetics of integrin-based adhesion, from single molecule dynamics to stability of macromolecular complexes

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Dynamics of Mechanosensitive Nascent Adhesion Formation

Cellular migration is a tightly regulated process that involves actin cytoskeleton, adaptor proteins, and integrin receptors. Forces are transmitted extracellularly through protein complexes of these molecules, called adhesions. Adhesions anchor the cell to its substrate, allowing it to migrate. In Chinese hamster ovary cells, three classes of adhesion can be identified: nascent adhesions (NAs), focal complexes, and focal adhesions, ranked here ascendingly based on size and stability. To understand the dynamics and mechanosensitive properties of NAs, a biophysical model of these NAs as colocalized clusters of integrins and adaptor proteins is developed. The model is then analyzed to characterize the dependence of NA area on biophysical parameters that regulate the number of integrins and adaptor proteins within NAs through a mechanosensitive coaggregation mechanism. Our results reveal that NA formation is triggered beyond a threshold of adaptor protein, integrin, or extracellular ligand densities, with these three factors listed in descending order of their relative influence on NA area. Further analysis of the model also reveals that an increase in coaggregation or reductions in integrin mobility inside the adhesion potentiate NA formation. By extending the model to consider the mechanosensitivity of the integrin bond, we identify mechanical stress, rather than mechanical load, as a permissive mechanical parameter that allows for noise-dependent and independent NA assembly, despite both parameters producing a bistable switch possessing a hysteresis. Stochastic simulations of the model confirm these results computationally. This study thus provides insight into the mechanical conditions defining NA dynamics.

Mechanosensitivity Occurs along the Adhesome's Force Train and Affects Traction Stress

Herein, we consider the process of force development along the adhesome within cell focal adhesions. Our model adhesome consists of the actin cytoskeleton-vinculin-talin-integrin-ligand-extracellular matrix-substrate force train. We specifically consider the effects of substrate stiffness on the force levels expected along the train and on the traction stresses they create at the substrate. We find that significant effects of substrate stiffness are manifest within each constitutive component of the force train and on the density and distribution of integrin/ligand anchorage points with the substrate. By following each component of the force train, we are able to delineate specific gaps in the quantitative descriptions of bond survival that must be addressed so that improved quantitative forecasts become possible. Our analysis provides, however, a rational description for the various levels of traction stresses that have been reported and of the effect of substrate stiffness. Our approach has the advantage of being quite clear as to how each constituent contributes to the net development of force and traction stress. We demonstrate that to provide truly quantitative forecasts for traction stress, a far more detailed description of integrin/ligand density and distribution is required. Although integrin density is already a well-recognized important feature of adhesion, our analysis places a finer point on it in the manner of how we evaluate the magnitude of traction stress. We provide mechanistic insight into how understanding of this vital element of the adhesion process may proceed by addressing mechanistic causes of integrin clustering that may lead to patterning.

Effect of Loading History on Airway Smooth Muscle Cell-Matrix Adhesions

Integrin-mediated adhesions between airway smooth muscle (ASM) cells and the extracellular matrix (ECM) regulate how contractile forces generated within the cell are transmitted to its external environment. Environmental cues are known to influence the formation, size, and survival of cell-matrix adhesions, but it is not yet known how they are affected by dynamic fluctuations associated with tidal breathing in the intact airway. Here, we develop two closely related theoretical models to study adhesion dynamics in response to oscillatory loading of the ECM, representing the dynamic environment of ASM cells in vivo. Using a discrete stochastic-elastic model, we simulate individual integrin binding and rupture events and observe two stable regimes in which either bond formation or bond rupture dominate, depending on the amplitude of the oscillatory loading. These regimes have either a high or low fraction of persistent adhesions, which could affect the level of strain transmission between contracted ASM cells and the airway tissue. For intermediate loading, we observe a region of bistability and hysteresis due to shared loading between existing bonds; the level of adhesion depends on the loading history. These findings are replicated in a related continuum model, which we use to investigate the effect of perturbations mimicking deep inspirations (DIs). Because of the bistability, a DI applied to the high adhesion state could either induce a permanent switch to a lower adhesion state or allow a return of the system to the high adhesion state. Transitions between states are further influenced by the frequency of oscillations, cytoskeletal or ECM stiffnesses, and binding affinities, which modify the magnitudes of the stable adhesion states as well as the region of bistability. These findings could explain (in part) the transient bronchodilatory effect of a DI observed in asthmatics compared to a more sustained effect in normal subjects.

On Stability of Specific Adhesion of Particles to Membranes in Simple Shear Flow

Adhesion of carrier particles to the luminal surface of endothelium under hemodynamic flow conditions is critical for successful vascular drug delivery. Endothelial cells line the inner surface of blood vessels. The effect of mechanical behavior of this compliant surface on the adhesion of blood-borne particles is unknown. In this contribution, we use a phase-plane method, first developed by Hammer and Lauffenburger [Biophysical Journal, 52, 475 (1987)], to analyze the stability of specific adhesion of a spherical particle to a compliant interface layer. We construct a phase diagram that predicts the state of particle adhesion, subjected to an incident simple shear flow, in terms of interfacial elasticity, shear rate, binding affinity of cell adhesive molecules, and their surface density. The main conclusion is that the local deformation of the flexible interface inhibits the stable adhesion of the particle. In comparison with adhesion to a rigid substrate, a greater ligand density is required to establish a stable adhesion between a particle and a compliant interface. The results can be used for the rational design of particles in vascular drug delivery.

Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates

Recent evidence has shown that, in addition to rigidity, the viscous response of the extracellular matrix (ECM) significantly affects the behavior and function of cells. However, the mechanism behind such mechanosensitivity toward viscoelasticity remains unclear. In this study, we systematically examined the dynamics of motor clutches (i.e., focal adhesions) formed between the cell and a viscoelastic substrate using analytical methods and direct Monte Carlo simulation. Interestingly, we observe that, for low ECM rigidity, maximum cell spreading is achieved at an optimal level of viscosity in which the substrate relaxation time falls between the timescale for clutch binding and its characteristic binding lifetime. That is, viscosity serves to stiffen soft substrates on a timescale faster than the clutch off-rate, which enhances cell-ECM adhesion and cell spreading. On the other hand, for substrates that are stiff, our model predicts that viscosity will not influence cell spreading, since the bound clutches are saturated by the elevated stiffness. The model was tested and validated using experimental measurements on three different material systems and explained the different observed effects of viscosity on each substrate. By capturing the mechanism by which substrate viscoelasticity affects cell spreading across a wide range of material parameters, our analytical model provides a useful tool for designing biomaterials that optimize cellular adhesion and mechanosensing.

Cell-Extracellular Matrix Mechanobiology: Forceful Tools and Emerging Needs for Basic and Translational Research

Extracellular biophysical cues have a profound influence on a wide range of cell behaviors, including growth, motility, differentiation, apoptosis, gene expression, adhesion, and signal transduction. Cells not only respond to definitively mechanical cues from the extracellular matrix (ECM) but can also sometimes alter the mechanical properties of the matrix and hence influence subsequent matrix-based cues in both physiological and pathological processes. Interactions between cells and materials in vitro can modify cell phenotype and ECM structure, whether intentionally or inadvertently. Interactions between cell and matrix mechanics in vivo are of particular importance in a wide variety of disorders, including cancer, central nervous system injury, fibrotic diseases, and myocardial infarction. Both the in vitro and in vivo effects of this coupling between mechanics and biology hold important implications for clinical applications.

Nuclear lamin A/C harnesses the perinuclear apical actin cables to protect nuclear morphology

The distinct spatial architecture of the apical actin cables (or actin cap) facilitates rapid biophysical signaling between extracellular mechanical stimuli and intracellular responses, including nuclear shaping, cytoskeletal remodeling, and the mechanotransduction of external forces into biochemical signals. These functions are abrogated in lamin A/C-deficient mouse embryonic fibroblasts that recapitulate the defective nuclear organization of laminopathies, featuring disruption of the actin cap. However, how nuclear lamin A/C mediates the ability of the actin cap to regulate nuclear morphology remains unclear. Here, we show that lamin A/C expressing cells can form an actin cap to resist nuclear deformation in response to physiological mechanical stresses. This study reveals how the nuclear lamin A/C-mediated formation of the perinuclear apical actin cables protects the nuclear structural integrity from extracellular physical disturbances. Our findings highlight the role of the physical interactions between the cytoskeletal network and the nucleus in cellular mechanical homeostasis.

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

Cells in vivo reside within complex microenvironments composed of both biochemical and biophysical cues. The dynamic feedback between cells and their microenvironments hinges upon biophysical cues that regulate critical cellular behaviors. Understanding this regulation from sensing to reaction to feedback is therefore critical, and a large effort is afoot to identify and mathematically model the fundamental mechanobiological mechanisms underlying this regulation. This review provides a critical perspective on recent progress in mathematical models for the responses of cells to the biophysical cues in their microenvironments, including dynamic strain, osmotic shock, fluid shear stress, mechanical force, matrix rigidity, porosity, and matrix shape. The review highlights key successes and failings of existing models, and discusses future opportunities and challenges in the field.

Mechanoregulated inhibition of formin facilitates contractile actomyosin ring assembly

Cytokinesis physically separates dividing cells by forming a contractile actomyosin ring. The fission yeast contractile ring has been proposed to assemble by Search-Capture-Pull-Release from cytokinesis precursor nodes that include the molecular motor type-II myosin Myo2 and the actin assembly factor formin Cdc12. By successfully reconstituting Search-Capture-Pull in vitro, we discovered that formin Cdc12 is a mechanosensor, whereby myosin pulling on formin-bound actin filaments inhibits Cdc12-mediated actin assembly. We mapped Cdc12 mechanoregulation to its formin homology 1 domain, which facilitates delivery of new actin subunits to the elongating actin filament. Quantitative modeling suggests that the pulling force of the myosin propagates through the actin filament, which behaves as an entropic spring, and thereby may stretch the disordered formin homology 1 domain and impede formin-mediated actin filament elongation. Finally, live cell imaging of mechano-insensitive formin mutant cells established that mechanoregulation of formin Cdc12 is required for efficient contractile ring assembly in vivo.

The fission yeast cytokinetic ring assembles by Search-Capture-Pull-Release from precursor nodes that include formin Cdc12 and myosin Myo2. The authors reconstitute Search-Capture-Pull in vitro and find that Myo2 pulling on Cdc12-associated actin filaments mechano-inhibits Cdc12-mediated assembly, which enables proper ring assembly in vivo.

Scattering of Cell Clusters in Confinement

Epithelial-to-mesenchymal transition (EMT) enables scattering of cell clusters and disseminates motile cells to distant locations in vivo during embryonic development and cancer metastasis. Both stiffness and topography of the extracellular matrix (ECM) have been shown to influence EMT. In this work, we examine how the integrity of epithelial cell clusters is regulated by subcellular forces, protrusions, and adhesions for varying ECM inputs, such as stiffness, topography, and dimensionality. Our model simulates multicell networks of defined sizes and shapes in ECMs of varied stiffness and geometry. The integrity of cell clusters is dictated by cell-cell junctions, which depend on subcellular forces and adhesion dynamics within each cell of the cluster. Our simulations demonstrate an enhanced dissociation of cell-cell junctions in stiffer and more confined three-dimensional (3D) environments, consistent with experimental findings. In narrow channels, the cell edges parallel to the axis of channels lose their cell-cell junctions more readily than those oriented in the perpendicular direction. The inhibition of protrusive activity and cell polarity disables confinement-dependent cell scattering. Here, cell adhesion and spreading along channel walls is found to be essential for scattering. The model also predicts that two-dimensional (2D) confinement of clusters restricts cell spreading and simultaneously blunts the confinement-sensitive cell scattering. This new, to our knowledge, multiscale model integrates molecular adhesion dynamics, subcellular forces, cellular deformation, and macroscale mechanical properties of the ECM to predict the state of cell clusters of defined shapes and sizes. The predictions made by our model not only match experimental findings from a number of experimental setups, but also provide a new conceptual framework for understanding mechanosensitive cell scattering and EMT.

Center or periphery? Modeling the effects of focal adhesion placement during cell spreading

Focal adhesions are often observed at the cell's periphery. We provide an explanation for this observation using a system-level mathematical model of a cell interacting with a two-dimensional substrate. The model describes the biological cell as a hypoelastic continuum material whose behavior is coupled to a deformable, linear elastic substrate via focal adhesions that are represented by collections of linear elastic attachments between the cell and the substrate. The evolution of the focal adhesions is coupled to local intracellular stresses which arise from mechanical cell-substrate interactions. Using this model we show that the cell has at least three mechanisms through which it can control its intracellular stresses: focal adhesion position, size, and attachment strength. We also propose that one reason why focal adhesions are typically located on the cell periphery instead of its center is because peripheral focal adhesions allow the cell to be more sensitive to changes in the microenvironment. This increased sensitivity is caused by the fact that peripherally located focal adhesions allow the cells to modulate its intracellular properties over a much larger portion of the cell area.

Computational simulation of formin-mediated actin polymerization predicts homologue-dependent mechanosensitivity

Many actin structures are nucleated and assembled by the barbed-end tracking polymerase formin family, including filopodia, focal adhesions, the cytokinetic ring and cell cortex. These structures respond to forces in distinct ways. Formins typically have profilin-actin binding sites embedded in highly flexible disordered FH1 domains, hypothesized to diffusively explore space to rapidly capture actin monomers for delivery to the barbed end. Recent experiments demonstrate that formin-mediated polymerization accelerates when under tension. The acceleration has been attributed to modifying the state of the FH2 domain of formin. Intriguingly, the same acceleration is reported when tension is applied to the FH1 domains, ostensibly pulling monomers away from the barbed end. Here we develop a mesoscale coarse-grain model of formin-mediated actin polymerization, including monomer capture and delivery by FH1, which sterically interacts with actin along its entire length. The binding of actin monomers to their specific sites on FH1 is entropically disfavored by the high disorder. We find that this penalty is attenuated when force is applied to the FH1 domain by revealing the binding site, increasing monomer capture efficiency. Overall polymerization rates can decrease or increase with increasing force, depending on the length of FH1 domain and location of binding site. Our results suggest that the widely varying FH1 lengths and binding site locations found in known formins could be used to differentially respond to force, depending on the actin structure being assembled. © 2016 Wiley Periodicals, Inc.

A Chemomechanical Model of Matrix and Nuclear Rigidity Regulation of Focal Adhesion Size

In this work, a chemomechanical model describing the growth dynamics of cell-matrix adhesion structures (i.e., focal adhesions (FAs)) is developed. We show that there are three regimes for FA evolution depending on their size. Specifically, nascent adhesions with initial lengths below a critical value that are yet to engage in actin fibers will dissolve, whereas bigger ones will grow into mature FAs with a steady state size. In adhesions where growth surpasses the steady state size, disassembly will occur until their sizes are reduced to the equilibrium state. This finding arises from the fact that polymerization of adhesion proteins is force-dependent. Under actomyosin contraction, individual integrin bonds within small FAs (i.e., nascent adhesions or focal complexes) must transmit higher loads while the phenomenon of stress concentration occurs at the edge of large adhesion patches. As such, an effective stiffness of the FA-extracellular matrix complex that is either too small or too large will be relatively low, resulting in a limited actomyosin pulling force developed at the edge that is insufficient to prevent disassembly. Furthermore, it is found that a stiffer extracellular matrix and/or nucleus, as well as a stronger chemomechanical feedback, will induce larger adhesions along with a higher level of contraction force. Interestingly, switching the extracellular side from an elastic half-space, corresponding to some widely used in vitro gel substrates, to a one-dimensional fiber (as in the case of cells anchoring to a fibrous scaffold in vivo) does not qualitative change these conclusions. Our model predictions are in good agreement with a variety of experimental observations obtained in this study as well as those reported in the literature. Furthermore, this new model, to our knowledge, provides a framework with which to understand how both intracellular and extracellular perturbations lead to changes in adhesion structure number and size.

Molecular-Scale Tools for Studying Mechanotransduction

Mechanical stimuli are known to be potent regulators of the form and function of cells and organisms. Although biological regulation has classically been understood in terms of principles from solution biochemistry, advancements in many fields have led to the development of a suite of techniques that are able to reveal the interplay between mechanical loading and changes in the biochemical properties of proteins in systems ranging from single molecules to living organisms. Here, we review these techniques and highlight the emergence of a new molecular-scale understanding of the mechanisms mediating the detection and response of cells to mechanical stimuli, a process termed mechanotransduction. Specifically, we focus on the role of subcellular adhesion structures in sensing the stiffness of the surrounding environment because this process is pertinent to applications in tissue engineering as well the onset of several mechanosensitive disease states, including cancer.

Crosstalk between focal adhesions and material mechanical properties governs cell mechanics and functions

Mechanical properties of materials strongly influence cell fate and functions. Focal adhesions are involved in the extremely important processes of mechanosensing and mechanotransduction. To address the relationship between the mechanical properties of cell substrates, focal adhesion/cytoskeleton assembly and cell functions, we investigated the behavior of NIH/3T3 cells over a wide range of stiffness (3-1000kPa) using two of the most common synthetic polymers for cell cultures: polyacrylamide and polydimethylsiloxane. An overlapping stiffness region was created between them to compare focal adhesion characteristics and cell functions, taking into account their different time-dependent behavior. Indeed, from a rheological point of view, polyacrylamide behaves like a strong gel (elastically), whereas polydimethylsiloxane like a viscoelastic solid. First, focal adhesion characteristics and dynamics were addressed in terms of material stiffness, then cell spreading area, migration rate and cell mechanical properties were correlated with focal adhesion size and assembly. Focal adhesion size was found to increase in the whole range of stiffness and to be in agreement in the overlapping rigidity region for the investigated materials. Cell mechanics directly correlated with focal adhesion lengths, whereas migration rate followed an inverse correlation. Cell spreading correlated with the substrate stiffness on polyacrylamide hydrogel, while no specific trend was found on polydimethylsiloxane. Substrate mechanics can be considered as a key physical cue that regulates focal adhesion assembly, which in turn governs important cellular properties and functions.

Regulation of matrix remodelling phenotype in gingival fibroblasts by substratum topography

Gingival connective tissue often has a composition resembling that of scar surrounding dental implant abutments. Increased cell adhesion, α-smooth muscle actin (α-SMA) expression and increased extracellular matrix deposition are a hallmark of fibrotic cells, but how topographic features influence gingival fibroblast adhesion and adoption of the α-SMA positive myofibroblast phenotype associated with scarring is unknown. The purpose of the present study was to demonstrate whether implant topographies that limit adhesion formation would reduce myofibroblast differentiation and extracellular matrix deposition. Human gingival fibroblasts were cultured on PT (smooth) and SLA (roughened) titanium discs for varying time-points. At 1 and 2 weeks after seeding, incorporation of α-SMA into stress-fibre bundles and fibronectin deposition was significantly higher on PT than SLA surfaces indicating differentiation of the cells towards a myofibroblast phenotype. Analysis of adhesion formation demonstrated that cells formed larger adhesions and more stable adhesions on PT, with more nascent adhesions observed on SLA. Gene expression analysis identified up-regulation of 15 genes at 24 hrs on SLA versus PT associated with matrix remodelling. Pharmacological inhibition of Src/FAK signalling in gingival fibroblasts on PT reduced fibronectin deposition and CCN2 expression. We conclude that topographical features that reduce focal adhesion stability could be applied to inhibit myofibroblast differentiation in gingival fibroblasts.

Master equation-based analysis of a motor-clutch model for cell traction force

Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell's optimum stiffness (i.e. the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on-off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours-days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.

Mathematical modeling of eukaryotic cell migration: insights beyond experiments

A migrating cell is a molecular machine made of tens of thousands of short-lived and interacting parts. Understanding migration means understanding the self-organization of these parts into a system of functional units. This task is one of tackling complexity: First, the system integrates numerous chemical and mechanical component processes. Second, these processes are connected in feedback interactions and over a large range of spatial and temporal scales. Third, many processes are stochastic, which leads to heterogeneous migration behaviors. Early on in the research of cell migration it became evident that this complexity exceeds human intuition. Thus, the cell migration community has led the charge to build mathematical models that could integrate the diverse experimental observations and measurements in consistent frameworks, first in conceptual and more recently in molecularly explicit models. The main goal of this review is to sift through a series of important conceptual and explicit mathematical models of cell migration and to evaluate their contribution to the field in their ability to integrate critical experimental data.

The multi-faceted role of the actin cap in cellular mechanosensation and mechanotransduction

The perinuclear actin cap (or actin cap) is a recently characterized cytoskeletal organelle composed of thick, parallel, and highly contractile acto-myosin filaments that are specifically anchored to the apical surface of the interphase nucleus. The actin cap is present in a wide range of adherent eukaryotic cells, but is disrupted in several human diseases, including laminopathies and cancer. Through its large terminating focal adhesions and anchorage to the nuclear lamina and nuclear envelope through LINC complexes, the perinuclear actin cap plays a critical role both in mechanosensation and mechanotransduction, the ability of cells to sense changes in matrix compliance and to respond to mechanical forces, respectively.

Predicting how cells spread and migrate: focal adhesion size does matter

Efficient cell migration is central to the normal development of tissues and organs and is involved in a wide range of human diseases, including cancer metastasis, immune responses, and cardiovascular disorders. Mesenchymal migration is modulated by focal-adhesion proteins, which organize into large integrin-rich protein complexes at the basal surface of adherent cells. Whether the extent of clustering of focal-adhesion proteins is actually required for effective migration is unclear. We recently demonstrated that the depletion of major focal-adhesion proteins, as well as modulation of matrix compliance, actin assembly, mitochondrial activity, and DNA recombination, all converged into highly predictable, inter-related, biphasic changes in focal adhesion size and cell migration. Herein, we further discuss the role of focal adhesions in controlling cell spreading and test their potential role in cell migration.

A kinetic model for RNA-interference of focal adhesions

BACKGROUND

Focal adhesions are integrin-based cell-matrix contacts that transduce and integrate mechanical and biochemical cues from the environment. They develop from smaller and more numerous focal complexes under the influence of mechanical force and are key elements for many physiological and disease-related processes, including wound healing and metastasis. More than 150 different proteins localize to focal adhesions and have been systematically classified in the adhesome project (http://www.adhesome.org). First RNAi-screens have been performed for focal adhesions and the effect of knockdown of many of these components on the number, size, shape and location of focal adhesions has been reported.

RESULTS

We have developed a kinetic model for RNA interference of focal adhesions which represents some of its main elements: a spatially layered structure, signaling through the small GTPases Rac and Rho, and maturation from focal complexes to focal adhesions under force. The response to force is described by two complementary scenarios corresponding to slip and catch bond behavior, respectively. Using estimated and literature values for the model parameters, three time scales of the dynamics of RNAi-influenced focal adhesions are identified: a sub-minute time scale for the assembly of focal complexes, a sub-hour time scale for the maturation to focal adhesions, and a time scale of days that controls the siRNA-mediated knockdown. Our model shows bistability between states dominated by focal complexes and focal adhesions, respectively. Catch bonding strongly extends the range of stability of the state dominated by focal adhesions. A sensitivity analysis predicts that knockdown of focal adhesion components is more efficient for focal adhesions with slip bonds or if the system is in a state dominated by focal complexes. Knockdown of Rho leads to an increase of focal complexes.

CONCLUSIONS

The suggested model provides a kinetic description of the effect of RNA-interference of focal adhesions. Its predictions are in good agreement with known experimental results and can now guide the design of RNAi-experiments. In the future, it can be extended to include more components of the adhesome. It also could be extended by spatial aspects, for example by the differential activation of the Rac- and Rho-pathways in different parts of the cell.

Physically based principles of cell adhesion mechanosensitivity in tissues

The minimal structural unit that defines living organisms is a single cell. By proliferating and mechanically interacting with each other, cells can build complex organization such as tissues that ultimately organize into even more complex multicellular living organisms, such as mammals, composed of billions of single cells interacting with each other. As opposed to passive materials, living cells actively respond to the mechanical perturbations occurring in their environment. Tissue cell adhesion to its surrounding extracellular matrix or to neighbors is an example of a biological process that adapts to physical cues. The adhesion of tissue cells to their surrounding medium induces the generation of intracellular contraction forces whose amplitude adapts to the mechanical properties of the environment. In turn, solicitation of adhering cells with physical forces, such as blood flow shearing the layer of endothelial cells in the lumen of arteries, reinforces cell adhesion and impacts cell contractility. In biological terms, the sensing of physical signals is transduced into biochemical signaling events that guide cellular responses such as cell differentiation, cell growth and cell death. Regarding the biological and developmental consequences of cell adaptation to mechanical perturbations, understanding mechanotransduction in tissue cell adhesion appears as an important step in numerous fields of biology, such as cancer, regenerative medicine or tissue bioengineering for instance. Physicists were first tempted to view cell adhesion as the wetting transition of a soft bag having a complex, adhesive interaction with the surface. But surprising responses of tissue cell adhesion to mechanical cues challenged this view. This, however, did not exclude that cell adhesion could be understood in physical terms. It meant that new models and descriptions had to be created specifically for these biological issues, and could not straightforwardly be adapted from dead matter. In this review, we present physical concepts of tissue cell adhesion and the unexpected cellular responses to mechanical cues such as external forces and stiffness sensing. We show how biophysical approaches, both experimentally and theoretically, have contributed to our understanding of the regulation of cellular functions through physical force sensing mechanisms. Finally, we discuss the different physical models that could explain how tissue cell adhesion and force sensing can be coupled to internal mechanosensitive processes within the cell body.

United we stand: integrating the actin cytoskeleton and cell-matrix adhesions in cellular mechanotransduction

Many essential cellular functions in health and disease are closely linked to the ability of cells to respond to mechanical forces. In the context of cell adhesion to the extracellular matrix, the forces that are generated within the actin cytoskeleton and transmitted through integrin-based focal adhesions are essential for the cellular response to environmental clues, such as the spatial distribution of adhesive ligands or matrix stiffness. Whereas substantial progress has been made in identifying mechanosensitive molecules that can transduce mechanical force into biochemical signals, much less is known about the nature of cytoskeletal force generation and transmission that regulates the magnitude, duration and spatial distribution of forces imposed on these mechanosensitive complexes. By focusing on cell-matrix adhesion to flat elastic substrates, on which traction forces can be measured with high temporal and spatial resolution, we discuss our current understanding of the physical mechanisms that integrate a large range of molecular mechanotransduction events on cellular scales. Physical limits of stability emerge as one important element of the cellular response that complements the structural changes affected by regulatory systems in response to mechanical processes.