Model for adhesion clutch explains biphasic relationship between actin flow and traction at the cell leading edge

A simple active fluid model unites cytokinesis, cell crawling, and axonal outgrowth

Axonal outgrowth, cell crawling, and cytokinesis utilize actomyosin, microtubule-based motors, cytoskeletal dynamics, and substrate adhesions to produce traction forces and bulk cellular motion. While it has long been appreciated that growth cones resemble crawling cells and that the mechanisms that drive cytokinesis help power cell crawling, they are typically viewed as unique processes. To better understand the relationship between these modes of motility, here, we developed a unified active fluid model of cytokinesis, amoeboid migration, mesenchymal migration, neuronal migration, and axonal outgrowth in terms of cytoskeletal flow, adhesions, viscosity, and force generation. Using numerical modeling, we fit subcellular velocity profiles of the motions of cytoskeletal structures and docked organelles from previously published studies to infer underlying patterns of force generation and adhesion. Our results indicate that, during cytokinesis, there is a primary converge zone at the cleavage furrow that drives flow towards it; adhesions are symmetric across the cell, and as a result, cells are stationary. In mesenchymal, amoeboid, and neuronal migration, the site of the converge zone shifts, and differences in adhesion between the front and back of the cell drive crawling. During neuronal migration and axonal outgrowth, the primary convergence zone lies within the growth cone, which drives actin retrograde flow in the P-domain and bulk anterograde flow of the axonal shaft. They differ in that during neuronal migration, the cell body is weakly attached to the substrate and thus moves forward at the same velocity as the axon. In contrast, during axonal outgrowth, the cell body strongly adheres to the substrate and remains stationary, resulting in a decrease in flow velocity away from the growth cone. The simplicity with which cytokinesis, cell crawling, and axonal outgrowth can be modeled by varying coefficients in a simple model suggests a deep connection between them.

Clutch model for focal adhesions predicts reduced self-stabilization under oblique pulling

Cell-matrix adhesions connect the cytoskeleton to the extracellular environment and are essential for maintaining the integrity of tissue and whole organisms. Remarkably, cell adhesions can adapt their size and composition to an applied force such that their size and strength increases proportionally to the load. Mathematical models for the clutch-like force transmission at adhesions are frequently based on the assumption that mechanical load is applied tangentially to the adhesion plane. Recently, we suggested a molecular mechanism that can explain adhesion growth under load for planar cell adhesions. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which for thermodynamic reasons, leads to the association of further molecules with the cluster, which we refer to as self-stabilization. Here, we generalize this model to forces that pull at an oblique angle to the plane supporting the cell, and examine if this idealized model also predicts self-stabilization. We also allow for a variable distance between the parallel planes representing cytoskeletal F-actin and transmembrane integrins. Simulation results demonstrate that the binding mechanism and the geometry of the cluster have a strong influence on the response of adhesion clusters to force. For oblique angles smaller than about 40∘, we observe a growth of the adhesion site under force. However this self-stabilization is reduced as the angle between the force and substrate plane increases, with vanishing self-stabilization for normal pulling. Overall, these results highlight the fundamental difference between the assumption of pulling and shearing forces in commonly used models of cell adhesion.

Mesenchymal cell migration on one-dimensional micropatterns

Quantitative studies of mesenchymal cell motion are important to elucidate cytoskeleton function and mechanisms of cell migration. To this end, confinement of cell motion to one dimension (1D) significantly simplifies the problem of cell shape in experimental and theoretical investigations. Here we review 1D migration assays employing micro-fabricated lanes and reflect on the advantages of such platforms. Data are analyzed using biophysical models of cell migration that reproduce the rich scenario of morphodynamic behavior found in 1D. We describe basic model assumptions and model behavior. It appears that mechanical models explain the occurrence of universal relations conserved across different cell lines such as the adhesion-velocity relation and the universal correlation between speed and persistence (UCSP). We highlight the unique opportunity of reproducible and standardized 1D assays to validate theory based on statistical measures from large data of trajectories and discuss the potential of experimental settings embedding controlled perturbations to probe response in migratory behavior.

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.

G-actin diffusion is insufficient to achieve F-actin assembly in fast-treadmilling protrusions

To generate forces that drive migration of a eukaryotic cell, arrays of actin filaments (F-actin) are assembled at the cell's leading membrane edge. To maintain cell propulsion and respond to dynamic external cues, actin filaments must be disassembled to regenerate the actin monomers (G-actin), and transport of G-actin from sites of disassembly back to the leading edge completes the treadmilling cycle and limits the flux of F-actin assembly. Whether or not molecular diffusion is sufficient for G-actin transport has been a long-standing topic of debate, in part because the dynamic nature of cell motility and migration hinders the estimation of transport parameters. In this work, we applied an experimental system in which cells adopt an approximately constant and symmetrical shape; they cannot migrate but exhibit fast, steady treadmilling in the thin region protruding from the cell. Using fluorescence recovery after photobleaching, we quantified the relative concentrations and corresponding fluxes of F- and G-actin in this system. In conjunction with mathematical modeling, constrained by measured features of each region of interest, this approach revealed that diffusion alone cannot account for the transport of G-actin to the leading edge. Although G-actin diffusion and vectorial transport might vary with position in the protruding region, good agreement with the fluorescence recovery after photobleaching measurements was achieved by a model with constant G-actin diffusivity ∼2 μm2/s and anterograde G-actin velocity less than 1 μm/s.

Optimal cell traction forces in a generalized motor-clutch model

Cells exert forces on mechanically compliant environments to sense stiffness, migrate, and remodel tissue. Cells can sense environmental stiffness via myosin-generated pulling forces acting on F-actin, which is in turn mechanically coupled to the environment via adhesive proteins, akin to a clutch in a drivetrain. In this "motor-clutch" framework, the force transmitted depends on the complex interplay of motor, clutch, and environmental properties. Previous mean-field analysis of the motor-clutch model identified the conditions for optimal stiffness for maximal force transmission via a dimensionless number that combines motor-clutch parameters. However, in this and other previous mean-field analyses, the motor-clutch system is assumed to have balanced motors and clutches and did not consider force-dependent clutch reinforcement and catch bond behavior. Here, we generalize the motor-clutch analytical framework to include imbalanced motor-clutch regimes, with clutch reinforcement and catch bonding, and investigate optimality with respect to all parameters. We found that traction force is strongly influenced by clutch stiffness, and we discovered an optimal clutch stiffness that maximizes traction force, suggesting that cells could tune their clutch mechanical properties to perform a specific function. The results provide guidance for maximizing the accuracy of cell-generated force measurements via molecular tension sensors by designing their mechanosensitive linker peptide to be as stiff as possible. In addition, we found that, on rigid substrates, the mean-field analysis identifies optimal motor properties, suggesting that cells could regulate their myosin repertoire and activity to maximize force transmission. Finally, we found that clutch reinforcement shifts the optimum substrate stiffness to larger values, whereas the optimum substrate stiffness is insensitive to clutch catch bond properties. Overall, our work reveals novel features of the motor-clutch model that can affect the design of molecular tension sensors and provide a generalized analytical framework for predicting and controlling cell adhesion and migration in immunotherapy and cancer.

A minimal cell model for lamellipodia-based cellular dynamics and migration

One ubiquitous cellular structure for performing various tasks, such as spreading and migration over external surfaces, is the sheet-like protrusion called a lamellipodium, which propels the leading edge of the cell. Despite the detailed knowledge about the many components of this cellular structure, it is not yet fully understood how these components self-organize spatiotemporally to form lamellipodia. We review here recent theoretical works where we have demonstrated that membrane-bound protein complexes that have intrinsic curvature and recruit the protrusive forces of the cytoskeleton result in a simple, yet highly robust, organizing feedback mechanism that organizes the cytoskeleton and the membrane. This self-organization mechanism accounts for the formation of flat lamellipodia at the leading edge of cells spreading over adhesive substrates, allowing for the emergence of a polarized, motile 'minimal cell' model. The same mechanism describes how lamellipodia organize to drive robust engulfment of particles during phagocytosis and explains in simple physical terms the spreading and migration of cells over fibers and other curved surfaces. This Review highlights that despite the complexity of cellular composition, there might be simple general physical principles that are utilized by the cell to drive cellular shape dynamics.

A multi-scale clutch model for adhesion complex mechanics

Cell-matrix adhesion is a central mechanical function to a large number of phenomena in physiology and disease, including morphogenesis, wound healing, and tumor cell invasion. Today, how single cells respond to different extracellular cues has been comprehensively studied. However, how the mechanical behavior of the main individual molecules that form an adhesion complex cooperatively responds to force within the adhesion complex is still poorly understood. This is a key aspect of cell adhesion because how these cell adhesion molecules respond to force determines not only cell adhesion behavior but, ultimately, cell function. To answer this question, we develop a multi-scale computational model for adhesion complexes mechanics. We extend the classical clutch hypothesis to model individual adhesion chains made of a contractile actin network, a talin rod, and an integrin molecule that binds at individual adhesion sites on the extracellular matrix. We explore several scenarios of integrins dynamics and analyze the effects of diverse extracellular matrices on the behavior of the adhesion molecules and on the whole adhesion complex. Our results describe how every single component of the adhesion chain mechanically responds to the contractile actomyosin force and show how they control the traction forces exerted by the cell on the extracellular space. Importantly, our computational results agree with previous experimental data at the molecular and cellular levels. Our multi-scale clutch model presents a step forward not only to further understand adhesion complexes mechanics but also to impact, e.g., the engineering of biomimetic materials, tissue repairment, or strategies to arrest tumor progression.

On multistability and constitutive relations of cell motion on fibronectin lanes

Cell motility on flat substrates exhibits coexisting steady and oscillatory morphodynamics, the biphasic adhesion-velocity relation, and the universal correlation between speed and persistence (UCSP) as simultaneous observations common to many cell types. Their universality and concurrency suggest a unifying mechanism causing all three of them. Stick-slip models for cells on one-dimensional lanes suggest multistability to arise from the nonlinear friction of retrograde flow. This study suggests a mechanical mechanism controlled by integrin signaling on the basis of a biophysical model and analysis of trajectories of MDA-MB-231 cells on fibronectin lanes, which additionally explains the constitutive relations. The experiments exhibit cells with steady or oscillatory morphodynamics and either spread or moving with spontaneous transitions between the dynamic regimes, spread and moving, and spontaneous direction reversals. Our biophysical model is based on the force balance at the protrusion edge, the noisy clutch of retrograde flow, and a response function of friction and membrane drag to integrin signaling. The theory reproduces the experimentally observed cell states, characteristics of oscillations, and state probabilities. Analysis of experiments with the biophysical model establishes a stick-slip oscillation mechanism, and explains multistability of cell states and the statistics of state transitions. It suggests protrusion competition to cause direction reversal events, the statistics of which explain the UCSP. The effect of integrin signaling on drag and friction explains the adhesion-velocity relation and cell behavior at fibronectin density steps. The dynamics of our mechanism are nonlinear flow mechanics driven by F-actin polymerization and shaped by the noisy clutch of retrograde flow friction, protrusion competition via membrane tension, and drag forces. Integrin signaling controls the parameters of the mechanical system.

Glioblastoma Spheroid Invasion through Soft, Brain-Like Matrices Depends on Hyaluronic Acid-CD44 Interactions

Increased secretion of hyaluronic acid (HA), a glycosaminoglycan abundant in the brain extracellular matrix (ECM), correlates with worse clinical outcomes for glioblastoma (GBM) patients. GBM cells aggressively invade the brain parenchyma while encountering spatiotemporal changes in their local ECM, including HA concentration. To investigate how varying HA concentrations affect GBM invasion, patient-derived GBM cells are cultured within a soft, 3D matrix in which HA concentration is precisely varied and cell migration observed. Data demonstrate that HA concentration can determine the invasive activity of patient-derived GBM cells in a biphasic and highly sensitive manner, where the absolute concentration of HA at which cell migration peaked is specific to each patient-derived line. Furthermore, evidence that this response relies on phosphorylated ezrin, which interacts with the intracellular domain of HA-engaged CD44 to effectively link the actin cytoskeleton to the local ECM is provided. Overall, this study highlights CD44-HA binding as a major mediator of GBM cell migration that acts independently of integrins and focal adhesion complexes and suggests that targeting HA-CD44-ezrin interactions represents a promising therapeutic strategy to prevent tumor cell invasion in the brain.

Regulation of actin filament assembly and disassembly in growth cone motility and axon guidance

Directed outgrowth of axons is fundamental for the establishment of neuronal networks. Axon outgrowth is guided by growth cones, highly motile structures enriched in filamentous actin (F-actin) located at the axons' distal tips. Growth cones exploit F-actin-based protrusions to scan the environment for guidance cues, and they contain the sensory apparatus to translate guidance cue information into intracellular signaling cascades. These cascades act upstream of actin-binding proteins (ABP) and thereby control assembly and disassembly of F-actin. Spatiotemporally controlled F-actin dis-/assembly in growth cones steers the axon towards attractants and away from repellents, and it thereby navigates the axon through the developing nervous system. Hence, ABP that control F-actin dynamics emerged as critical regulators of neuronal network formation. In the present review article, we will summarize and discuss current knowledge of the mechanisms that control remodeling of the actin cytoskeleton in growth cones, focusing on recent progress in the field. Further, we will introduce tools and techniques that allow to study actin regulatory mechanism in growth cones.

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.

Deconstructing the role of myosin contractility in force fluctuations within focal adhesions

Force fluctuations exhibited in focal adhesions that connect a cell to its extracellular environment point to the complex role of the underlying machinery that controls cell migration. To elucidate the explicit role of myosin motors in the temporal traction force oscillations, we vary the contractility of these motors in a dynamical model based on the molecular clutch hypothesis. As the contractility is lowered, effected both by changing the motor velocity and the rate of attachment/detachment, we show analytically in an experimentally relevant parameter space, that the system goes from decaying oscillations to stable limit cycle oscillations through a supercritical Hopf bifurcation. As a function of the motor activity and the number of clutches, the system exhibits a rich array of dynamical states. We corroborate our analytical results with stochastic simulations of the motor-clutch system. We obtain limit cycle oscillations in the parameter regime as predicted by our model. The frequency range of oscillations in the average clutch and motor deformation compares well with experimental results.

Modeling cell protrusion predicts how myosin II and actin turnover affect adhesion-based signaling

Orchestration of cell migration is essential for development, tissue regeneration, and the immune response. This dynamic process integrates adhesion, signaling, and cytoskeletal subprocesses across spatial and temporal scales. In mesenchymal cells, adhesion complexes bound to extracellular matrix mediate both biochemical signal transduction and physical interaction with the F-actin cytoskeleton. Here, we present a mathematical model that offers insight into both aspects, considering spatiotemporal dynamics of nascent adhesions, active signaling molecules, mechanical clutching, actin treadmilling, and nonmuscle myosin II contractility. At the core of the model is a positive feedback loop, whereby adhesion-based signaling promotes generation of barbed ends at, and protrusion of, the cell's leading edge, which in turn promotes formation and stabilization of nascent adhesions. The model predicts a switch-like transition and optimality of membrane protrusion, determined by the balance of actin polymerization and retrograde flow, with respect to extracellular matrix density. The model, together with new experimental measurements, explains how protrusion can be modulated by mechanical effects (nonmuscle myosin II contractility and adhesive bond stiffness) and F-actin turnover.

Discrete mechanical model of lamellipodial actin network implements molecular clutch mechanism and generates arcs and microspikes

Mechanical forces, actin filament turnover, and adhesion to the extracellular environment regulate lamellipodial protrusions. Computational and mathematical models at the continuum level have been used to investigate the molecular clutch mechanism, calculating the stress profile through the lamellipodium and around focal adhesions. However, the forces and deformations of individual actin filaments have not been considered while interactions between actin networks and actin bundles is not easily accounted with such methods. We develop a filament-level model of a lamellipodial actin network undergoing retrograde flow using 3D Brownian dynamics. Retrograde flow is promoted in simulations by pushing forces from the leading edge (due to actin polymerization), pulling forces (due to molecular motors), and opposed by viscous drag in cytoplasm and focal adhesions. Simulated networks have densities similar to measurements in prior electron micrographs. Connectivity between individual actin segments is maintained by permanent and dynamic crosslinkers. Remodeling of the network occurs via the addition of single actin filaments near the leading edge and via filament bond severing. We investigated how several parameters affect the stress distribution, network deformation and retrograde flow speed. The model captures the decrease in retrograde flow upon increase of focal adhesion strength. The stress profile changes from compression to extension across the leading edge, with regions of filament bending around focal adhesions. The model reproduces the observed reduction in retrograde flow speed upon exposure to cytochalasin D, which halts actin polymerization. Changes in crosslinker concentration and dynamics, as well as in the orientation pattern of newly added filaments demonstrate the model's ability to generate bundles of filaments perpendicular (actin arcs) or parallel (microspikes) to the protruding direction.

Focal adhesion dynamics in cellular function and disease

Acting as a bridge between the cytoskeleton of the cell and the extra cellular matrix (ECM), the cell-ECM adhesions with integrins at their core, play a major role in cell signalling to direct mechanotransduction, cell migration, cell cycle progression, proliferation, differentiation, growth and repair. Biochemically, these adhesions are composed of diverse, yet an organised group of structural proteins, receptors, adaptors, various enzymes including protein kinases, phosphatases, GTPases, proteases, etc. as well as scaffolding molecules. The major integrin adhesion complexes (IACs) characterised are focal adhesions (FAs), invadosomes (podosomes and invadopodia), hemidesmosomes (HDs) and reticular adhesions (RAs). The varied composition and regulation of the IACs and their signalling, apart from being an integral part of normal cell survival, has been shown to be of paramount importance in various developmental and pathological processes. This review per-illustrates the recent advancements in the research of IACs, their crucial roles in normal as well as diseased states. We have also touched on few of the various methods that have been developed over the years to visualise IACs, measure the forces they exert and study their signalling and molecular composition. Having such pertinent roles in the context of various pathologies, these IACs need to be understood and studied to develop therapeutical targets. We have given an update to the studies done in recent years and described various techniques which have been applied to study these structures, thereby, providing context in furthering research with respect to IAC targeted therapeutics.

Stick-slip model for actin-driven cell protrusions, cell polarization, and crawling

Cell crawling requires the generation of intracellular forces by the cytoskeleton and their transmission to an extracellular substrate through specific adhesion molecules. Crawling cells show many features of excitable systems, such as spontaneous symmetry breaking and crawling in the absence of external cues, and periodic and propagating waves of activity. Mechanical instabilities in the active cytoskeleton network and feedback loops in the biochemical network of activators and repressors of cytoskeleton dynamics have been invoked to explain these dynamical features. Here, I show that the interplay between the dynamics of cell-substrate adhesion and linear cellular mechanics is sufficient to reproduce many nonlinear dynamical patterns observed in spreading and crawling cells. Using an analytical formalism of the molecular clutch model of cell adhesion, regulated by local mechanical forces, I show that cellular traction forces exhibit stick-slip dynamics resulting in periodic waves of protrusion/retraction and propagating waves along the cell edge. This can explain spontaneous symmetry breaking and polarization of spreading cells, leading to steady crawling or bipedal motion, and bistability, where persistent cell motion requires a sufficiently strong transient external stimulus. The model also highlights the role of membrane tension in providing the long-range mechanical communication across the cell required for symmetry breaking.

Predicting Confined 1D Cell Migration from Parameters Calibrated to a 2D Motor-Clutch Model

Biological tissues contain micrometer-scale gaps and pores, including those found within extracellular matrix fiber networks, between tightly packed cells, and between blood vessels or nerve bundles and their associated basement membranes. These spaces restrict cell motion to a single-spatial dimension (1D), a feature that is not captured in traditional in vitro cell migration assays performed on flat, unconfined two-dimensional (2D) substrates. Mechanical confinement can variably influence cell migration behaviors, and it is presently unclear whether the mechanisms used for migration in 2D unconfined environments are relevant in 1D confined environments. Here, we assessed whether a cell migration simulator and associated parameters previously measured for cells on 2D unconfined compliant hydrogels could predict 1D confined cell migration in microfluidic channels. We manufactured microfluidic devices with narrow channels (60-μm2 rectangular cross-sectional area) and tracked human glioma cells that spontaneously migrated within channels. Cell velocities (vexp = 0.51 ± 0.02 μm min-1) were comparable to brain tumor expansion rates measured in the clinic. Using motor-clutch model parameters estimated from cells on unconfined 2D planar hydrogel substrates, simulations predicted similar migration velocities (vsim = 0.37 ± 0.04 μm min-1) and also predicted the effects of drugs targeting the motor-clutch system or cytoskeletal assembly. These results are consistent with glioma cells utilizing a motor-clutch system to migrate in confined environments.

Feeling Things Out: Bidirectional Signaling of the Cell-ECM Interface, Implications in the Mechanobiology of Cell Spreading, Migration, Proliferation, and Differentiation

Biophysical cues stemming from the extracellular environment are rapidly transduced into discernible chemical messages (mechanotransduction) that direct cellular activities-placing the extracellular matrix (ECM) as a potent regulator of cell behavior. Dynamic reciprocity between the cell and its associated matrix is essential to the maintenance of tissue homeostasis and dysregulation of both ECM mechanical signaling, via pathological ECM turnover, and internal mechanotransduction pathways contribute to disease progression. This review covers the current understandings of the key modes of signaling used by both the cell and ECM to coregulate one another. By taking an outside-in approach, the inherent complexities and regulatory processes at each level of signaling (ECM, plasma membrane, focal adhesion, and cytoplasm) are captured to give a comprehensive picture of the internal and external mechanoregulatory environment. Specific emphasis is placed on the focal adhesion complex which acts as a central hub of mechanical signaling, regulating cell spreading, migration, proliferation, and differentiation. In addition, a wealth of available knowledge on mechanotransduction is curated to generate an integrated signaling network encompassing the central components of the focal adhesion, cytoplasm and nucleus that act in concert to promote durotaxis, proliferation, and differentiation in a stiffness-dependent manner.

Scaling up single-cell mechanics to multicellular tissues - the role of the intermediate filament-desmosome network

Cells and tissues sense, respond to and translate mechanical forces into biochemical signals through mechanotransduction, which governs individual cell responses that drive gene expression, metabolic pathways and cell motility, and determines how cells work together in tissues. Mechanotransduction often depends on cytoskeletal networks and their attachment sites that physically couple cells to each other and to the extracellular matrix. One way that cells associate with each other is through Ca2+-dependent adhesion molecules called cadherins, which mediate cell-cell interactions through adherens junctions, thereby anchoring and organizing the cortical actin cytoskeleton. This actin-based network confers dynamic properties to cell sheets and developing organisms. However, these contractile networks do not work alone but in concert with other cytoarchitectural elements, including a diverse network of intermediate filaments. This Review takes a close look at the intermediate filament network and its associated intercellular junctions, desmosomes. We provide evidence that this system not only ensures tissue integrity, but also cooperates with other networks to create more complex tissues with emerging properties in sensing and responding to increasingly stressful environments. We will also draw attention to how defects in intermediate filament and desmosome networks result in both chronic and acquired diseases.

Modeling the Shape of Synaptic Spines by Their Actin Dynamics

Dendritic spines are the morphological basis of excitatory synapses in the cortex and their size and shape correlates with functional synaptic properties. Recent experiments show that spines exhibit large shape fluctuations that are not related to activity-dependent plasticity but nonetheless might influence memory storage at their synapses. To investigate the determinants of such spontaneous fluctuations, we propose a mathematical model for the dynamics of the spine shape and analyze it in 2D-related to experimental microscopic imagery-and in 3D. We show that the spine shape is governed by a local imbalance between membrane tension and the expansive force from actin bundles that originates from discrete actin polymerization foci. Experiments have shown that only few such polymerization foci co-exist at any time in a spine, each having limited life time. The model shows that the momentarily existing set of such foci pushes the membrane along certain directions until foci are replaced and other directions may now be affected. We explore these relations in depth and use our model to predict shape and temporal characteristics of spines from the different biophysical parameters involved in actin polymerization. Approximating the model by a single recursive equation we finally demonstrate that the temporal evolution of the number of active foci is sufficient to predict the size of the model-spines. Thus, our model provides the first platform to study the relation between molecular and morphological properties of the spine with a high degree of biophysical detail.

Stick-slip dynamics of migrating cells on viscoelastic substrates

Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviors have previously been investigated typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model, based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force-dependent assembly, and disassembly of focal adhesions coupled with cell-substrate interaction. We show that consideration of a viscoelastic substrate not only captures the usually observed stick-slip jumps but also predicts the existence of an optimal substrate viscosity corresponding to maximum traction force and minimum retrograde flow which was hitherto unexplored. Moreover, our theory predicts the time evolution of individual bond force that characterizes the stick-slip patterns on soft versus stiff substrates. Our analysis also elucidates how the duration of the stick-slip cycles are affected by various cellular parameters.

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.

Modeling Cell Migration Mechanics

Cell migration is the physical movement of cells and is responsible for the extensive cellular invasion and metastasis that occur in high-grade tumors. Motivated by decades of direct observation of cell migration via light microscopy, theoretical models have emerged to capture various aspects of the fundamental physical phenomena underlying cell migration. Yet, the motility mechanisms actually used by tumor cells during invasion are still poorly understood, as is the role of cellular interactions with the extracellular environment. In this chapter, we review key physical principles of cytoskeletal self-assembly and force generation, membrane tension, biological adhesion, hydrostatic and osmotic pressures, and their integration in mathematical models of cell migration. With the goal of modeling-driven cancer therapy, we provide examples to guide oncologists and physical scientists in developing next-generation models to predict disease progression and treatment.

Multiscale model of integrin adhesion assembly

The ability of adherent cells to form adhesions is critical to numerous phases of their physiology. The assembly of adhesions is mediated by several types of integrins. These integrins differ in physical properties, including rate of diffusion on the plasma membrane, rapidity of changing conformation from bent to extended, affinity for extracellular matrix ligands, and lifetimes of their ligand-bound states. However, the way in which nanoscale physical properties of integrins ensure proper adhesion assembly remains elusive. We observe experimentally that both β-1 and β-3 integrins localize in nascent adhesions at the cell leading edge. In order to understand how different nanoscale parameters of β-1 and β-3 integrins mediate proper adhesion assembly, we therefore develop a coarse-grained computational model. Results from the model demonstrate that morphology and distribution of nascent adhesions depend on ligand binding affinity and strength of pairwise interactions. Organization of nascent adhesions depends on the relative amounts of integrins with different bond kinetics. Moreover, the model shows that the architecture of an actin filament network does not perturb the total amount of integrin clustering and ligand binding; however, only bundled actin architectures favor adhesion stability and ultimately maturation. Together, our results support the view that cells can finely tune the expression of different integrin types to determine both structural and dynamic properties of adhesions.

Regulation of axon growth by myosin II-dependent mechanocatalysis of cofilin activity

Synergism between myosin II contractility and cofilin activity modulates serotonin-dependent axon growth. Normally, cofilin-dependent decreases in actin density are compensated by increases in point contact density and traction force; however, myosin hyperactivation leads to catastrophic decreases in actin network density and neurite retraction.

Serotonin (5-HT) is known to increase the rate of growth cone advance via cofilin-dependent increases in retrograde actin network flow and nonmuscle myosin II activity. We report that myosin II activity is regulated by PKC during 5-HT responses and that PKC activity is necessary for increases in traction force normally associated with these growth responses. 5-HT simultaneously induces cofilin-dependent decreases in actin network density and PKC-dependent increases in point contact density. These reciprocal effects facilitate increases in traction force production in domains exhibiting decreased actin network density. Interestingly, when PKC activity was up-regulated, 5-HT treatments resulted in myosin II hyperactivation accompanied by catastrophic cofilin-dependent decreases in actin filament density, sudden decreases in traction force, and neurite retraction. These results reveal a synergistic relationship between cofilin and myosin II that is spatiotemporally regulated in the growth cone via mechanocatalytic effects to modulate neurite growth.

Model for Coordination of Microtubule and Actin Dynamics in Growth Cone Turning

In the developing nervous system, axons are guided to their synaptic targets by motile structures at the axon tip called growth cones, which reorganize their cytoskeleton in order to steer in response to chemotactic cues. Growth cone motility is mediated by an actin-adhesion “clutch” mechanism, in which mechanical attachment to a substrate, coupled with polarized actin growth, produces leading-edge protrusion. Several studies suggest that dynamic microtubules (MTs) in the growth cone periphery play an essential role in growth cone steering. It is not yet well-understood how the MT cytoskeleton and the dynamic actin-adhesion clutch system are coordinated to promote growth cone navigation. I introduce an experimentally motivated stochastic model of the dynamic reorganization of the growth cone cytoskeleton in response to external guidance cues. According to this model, asymmetric decoupling of MTs from actin retrograde flow leads to a local influx of MTs to the growth cone leading edge, and the leading-edge MT accumulation is amplified by positive feedback between MTs and the actin-adhesion clutch system. Local accumulation of MTs at the leading edge is hypothesized to increase actin adhesion to the substrate, which attenuates actin retrograde flow and promotes leading-edge protrusion. Growth cone alignment with the chemotactic gradient is predicted to be most effective for intermediate levels of sensitivity of the adhesion strength to the presence of leading-edge MTs. Quantitative predictions of the MT distribution and the local rate of retrograde actin flow will allow the hypothetical positive feedback mechanism to be experimentally tested.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

Collective gradient sensing and chemotaxis: modeling and recent developments

Cells measure a vast variety of signals, from their environment's stiffness to chemical concentrations and gradients; physical principles strongly limit how accurately they can do this. However, when many cells work together, they can cooperate to exceed the accuracy of any single cell. In this topical review, I will discuss the experimental evidence showing that cells collectively sense gradients of many signal types, and the models and physical principles involved. I also propose new routes by which experiments and theory can expand our understanding of these problems.

Control of Mechanotransduction by Molecular Clutch Dynamics

The linkage of cells to their microenvironment is mediated by a series of bonds that dynamically engage and disengage, in what has been conceptualized as the molecular clutch model. Whereas this model has long been employed to describe actin cytoskeleton and cell migration dynamics, it has recently been proposed to also explain mechanotransduction (i.e., the process by which cells convert mechanical signals from their environment into biochemical signals). Here we review the current understanding on how cell dynamics and mechanotransduction are driven by molecular clutch dynamics and its master regulator, the force loading rate. Throughout this Review, we place a specific emphasis on the quantitative prediction of cell response enabled by combined experimental and theoretical approaches.

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.

Theoretical modeling of actin-retrograde-flow passing clusters of confined T cell receptors

Through the activation process of T cells, actin filaments move from the cell periphery toward the cell center. The moving filaments engage with T cell receptors and thus contribute to transportation of the signaling molecules. To study the connection between the moving actin filaments and T cell receptors, an experiment available in the literature has measured filaments flow velocity passing over a region of confined clusters of receptors. It shows that flow velocity decreases in the proximity of the receptors, and then regains its normal value after traversing the region, suggesting a dissipative friction-like connection. In this work, we develop a minimal theoretical model to re-examine this experiment. The model brings the insight that, in contrast to the first impression that the experiment gives, the direct necessity of having a minimum in the velocity profile is not the locally high friction region, but a combined driving force of push from upstream and pull from within and downstream of the system. The predicted driving force integrates our current understanding of the spatially dependent role of the myosin motor proteins and the actin-polymerization-machinery, which make the pulling and pushing forces, respectively.

ATRA mechanically reprograms pancreatic stellate cells to suppress matrix remodelling and inhibit cancer cell invasion

Pancreatic ductal adenocarcinoma (PDAC) is a highly aggressive malignancy with a dismal survival rate. Persistent activation of pancreatic stellate cells (PSCs) can perturb the biomechanical homoeostasis of the tumour microenvironment to favour cancer cell invasion. Here we report that ATRA, an active metabolite of vitamin A, restores mechanical quiescence in PSCs via a mechanism involving a retinoic acid receptor beta (RAR-β)-dependent downregulation of actomyosin (MLC-2) contractility. We show that ATRA reduces the ability of PSCs to generate high traction forces and adapt to extracellular mechanical cues (mechanosensing), as well as suppresses force-mediated extracellular matrix remodelling to inhibit local cancer cell invasion in 3D organotypic models. Our findings implicate a RAR-β/MLC-2 pathway in peritumoural stromal remodelling and mechanosensory-driven activation of PSCs, and further suggest that mechanical reprogramming of PSCs with retinoic acid derivatives might be a viable alternative to stromal ablation strategies for the treatment of PDAC.

Persistent activation of pancreatic stellate cells (PSCs) can perturb the biomechanical homeostasis of the tumour microenvironment. Here the authors show that all-trans retinoic acid reduces retinoic acid receptor beta dependent-actomyosin contractility and restores mechanical quiescence in PSCs.

Identification of a shootin1 isoform expressed in peripheral tissues

Shootin1 is a brain-specific cytoplasmic protein involved in neuronal polarity formation and axon outgrowth. It accumulates at the leading edge of axonal growth cones, where it mediates the mechanical coupling between F-actin retrograde flow and cell adhesions as a clutch molecule, thereby producing force for axon outgrowth. In this study, we report a novel splicing isoform of shootin1 which is expressed not only in the brain but also in peripheral tissues. We have renamed the brain-specific shootin1 as shootin1a and termed the novel isoform as shootin1b. Immunoblot and immunohistochemical analyses with a shootin1b-specific antibody revealed that shootin1b is distributed in various mouse tissues including the lung, liver, stomach, intestines, spleen, pancreas, kidney and skin. Interestingly, shootin1b immunoreactivity was widely detected in epithelial cells that constitute simple and stratified epithelia; in some cells, it colocalized with E-cadherin and cortactin at cell-cell contact sites. Shootin1b also localized in dendritic cells in the spleen. These results suggest that shootin1b may function in various peripheral tissues including epithelial cells.