Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility

Nascent adhesions shorten the period of lamellipodium protrusion through the Brownian ratchet mechanism

Directional cell migration is driven by the conversion of oscillating edge motion into lasting periods of leading edge protrusion. Actin polymerization against the membrane and adhesions control edge motion, but the exact mechanisms that determine protrusion period remain elusive. We addressed this by developing a computational model in which polymerization of actin filaments against a deformable membrane and variable adhesion dynamics support edge motion. Consistent with previous reports, our model showed that actin polymerization and adhesion lifetime power protrusion velocity. However, increasing adhesion lifetime decreased the protrusion period. Measurements of adhesion lifetime and edge motion in migrating cells confirmed that adhesion lifetime is associated with and promotes protrusion velocity, but decreased duration. Our model showed that adhesions' control of protrusion persistence originates from the Brownian ratchet mechanism for actin filament polymerization. With longer adhesion lifetime or increased-adhesion density, the proportion of actin filaments tethered to the substrate increased, maintaining filaments against the cell membrane. The reduced filament-membrane distance generated pushing force for high edge velocity, but limited further polymerization needed for protrusion duration. We propose a mechanism for cell edge protrusion in which adhesion strength regulates actin filament polymerization to control the periods of leading edge protrusion.

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.

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.

Actin-Membrane Release Initiates Cell Protrusions

Despite the well-established role of actin polymerization as a driving mechanism for cell protrusion, upregulated actin polymerization alone does not initiate protrusions. Using a combination of theoretical modeling and quantitative live-cell imaging experiments, we show that local depletion of actin-membrane links is needed for protrusion initiation. Specifically, we show that the actin-membrane linker ezrin is depleted prior to protrusion onset and that perturbation of ezrin's affinity for actin modulates protrusion frequency and efficiency. We also show how actin-membrane release works in concert with actin polymerization, leading to a comprehensive model for actin-driven shape changes. Actin-membrane release plays a similar role in protrusions driven by intracellular pressure. Thus, our findings suggest that protrusion initiation might be governed by a universal regulatory mechanism, whereas the mechanism of force generation determines the shape and expansion properties of the protrusion.

Cell-substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model

During the process of tissue formation and regeneration, cells migrate collectively while remaining connected through intercellular adhesions. However, the roles of cell-substrate and cell-cell mechanical interactions in regulating collective cell migration are still unclear. In this study, we employ a newly developed finite element cellular model to study collective cell migration by exploring the effects of mechanical feedback between cell and substrate and mechanical signal transmission between adjacent cells. Our viscoelastic model of cells consists many triangular elements and is of high resolution. Cadherin adhesion between cells is modeled explicitly as linear springs at subcellular level. In addition, we incorporate a mechano-chemical feedback loop between cell-substrate mechanics and Rac-mediated cell protrusion. Our model can reproduce a number of experimentally observed patterns of collective cell migration during wound healing, including cell migration persistence, separation distance between cell pairs and migration direction. Moreover, we demonstrate that cell protrusion determined by the cell-substrate mechanics plays an important role in guiding persistent and oriented collective cell migration. Furthermore, this guidance cue can be maintained and transmitted to submarginal cells of long distance through intercellular adhesions. Our study illustrates that our finite element cellular model can be employed to study broad problems of complex tissue in dynamic changes at subcellular level.

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.

Paxillin phosphorylation at serine 273 and its effects on Rac, Rho and adhesion dynamics

Focal adhesions are protein complexes that anchor cells to the extracellular matrix. During migration, the growth and disassembly of these structures are spatiotemporally regulated, with new adhesions forming at the leading edge of the cell and mature adhesions disassembling at the rear. Signalling proteins and structural cytoskeletal components tightly regulate adhesion dynamics. Paxillin, an adaptor protein within adhesions, is one of these proteins. Its phosphorylation at serine 273 (S273) is crucial for maintaining fast adhesion assembly and disassembly. Paxillin is known to bind to a GIT1-βPIX-PAK1 complex, which increases the local activation of the small GTPase Rac. To understand quantitatively the behaviour of this system and how it relates to adhesion assembly/disassembly, we developed a mathematical model describing the dynamics of the small GTPases Rac and Rho as determined by paxillin S273 phosphorylation. Our model revealed that the system possesses bistability, where switching between uninduced (active Rho) and induced (active Rac) states can occur through a change in rate of paxillin phosphorylation or PAK1 activation. The bistable switch is characterized by the presence of memory, minimal change in the levels of active Rac and Rho within the induced and uninduced states, respectively, and the limited regime of monostability associated with the uninduced state. These results were validated experimentally by showing the presence of bimodality in adhesion assembly and disassembly rates, and demonstrating that Rac activity increases after treating Chinese Hamster Ovary cells with okadaic acid (a paxillin phosphatase inhibitor), followed by a modest recovery after 20 min washout. Spatial gradients of phosphorylated paxillin in a reaction-diffusion model gave rise to distinct regions of Rac and Rho activities, resembling polarization of a cell into front and rear. Perturbing several parameters of the model also revealed important insights into how signalling components upstream and downstream of paxillin phosphorylation affect dynamics.

Cellular migration is crucial in both physiological and pathological functions. Maintenance of proper migration and development of aberrant migration are effectuated by cellular machinery involving protein complexes, called adhesions, that anchor the cell to its environment. Over time, these adhesions assemble at the leading edge, as the cell extends forward, anchoring the front of the cells to its substrate, while those at the cell rear disassemble, allowing detachment and forward movement. Their dynamics are controlled by a number of regulatory factors, occurring on both cell-wide and adhesion-level scales. The coordination of these regulatory factors is complex, but insights about their dynamics can be gained from the use of mathematical modeling techniques which integrate many of these components together. Here, we developed several molecularly explicit models to explore how local regulation of paxillin, an adhesion protein, interacts with the activities of Rac and Rho to produce cell-wide polarization associated with motility and directionality. By altering paxillin phosphorylation/dephosphorylation within such models, we have advanced our understanding of how a shift from a non-motile state to a highly motile state occurs. Deciphering these key processes quantitatively thus helped us gain insight into the subcellular factors underlying polarity and movement.

Cell protrusion and retraction driven by fluctuations in actin polymerization: A two-dimensional model

Animal cells that spread onto a surface often rely on actin-rich lamellipodial extensions to execute protrusion. Many cell types recently adhered on a two-dimensional substrate exhibit protrusion and retraction of their lamellipodia, even though the cell is not translating. Travelling waves of protrusion have also been observed, similar to those observed in crawling cells. These regular patterns of protrusion and retraction allow quantitative analysis for comparison to mathematical models. The periodic fluctuations in leading edge position of XTC cells have been linked to excitable actin dynamics using a one-dimensional model of actin dynamics, as a function of arc-length along the cell. In this work we extend this earlier model of actin dynamics into two dimensions (along the arc-length and radial directions of the cell) and include a model membrane that protrudes and retracts in response to the changing number of free barbed ends of actin filaments near the membrane. We show that if the polymerization rate at the barbed ends changes in response to changes in their local concentration at the leading edge and/or the opposing force from the cell membrane, the model can reproduce the patterns of membrane protrusion and retraction seen in experiment. We investigate both Brownian ratchet and switch-like force-velocity relationships between the membrane load forces and actin polymerization rate. The switch-like polymerization dynamics recover the observed patterns of protrusion and retraction as well as the fluctuations in F-actin concentration profiles. The model generates predictions for the behavior of cells after local membrane tension perturbations.

Nanoscale mechanobiology of cell adhesions

Proper physiological functions of cells and tissues depend upon their abilities to sense, transduce, integrate, and generate mechanical and biochemical signals. Although such mechanobiological phenomena are widely observed, the molecular mechanisms driving these outcomes are still not fully understood. Cell adhesions formed by integrins and cadherins receptors are key structures that process diverse sources of signals to elicit complex mechanobiological responses. Since the nanoscale is the length scale at which molecules interact to relay force and information, the understanding of cell adhesions at the nanoscale level is important for grasping the inner logics of cellular decision making. Until recently, the study of the biological nanoscale has been restricted by available molecular and imaging tools. Fortunately, rapid technological advances have increasingly opened up the nanoscale realm to systematic investigations. In this review, we discuss current insights and key open questions regarding the nanoscale structure and function relationship of cell adhesions, focusing on recent progresses in characterizing their composition, spatial organization, and cytomechanical operation.

Interstitial fluid flow-induced growth potential and hyaluronan synthesis of fibroblasts in a fibroblast-populated stretched collagen gel culture

BACKGROUND

Tensioned collagen gels with dermal fibroblasts (DFs) as a dermis model are usually utilized in a static culture (SC) that lacks medium flowing. To make the model closer to its in vivo state, we created a device to perfuse the model with media flowing at a physiological velocity and examined the effects of medium flow (MF) on the cultures.

METHODS

We constructed a medium perfusion device for human DF-embedded stretched collagen gels (human dermis model), exposed the model to media that flows upwardly at ~1mL/day, and examined water retention of the gels, cells' growth ability, metabolic activity, expression profiles of nine extracellular matrix (ECM)-related genes. The obtained data were compared with those from the model in SC.

RESULTS

MF increases the gels' water retention and cells' growth potential but had little effect on their metabolic activities. MF robustly enhanced hyaluronan synthase 2 (HAS2) and matrix metalloprotease 1 (MMP1) gene expressions but not of the other genes (MMP2, HYAL1, HYAL2, HYAL3, COL1A1, COL3A1, and CD44). MF significantly increased the amounts of cellular hyaluronan and adenosine triphosphate.

CONCLUSIONS

The MF at a physiological speed significantly influences the nature of ECMs and their resident fibroblasts and remodels ECMs by regulating hyaluronan metabolism.

GENERAL SIGNIFICANCE

Fibroblasts in tensioned collagen gels altered their phenotypes in a MF rate-dependent manner. Collagen gel culture with tension and MF could be utilized as an appropriate in vitro model of interstitial connective tissues to evaluate the pathophysiological significance of mechanosignals generated by fluid flow and cellular/extracellular tension.

An Integrated Stochastic Model of Matrix-Stiffness-Dependent Filopodial Dynamics

The ways that living cells regulate their behavior in response to their local mechanical environment underlie growth, development, and healing and are important to critical pathologies such as metastasis and fibrosis. Although extensive experimental evidence supports the hypothesis that this regulation is governed by the dependence of filopodial dynamics upon extracellular matrix stiffness, the pathways for this dependence are unclear. We therefore developed a model to relate filopodial focal adhesion dynamics to integrin-mediated Rho signaling kinetics. Results showed that focal adhesion maturation, i.e., focal adhesion links reinforcement and integrin clustering, dominates over filopodial dynamics. Downregulated focal adhesion maturation leads to the biphasic relationship between extracellular matrix stiffness and retrograde flow that has been observed in embryonic chick forebrain neurons, whereas upregulated maturation leads to the monotonically decreasing relationship that has been observed in mouse embryonic fibroblasts. When integrin-mediated Rho activation and stress-dependent focal adhesion maturation are combined, the model shows how filopodial dynamics endows cells with exquisite mechanosensing. Taken together, the results support the hypothesis that mechanical and structural factors combine with signaling kinetics to enable cells to probe their environments via filopodial dynamics.

Linking morphodynamics and directional persistence of T lymphocyte migration

T cells play a central role in the adaptive immune response, and their directed migration is essential for homing to sites of antigen presentation. Like neutrophils, T lymphocytes are rapidly moving cells that exhibit amoeboid movement, characterized by a definitive polarity with F-actin concentrated at the front and myosin II elsewhere. In this study, we used total internal reflection fluorescence (TIRF) microscopy to monitor the cells' areas of contact with a surface presenting adhesive ICAM-1 and the chemokine, CXCL12/SDF-1. Our analysis reveals that T-cell migration and reorientation are achieved by bifurcation and lateral separation of protrusions along the leading membrane edge, followed by cessation of one of the protrusions, which acts as a pivot for cell turning. We show that the distribution of bifurcation frequencies exhibits characteristics of a random, spontaneous process; yet, the waiting time between bifurcation events depends on whether or not the pivot point remains on the same side of the migration axis. Our analysis further suggests that switching of the dominant protrusion between the two sides of the migration axis is associated with persistent migration, whereas the opposite is true of cell turning. To help explain the bifurcation phenomenon and how distinct migration behaviours might arise, a spatio-temporal, stochastic model describing F-actin dynamics is offered.

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

Cell motility relies on the continuous reorganization of a dynamic actin-myosin-adhesion network at the leading edge of the cell, in order to generate protrusion at the leading edge and traction between the cell and its external environment. We analyze experimentally measured spatial distributions of actin flow, traction force, myosin density, and adhesion density in control and pharmacologically perturbed epithelial cells in order to develop a mechanical model of the actin-adhesion-myosin self-organization at the leading edge. A model in which the F-actin network is treated as a viscous gel, and adhesion clutch engagement is strengthened by myosin but weakened by actin flow, can explain the measured molecular distributions and correctly predict the spatial distributions of the actin flow and traction stress. We test the model by comparing its predictions with measurements of the actin flow and traction stress in cells with fast and slow actin polymerization rates. The model predicts how the location of the lamellipodium-lamellum boundary depends on the actin viscosity and adhesion strength. The model further predicts that the location of the lamellipodium-lamellum boundary is not very sensitive to the level of myosin contraction.

F-actin bundles direct the initiation and orientation of lamellipodia through adhesion-based signaling

Mesenchymal cells such as fibroblasts are weakly polarized and reorient directionality by a lamellipodial branching mechanism that is stabilized by phosphoinositide 3-kinase (PI3K) signaling. However, the mechanisms by which new lamellipodia are initiated and directed are unknown. Using total internal reflection fluorescence microscopy to monitor cytoskeletal and signaling dynamics in migrating cells, we show that peripheral F-actin bundles/filopodia containing fascin-1 serve as templates for formation and orientation of lamellipodia. Accordingly, modulation of fascin-1 expression tunes cell shape, quantified as the number of morphological extensions. Ratiometric imaging reveals that F-actin bundles/filopodia play both structural and signaling roles, as they prime the activation of PI3K signaling mediated by integrins and focal adhesion kinase. Depletion of fascin-1 ablated fibroblast haptotaxis on fibronectin but not platelet-derived growth factor chemotaxis. Based on these findings, we conceptualize haptotactic sensing as an exploration, with F-actin bundles directing and lamellipodia propagating the process and with signaling mediated by adhesions playing the role of integrator.

Using fluctuation analysis to establish causal relations between cellular events without experimental perturbation

Experimental perturbations are commonly used to establish causal relationships between the molecular components of a pathway and their cellular functions; however, this approach suffers inherent limitations. Especially in pathways with a significant level of nonlinearity and redundancy among components, such perturbations induce compensatory responses that obscure the actual function of the targeted component in the unperturbed pathway. A complementary approach uses constitutive fluctuations in component activities to identify the hierarchy of information flow through pathways. Here, we review the motivation for using perturbation-free approaches and highlight recent advances made in using perturbation-free fluctuation analysis as a means to establish causality among cellular events.

Intrinsic activity in cells and the brain

Motile cells such as bacteria, amoebae, and fibroblasts display a continual level of energy-consuming reactions involving the cytoskeleton and signal pathways, regardless of whether or not they are actually migrating. I draw parallels between these "silent signals" and the intrinsic activity of the human brain, especially that associated with the brain stem. In both cases, it can be argued that the organism continually rehearses possible future actions, so it can act quickly and accurately when suitable cues are received from the environment.

Extending the molecular clutch beyond actin-based cell motility

Many cell movements occur via polymerization of the actin cytoskeleton beneath the plasma membrane at the front of the cell, forming a protrusion called a lamellipodium, while myosin contraction squeezes forward the back of the cell. In what is known as the "molecular clutch" description of cell motility, forward movement results from the engagement of the acto-myosin motor with cell-matrix adhesions, thus transmitting force to the substrate and producing movement. However during cell translocation, clutch engagement is not perfect, and as a result, the cytoskeleton slips with respect to the substrate, undergoing backward (retrograde) flow in the direction of the cell body. Retrograde flow is therefore inversely proportional to cell speed and depends on adhesion and acto-myosin dynamics. Here we asked whether the molecular clutch was a general mechanism by measuring motility and retrograde flow for the Caenorhabditis elegans sperm cell in different adhesive conditions. These cells move by adhering to the substrate and emitting a dynamic lamellipodium, but the sperm cell does not contain an acto-myosin cytoskeleton. Instead the lamellipodium is formed by the assembly of Major Sperm Protein (MSP), which has no biochemical or structural similarity to actin. We find that these cells display the same molecular clutch characteristics as acto-myosin containing cells. We further show that retrograde flow is produced both by cytoskeletal assembly and contractility in these cells. Overall this study shows that the molecular clutch hypothesis of how polymerization is transduced into motility via adhesions is a general description of cell movement regardless of the composition of the cytoskeleton.