Kinetic model for lamellipodal actin-integrin 'clutch' dynamics

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.

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.

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.

Win, Lose, or Tie: Mathematical Modeling of Ligand Competition at the Cell-Extracellular Matrix Interface

Integrin transmembrane proteins conduct mechanotransduction at the cell–extracellular matrix (ECM) interface. This process is central to cellular homeostasis and therefore is particularly important when designing instructive biomaterials and organoid culture systems. Previous studies suggest that fine-tuning the ECM composition and mechanical properties can improve organoid development. Toward the bigger goal of fully functional organoid development, we hypothesize that resolving the dynamics of ECM–integrin interactions will be highly instructive. To this end, we developed a mathematical model that enabled us to simulate three main interactions, namely integrin activation, ligand binding, and integrin clustering. Different from previously published computational models, we account for the binding of more than one type of ligand to the integrin. This competition between ligands defines the fate of the system. We have demonstrated that an increase in the initial concentration of ligands does not ensure an increase in the steady state concentration of ligand-bound integrins. The ligand with higher binding rate occupies more integrins at the steady state than does the competing ligand. With cell type specific, quantitative input on integrin-ligand binding rates, this model can be used to develop instructive cell culture systems.

Pre-complexation of talin and vinculin without tension is required for efficient nascent adhesion maturation

Talin and vinculin are mechanosensitive proteins that are recruited early to integrin-based nascent adhesions (NAs). In two epithelial cell systems with well-delineated NA formation, we find these molecules concurrently recruited to the subclass of NAs maturing to focal adhesions. After the initial recruitment under minimal load, vinculin accumulates in maturing NAs at a ~ fivefold higher rate than in non-maturing NAs, and is accompanied by a faster traction force increase. We identify the R8 domain in talin, which exposes a vinculin-binding-site (VBS) in the absence of load, as required for NA maturation. Disruption of R8 domain function reduces load-free vinculin binding to talin, and reduces the rate of additional vinculin recruitment. Taken together, these data show that the concurrent recruitment of talin and vinculin prior to mechanical engagement with integrins is essential for the traction-mediated unfolding of talin, exposure of additional VBSs, further recruitment of vinculin, and ultimately, NA maturation.

Towards understanding the messengers of extracellular space: Computational models of outside-in integrin reaction networks

The interactions between cells and their extracellular matrix (ECM) are critically important for homeostatic control of cell growth, proliferation, differentiation and apoptosis. Transmembrane integrin molecules facilitate the communication between ECM and the cell. Since the characterization of integrins in the late 1980s, there has been great advancement in understanding the function of integrins at different subcellular levels. However, the versatility in molecular pathways integrins are involved in, the high diversity in their interaction partners both outside and inside the cell as well as on the cell membrane and the short lifetime of events happening at the cell-ECM interface make it difficult to elucidate all the details regarding integrin function experimentally. To overcome the experimental challenges and advance the understanding of integrin biology, computational modeling tools have been used extensively. In this review, we summarize the computational models of integrin signaling while we explain the function of integrins at three main subcellular levels (outside the cell, cell membrane, cytosol). We also discuss how these computational modeling efforts can be helpful in other disciplines such as biomaterial design. As such, this review is a didactic modeling summary for biomaterial researchers interested in complementing their experimental work with computational tools or for seasoned computational scientists that would like to advance current in silico integrin models.

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.

Cell mechanosensing is regulated by substrate strain energy rather than stiffness

The ability of cells to perceive the mechanical identity of extracellular matrix, generally known as mechanosensing, is generally depicted as a consequence of an intricate balance between pulling forces actuated by the actin fibers on the adhesion plaques and the mechanical reaction of the supporting material. However, whether the cell is sensitive to the stiffness or to the energy required to deform the material remains unclear. To address this important issue, here the cytoskeleton mechanics of BALB/3T3 and MC3T3 cells seeded on linearly elastic substrates under different levels of deformation were studied. In particular, the effect of prestrain on cell mechanics was evaluated by seeding cells both on substrates with no prestrain and on substrates with different levels of prestrain. Results indicated that cells recognize the existence of prestrain, exhibiting a stiffer cytoskeleton on stretched material compared to cells seeded on unstretched substrate. Cytoskeleton mechanics of cells seeded on stretched material were, in addition, comparable to those measured after the stretching of the substrate and cells together to the same level of deformation. This observation clearly suggests that cell mechanosensing is not mediated only by the stiffness of the substrate, as widely assumed in the literature, but also by the deformation energy associated with the substrate. Indeed, the clutch model, based on the exclusive dependence of cell mechanics upon substrate stiffness, fails to describe our experimental results. By modifying the clutch model equations to incorporate the dependence on the strain energy, we were able to correctly interpret the experimental evidence.

Biphasic mechanosensitivity of T cell receptor-mediated spreading of lymphocytes

Mechanosensing by T cells through the T cell receptor (TCR) is at the heart of immune recognition. While the mechanobiology of the TCR at the molecular level is increasingly well documented, its link to cell-scale response is poorly understood. Here we explore T cell spreading response as a function of substrate rigidity and show that remarkably, depending on the surface receptors stimulated, the cellular response may be either biphasic or monotonous. When adhering solely via the TCR complex, T cells respond to environmental stiffness in an unusual fashion, attaining maximal spreading on an optimal substrate stiffness comparable to that of professional antigen-presenting cells. However, in the presence of additional ligands for the integrin LFA-1, this biphasic response is abrogated and the cell spreading increases monotonously with stiffness up to a saturation value. This ligand-specific mechanosensing is effected through an actin-polymerization-dependent mechanism. We construct a mesoscale semianalytical model based on force-dependent bond rupture and show that cell-scale biphasic or monotonous behavior emerges from molecular parameters. As the substrate stiffness is increased, there is a competition between increasing effective stiffness of the bonds, which leads to increased cell spreading and increasing bond breakage, which leads to decreased spreading. We hypothesize that the link between actin and the receptors (TCR or LFA-1), rather than the ligand/receptor linkage, is the site of this mechanosensing.

Lamellipodium is a myosin-independent mechanosensor

The ability of adherent cells to sense changes in the mechanical properties of their extracellular environments is critical to numerous aspects of their physiology. It has been well documented that cell attachment and spreading are sensitive to substrate stiffness. Here, we demonstrate that this behavior is actually biphasic, with a transition that occurs around a Young's modulus of ∼7 kPa. Furthermore, we demonstrate that, contrary to established assumptions, this property is independent of myosin II activity. Rather, we find that cell spreading on soft substrates is inhibited due to reduced myosin-II independent nascent adhesion formation within the lamellipodium. Cells on soft substrates display normal leading-edge protrusion activity, but these protrusions are not stabilized due to impaired adhesion assembly. Enhancing integrin-ECM affinity through addition of Mn²⁺ recovers nascent adhesion assembly and cell spreading on soft substrates. Using a computational model to simulate nascent adhesion assembly, we find that biophysical properties of the integrin-ECM bond are optimized to stabilize interactions above a threshold matrix stiffness that is consistent with the experimental observations. Together, these results suggest that myosin II-independent forces in the lamellipodium are responsible for mechanosensation by regulating new adhesion assembly, which, in turn, directly controls cell spreading. This myosin II-independent mechanism of substrate stiffness sensing could potentially regulate a number of other stiffness-sensitive processes.

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.

Talin determines the nanoscale architecture of focal adhesions

Insight into how molecular machines perform their biological functions depends on knowledge of the spatial organization of the components, their connectivity, geometry, and organizational hierarchy. However, these parameters are difficult to determine in multicomponent assemblies such as integrin-based focal adhesions (FAs). We have previously applied 3D superresolution fluorescence microscopy to probe the spatial organization of major FA components, observing a nanoscale stratification of proteins between integrins and the actin cytoskeleton. Here we combine superresolution imaging techniques with a protein engineering approach to investigate how such nanoscale architecture arises. We demonstrate that talin plays a key structural role in regulating the nanoscale architecture of FAs, akin to a molecular ruler. Talin diagonally spans the FA core, with its N terminus at the membrane and C terminus demarcating the FA/stress fiber interface. In contrast, vinculin is found to be dispensable for specification of FA nanoscale architecture. Recombinant analogs of talin with modified lengths recapitulated its polarized orientation but altered the FA/stress fiber interface in a linear manner, consistent with its modular structure, and implicating the integrin-talin-actin complex as the primary mechanical linkage in FAs. Talin was found to be ∼97 nm in length and oriented at ∼15° relative to the plasma membrane. Our results identify talin as the primary determinant of FA nanoscale organization and suggest how multiple cellular forces may be integrated at adhesion sites.

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.

Protein interactions of cortactin in relation to invadopodia formation in metastatic renal clear cell carcinoma

In the present study, we wanted to examine the predominant factor/s in the initiation of metastasis. We used samples of advanced grades of renal clear cell carcinoma with documented clinical history of vena caval spread as the experimental group. The major rationale for this selection is the fact that renal cell carcinoma metastasize extensively through the inferior vena cava up to the pulmonary bed and often exist as a continuous mass of metastatic tissue. As cortactin plays a significant role in invadopodia formation during initiation of metastasis, in the present study, we tested expression of cortactin and phospho(tyr421)-cortactin in different grades of renal cell clear carcinoma and examined its property to bind to actin. The findings of the present study suggest that the variations of the local physiological milieu are the driving forces for metastasis by enhancing molecular mechanisms for lamellipodia formation. We conclude that localization of cortactin in cancer cells and interaction between actin and its nucleators are crucial for cancer progression.

Second messenger signaling for neuronal polarization: cell mechanics-dependent pattern formation

Neuronal polarization is a critical step in the neuronal morphogenesis. Despite the identification of several evolutionarily conserved factors for neural polarization, the exact mechanisms by which cells initiate and maintain polarity remain to be characterized. Here, we review the recent progress on the roles of second messengers, specifically the cyclic nucleotides and membrane-associated phospholipids, in the initiation, propagation, and integration of polarization signals, and propose an inhibitor-free model for neural polarization. The characteristic features of neuron polarization include the formation of single axon and multiple dendrites. These features involve chemical and mechanical mechanisms such as reaction-diffusion and tug-of-war, by which second messengers can act in concert to initiate and stabilize the cellular asymmetry. Nevertheless, biochemical factors eliciting the long-range inhibition remain ambiguous. Thus, we provide a simple, inhibitor-free model that can incorporate known cytochemical and cytomechanical factors, and produce features of neuronal polarization in environments provided with minimized extracellular regulators.

Determinants of maximal force transmission in a motor-clutch model of cell traction in a compliant microenvironment

The mechanical stiffness of a cell's environment exerts a strong, but variable, influence on cell behavior and fate. For example, different cell types cultured on compliant substrates have opposite trends of cell migration and traction as a function of substrate stiffness. Here, we describe how a motor-clutch model of cell traction, which exhibits a maximum in traction force with respect to substrate stiffness, may provide a mechanistic basis for understanding how cells are tuned to sense the stiffness of specific microenvironments. We find that the optimal stiffness is generally more sensitive to clutch parameters than to motor parameters, but that single parameter changes are generally only effective over a small range of values. By contrast, dual parameter changes, such as coordinately increasing the numbers of both motors and clutches offer a larger dynamic range for tuning the optimum. The model exhibits distinct regimes: at high substrate stiffness, clutches quickly build force and fail (so-called frictional slippage), whereas at low substrate stiffness, clutches fail spontaneously before the motors can load the substrate appreciably (a second regime of frictional slippage). Between the two extremes, we find the maximum traction force, which occurs when the substrate load-and-fail cycle time equals the expected time for all clutches to bind. At this stiffness, clutches are used to their fullest extent, and motors are therefore resisted to their fullest extent. The analysis suggests that coordinate parameter shifts, such as increasing the numbers of motors and clutches, could underlie tumor progression and collective cell migration.

Extracellular matrix density promotes EMT by weakening cell–cell adhesions

This paper probes the influence of extracellular matrix density on cell–cell adhesion and its relevance to EMT.

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

A physicochemical model is used to describe the coupling of adhesion, cytoskeletal, and signaling dynamics during cell migration. Analysis of stochastic simulations predicts relationships between measurable quantities that reflect partitioning of stress between F-actin–bound adhesions, which act as a molecular clutch, and retrograde F-actin flow.

Animal cell migration is a complex process characterized by the coupling of adhesion, cytoskeletal, and signaling dynamics. Here we model local protrusion of the cell edge as a function of the load-bearing properties of integrin-based adhesions, actin polymerization fostered by adhesion-mediated signaling, and mechanosensitive activation of RhoA that promotes myosin II–generated stress on the lamellipodial F-actin network. Analysis of stochastic model simulations illustrates how these pleiotropic functions of nascent adhesions may be integrated to govern temporal persistence and frequency of protrusions. The simulations give mechanistic insight into the documented effects of extracellular matrix density and myosin abundance, and they show characteristic, nonnormal distributions of protrusion duration times that are similar to those extracted from live-cell imaging experiments. Analysis of the model further predicts relationships between measurable quantities that reflect the partitioning of stress between tension on F-actin–bound adhesions, which act as a molecular clutch, and dissipation by retrograde F-actin flow.

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.

Perturbations of mechanotransduction and aneurysm formation in heritable aortopathies

Thoracic aortic aneurysm and dissection in young and middle aged patients is increasingly recognised as due to genetic aortopathy. Mutations in multiple genes affecting proteins in the extracellular matrix, microfibrillar structure, the endothelium and cell signalling pathways have been associated with thoracic aortic disease. The TGFß signalling pathway appears to play a key role in mediating abnormal aortic growth and aneurysm formation. A challenge remains in understanding how the many different gene mutations can result in deranged TGFß signalling. This review examines the functional relationships between key structural and signalling proteins, with reference to the need for maintenance of homeostasis in mechanotransduction within the aortic wall. A mechanism, through which perturbations in mechanotransduction, arising from different gene mutations, results in altered TGFß signalling is described.

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.

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.

Steady state dynamics of a moving model cell

Crawling cell motility results due to treadmilling of a polymerized actin network at the leading edge. Steady state dynamics of a moving cell are governed by actin concentration profiles across the cell. Branching of new filaments implicating Arp2/3 and capping of existing filaments with capZ or Gelsolin are central to the robust functioning of the actin network. Using computer simulations, steady state concentration profiles of globular actin (G actin) and filamentous actin (F actin) are computed. The profiles are in agreement with experimentally observed ones. Simulations unveil that there is an optimal capping and branching rate for which the velocity of the model cell is maximum. Our simulations also indicate that the capping of actin filaments results in an increase in nucleation of new filaments by Arp2/3-induced branching and is in agreement with a recently observed monomer gating model. We observe that Arp2/3 and capping protein exhibit a functional antagonism with respect to the actin network treadmilling.

Fibronectin expression determines skin cell motile behavior

Mouse keratinocytes migrate significantly slower than their human counterparts in vitro on uncoated surfaces. We tested the hypothesis that this is a consequence of differences in the extracellular matrix (ECM) that cells deposit. In support of this, human keratinocyte motility was markedly reduced when plated onto the ECM of mouse skin cells, whereas the latter cells migrated faster when plated onto human keratinocyte ECM. The ECM of mouse and human keratinocytes contained similar levels of the α3 laminin subunit of laminin-332. However, mouse skin cells expressed significantly more fibronectin (FN) than human cells. To assess whether FN is a motility regulator, we used small interfering RNA (siRNA) to reduce the expression of FN in mouse keratinocytes. The treated mouse keratinocytes moved significantly more rapidly than wild-type mouse skin cells. Moreover, the FN-depleted mouse cell ECM supported increased migration of both mouse and human keratinocytes. Furthermore, the motility of human keratinocytes was slowed when plated onto FN-coated substrates or human keratinocyte ECM supplemented with FN in a dose-dependent manner. Consistent with these findings, the ECM of α3 integrin-null keratinocytes, which also migrated faster than wild-type cells, was FN deficient. Our results provide evidence that FN is a brake to skin cell migration supported by laminin-332-rich matrices.

Signaling pathways that control cell migration: models and analysis

Dissecting the intracellular signaling mechanisms that govern the movement of eukaryotic cells presents a major challenge, not only because of the large number of molecular players involved, but even more so because of the dynamic nature of their regulation by both biochemical and mechanical interactions. Computational modeling and analysis have emerged as useful tools for understanding how the physical properties of cells and their microenvironment are coupled with certain biochemical pathways to actuate and control cell motility. In this focused review, we highlight some of the more recent applications of quantitative modeling and analysis in the field of cell migration. Both in modeling and experiment, it has been prudent to follow a reductionist approach in order to characterize what are arguably the principal modules: spatial polarization of signaling pathways, regulation of the actin cytoskeleton, and dynamics of focal adhesions. While it is important that we 'cut our teeth' on these subsystems, focusing on the details of certain aspects while ignoring or coarse-graining others, it is clear that the challenge ahead will be to characterize the couplings between them in an integrated framework.

Probing mechanical principles of focal contacts in cell-matrix adhesion with a coupled stochastic-elastic modelling framework

Cell-matrix adhesion depends on the collective behaviours of clusters of receptor-ligand bonds called focal contacts between cell and extracellular matrix. While the behaviour of a single molecular bond is governed by statistical mechanics at the molecular scale, continuum mechanics should be valid at a larger scale. This paper presents an overview of a series of recent theoretical studies aimed at probing the basic mechanical principles of focal contacts in cell-matrix adhesion via stochastic-elastic models in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial traction-separation are unified in a single modelling framework. The intention here is to illustrate these principles using simple analytical and numerical models. The aim of the discussions is to provide possible clues to the following questions: why does the size of focal adhesions (FAs) fall into a narrow range around the micrometre scale? How can cells sense and respond to substrates of varied stiffness via FAs? How do the magnitude and orientation of mechanical forces affect the binding dynamics of FAs? The effects of cluster size, cell-matrix elastic modulus, loading direction and cytoskeletal pretension on the lifetime of FA clusters have been investigated by theoretical arguments as well as Monte Carlo numerical simulations, with results showing that intermediate adhesion size, stiff substrate, cytoskeleton stiffening, low-angle pulling and moderate cytoskeletal pretension are factors that contribute to stable FAs. From a mechanistic point of view, these results provide possible explanations for a wide range of experimental observations and suggest multiple mechanisms by which cells can actively control adhesion and de-adhesion via cytoskeletal contractile machinery in response to mechanical properties of their surroundings.

An adhesion-dependent switch between mechanisms that determine motile cell shape

Keratocytes are fast-moving cells in which adhesion dynamics are tightly coupled to the actin polymerization motor that drives migration, resulting in highly coordinated cell movement. We have found that modifying the adhesive properties of the underlying substrate has a dramatic effect on keratocyte morphology. Cells crawling at intermediate adhesion strengths resembled stereotypical keratocytes, characterized by a broad, fan-shaped lamellipodium, clearly defined leading and trailing edges, and persistent rates of protrusion and retraction. Cells at low adhesion strength were small and round with highly variable protrusion and retraction rates, and cells at high adhesion strength were large and asymmetrical and, strikingly, exhibited traveling waves of protrusion. To elucidate the mechanisms by which adhesion strength determines cell behavior, we examined the organization of adhesions, myosin II, and the actin network in keratocytes migrating on substrates with different adhesion strengths. On the whole, our results are consistent with a quantitative physical model in which keratocyte shape and migratory behavior emerge from the self-organization of actin, adhesions, and myosin, and quantitative changes in either adhesion strength or myosin contraction can switch keratocytes among qualitatively distinct migration regimes.

Cell migration is important for many biological processes: white blood cells chase down and kill bacteria to guard against infection, epithelial cells crawl across open wounds to promote healing, and embryonic cells move collectively to form organs and tissues during embryogenesis. In all of these cases, migration depends on the spatial and temporal organization of multiple forces, including actin-driven protrusion of the cell membrane, membrane tension, cell-substrate adhesion, and myosin-mediated contraction of the actin network. In this work, we have used a simple cell type, the fish epithelial keratocyte, as a model system to investigate the manner in which these forces are integrated to give rise to large-scale emergent properties such as cell shape and movement. Keratocytes are normally fan-shaped and fast-moving, but we have found that keratocytes migrate more slowly and assume round or asymmetric shapes when cell-substrate adhesion strength is too high or too low. By correlating measurements of adhesion-dependent changes in cell shape and speed with measurements of adhesion and myosin localization patterns and actin network organization, we have developed a mechanical model in which keratocyte shape and movement emerge from adhesion and myosin-dependent regulation of the dynamic actin cytoskeleton.

Cell-matrix adhesion: slip and immobilization under force

When force is applied to cell-matrix adhesion complexes, they respond by growing larger and stronger. It emerges that strengthening involves transient motion of the transmembrane integrin receptors and their eventual immobilization to the extracellular matrix.

Conserved F-actin dynamics and force transmission at cell adhesions

Adhesions are a central mechanism by which cells mechanically interact with the surrounding extracellular matrix (ECM) and neighboring cells. In both cell-ECM and cell-cell adhesions, forces generated within the actin cytoskeleton are transmitted to the surrounding environment and are essential for numerous morphogenic processes. Despite differences in many molecular components that regulate cell-cell and cell-ECM adhesions, the roles of F-actin dynamics and mechanical forces in adhesion regulation are surprisingly similar. Moreover, force transmission at adhesions occurs concomitantly with dynamic F-actin; proteins comprising the adhesion of F-actin to the plasma membrane must accommodate this movement while still facilitating force transmission. Thus, despite different molecular architectures, integrin and cadherin-mediated adhesions operate with common biophysical characteristics to transmit and respond to mechanical forces in multicellular tissue.

Transient frictional slip between integrin and the ECM in focal adhesions under myosin II tension

BACKGROUND

The spatiotemporal regulation of adhesion to the extracellular matrix is important in metazoan cell migration and mechanosensation. Although adhesion assembly depends on intracellular and extracellular tension, the biophysical regulation of force transmission between the actin cytoskeleton and extracellular matrix during this process remains largely unknown.

RESULTS

To elucidate the nature of force transmission as myosin II tension is applied to focal adhesions, we correlated the dynamics of focal adhesion proteins and the actin cytoskeleton to local traction stresses. Under low extracellular tension, newly formed adhesions near the cell periphery underwent a transient retrograde displacement preceding elongation. We found that myosin II-generated tension drives this mobility, and we determine the interface of differential motion, or "slip," to be between integrin and the ECM. The magnitude and duration of both adhesion slip and associated F-actin dynamics is strongly modulated by ECM compliance. Traction forces are generated throughout the slip period, and adhesion immobilization occurs at a constant tension.

CONCLUSIONS

We have identified a tension-dependent, extracellular "clutch" between integrins and the extracellular matrix; this clutch stabilizes adhesions under myosin II driven tension. The current work elucidates a mechanism by which force transmission is modulated during focal adhesion maturation.

Modeling cytoskeletal flow over adhesion sites: competition between stochastic bond dynamics and intracellular relaxation

In migrating cells, retrograde flow of the actin cytoskeleton is related to traction at adhesion sites located at the base of the lamellipodium. The coupling between the moving cytoskeleton and the stationary adhesions is mediated by the continuous association and dissociation of molecular bonds. We introduce a simple model for the competition between the stochastic dynamics of elastic bonds at the moving interface and relaxation within the moving actin cytoskeleton represented by an internal viscous friction coefficient. Using exact stochastic simulations and an analytical mean field theory, we show that the stochastic bond dynamics lead to biphasic friction laws as observed experimentally. At low internal dissipation, stochastic bond dynamics lead to a regime of irregular stick-and-slip motion. High internal dissipation effectively suppresses cooperative effects among bonds and hence stabilizes the adhesion.

Multi-level molecular clutches in motile cell processes

To trigger cell motility, forces generated by the cytoskeleton must be transmitted physically to the external environment through transmembrane adhesion molecules. One model put forward twenty years ago to describe this process is the molecular clutch by which a modular interface of adaptor proteins mediates a dynamic mechanical connection between the actin flow and cell adhesion complexes. Recent optical imaging experiments have identified key clutch molecules linked to specific chemical and mechanical signal transduction pathways, particularly regarding integrins in migrating cells, IgCAMs in neuronal growth cones, and cadherins at intercellular junctions. We propose here the concept of a multi-level clutch as a useful analogy to grasp the complexity of the dynamic molecular interactions involved in a panel of motile behaviors and shapes.