Fig 2 - available via license: Creative Commons Attribution 4.0 International
Content may be subject to copyright.
Phase-portrait of the bistable spatially uniform system described by Eq (1). The steady states are at the intersections of the nullclines (red and yellow curves), the light green/blue curves show the stable/ unstable manifolds of the unstable steady state, and the arrows show the direction and rate of change at different locations on the RhoA-NMIIA phase-plane. The parameters are: α = 1, κ 1 = κ 2 = 0.4, n = 4. For this choice of parameters the location of the unstable saddle point is closer to the low fixed point at origin. https://doi.org/10.1371/journal.pcbi.1005411.g002
Source publication
Mechanical coherence of cell layers is essential for epithelia to function as tissue barriers and to control active tissue dynamics during morphogenesis. RhoA signaling at adherens junctions plays a key role in this process by coupling cadherin-based cell-cell adhesion together with actomyosin contractility. Here we propose and analyze a mathematic...
Contexts in source publication
Context 1
... RhoA is a lipid-anchored molecule, which can potentially diffuse in the mem- brane away from its source of activation [12,13]. Furthermore, mathematical models have revealed that reaction-diffusion systems of membrane-bound proteins can generate dynamic zones that exhibit travelling wave fronts that are not static or confined. In particular, these occur when diffusion is combined with bistability in the underlying dynamical system of non- linear interactions [14,15], akin to what we identified for the NMIIA-RhoA feedback network of the ZA [6]. Despite this, we observed that the morphology of the RhoA zone at the ZA was stable (Fig 1, S1 Movie), both in its width and the definition of its borders, over time scales (10s min) that are much longer than that of its constituent molecules (RhoA T 1/2 ~ 0.5 sec) DP160104342), Cancer Council Queensland (1086857), and Human Frontiers Science Program (http://www.hfsp.org/ RGP0023/2014). ZN is supported by an Australian Research Council Future Fellowship (FT130100659). GAG is supported by an Australian Research Council Future Fellowship (FT160100366) Optical imaging was performed at the ACRF/IMB Cancer Biology Imaging Facility, established with the generous support of the Australian Cancer Research Foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the ...
Context 2
... seeking to understand how meso-scale stability of an NMIIA-RhoA system is achieved at adherens junctions (Fig 1) we considered a minimal model of a RhoA-NMIIA positive feed- back loop that can exhibit bi-stability. This corresponds to the case in which RhoA and NMIIA mutually recruit each other to the cell cortex following a Hill type process of cortical adsorption, and dissociate from the cortex with the dissociation rates, k RhoA and k NMIIA, respec- tively ...
Context 3
... then sought to test the predictions of this model for the RhoA zone of the ZA. We imaged active, GTP-loaded RhoA (GTP-RhoA) using a location biosensor derived from the C-termi- nus of anillin (GFP-AHPH, Fig 7). This reporter binds specifically to GTP-RhoA, and thus its localization identifies the location of GTP-RhoA [6]. As previously described [6], GTP-RhoA localized in a prominent ring-like zone at the apical poles of confluent MCF7 mammary epi- thelial cells (Figs 1 and 7A). Kymographic analysis of live-cell movies further confirmed that both the spatial definition of the zone (its width and definition of boundaries) and its signal intensity were stable over the 2 hr duration of the movies (Fig 7A and 7D-7F, S1 Movie). Based on our computational analysis we now predicted that diffusion driven by bistable signal- ing between NMIIA and RhoA would tend to cause an outward-travelling front of GTP-RhoA, unless this was counteracted by local mechanical stress (advective flow) at the ZA. Travelling wave and cortical advection define stable zones of RhoA ...
Context 4
... tested this prediction qualitatively by monitoring the spatiotemporal response of the GTP-RhoA zone when NMII was inhibited. For technical reasons, we blocked contractility using the ROCK inhibitor, Y-27632, as this drug is compatible with live-cell imaging. More- over, due to the geometry of cell in the monolayer and the position of the Rho zone (Fig 1), measurements could be only done in the XY plane of the cortex parallel to the plane of the microscope stage, which corresponds to the apical surface of the epithelial monolayer. Whereas control cells (Fig 7A, 7D and 7E), retained GTP-RhoA as a tightly defined band at apical junctions, addition of Y-27632 caused cortical GTP-RhoA to diffuse progressively out- wards from the junction, leading to a broader zone within ~50 min of adding the drug (Fig 7B and 7D-7F, S2 Movie). This broadened zone then faded after 2 hrs treatment, likely due to inactivation of GTP-RhoA by the cortical recruitment of p190B RhoGAP [6]. Indeed, when this experiment was performed in p190B RhoGAP RNAi cells, we found that the GTP-RhoA zone persisted and displayed even more pronounced outward flux from the junction after treatment with Y-27632 (S3 ...
Similar publications
The coordination between cell proliferation and cell polarity is crucial to orient the asymmetric cell divisions to generate cell diversity in epithelia. In many instances, the Frizzled/Dishevelled planar cell polarity pathway is involved in mitotic spindle orientation, but how this is spatially and temporally coordinated with cell cycle progressio...
Citations
... Another mechanism that regulates junctional RHOA dynamics is a complex but fascinating feedback mechanism in which junctional myosin 2 maintains a balance of Rho activation and inactivation via ROCK-dependent phosphorylation of the non-canonical Rho GTPase RND3, which, in turn, modulates the recruitment of p190B-RhoGAP to the junctions 80 (Fig. 4d). A model based on diffusion counteracted by myosin 2-powered advection explains how the tight localization of RHOA-GTP to the junction is maintained in the face of rapid turnover 230 . ...
The Rho GTPases — RHOA, RAC1 and CDC42 — are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.
... A front of highly concentrated RhoA travels away from the source, increasing the total RhoA and actomyosin in the system (Fig 4B). This is reminiscent of a bistable front propagation in classical excitable systems [50,51], where the system switches to the high concentration stationary state ( Fig 2C). ...
The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate, and transmit mechanical forces. The cortex exhibits a wide range of dynamic behaviours, from generating pulsatory contractions and travelling waves to forming organised structures. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, the emergent dynamics of this mechanochemical system is poorly understood. Here we develop a reaction-diffusion model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active actomyosin gel, to investigate how the interplay between chemical signalling and mechanical forces regulate stresses and patterns in the cortex. We demonstrate that mechanochemical feedback in the cortex acts to destabilise homogeneous states and robustly generate pulsatile contractions. By tuning active stress in the system, we show that the cortex can generate propagating contraction pulses, form network structures, or exhibit topological turbulence.
... As a result, the force is divided between the two chains, and the junction can strengthen (Figure 1.2B) (42). Further, when mechanosensors at the junction detect stress increase at a specific location, the signaling pathway leads to an increase in the number of bonds (43), and therefore the average force within each bond drops (Figure 1.2C) (44)(45)(46). ...
Cell-cell adhesion complexes are macromolecular adhesive organelles that integrate cells into tissues. Perturbations of the cell-cell adhesion structure or relatedmechanotransduction pathways lead to pathological conditions such as skin and heart diseases, arthritis, and cancer. Mechanical stretching has been used to stimulate the mechanotransduction process originating from the cell-cell adhesion and cell-extracellular matrix (ECM) complexes. The current techniques, however, have limitations on their ability to measure the cell-cell adhesion force directly and quantitatively. These methods use a monolayer of cells, which makes it impossible to quantify the forces within a single cell-cell adhesion complex. Other methods using single cells or cell pairs rely on cell-ECM adhesion to find the cell-cell adhesion forces and consequently, they indirectly measure the junctional forces. In the current study, we designed and developed a single cell-cell adhesion interrogation and stimulation platform based on nanofabricated polymeric structures. The platform employs microstructures fabricated from biocompatible materials using two photon polymerization (TPP), a process that enables direct 3D structure writing with nanometer precision. The microdevice allows a pair of epithelial cells to form a mature cell junction. The single matured cell junction is stretched with controlled strain until cell-cell junction ruptures while the forces within the cell-junction-cell system are recorded. Using this platform, we have conducted mechanical characterization of a single cell junction with strain-stress analysis. The strain dependency of the junction has been investigated through the stretch test with four different strain rates. The results showed that the junction behaves in a strain-rate dependent manner, where high strain-rates lead to decreased viscosity property, a characteristic for a shear-thinning viscoelastic material. This also confirms our hypothesis that strain-rate plays an important role in the cell mechanical behavior, particularly the cytoskeleton dominant cell mechanics. The maturation of this technology can pave the way for the in situ investigation of mechano-chemical signaling pathways mediated by cell-cell junctions and potentially reveal novel disease mechanisms in which defects in cell-cell adhesion play a significant role in the disease pathology. Advisor: Ruiguo Yang
... A front of highly concentrated RhoA travels away from the source, increasing the total RhoA and actomyosin in the system (Fig. 4b). This is reminiscent of a bistable front propagation in classical excitable systems [39,40], where the system switches to the high concentration stationary state (Fig. 2c). ...
The actin cortex is an active adaptive material, embedded with complex regulatory networks that can sense, generate and transmit mechanical forces. The cortex can exhibit a wide range of dynamic behaviours, from generating pulsatory contractions and traveling waves to forming highly organised structures such as ordered fibers, contractile rings and networks that must adapt to the local cellular environment. Despite the progress in characterising the biochemical and mechanical components of the actin cortex, our quantitative understanding of the emergent dynamics of this mechanochemical system is limited. Here we develop a mathematical model for the RhoA signalling network, the upstream regulator for actomyosin assembly and contractility, coupled to an active polymer gel, to investigate how the interplay between chemical signalling and mechanical forces govern the propagation of contractile stresses and patterns in the cortex. We demonstrate that mechanical feedback in the excitable RhoA system, through dilution and concentration of chemicals, acts to destabilise homogeneous states and robustly generate pulsatile contractions. While moderate active stresses generate spatial propagation of contraction pulses, higher active stresses assemble localised contractile structures. Moreover, mechanochemical feedback induces memory in the active gel, enabling long-range propagation of transient local signals.
... Adhesion enhancement at the cell-cell contact is more complex in terms of timescale. Load-induced cell-cell adhesion strengthening has been shown via the increase in the number of adhesion complexes (33)(34)(35) or by the clustering of adhesion complexes (36)(37)(38)(39), which occurs on a timescale ranging from a few minutes up to a few hours after cells experience an initial load (28). External load on the cell-cell contact also results in a prolonged cell-cell adhesion dissociation time (40,41), suggesting cadherin bonds may transition to catch bonds under certain loading conditions (42,43), which can occur within seconds (44). ...
Significance
Cell–cell junctions are essential components in multicellular structures and often experience strains of different magnitudes and rates. However, their mechanical behavior is currently underexplored due to the lack of techniques to quantitatively characterize junctional stress–strain relationships. We developed a polymeric microstructure to strain the mutual junction of a single cell pair while simultaneously recording the junction stress and observed previously unseen strain-rate–dependent junction responses. We showed that cytoskeleton growth could relax the stress buildup and prevent junction failure at low strain rates, while high strain rates led to synchronized junction failures at remarkably large strains (over 200%). We expect this platform and our biophysical understanding to form the foundation for the rate-dependent mechanics of cell–cell junctions.
... 60 Furthermore, when mechanosensors at the junction detect stress increase at a specific location, the signaling pathway leads to an increase in the number of bonds, 61 and therefore, the average force within each bond drops (Fig. 3C). [62][63][64] In epithelia, E-cadherin is concentrated at regions of greatest tension within the AJ, 65 suggesting the presence of several mechanisms that couple the spreading of cadherins to cortical actomyosin. These may include moving cadherins linked to the cytoskeleton toward sites of higher contractile stress, 66 clustering of cadherin by F-actin 67 and myosin, 68 and regulating cortical actin. ...
Cell-cell adhesion complexes are macromolecular adhesive organelles that integrate cells into tissues. This mechano-chemical coupling in cell-cell adhesion is required for a large number of cell behaviors, and perturbations of the cell-cell adhesion structure or related mechanotransduction pathways can lead to critical pathological conditions such as skin and heart diseases, arthritis, and cancer. Mechanical stretching has been a widely used method to stimulate the mechanotransduction process originating from the cell-cell adhesion and cell-extracellular matrix (ECM) complexes. These studies aimed to reveal the biophysical processes governing cell proliferation, wound healing, gene expression regulation, and cell differentiation in various tissues, including cardiac, muscle, vascular, and bone. This review explores techniques in mechanical stretching in two-dimensional (2D) settings with different stretching regimens on different cell types. The mechanotransduction responses from these different cell types will be discussed with an emphasis on their biophysical transformations during mechanical stretching and the crosstalk between the cell-cell and cell-ECM adhesion complexes. Therapeutic aspects of mechanical stretching are reviewed considering these cellular responses after the application of mechanical forces, with a focus on wound healing and tissue regeneration.
... This positive feedback amongst downstream components in the pathway may allow for amplification of the relatively subtle enhancements of Rho-GTP I have observed in alignment. Additionally, positive feedback may buffer against small fluctuations in Rho activity that may arise from negative feedback [103,114]. ...
Rho signaling is a conserved mechanism for generating forces through activation of contractile actomyosin. How this pathway can produce different cell morphologies is poorly understood. In the Drosophila embryonic epithelium, we investigate how Rho signaling controls force asymmetry to drive morphogenesis.We study a distinct morphogenetic process termed 'alignment'. This process results in striking columns of rectilinear cells connected by aligned cell-cell contacts.We found that this is driven by contractile actomyosin cables that elevate tension along aligning interfaces. Our data show that polarization of Rho effectors, Rok and Dia, directs formation of these cables. Constitutive activation of these effectors causes aligning cells to instead invaginate. This suggests that moderating Rho signaling is essential to producing the aligned geometry. Therefore, we tested for feedback that could fine-tune Rho signaling. We discovered that F-actin exerts negative feedback on multiple nodes in the pathway. Further, we present evidence that suggests that Rok in part mediates feedback from F-actin to Rho in a manner independent of Myo-II. Collectively, our work suggests that multiple feedback mechanisms regulate Rho signaling, which may account for diverse morphological outcomes.
... Once localized in response to force, myosins also possess a diverse capacity to influence cell signaling. Non-muscle Myosin IIA can regulate the availability of Rho-family GEFs [102,103] and scaffold bistable feedback networks that reinforce RhoA signaling [82,104]; while Myosin IXA bears a RhoGAP domain that limits RhoA signaling when cells first contact one another [105]. As motors such as Myosin II have been identified as cortical mechanosensors in single cells [99], their role in junctional mechanotransduction may then represent another instance where fundamental mechanical elements of the cell cortex become co-opted in the specialized case of an adhesive junction. ...
... Such coordination may reflect several mechanisms that couple the distribution of cadherins to cortical actomyosin ( Figure 4A). These include movement of cadherins linked to the cytoskeleton [117], which are predicted to flow towards sites of higher contractile stress [104,118,119]; clustering of cadherin by F-actin [54] and myosin [120]; and cortical actin regulation [9,54,73]. Some of the recently-identified stress-responsive mechanotransductory pathways can reinforce junctions by these means. ...
Cell-cell junctions are specializations of the plasma membrane responsible for physically integrating cells into tissues. We are now beginning to appreciate the diverse impacts that mechanical forces exert upon the integrity and function of these junctions. Currently, this is best understood for cadherin-based adherens junctions in epithelia and endothelia, where cell-cell adhesion couples the contractile cytoskeletons of cells together to generate tissue-scale tension. Junctional tension participates in morphogenesis and tissue homeostasis. Changes in tension can also be detected by mechanotransduction pathways that allow cells to communicate with each other. In this review, we discuss progress in characterising the forces present at junctions in physiological conditions; the cellular mechanisms that generate intrinsic tension and detect changes in tension; and, finally, we consider how tissue integrity is maintained in the face of junctional stresses.
... Altering the actin network geometry by overexpressing Rac1 GTPase so precursor actin bundles are suppressed at free borders, changes adherens junction shape, and increases lamellae protrusions (182,183). RhoA signaling couples cadherin based adhesion with actimyosin contractility (184). Rac1 and RhoA interact in a spatiotemporal manner with adherens junction proteins to coordinate opening and closing of endothelial junctions (185). ...
The mitral valve exists in a mechanically demanding environment, with the stress of each cardiac cycle deforming and shearing the native fibroblasts and endothelial cells. Cells and their extracellular matrix exhibit a dynamic reciprocity in the growth and formation of tissue through mechanotransduction and continuously adapt to physical cues in their environment through gene, protein, and cytokine expression. Valve disease is the most common congenital heart defect with watchful waiting and valve replacement surgery the only treatment option. Mitral valve disease (MVD) has been linked to a variety of mechano-active genes ranging from extracellular components, mechanotransductive elements, and cytoplasmic and nuclear transcription factors. Specialized cell receptors, such as adherens junctions, cadherins, integrins, primary cilia, ion channels, caveolae, and the glycocalyx, convert mechanical cues into biochemical responses via a complex of mechanoresponsive elements, shared signaling modalities, and integrated frameworks. Understanding mechanosensing and transduction in mitral valve-specific cells may allow us to discover unique signal transduction pathways between cells and their environment, leading to cell or tissue specific mechanically targeted therapeutics for MVD.
The Rho family of GTPases are known to play pivotal roles in the regulation of fundamental cellular processes, ranging from cell migration and polarity to wound healing and regulation of actin cytoskeleton. Over the past decades, accumulating experimental work has increasingly mapped out the mechanistic details and interactions between members of the family and their regulators, establishing detailed interaction circuits within the Rho GTPase signaling network. These circuits have served as a vital foundation based on which a multitude of mathematical models have been developed to explain experimental data, gain deeper insights into the biological phenomenon they describe, as well as make new testable predictions and hypotheses. Due to the diverse nature and purpose of these models, they often vary greatly in size, scope, complexity, and formulation. Here, we provide a systematic, categorical, and comprehensive account of the recent modeling studies of Rho family GTPases, with an aim to offer a broad perspective of the field. The modeling limitations and possible future research directions are also discussed.
