A mathematical model of GTPase pattern formation during single-cell wound repair

A biomechanical model for cell sensing and migration

We developed an original computational model for cell deformation and migration capable of accounting for the cell sensitivity to the environment and its appropriate adaptation. This cell model is ultimately intended to be used to address tissue morphogenesis. Hence it has been designed to comply with four requirements: (1) the cell should be able to probe and sense its environment and respond accordingly; (2) the model should be easy to parametrize to adapt to different cell types; (3) the model should be able to extend to 3D cases; (4) simulations should be fast enough to integrate many interacting cells. The simulations carried out focused on two aspects: first, the general behaviour of the cell on a homogeneous substrate, as observed experimentally, for model validation. This enabled us to decipher the mechanisms by which the cell can migrate, highlighting respective influences of the adhesions lifetimes and their sensitivity to traction; second, it predicts the sensitivity of the cell to an anisotropic patterned substrate, in agreement with recently published experiments. The results show that mechanosensors simulated by the model make it possible to reproduce such experiments in terms of migration bias generated by the substrate anisotropy. Here again, the model provides a biomechanical explanation of this phenomenon, depending on cell-matrix interactions and adhesion maturation rate.

Patterning of the cell cortex by Rho GTPases

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.

Wound Repair of the Cell Membrane: Lessons from Dictyostelium Cells

The cell membrane is frequently subjected to damage, either through physical or chemical means. The swift restoration of the cell membrane's integrity is crucial to prevent the leakage of intracellular materials and the uncontrolled influx of extracellular ions. Consequently, wound repair plays a vital role in cell survival, akin to the importance of DNA repair. The mechanisms involved in wound repair encompass a series of events, including ion influx, membrane patch formation, endocytosis, exocytosis, recruitment of the actin cytoskeleton, and the elimination of damaged membrane sections. Despite the absence of a universally accepted general model, diverse molecular models have been proposed for wound repair in different organisms. Traditional wound methods not only damage the cell membrane but also impact intracellular structures, including the underlying cortical actin networks, microtubules, and organelles. In contrast, the more recent improved laserporation selectively targets the cell membrane. Studies on Dictyostelium cells utilizing this method have introduced a novel perspective on the wound repair mechanism. This review commences by detailing methods for inducing wounds and subsequently reviews recent developments in the field.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

Bifurcation analysis of critical values for wound closure outcomes in wound healing experiments

A nonlinear partial differential equation containing a nonlocal advection term and a diffusion term is analyzed to study wound closure outcomes in wound healing experiments. There is an extensive literature of similar models for wound healing experiments. In this paper we study the character of wound closure in these experiments in terms of the sensing radius of cells and the force of cell-cell adhesion. We prove a bifurcation result which differentiates uniform closure of the wound from nonuniform closure of the wound, based on a critical value [Formula: see text] of the force of cell-cell adhesion parameter [Formula: see text]. For [Formula: see text] the steady state solution [Formula: see text] of the model is stable and the wound closes uniformly. For [Formula: see text] the steady state solution [Formula: see text] of the model is unstable and the wound closes nonuniformly. We provide numerical simulations of the model to illustrate our results.

Spatial models of pattern formation during phagocytosis

Phagocytosis, the biological process in which cells ingest large particles such as bacteria, is a key component of the innate immune response. Fcγ receptor (FcγR)-mediated phagocytosis is initiated when these receptors are activated after binding immunoglobulin G (IgG). Receptor activation initiates a signaling cascade that leads to the formation of the phagocytic cup and culminates with ingestion of the foreign particle. In the experimental system termed "frustrated phagocytosis", cells attempt to internalize micropatterned disks of IgG. Cells that engage in frustrated phagocytosis form "rosettes" of actin-enriched structures called podosomes around the IgG disk. The mechanism that generates the rosette pattern is unknown. We present data that supports the involvement of Cdc42, a member of the Rho family of GTPases, in pattern formation. Cdc42 acts downstream of receptor activation, upstream of actin polymerization, and is known to play a role in polarity establishment. Reaction-diffusion models for GTPase spatiotemporal dynamics exist. We demonstrate how the addition of negative feedback and minor changes to these models can generate the experimentally observed rosette pattern of podosomes. We show that this pattern formation can occur through two general mechanisms. In the first mechanism, an intermediate species forms a ring of high activity around the IgG disk, which then promotes rosette organization. The second mechanism does not require initial ring formation but relies on spatial gradients of intermediate chemical species that are selectively activated over the IgG patch. Finally, we analyze the models to suggest experiments to test their validity.

Cross-talk-dependent cortical patterning of Rho GTPases during cell repair

Rho GTPases such as Rho, Rac, and Cdc42 are important regulators of the cortical cytoskeleton in processes including cell division, locomotion, and repair. In these processes, Rho GTPases assume characteristic patterns wherein the active GTPases occupy mutually exclusive "zones" in the cell cortex. During cell wound repair, for example, a Rho zone encircles the wound edge and is in turn encircled by a Cdc42 zone. Here we evaluated the contributions of cross-talk between Rho and Cdc42 to the patterning of their respective zones in wounded Xenopus oocytes using experimental manipulations in combination with mathematical modeling. The results show that the position of the Cdc42 zone relative to the Rho zone and relative to the wound edge is controlled by the level of Rho activity. In contrast, the outer boundary of the Rho zone is limited by the level of Cdc42 activity. Models based on positive feedback within zones and negative feedback from Rho to the GEF-GAP Abr to Cdc42 capture some, but not all, of the observed behaviors. We conclude that GTPase zone positioning is controlled at the level of Rho activity and we speculate that the Cdc42 zone or something associated with it limits the spread of Rho activity.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.

Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape

Migratory cells exhibit a variety of morphologically distinct responses to their environments that manifest in their cell shape. Some protrude uniformly to increase substrate contacts, others are broadly contractile, some polarize to facilitate migration, and yet others exhibit mixtures of these responses. Prior studies have identified a discrete collection of shapes that the majority of cells display and demonstrated that activity levels of the cytoskeletal regulators Rac1 and RhoA GTPase regulate those shapes. Here, we use computational modeling to assess whether known GTPase dynamics can give rise to a sufficient diversity of spatial signaling states to explain the observed shapes. Results show that the combination of autoactivation and mutually antagonistic cross talk between GTPases, along with the conservative membrane binding, generates a wide array of distinct homogeneous and polarized regulatory phenotypes that arise for fixed model parameters. From a theoretical perspective, these results demonstrate that simple GTPase dynamics can generate complex multistability in which six distinct stable steady states (three homogeneous and three polarized) coexist for a fixed set of parameters, each of which naturally maps to an observed morphology. From a biological perspective, although we do not explicitly model the cytoskeleton or resulting cell morphologies, these results, along with prior literature linking GTPase activity to cell morphology, support the hypothesis that GTPase signaling dynamics can generate the broad morphological characteristics observed in many migratory cell populations. Further, the observed diversity may be the result of cells populating a complex morphological landscape generated by GTPase regulation rather than being the result of intrinsic cell-cell variation. These results demonstrate that Rho GTPases may have a central role in regulating the broad characteristics of cell shape (e.g., expansive, contractile, polarized, etc.) and that shape heterogeneity may be (at least partly) a reflection of the rich signaling dynamics regulating the cytoskeleton rather than intrinsic cell heterogeneity.

Extraction of active RhoGTPases by RhoGDI regulates spatiotemporal patterning of RhoGTPases

The RhoGTPases are characterized as membrane-associated molecular switches that cycle between active, GTP-bound and inactive, GDP-bound states. However, 90-95% of RhoGTPases are maintained in a soluble form by RhoGDI, which is generally viewed as a passive shuttle for inactive RhoGTPases. Our current understanding of RhoGTPase:RhoGDI dynamics has been limited by two experimental challenges: direct visualization of the RhoGTPases in vivo and reconstitution of the cycle in vitro. We developed methods to directly image vertebrate RhoGTPases in vivo or on lipid bilayers in vitro. Using these methods, we identified pools of active and inactive RhoGTPase associated with the membrane, found that RhoGDI can extract both inactive and active RhoGTPases, and found that extraction of active RhoGTPase contributes to their spatial regulation around cell wounds. These results indicate that RhoGDI directly contributes to the spatiotemporal patterning of RhoGTPases by removing active RhoGTPases from the plasma membrane.

Actin dynamics and myosin contractility during plasma membrane repair and restoration: Does one ring really heal them all?

In order to survive daily insults, cells have evolved various mechanisms that detect, stabilize and repair damages done to their plasma membrane and cytoskeletal structures. Damage to the PM endangers wounded cells by exposing them to uncontrolled exchanges with the extracellular milieu. The processes and molecular machinery enabling PM repair are therefore at the center of the bulk of the investigations into single-cell repair program. Wounds are repaired by dynamically remodeling the composition and shape of the injured area through exocytosis-mediated release of intracellular membrane components to the wounded area, endocytosis-mediated removal of the injured area, or the shedding of the injury. The wound healing program of Xenopus oocytes and early Drosophila embryos is by contrast, mostly characterized by the rapid formation of a large membrane patch over the wound that eventually fuse with the plasma membrane which restores plasma membrane continuity and lead to the shedding of patch material into the extracellular space. Formation and contraction of actomyosin ring restores normal plasma membrane composition and organizes cytoskeletal repairs. The extend of the contributions of the cytoskeleton to the wound healing program of somatic cells have comparatively received little attention. This review offers a survey of the current knowledge on how actin dynamics, myosin-based contraction and other cytoskeletal structures affects PM and cortical cytoskeleton repair of somatic cells.

Computational modeling of single-cell mechanics and cytoskeletal mechanobiology

Cellular cytoskeletal mechanics plays a major role in many aspects of human health from organ development to wound healing, tissue homeostasis and cancer metastasis. We summarize the state-of-the-art techniques for mathematically modeling cellular stiffness and mechanics and the cytoskeletal components and factors that regulate them. We highlight key experiments that have assisted model parameterization and compare the advantages of different models that have been used to recapitulate these experiments. An overview of feed-forward mechanisms from signaling to cytoskeleton remodeling is provided, followed by a discussion of the rapidly growing niche of encapsulating feedback mechanisms from cytoskeletal and cell mechanics to signaling. We discuss broad areas of advancement that could accelerate research and understanding of cellular mechanobiology. A precise understanding of the molecular mechanisms that affect cell and tissue mechanics and function will underpin innovations in medical device technologies of the future. WIREs Syst Biol Med 2018, 10:e1407. doi: 10.1002/wsbm.1407 This article is categorized under: Models of Systems Properties and Processes > Mechanistic Models Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.