Stick-slip model for actin-driven cell protrusions, cell polarization, and crawling
Résumé
Cell crawling requires the generation of intracellular forces by the cytoskeleton and their transmission to an extracellular sub-strate through specific adhesion molecules. Crawling cells show many features of excitable systems, such as spontaneous symmetry breaking and crawling in the absence of external cues, and periodic and propagating waves of activity. Mechanical instabili-ties in the active cytoskeleton network and feedback loops in the biochemical network of activators and repressors of cytoskele-ton dynamics have been invoked to explain these dynamical features. Here, I show that the interplay between the dynamics of cell-substrate adhesion and linear cellular mechanics is sufficient to reproduce many nonlinear dynamical patterns observed in spreading and crawling cells. Using an analytical formalism of the molecular clutch model of cell adhesion, regulated by local mechanical forces, I show that cellular traction forces exhibit stick-slip dynamics resulting in periodic waves of protru-sion/retraction and propagating waves along the cell edge. This can explain spontaneous symmetry breaking and polarization of spreading cells, leading to steady crawling or bipedal motion, and bistability, where persistent cell motion requires a sufficiently strong transient external stimulus. The model also highlights the role of membrane tension in providing the long-range mechanical communication across the cell required for symmetry breaking. cell motility | symmetry breaking | stick-slip | membrane tension C ell crawling is ubiquitous in many biological processes from development to cancer. It is inherently a problem of mechanics , in which forces generated by the cytoskeleton are transmitted to the environment through transient adhesion to allow for cell translocation (1). The cytoskeleton is a highly dynamical active gel able to exert pushing forces through the polymerization of actin filaments and contractile forces through the interaction between actin and myosin motors. In a schematic description of cell crawling, the protrusion of the cell front is driven by actin polymerization while actomyosin contraction retracts the cell rear (2). In their physiological context, cells often polarize and crawl in response to external cues, such as gradients of chemoat-tractants or of mechanical properties of their environment (3, 4). However, many cells also crawl as a result of spontaneous symmetry breaking and exhibit periodic and/or propagating waves of activity (5). Even cell fragments devoid of nucleus show spontaneous symmetry breaking and bistability and can be driven into a persistent motile state by transient mechanical stimuli (6). These nonlinear features call for a description of motile cells as self-organized systems in which feedback loops lead to dynam-ical phase transitions (7-9). Many such descriptions have been proposed, most of which focus on the behavior of the cytoskele-ton itself. One class of models, which include bistability, polarization , and wave propagation, is based on the existence of feedback loops within the biochemical network of proteins regulating cytoskeletal activity, such as Rac GTPases which activate actin polymerization and protrusion or Rho GTPases which activate actomyosin contractility (10-12). This includes possible mechanical feedback, for instance through modulations of the cell membrane tension (13, 14). Another class of models focuses on the mechanics of the cytoskeleton, an active viscoelastic gel made of polar filaments which can spontaneously form asters and vortices (15). Symmetry breaking (16) and spontaneous motility (17) can be obtained by coupling filament orientation to the cell boundary , and waves can arise from the reaction-diffusion dynamics of actin nucleators and inhibitors (18). Modulations of the myosin distribution by the actin flow have also been studied extensively and can lead to instabilities (19) and spontaneous polarization and motion (20-24). In fast-moving, crescent-shaped cells such as keratocytes and cell fragments, the actin cytoskeleton often forms a branched network at the cell front and contractile bundles enriched in myosin at the back. A switch-like transition between these two structures has been described using phe-nomenological models (25, 26). Finally, many models have also addressed the shape, dynamics, and speed of motile cells through feedback between shape and the rate of actin polymerization and depolymerization (27-31). The models above generally treat force transmission with the substrate as a simple linear friction. The present work focuses on the nonlinear dynamics of cell-substrate adhesion. More specifically , it concentrates on so-called mesenchymal cell motility on a flat substrate, where a thin protrusion called the lamellipodium forms the leading edge of spreading and crawling cells, powered by actin polymerization (32). Polymerization is often offset by a retrograde flow of actin away from the cell edge, driven by actomyosin contraction and the cell membrane tension. According to the "molecular clutch" model (33, 34), these retrograde forces are balanced by frictional traction forces resulting from the transient linkage between actin filaments and the substrate through the binding and unbinding of adhesion molecules such Significance Spreading and crawling cells display rich nonlinear dynamics , which include periodic phases of growth and retraction of cellular protrusion, traveling waves along the cell edges, and spontaneous cell polarization and crawling. Using a theoretical model combining the mechanosensitivity of cell-substrate adhesion kinetics and linear cell viscoelastic mechanics, I show that the force-sensitive unbinding of adhesion bonds leads to stick-slip dynamics that recapitulate these dynamics' features. The model also highlights the role of the cell membrane tension in controlling spontaneous symmetry breaking and the transition between spreading and crawling. This suggests that purely mechanical feedback loops, in addition to those involved in biochemical signaling networks, are key regulators of cell crawling.
Domaines
Autre [cond-mat.other]
Origine : Fichiers produits par l'(les) auteur(s)