From pulsatile apicomedial contractility to effective epithelial mechanics

Motility and swimming: universal description and generic trajectories

Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimming) and artificial swimmers. An outstanding feature is the ability of these entities to follow complex trajectories, ranging from straight, curved (circular, helical...), to random-like ones. The non-straight nature of these trajectories is often explained as a consequence of the asymmetry of the particle or the medium in which it moves, or due to the presence of bounding walls, etc... Here, we show that for a particle driven by a concentration field of an active species, straight, circular and helical trajectories emerge naturally in the absence of asymmetry of the particle or that of suspending medium. Our proof is based on general considerations, without referring to an explicit form of a model. We show that these three trajectories correspond to self-congruent solutions. Self-congruency means that the states of the system at different moments of time can be made identical by an appropriate combination of rotation and translation of the coordinate space. We show that these solutions are exhibited by spherically symmetric particles as a result of a series of pitchfork bifurcations, leading to spontaneous symmetry breaking in the concentration field driving the particle motility. Self-congruent dynamics in one and two dimensions are analyzed as well. Finally, we present a simple explicit nonlinear exactly solvable model of fully isotropic phoretic particle that shows the transitions from a non-motile state to straight motion to circular motion to helical motion as a series of spontaneous symmetry-breaking bifurcations. Whether a system exhibits or not a given trajectory only depends on the numerical values of parameters entering the model, while asymmetry of swimmer shape, or anisotropy of the suspending medium, or influence of bounding walls are not necessary.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

The Lateral Epidermis Actively Counteracts Pulling by the Amnioserosa During Dorsal Closure

Dorsal closure is a prominent morphogenetic process during Drosophila embryogenesis, which involves two epithelial tissues, that is, the squamous amnioserosa and the columnar lateral epidermis. Non-muscle myosin II-driven constriction in the amnioserosa leads to a decrease in the apical surface area and pulls on the adjacent lateral epidermis, which subsequently moves dorsally. The pull by the amnioserosa becomes obvious in an elongation of the epidermal cells, especially of those in the first row. The contribution of the epidermal cell elongation has remained unclear to dorsal closure. Cell elongation may be a mere passive consequence or an active response to the pulling by the amnioserosa. Here, we found that the lateral epidermis actively responds. We analyzed tensions within tissues and cell junctions by laser ablation before and during dorsal closure, the elliptical and dorsal closure stages, respectively. Furthermore, we genetically and optochemically induced chronic and acute cell contraction, respectively. In this way, we found that tension in the epidermis increased during dorsal closure. A correspondingly increased tension was not observed at individual junctions, however. Junctional tension even decreased during dorsal closure in the epidermis. We strikingly observed a strong increase of the microtubule amount in the epidermis, while non-muscle myosin II increased in both tissues. Our data suggest that the epidermis actively antagonizes the pull from the amnioserosa during dorsal closure and the increased microtubules might help the epidermis bear part of the mechanical force.

Pulsatile contractions and pattern formation in excitable actomyosin cortex

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 regulates 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.

The cellular actin cortex is a dynamic sub-membranous network of filamentous actin, myosin motors, and other accessory proteins that regulates the ability of cells to maintain or change shapes. While the key molecular components and mechanical properties of the actin cortex have been characterized, the ways in which biochemical signalling and mechanical forces interact to regulate cortex behaviours remain poorly understood. In this article, we develop a mathematical model for the actomyosin cortex that combines the reaction-diffusion dynamics of signalling proteins with active force generation by actomyosin networks. Using this model, we investigate how the feedback between mechanics and biochemical signalling regulates the propagation of actomyosin flows, mechanical stresses, and pattern formation in the cortex. Our work reveals a variety of ways in which the cortex can tune the dynamic coupling between biochemical activity, force production, and advective transport to control mechanical behaviours.

Appreciating the role of cell shape changes in the mechanobiology of epithelial tissues

The wide range of epithelial cell shapes reveals the complexity and diversity of the intracellular mechanisms that serve to construct their morphology and regulate their functions. Using mechanosensitive steps, epithelial cells can sense a variety of different mechanochemical stimuli and adapt their behavior by reshaping their morphology. These changes of cell shape rely on a structural reorganization in space and time that generates modifications of the tensional state and activates biochemical cascades. Recent studies have started to unveil how the cell shape maintenance is involved in mechanical homeostatic tasks to sustain epithelial tissue folding, identity, and self-renewal. Here, we review relevant works that integrated mechanobiology to elucidate some of the core principles of how cell shape may be conveyed into spatial information to guide collective processes such as epithelial morphogenesis. Among many other parameters, we show that the regulation of the cell shape can be understood as the result of the interplay between two counteracting mechanisms: actomyosin contractility and intercellular adhesions, and that both do not act independently but are functionally integrated to operate on molecular, cellular, and tissue scales. We highlight the role of cadherin-based adhesions in force-sensing and mechanotransduction, and we report recent developments that exploit physics of liquid crystals to connect cell shape changes to orientational order in cell aggregates. Finally, we emphasize that the further intermingling of different disciplines to develop new mechanobiology assays will lead the way toward a unified picture of the contribution of cell shape to the pathophysiological behavior of epithelial tissues.

Modulating RhoA effectors induces transitions to oscillatory and more wavelike RhoA dynamics in C. elegans zygotes

Pulsatile RhoA dynamics underlie a wide range of cell and tissue behaviors. The circuits that produce these dynamics in different cells share common architectures based on fast positive and delayed negative feedback through F-actin, but they can produce very different spatiotemporal patterns of RhoA activity. However, the underlying causes of this variation remain poorly understood. Here we asked how this variation could arise through modulation of actin network dynamics downstream of active RhoA in early C. elegans embryos. We find that perturbing two RhoA effectors - formin and anillin - induce transitions from non-recurrent focal pulses to either large noisy oscillatory pulses (formin depletion) or noisy oscillatory waves (anillin depletion). In both cases these transitions could be explained by changes in local F-actin levels and depletion dynamics, leading to changes in spatial and temporal patterns of RhoA inhibition. However, the underlying mechanisms for F-actin depletion are distinct, with different dependencies on myosin II activity. Thus, modulating actomyosin network dynamics could shape the spatiotemporal dynamics of RhoA activity for different physiological or morphogenetic functions. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Mechanical processes underlying precise and robust cell matching

During the development of complicated multicellular organisms, the robust formation of specific cell-cell connections (cell matching) is required for the generation of precise tissue structures. Mismatches or misconnections can lead to various diseases. Diverse mechanical cues, including differential adhesion and temporally varying cell contractility, are involved in regulating the process of cell-cell recognition and contact formation. Cells often start the process of cell matching through contact via filopodia protrusions, mediated by specific adhesion interactions at the cell surface. These adhesion interactions give rise to differential mechanical signals that can be further perceived by the cells. In conjunction with contractions generated by the actomyosin networks within the cells, this differentially coded adhesion information can be translated to reposition and sort cells. Here, we review the role of these different cell matching components and suggest how these mechanical factors cooperate with each other to facilitate specificity in cell-cell contact formation.

Microtubules enter centre stage for morphogenesis

Cell shape changes are key to observable changes at the tissue level during morphogenesis and organ formation. The major driver of cell shape changes in turn is the actin cytoskeleton, both in the form of protrusive linear or branched dynamic networks and in the form of contractile actomyosin. Over the last 20 years, actomyosin has emerged as the major cytoskeletal system that deforms cells in epithelial sheets during morphogenesis. By contrast, the second major cytoskeletal system, microtubules, have so far mostly been assumed to serve 'house-keeping' functions, such as directed transport or cell division, during morphogenetic events. Here, I will reflect on a subset of studies over the last 10 years that have clearly shown a major direct role for the microtubule cytoskeleton in epithelial morphogenesis, suggesting that our focus will need to be widened to give more attention and credit to this cytoskeletal system in playing an active morphogenetic role. This article is part of a discussion meeting issue 'Contemporary morphogenesis'.

The pulse of morphogenesis: actomyosin dynamics and regulation in epithelia

Actomyosin networks are some of the most crucial force-generating components present in developing tissues. The contractile forces generated by these networks are harnessed during morphogenesis to drive various cell and tissue reshaping events. Recent studies of these processes have advanced rapidly, providing us with insights into how these networks are initiated, positioned and regulated, and how they act via individual contractile pulses and/or the formation of supracellular cables. Here, we review these studies and discuss the mechanisms that underlie the construction and turnover of such networks and structures. Furthermore, we provide an overview of how ratcheted processivity emerges from pulsed events, and how tissue-level mechanics are the coordinated output of many individual cellular behaviors.

Caenorhabditis elegans Gastrulation: A Model for Understanding How Cells Polarize, Change Shape, and Journey Toward the Center of an Embryo

Gastrulation is fundamental to the development of multicellular animals. Along with neurulation, gastrulation is one of the major processes of morphogenesis in which cells or whole tissues move from the surface of an embryo to its interior. Cell internalization mechanisms that have been discovered to date in Caenorhabditis elegans gastrulation bear some similarity to internalization mechanisms of other systems including Drosophila, Xenopus, and mouse, suggesting that ancient and conserved mechanisms internalize cells in diverse organisms. C. elegans gastrulation occurs at an early stage, beginning when the embryo is composed of just 26 cells, suggesting some promise for connecting the rich array of developmental mechanisms that establish polarity and pattern in embryos to the force-producing mechanisms that change cell shapes and move cells interiorly. Here, we review our current understanding of C. elegans gastrulation mechanisms. We address how cells determine which direction is the interior and polarize with respect to that direction, how cells change shape by apical constriction and internalize, and how the embryo specifies which cells will internalize and when. We summarize future prospects for using this system to discover some of the general principles by which animal cells change shape and internalize during development.

RhoA Mediates Epithelial Cell Shape Changes via Mechanosensitive Endocytosis

Epithelial remodeling involves ratcheting behavior whereby periodic contractility produces transient changes in cell-cell contact lengths, which stabilize to produce lasting morphogenetic changes. Pulsatile RhoA activity is thought to underlie morphogenetic ratchets, but how RhoA governs transient changes in junction length, and how these changes are rectified to produce irreversible deformation, remains poorly understood. Here, we use optogenetics to characterize responses to pulsatile RhoA in model epithelium. Short RhoA pulses drive reversible junction contractions, while longer pulses produce irreversible junction length changes that saturate with prolonged pulse durations. Using an enhanced vertex model, we show this is explained by two effects: thresholded tension remodeling and continuous strain relaxation. Our model predicts that structuring RhoA into multiple pulses overcomes the saturation of contractility and confirms this experimentally. Junction remodeling also requires formin-mediated E-cadherin clustering and dynamin-dependent endocytosis. Thus, irreversible junction deformations are regulated by RhoA-mediated contractility, membrane trafficking, and adhesion receptor remodeling.

Active gel segment behaving as an active particle

We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.