Cell motility as an energy minimization process

The dynamics of active matter driven by interacting molecular motors has a nonpotential structure at the local scale. However, we show that there exists a quasipotential effectively describing the collective self-organization of the motors propelling a cell at a continuum active gel level. Such a model allows us to understand cell motility as an active phase transition problem between the static and motile steady-state configurations that minimize the quasipotential. In particular, both configurations can coexist in a metastable fashion and a small stochastic disorder in the gel is sufficient to trigger an intermittent cell dynamics where either static or motile phases are more probable, depending on which state is the global minimum of the quasipotential.

Direction of epithelial folding defines impact of mechanical forces on epithelial state

Cell shape dynamics during development is tightly regulated and coordinated with cell fate determination. Triggered by an interplay between biochemical and mechanical signals, epithelia form complex tissues by undergoing coordinated cell shape changes, but how such spatiotemporal coordination is controlled remains an open question. To dissect biochemical signaling from purely mechanical cues, we developed a microfluidic system that experimentally triggers epithelial folding to recapitulate stereotypic deformations observed in vivo. Using this system, we observe that the apical or basal direction of folding results in strikingly different mechanical states at the fold boundary, where the balance between tissue tension and torque (arising from the imposed curvature) controls the spread of folding-induced calcium waves at a short timescale and induces spatial patterns of gene expression at longer timescales. Our work uncovers that folding-associated gradients of cell shape and their resulting mechanical stresses direct spatially distinct biochemical responses within the monolayer.

Extracellular matrix in multicellular aggregates acts as a pressure sensor controlling cell proliferation and motility

Imposed deformations play an important role in morphogenesis and tissue homeostasis, both in normal and pathological conditions. To perceive mechanical perturbations of different types and magnitudes, tissues need appropriate detectors, with a compliance that matches the perturbation amplitude. By comparing results of selective osmotic compressions of CT26 mouse cells within multicellular aggregates and global aggregate compressions, we show that global compressions have a strong impact on the aggregates growth and internal cell motility, while selective compressions of same magnitude have almost no effect. Both compressions alter the volume of individual cells in the same way over a shor-timescale, but, by draining the water out of the extracellular matrix, the global one imposes a residual compressive mechanical stress on the cells over a long-timescale, while the selective one does not. We conclude that the extracellular matrix is as a sensor that mechanically regulates cell proliferation and migration in a 3D environment.

Tug-of-war between stretching and bending in living cell sheets

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness e of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like 1/e, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Curling of epithelial monolayers reveals coupling between active bending and tissue tension

Epithelial monolayers are two-dimensional cell sheets which compartmentalize the body and organs of multicellular organisms. Their morphogenesis during development or pathology results from patterned endogenous and exogenous forces and their interplay with tissue mechanical properties. In particular, bending of epithelia is thought to result from active torques generated by the polarization of myosin motors along their apicobasal axis. However, the contribution of these out-of-plane forces to morphogenesis remains challenging to evaluate because of the lack of direct mechanical measurement. Here we use epithelial curling to characterize the out-of-plane mechanics of epithelial monolayers. We find that curls of high curvature form spontaneously at the free edge of epithelial monolayers devoid of substrate in vivo and in vitro. Curling originates from an enrichment of myosin in the basal domain that generates an active spontaneous curvature. By measuring the force necessary to flatten curls, we can then estimate the active torques and the bending modulus of the tissue. Finally, we show that the extent of curling is controlled by the interplay between in-plane and out-of-plane stresses in the monolayer. Such mechanical coupling emphasizes a possible role for in-plane stresses in shaping epithelia during morphogenesis.

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.

Actomyosin controls planarity and folding of epithelia in response to compression

Throughout embryonic development and adult life, epithelia are subjected to compressive deformations. While these have been shown to trigger mechanosensitive responses such as cell extrusion and differentiation, which span tens of minutes, little is known about how epithelia adapt to compression over shorter timescales. Here, using suspended epithelia, we uncover the immediate response of epithelial tissues to the application of in-plane compressive strains (5-80%). We show that fast compression induces tissue buckling followed by actomyosin-dependent tissue flattening that erases the buckle within tens of seconds, in both mono- and multi-layered epithelia. Strikingly, we identify a well-defined limit to this response, so that stable folds form in the tissue when compressive strains exceed a 'buckling threshold' of ~35%. A combination of experiment and modelling shows that this behaviour is orchestrated by adaptation of the actomyosin cytoskeleton as it re-establishes tissue tension following compression. Thus, tissue pre-tension allows epithelia to both buffer against deformation and sets their ability to form and retain folds during morphogenesis.

Actomyosin controls planarity and folding of epithelia in response to compression

Throughout embryonic development and adult life, epithelia are subjected to compressive deformations. While these have been shown to trigger mechanosensitive responses such as cell extrusion and differentiation, which span tens of minutes, little is known about how epithelia adapt to compression over shorter timescales. Here, using suspended epithelia, we uncover the immediate response of epithelial tissues to the application of in-plane compressive strains (5-80%). We show that fast compression induces tissue buckling followed by actomyosin-dependent tissue flattening that erases the buckle within tens of seconds, in both mono- and multi-layered epithelia. Strikingly, we identify a well-defined limit to this response, so that stable folds form in the tissue when compressive strains exceed a 'buckling threshold' of ~35%. A combination of experiment and modelling shows that this behaviour is orchestrated by adaptation of the actomyosin cytoskeleton as it re-establishes tissue tension following compression. Thus, tissue pre-tension allows epithelia to both buffer against deformation and sets their ability to form and retain folds during morphogenesis.

Crawling in a Fluid

There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a nonmotile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trends.

Mechanical stress as a regulator of cell motility

The motility of a cell can be triggered or inhibited not only by an applied force but also by a mechanically neutral force couple. This type of loading, represented by an applied stress and commonly interpreted as either squeezing or stretching, can originate from extrinsic interaction of a cell with its neighbors. To quantify the effect of applied stresses on cell motility we use an analytically transparent one-dimensional model accounting for active myosin contraction and induced actin turnover. We show that stretching can polarize static cells and initiate cell motility while squeezing can symmetrize and arrest moving cells. We show further that sufficiently strong squeezing can lead to the loss of cell integrity. The overall behavior of the system depends on the two dimensionless parameters characterizing internal driving (chemical activity) and external loading (applied stress). We construct a phase diagram in this parameter space distinguishing between static, motile, and collapsed states. The obtained results are relevant for the mechanical understanding of contact inhibition and the epithelial-to-mesenchymal transition.

The dynamic mechanical properties of cellularised aggregates

Cellularised materials are composed of cells interfaced through specialised intercellular junctions that link the cytoskeleton of one cell to that of its neighbours allowing for transmission of forces. Cellularised materials are common in early development and adult tissues where they can be found in the form of cell sheets, cysts, or amorphous aggregates and in pathophysiological conditions such as cancerous tumours. Given the growing realisation that forces can regulate cell physiology and developmental processes, understanding how cellularised materials deform under mechanical stress or dissipate stress appear as key biological questions. In this review, we will discuss the dynamic mechanical properties of cellularised materials devoid of extracellular matrix.

Rigidity generation by nonthermal fluctuations

Active stabilization in systems with zero or negative stiffness is an essential element of a wide variety of biological processes. We study a prototypical example of this phenomenon and show how active rigidity, interpreted as a formation of a pseudowell in the effective energy landscape, can be generated in an overdamped stochastic system. We link the transition from negative to positive rigidity with time correlations in the additive noise, and we show that subtle differences in the out-of-equilibrium driving may compromise the emergence of a pseudowell.

Publisher's Note: Growth, collapse, and stalling in a mechanical model for neurite motility [Phys. Rev. E 93, 032410 (2016)]

This corrects the article DOI: 10.1103/PhysRevE.93.032410.

Growth, collapse, and stalling in a mechanical model for neurite motility

Neurites, the long cellular protrusions that form the routes of the neuronal network, are capable of actively extending during early morphogenesis or regenerating after trauma. To perform this task, they rely on their cytoskeleton for mechanical support. In this paper, we present a three-component active gel model that describes neurites in the three robust mechanical states observed experimentally: collapsed, static, and motile. These states arise from an interplay between the physical forces driven by the growth of the microtubule-rich inner core of the neurite and the acto-myosin contractility of its surrounding cortical membrane. In particular, static states appear as a mechanical balance between traction and compression of these two parallel structures. The model predicts how the response of a neurite to a towing force depends on the force magnitude and recovers the response of neurites to several drug treatments that modulate the cytoskeleton active and passive properties.

One-dimensional collective migration of a proliferating cell monolayer

The importance of collective cellular migration during embryogenesis and tissue repair asks for a sound understanding of underlying principles and mechanisms. Here, we address recent in vitro experiments on cell monolayers, which show that the advancement of the leading edge relies on cell proliferation and protrusive activity at the tissue margin. Within a simple viscoelastic mechanical model amenable to detailed analysis, we identify a key parameter responsible for tissue expansion, and we determine the dependence of the monolayer velocity as a function of measurable rheological parameters. Our results allow us to discuss the effects of pharmacological perturbations on the observed tissue dynamics.

Assembly and positioning of actomyosin rings by contractility and planar cell polarity

The actomyosin cytoskeleton is a primary force-generating mechanism in morphogenesis, thus a robust spatial control of cytoskeletal positioning is essential. In this report, we demonstrate that actomyosin contractility and planar cell polarity (PCP) interact in post-mitotic Ciona notochord cells to self-assemble and reposition actomyosin rings, which play an essential role for cell elongation. Intriguingly, rings always form at the cells' anterior edge before migrating towards the center as contractility increases, reflecting a novel dynamical property of the cortex. Our drug and genetic manipulations uncover a tug-of-war between contractility, which localizes cortical flows toward the equator and PCP, which tries to reposition them. We develop a simple model of the physical forces underlying this tug-of-war, which quantitatively reproduces our results. We thus propose a quantitative framework for dissecting the relative contribution of contractility and PCP to the self-assembly and repositioning of cytoskeletal structures, which should be applicable to other morphogenetic events.

Cortical instability drives periodic supracellular actin pattern formation in epithelial tubes

An essential question of morphogenesis is how patterns arise without preexisting positional information, as inspired by Turing. In the past few years, cytoskeletal flows in the cell cortex have been identified as a key mechanism of molecular patterning at the subcellular level. Theoretical and in vitro studies have suggested that biological polymers such as actomyosin gels have the property to self-organize, but the applicability of this concept in an in vivo setting remains unclear. Here, we report that the regular spacing pattern of supracellular actin rings in the Drosophila tracheal tubule is governed by a self-organizing principle. We propose a simple biophysical model where pattern formation arises from the interplay of myosin contractility and actin turnover. We validate the hypotheses of the model using photobleaching experiments and report that the formation of actin rings is contractility dependent. Moreover, genetic and pharmacological perturbations of the physical properties of the actomyosin gel modify the spacing of the pattern, as the model predicted. In addition, our model posited a role of cortical friction in stabilizing the spacing pattern of actin rings. Consistently, genetic depletion of apical extracellular matrix caused strikingly dynamic movements of actin rings, mirroring our model prediction of a transition from steady to chaotic actin patterns at low cortical friction. Our results therefore demonstrate quantitatively that a hydrodynamical instability of the actin cortex can trigger regular pattern formation and drive morphogenesis in an in vivo setting.

Contraction-driven cell motility

We propose a mechanism for the initiation of cell motility that is based on myosin-induced contraction and does not require actin polymerization. The translocation of a cell is induced by symmetry breaking of the motor-driven flow, and the ensuing asymmetry gives rise to a steady motion of the center of mass of a cell. The predictions of the model are consistent with observations on keratocytes.

Asymmetry between pushing and pulling for crawling cells

Eukaryotic cells possess motility mechanisms allowing them not only to self-propel but also to exert forces on obstacles (to push) and to carry cargoes (to pull). To study the inherent asymmetry between active pushing and pulling we model a crawling acto-myosin cell extract as a one-dimensional layer of active gel subjected to external forces. We show that pushing is controlled by protrusion and that the macroscopic signature of the protrusion dominated motility mechanism is concavity of the force-velocity relation. In contrast, pulling is driven by protrusion only at small values of the pulling force and it is replaced by contraction when the pulling force is sufficiently large. This leads to more complex convex-concave structure of the force-velocity relation; in particular, competition between protrusion and contraction can produce negative mobility in a biologically relevant range. The model illustrates active readjustment of the force generating machinery in response to changes in the dipole structure of external forces. The possibility of switching between complementary active mechanisms implies that if necessary "pushers" can replace "pullers" and vice versa.