arXiv subjects

Pierre Recho

Publications and source records attributed to Pierre Recho.

At least 19 recordsLinked to original sources

arXiv2026

Spontaneous polarization for protrusion-driven cell crawling

We propose a minimal one-dimensional continuum model for the spontaneous initiation of protrusion-driven cell crawling on a rigid substrate. The cell cytoskeleton is represented as a viscous actin meshwork that turns over in the bulk and polymerizes at two moving cell edges. Symmetry breaking arises from the feedback between cell motion, an external chemical regulator of actin nucleation, and actin polymerization at the cell fronts. When the cell moves, the regulator becomes polarized around the moving boundaries, thereby imposing different actin nucleation densities at the two edges. This generates unequal protrusive rates, which in turn reinforce motion and sustain the chemical polarization. Above a critical protrusive activity, the static symmetric state loses stability and the system undergoes a bifurcation toward a motile polarized state. Depending on how the external cue controls actin nucleation, the transition can be either supercritical or subcritical, leading in the latter case to coexistence between static and motile states. Using parameter values appropriate for keratocyte cells, the model predicts realistic crawling speeds and actin-density profiles, including asymmetric edge-localized density peaks. These results identify a generic mechanism by which external biochemical regulation of actin nucleation can trigger spontaneous motility along a one-dimensional track without requiring molecular motors, specific adhesion dynamics, deformable substrates, or pre-existing polarity.

physics.bio-ph↗

arXiv2024

Optimal crawling: from mechanical to chemical actuation

Taking inspiration from the crawling motion of biological cells on a substrate, we consider a physical model of self-propulsion where the spatio-temporal driving can involve both, a mechanical actuation by active force couples, and a chemical actuation through controlled mass turnover. We show that the competition and cooperation between these two modalities of active driving can drastically broaden the performance repertoire of the crawler. When the material turnover is slow and the mechanical driving dominates, we find that the highest velocity at a given energetic cost is reached when actuation takes the form of an active force configuration propagating as a traveling wave. As the rate of material turnover increases, and the chemical driving starts to dominate the mechanical one, such a peristalsis-type control progressively loses its efficacy, yielding to a standing wave type driving which involves an interplay between the mechanical and chemical actuation. Our analysis suggests a new paradigm for the optimal design of crawling biomimetic robots where the conventional purely mechanical driving through distributed force actuators is complemented by a distributed chemical control of the material remodeling inside the force-transmitting machinery.

cond-mat.soft↗

arXiv2024

Mechanics and thermodynamics of contractile entropic biopolymer networks

Contractile biopolymer networks, such as the actomyosin meshwork of animal cells, are ubiquitous in living organisms. The active gel theory, which provides the thermodynamic framework for these materials, has been mostly used in conjunction with the assumption that the microstructure of the biopolymer network is based on rigid rods. However, experimentally, crosslinked actin network exhibits entropic elasticity. Here we combine an entropic elasticity kinetic theory, in the spirit of the Green and Tobolsky model of transiently crosslinked networks, with an active flux modelling biological activity. We determine this active flux using Onsager reciprocal relations and interpret the corresponding microscopic dynamics. We obtain a closed-form model of the macroscopic mechanical behaviour. We show how this model can be written using the framework of multiplicative strain gradient decomposition, which is convenient for the resolution of such problems.

cond-mat.soft↗

arXiv2023

Initiation of motility on a compliant substrate

The conditions under which biological cells switch from a static to a motile state are fundamental to the understanding of many healthy and pathological processes. In this paper, we show that even in the presence of a fully symmetric protrusive activity at the cell edges, such a spontaneous transition can result solely from the mechanical interaction of the cell traction forces with an elastic substrate. The loss of symmetry of the traction forces leading to the cell propulsion is rooted in the fact that the surface loading follows the substrate deformation. The bifurcation between the static and motile states is characterized analytically and, considering the measurements performed on two cell types, we show that such an instability can realistically occur on soft in vivo substrates.

physics.bio-ph↗

arXiv2021

Cell motility as an energy minimization process

The dynamics of active matter driven by interacting molecular motors has a non-potential structure at the local scale. However, we show that there exists a quasi-potential 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 quasi-potential. 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 quasi-potential.

physics.bio-ph↗

arXiv2021

Chemo-mechanical model of a cell as a stochastic active gel

While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we present a framework that couples an active gel model of the cell mechanical scaffold with the complex cell metabolic system stochastically delivering the chemical energy needed to sustain an active stress in the scaffold. Our closure assumption setting the magnitude of the fluctuations is that the chemo-mechanical free energy of the cell is controlled at a target homeostatic value. Our model rationalizes the experimental observation that the cell shape fluctuations depend on the mechanical environment that constraints the cell. We apply our framework to the simple case of a cell migrating on a one dimensional track to successfully capture the different regimes of the cell mean square displacement along the track as well as the magnitude of the long time scale effective diffusive motion of the cell.

physics.bio-ph↗

arXiv2020

Mechanical behavior of multi-cellular spheroids under osmotic compression

The internal and external mechanical environment plays an important role in tumorogenesis. As a proxy of an avascular early state tumor, we use multicellular spheroids, a composite material made of cells, extracellular matrix and permeating fluid. We characterize its effective rheology at the timescale of minutes to hours by compressing the aggregates with osmotic shocks and modeling the experimental results with an active poroelastic material that reproduces the stress and strain distributions in the aggregate. The model also predicts how the emergent bulk modulus of the aggregate as well as the hydraulic diffusion of the percolating interstitial fluid are modified by the preexisting active stress within the aggregate. We further show that the value of these two phenomenological parameters can be rationalized by considering that, in our experimental context, the cells are effectively impermeable and incompressible inclusions nested in a compressible and permeable matrix.

physics.bio-ph↗

arXiv2020

Mechanical Feedback in Regulating the Size of Growing Multicellular Spheroids

The mechanism by which cells measure the dimension of the organ in which they are embedded, and slow down their growth when the final size is reached, is a long-standing problem of developmental biology. The role of mechanics in this feedback is considered important. Morphoelasticity is a standard continuum framework for modeling growing elastic tissues. However, in this theory, in the absence of additional variables, the feedback between growth and mechanical stress leads to either a collapse or unbounded growth of the tissue, but usually prohibits reaching a finite asymptotic size ('size control'). In this article, we modify this classical setting to include an energetic cost associated with growth, leading to the physical effect of size control. The present model simultaneously provides a qualitatively correct residual stress profile and has a naturally emerging necrotic core, all of which have previously been experimentally established in multicellular spheroids. This is achieved through a local feedback mechanism derived from a thermodynamical framework. The model delivers testable predictions for experimental systems and could be a step towards the understanding of the role of mechanics in the multifaceted question of how growing organs attain their final size.

physics.bio-ph↗

arXiv2020

A 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 study, 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.

physics.bio-ph↗

arXiv2019

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 non-motile 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.

physics.bio-ph↗

arXiv2018

On the quasi-static effective behaviour of poroelastic media containing elastic inclusions

The aim of the present study is to derive the effective quasi-static behaviour of a composite medium, made of a poroelastic matrix containing elastic impervious inclusions. For this purpose, the asymptotic homogenisation method is used. On the local scale, the governing equations include Biot's model of poroelasticity in the porous matrix and Navier equations in the inclusions, with elastic properties of the same order of magnitude. Biot's diphasic model of poroelasticity is obtained on the macroscopic scale, but with effective parameters that are strongly impacted by the distribution of inclusions, even at low volume fraction. The impact on fluid flow is strictly geometrical, showing that the inclusions do not play the role of a porous network.

cond-mat.soft↗

arXiv2018

Colliding cells: when active segments behave as active particles

Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended objects with internal activity and then reducing this description to a model of size-less active particles characterized by their position and polarity. We show that, in the presence of an applied force, a cell can either be dragged along or self-propel against the force, depending on the polarity of the cell. The co-existence of these regimes offers a self-consistent mechanical explanation for cell re-polarization upon contact. We rationalize the experimentally observed collision scenarios within the extended and particle models and link the various outcomes with measurable biological parameters.

physics.bio-ph↗

arXiv2018

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.

cond-mat.soft↗

arXiv2016

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.

q-bio.QM↗

arXiv2015

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 to actively extend during early morphogenesis or to regenerate 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 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 traction/compression balance 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.

physics.bio-ph↗

arXiv2015

Pseudo energy wells in active systems

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 at a micro-scale and show how active rigidity, interpreted as a formation of a pseudo-well in the effective energy landscape, can be generated in an overdamped ratchet-type stochastic system. We link the transition from negative to positive rigidity with correlations in the noise and show that subtle differences in out-of-equilibrium driving may compromise the emergence of a pseudo-well.

physics.bio-ph↗

arXiv2015

Mechanics of motility initiation and motility arrest in crawling cells

Motility initiation in crawling cells requires transformation of a symmetric state into a polarized state. In contrast, motility arrest is associated with re-symmetrization of the internal configuration of a cell. Experiments on keratocytes suggest that polarization is triggered by the increased contractility of motor proteins but the conditions of re-symmetrization remain unknown. In this paper we show that if adhesion with the extra-cellular substrate is sufficiently low, the progressive intensification of motor-induced contraction may be responsible for both transitions: from static (symmetric) to motile (polarized) at a lower contractility threshold and from motile (polarized) back to static (symmetric) at a higher contractility threshold. Our model of lamellipodial cell motility is based on a 1D projection of the complex intra-cellular dynamics on the direction of locomotion. In the interest of analytical transparency we also neglect active protrusion and view adhesion as passive. Despite the unavoidable oversimplifications associated with these assumptions, the model reproduces quantitatively the motility initiation pattern in fish keratocytes and reveals a crucial role played in cell motility by the nonlocal feedback between the mechanics and the transport of active agents. A prediction of the model that a crawling cell can stop and re-symmetrize when contractility increases sufficiently far beyond the motility initiation threshold still awaits experimental verification.

physics.bio-ph↗

arXiv2015

Maximum velocity of self-propulsion for an active segment

The motor part of a crawling eukaryotic cell can be represented schematically as an active continuum layer. The main active processes in this layer are protrusion, originating from non-equilibrium polymerization of actin fibers, contraction, induced by myosin molecular motors and attachment due to active bonding of trans-membrane proteins to a substrate. All three active mechanisms are regulated by complex signaling pathways involving chemical and mechanical feedback loops whose microscopic functioning is still poorly understood. In this situation, it is instructive to take a reverse engineering approach and study a problem of finding the spatial organization of standard active elements inside a crawling layer ensuring an optimal cost-performance trade-off. In this paper we assume that (in the range of interest) the energetic cost of self-propulsion is velocity independent and adopt, as an optimality criterion, the maximization of the overall velocity. We then choose a prototypical setting, formulate the corresponding variational problem and obtain a set of bounds suggesting that radically different spatial distributions of adhesive complexes would be optimal depending on the domineering active mechanism of self-propulsion. Thus, for contraction-dominated motility, adhesion has to cooperate with 'pullers' which localize at the trailing edge of the cell, while for protrusion-dominated motility it must conspire with 'pushers' concentrating at the leading edge of the cell. Both types of crawling mechanisms were observed experimentally.

physics.bio-ph↗