On the mechanical interplay between intra- and inter-synchronization during collective cell migration : a numerical investigation

Collective cell migration is a fundamental process that takes place during several biological phenomena such as embryogenesis, immunity response, and tumorogenesis, but the mechanisms that regulate it are still unclear. Similarly to collective animal behavior, cells receive feedbacks in space and time, which control the direction of the migration and the synergy between the cells of the population, respectively. While in single cell migration intra-synchronization (i.e. the synchronization between the protrusion-contraction movement of the cell and the adhesion forces exerted by the cell to move forward) is a sufficient condition for an efficient migration, in collective cell migration the cells must communicate and coordinate their movement between each other in order to be as efficient as possible (i.e. inter-synchronization). Here, we propose a 2D mechanical model of a cell population, which is described as a continuum with embedded discrete cells with or without motility phenotype. The decomposition of the deformation gradient is employed to reproduce the cyclic active strains of each single cell (i.e. protrusion and contraction). We explore different modes of collective migration to investigate the mechanical interplay between intra- and inter-synchronization. The main objective of the paper is to evaluate the efficiency of the cell population in terms of covered distance and how the stress distribution inside the cohort and the single cells may in turn provide insights regarding such efficiency

Collagen fiber network infiltration : permeability and capillary infiltration

International audienceIn dentin restoration, collagen fiber network infiltration is an issue. Using data from the litterature, we have constructed a relevant numerical geometrical model of the network. The specificity of our model is that the fibers are taken into account implicitly using a regularized Heaviside function. This function is either used to set the viscosity or to localize the contact line where capillary forces are applied. A level set technique with respect to fluid infiltration front tracking in five fiber networks using the level set method and Navier-Stokes equations with capillary terms is used to point out efficient critical infiltration parameters. A variational formulation which can be implemented in FEM is proposed both for the infiltration front and the contact line. Because of lack of knowledge on fiber orientation, different configurations were tested through permeability assessment of the whole network. Fiber orientation, interfibrillar space and contact angle influence were investigated

Diffusion-reaction model for Drosophila embryo development

During the early stages of gastrulation in Drosophila embryo, the epithelial cells composing the single tissue layer of the egg undergo large strains and displacements. These movements have been usually modeled by decomposing the total deformation gradient in an (imposed or strain/stress dependent) active part and a passive response. Although the influence of the chemical and genetic activity in the mechanical response of the cell has been experimentally observed, the effects of the mechanical deformation on the latter has been far less studied, and much less modeled. Here, we propose a model which couples morphogen transport and the cell mechanics during embryogenesis. A diffusion-reaction equation is introduced as an additional mechanical regulator of morphogenesis. Consequently, the active deformations are not directly 2 imposed in the analytical formulation, but they rather depend on the morphogen concentration, which is introduced as a new variable. In this work, we show that similar strain patterns to those observed during biological experiments can be reproduced by properly combining the two phenomena. Additionally, we use a novel technique to parameterize the embryo geometry by solving two Laplace problems with specific boundary conditions. We apply the method to two morphogenetic movements: ventral furrow invagination and germ band extension. The matching between our results and the observed experimental deformations confirms that diffusion-reaction of morphogens can actually be controlling large morphogenetic movements.Preprin

Viscoelastoplastic model of cell nucleus under compression

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In silico approach to quantify nucleus self‑deformation on micropillared substrates

Considering the major role of confined cell migration in biological processes and diseases, such as embryogenesis or metastatic cancer, it has become increasingly important to design relevant experimental set-ups for in vitro studies. Microfluidic devices have recently presented great opportunities in their respect since they offer the possibility to study all the steps from a suspended to a spread, and eventually crawling cell or a cell with highly deformed nucleus. Here, we focus on the nucleus self-deformation over a micropillared substrate. Actin networks have been observed at two locations in this set-up: above the nucleus, forming the perinuclear actin cap (PAC), and below the nucleus, surrounding the pillars. We can then wonder which of these contractile networks is responsible for nuclear deformation. The cytoplasm and the nucleus are represented through the superposition of a viscous and a hyperelastic material and follow a series of processes. First, the suspended cell settles on the pillars due to gravity. Second, an adhesive spreading force comes into play, and then, active deformations contract one or both actin domains and consequently the nucleus. Our model is first tested on a flat substrate to validate its global behaviour before being confronted to a micropillared substrate. Overall, the nucleus appears to be mostly pulled towards the pillars, while the mechanical action of the PAC is weak. Eventually, we test the influence of gravity and prove that the gravitational force does not play a role in the final deformation of the nucleus

A Coupled Friction-Poroelasticity Model of Chimneying Shows that Confined Cells Can Mechanically Migrate Without Adhesions

Cell migration is the cornerstone of many biological phenomena such as cancer metastasis, immune response or organogenesis. Adhesion-based motility is the most renown and examined motility mode, but in an adhesion-free confined environment or simply to achieve a higher migration speed, cells can adopt a very interesting bleb-based migration mode called “chimneying”. This mode rests on the sharp synchronization between the active contraction of the cells uropod and the passive friction force between the cell and the confining surface. In this paper, we propose a one dimensional poroelastic model of chimneying which considers the active strains of the cell, but, as an improvement with respect to our previous works, the synchronization between such strains and the friction forces developed by the cell and necessary to move forward is self-determined. The present work allows to deepen our knowledge on chimneying which is still poorly understood from a mechanical point of view. Furthermore, our results emphasize the key role of poroelasticity in bleb formation and give new insights on the location and the time-synchronization of the friction force. Further development of this exploratory work could provide a major tool to test hypotheses beforehand and thus focus future experiments on mechanically relevant ones

A mechanical model to investigate the role of the nucleus during confined cell migration

1. Introduction Cell migration in confinement plays a fundamental role in biological processes such as embryogenesis, immune response and tumorogenesis. Specifically, tumor cells continuously adapt their migratory behaviour to their environment. Therefore, it has become timely and essential for diagnostic purposes to quanti- tatively evaluate the cell deformability in confinement. Here, we propose a two-dimensional mechanical model to simulate the migration of a HeLa cell through a micro- channel. We will evaluate both the invasiveness of the cell and the mechanical forces exerted by the cell according to the surrounding microstructure

A piecewise-linear reduced-order model of squeeze-film damping for deformable structures including large displacement effects

This paper presents a reduced-order model for the Reynolds equation for deformable structure and large displacements. It is based on the model established in [11] which is piece-wise linearized using two different methods. The advantages and drawbacks of each method are pointed out. The pull-in time of a microswitch is determined and compared to experimental and other simulation data.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838