laboratoire de physique statistique
 
 
laboratoire de physique statistique

Publications

Rechercher
 
2016
Collective chemotaxis and segregation of active bacterial colonies - Ben Amar, M.
SCIENTIFIC REPORTS 6 (2016) 
LPS


Abstract : Still recently, bacterial fluid suspensions have motivated a lot of works, both experimental and theoretical, with the objective to understand their collective dynamics from universal and simple rules. Since some species are active, most of these works concern the strong interactions that these bacteria exert on a forced flow leading to instabilities, chaos and turbulence. Here, we investigate the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction. We propose a simple model to understand and quantify the physical properties of these living organisms which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.
Multiscale modeling of fibrosis - What's next? Reply to Comments on ``Towards a unified approach in the modeling of fibrosis: A review with research perspective'' by Martine Ben Amar and Carlo Bianca - Ben Amar, Martine and Bianca, Carlo
PHYSICS OF LIFE REVIEWS 17118-123 (2016) 
LPS
Towards a unified approach in the modeling of fibrosis: A review with research perspectives - Ben Amar, Martine and Bianca, Carlo
PHYSICS OF LIFE REVIEWS 1761-85 (2016) 
LPS


Abstract : Pathological fibrosis is the result of a failure in the wound healing process. The comprehension and the related modeling of the different mechanisms that trigger fibrosis are a challenge of many researchers that work in the field of medicine and biology. The modern scientific analysis of a phenomenon generally consists of three major approaches: theoretical, experimental, and computational. Different theoretical tools coming from mathematics and physics have been proposed for the modeling of the physiological and pathological fibrosis. However a complete framework is missing and the development of a general theory is required. This review aims at finding a unified approach in the modeling of fibrosis diseases that takes into account the different phenomena occurring at each level: molecular, cellular and tissue. Specifically by means of a critical analysis of the different models that have been proposed in the mathematical, computational and physical biology, from molecular to tissue scales, a multiscale approach is proposed, an approach that has been strongly recommended by top level biologists in the past decades. (C) 2016 Elsevier B.V. All rights reserved.
Onset of nonlinearity in a stochastic model for auto-chemotactic advancing epithelia - Ben Amar, Martine and Bianca, Carlo
SCIENTIFIC REPORTS 6 (2016) 
LPS


Abstract : We investigate the role of auto-chemotaxis in the growth and motility of an epithelium advancing on a solid substrate. In this process, cells create their own chemoattractant allowing communications among neighbours, thus leading to a signaling pathway. As known, chemotaxis provokes the onset of cellular density gradients and spatial inhomogeneities mostly at the front, a phenomenon able to predict some features revealed in in vitro experiments. A continuous model is proposed where the coupling between the cellular proliferation, the friction on the substrate and chemotaxis is investigated. According to our results, the friction and proliferation stabilize the front whereas auto-chemotaxis is a factor of destabilization. This antagonist role induces a fingering pattern with a selected wavenumber k(0). However, in the planar front case, the translational invariance of the experimental set-up gives also a mode at k = 0 and the coupling between these two modes in the nonlinear regime is responsible for the onset of a Hopf-bifurcation. The time-dependent oscillations of patterns observed experimentally can be predicted simply in this continuous non-linear approach. Finally the effects of noise are also investigated below the instability threshold.
 
2015
Growth and remodelling for profound circular wounds in skin - Wu, Min and Ben Amar, Martine
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY 14357-370 (2015) 
LPS


Abstract : Wound healing studies both in vitro and in vivo have received a lot of attention recently. In vivo wound healing is a multi-step process involving physiological factors such as fibrinogen forming the clot, the infiltrated inflammatory cells, the recruited fibroblasts and the differentiated myofibroblasts as well as deposited collagens. All these actors play their roles at different times, aided by a cascade of morphogenetic agents and the result for the repair is approximatively successful but the imperfection is remained for large scars with fibrosis. Here, we want to study wound healing from the viewpoint of skin biomechanics, integrating the particular layered geometry of the skin, and the role of the neighbouring wound epidermis. After 2 days post-injury, it migrates towards the wound centre to cover the hole, the migration being coupled to proliferation at the wound border. Such a process is dominated by the skin properties which varies with ages, locations, pathologies, radiations, etc. It is also controlled by passive (actin, collagen) and active (myo-fibroblasts) fibres. We explore a growth model in finite elasticity of a bilayer surrounding a circular wound, only the interior one being proliferative and contractile. We discuss the occurrence of an irregular wound geometry generated by stresses and show quantitatively that it results from the combined effects of the stiffness, the size of the wound, eventually weakened by actin cables. Comparison of our findings is made with known observations or experiments in vivo.
Osmotic stress affects functional properties of human melanoma cell lines - La Porta, Caterina A. M. and Ghilardi, Anna and Pasini, Maria and Laurson, Lasse and Alava, Mikko J. and Zapperi, Stefano and Ben Amar, Martine
EUROPEAN PHYSICAL JOURNAL PLUS 130 (2015) 
LPS


Abstract : Understanding the role of microenvironment in cancer growth and metastasis is a key issue for cancer research. Here, we study the effect of osmotic pressure on the functional properties of primary and metastatic melanoma cell lines. In particular, we experimentally quantify individual cell motility and transmigration capability. We then perform a circular scratch assay to study how a cancer cell front invades an empty space. Our results show that primary melanoma cells are sensitive to a low osmotic pressure, while metastatic cells are less. To better understand the experimental results, we introduce and study a continuous model for the dynamics of a cell layer and a stochastic discrete model for cell proliferation and diffusion. The two models capture essential features of the experimental results and allow to make predictions for a wide range of experimentally measurable parameters.
Modelling fibers in growing disks of soft tissues - Wu, Min and Ben Amar, Martine
MATHEMATICS AND MECHANICS OF SOLIDS 20663-679 (2015) 
LPS


Abstract : Despite its simple geometry and pertinence to biological systems, the growth of soft tissue disks has not been studied systematically in finite elasticity. Here with this simple geometry, we perform theoretical studies of constitutive laws concerning fibrous samples in growth or atrophy. Considering the radial growth of an incompressible neo-Hookean disk of matter, reinforced by fibers, we focus on the possible shape bifurcation from the circular to the wavy geometry. By analytical means based on a variational formulation of the theory of elasticity with growth we show that the radial geometry is lost for a critical growth anisotropy coefficient which plays the role of a control bifurcation parameter. Above a threshold which depends on the fiber invariants, the border of the disk becomes undulated with selection of a low wavenumber for low anisotropic coefficient. Radially or circumferentially oriented fibers favor undulations, but not intermediate cross-linked fibers, which inhibit undulations. Our systematic analysis shows the key role of the anisotropic growth coefficient as well as the fiber orientation for the observation of undulated patterns. Such models can explain experimental observations for skin tumors, biofilms and yeast colonies.
Morphogenesis of early stage melanoma - Chatelain, Clement and Ben Amar, Martine
EUROPEAN PHYSICAL JOURNAL PLUS 130 (2015) 
LPS


Abstract : Melanoma early detection is possible by simple skin examination and can insure a high survival probability when successful. However it requires efficient methods for identifying malignant lesions from common moles. This paper provides an overview first of the biological and physical mechanisms controlling melanoma early evolution, and then of the clinical tools available today for detecting melanoma in vivo at an early stage. It highlights the lack of diagnosis methods rationally linking macroscopic observables to the microscopic properties of the tissue, which define the malignancy of the tumor. The possible inputs of multiscale models for improving these methods are shortly discussed.
Faraday instability in floating drops - Pucci, G. and Ben Amar, M. and Couder, Y.
PHYSICS OF FLUIDS 27 (2015) 
LPS
DOI
10
Morpho-elasticity of inflammatory fibrosis: the case of capsular contracture - Ben Amar, Martine and Wu, Min and Trejo, Miguel and Atlan, Michael
JOURNAL OF THE ROYAL SOCIETY INTERFACE 12 (2015) 
LPS


Abstract : Inflammatory fibrosis is a wound-healing reaction of the immune system in mammals against aggression. After a signalling cascade, fibroblasts and potentially myofibroblasts make a stiff collagenous tissue inside the body that modifies the original healthy tissue. We focus here on the implant-induced fibrosis that aims to encapsulate the implant with a typical fibrous tissue called the capsule. Focusing on breast capsules, we aim to understand the mechanical properties of these tissues, to test the validity of fibre models that have been established in other contexts such as arteries. For this purpose, we perform force-extension experiments and show that mechanical constitutive laws of these tissues are especially difficult to derive, because models are sensitive to fibre orientation and dispersion, independently of the variation between individuals. In addition, fibre breakdown, and possibly remodelling, occur during the extension experiments. However, the high stiffness of the capsular tissue, compared with the healthy tissue, added to the fact that an inflammatory process has no reason to cease, is at the origin of large compressive stresses in vivo, which explains the pain and unaesthetic deformity. We evaluate the stresses responsible for the pain and the buckling instability, which have no reason to stop if the inflammation persists.
DOI
11
The role of pressure in cancer growth - Taloni, Alessandro and Ben Amar, Martine and Zapperi, Stefano and La Porta, Caterina A. M.
EUROPEAN PHYSICAL JOURNAL PLUS 130 (2015) 
LPS


Abstract : The response to external mechanical forces is increasingly seen as a crucial aspect of cancer growth and a topic where the contribution of physics ideas and methods is important. Understanding if tumor progression towards increased malignancy reflects the geometry and mechanics of the microenvironment is an important issue still to be fully explored. In order to grow, tumors have to overcome the mechanical resistance posed by the tissues in which they originate, while cancer cells involved in metastasis are often subject to fluid pressure. Here we review the recent literature describing the role of solid and fluid pressure on tumor growth and progression. We discuss a variety of in vitro experiments as well as computational models used to interpret them. We conclude discussing future perspectives.
 
2014
DOI
12
Morphology of melanocytic lesions in situ - Balois, Thibaut and Ben Amar, Martine
SCIENTIFIC REPORTS 4 (2014) 
LPS


Abstract : Melanoma is a solid tumour with its own specificity from the biological and morphological viewpoint. On one hand, numerous mutations are already known affecting different pathways. They usually concern proliferation rate, apoptosis, cell senescence and cell behaviour. On the other hand, several visual criteria at the tissue level are used by physicians in order to diagnose skin lesions. Nevertheless, the mechanisms between the changes from the mutations at the cell level to the morphology exhibited at the tissue level are still not fully understood. Using physical tools, we develop a simple model. We demonstrate analytically that it contains the necessary ingredients to understand several specificities of melanoma such as the presence of microstructures inside a skin lesion or the absence of a necrotic core. We also explain the importance of senescence for growth arrest in benign skin lesions. Thanks to numerical simulations, we successfully compare this model to biological data.
DOI
13
Patterns in melanocytic lesions: impact of the geometry on growth and transport inside the epidermis - Balois, Thibaut and Chatelain, Clement and Ben Amar, Martine
JOURNAL OF THE ROYAL SOCIETY INTERFACE 11 (2014) 
LPS


Abstract : In glabrous skin, nevi and melanomas exhibit pigmented stripes during clinical dermoscopic examination. They find their origin in the basal layer geometry which periodically exhibits ridges, alternatively large (limiting ridges) and thin (intermediate ridges). However, nevus and melanoma lesions differ by the localization of the pigmented stripes along furrows or ridges of the epidermis surface. Here, we propose a biomechanical model of avascular tumour growth which takes into account this specific geometry in the epidermis where both kinds of lesions first appear. Simulations show a periodic distribution of tumour cells inside the lesion, with a global contour stretched out along the ridges. In order to be as close as possible to clinical observations, we also consider the melanin transport by the keratinocytes. Our simulations show that reasonable assumptions on melanocytic cell repartition in the ridges favour the limiting ridges of the basal compared with the intermediate ones in agreement with nevus observations but not really with melanomas. It raises the question of cell aggregation and repartition of melanocytic cells in acral melanomas and requires further biological studies of these cells in situ.
 
2013
DOI
14
Theoretical analysis of growth or swelling wrinkles on constrained soft slabs - Jia, Fei and Ben Amar, Martine
SOFT MATTER 98216-8226 (2013) 
LPS


Abstract : Growth or swelling of soft slabs attached to a rigid substrate generates large compressive stresses at their surfaces. When the stresses exceed a critical value, the smooth surface becomes unstable. For an in-plane isotropic material, a nonlinear three dimensional analysis is employed to ascertain the energy in the buckled state for different modes: stripes, squares and hexagons. When increasing the growth control parameter, we show that hexagonal patterns with a dimple at the center minimize the elastic energy and will be the dominant mode if the mode with minimal energy is the most likely to be observed. The growth of an anisotropic material reinforced by fibers is also considered. The results provide a way to understand surface wrinkling patterns induced by equi-biaxial growth or swelling of elastic layers, with possible applications for micro-patterns fabrication through an appropriate fiber arrangement.
DOI
15
Thin nematic films: Anchoring effects and stripe instability revisited - Manyuhina, O. V. and Ben Amar, M.
PHYSICS LETTERS A 3771003-1011 (2013) 
LPS


Abstract : We study theoretically the formation of long-wavelength instability patterns observed at spreading of nematic droplets on liquid substrates. The role of surface-like elastic terms in nematic films of submicron thickness is (re)examined by extending our previous work to hybrid aligned nematics. We identify the upper threshold for the formation of stripes and compare our results with experimental observations. We find that the wavelength and the amplitude of the in-plane director undulations can be related to the small but finite azimuthal anchoring. Within a simplified model we analyse the possibility of non-planar base state below the Barbero-Barberi critical thickness. (C) 2013 Elsevier B.V. All rights reserved.
DOI
16
Faraday instability in floating liquid lenses: the spontaneous mutual adaptation due to radiation pressure - Pucci, G. and Ben Amar, M. and Couder, Y.
JOURNAL OF FLUID MECHANICS 725402-427 (2013) 
LPS


Abstract : Fluid dynamics instabilities are usually investigated in two types of situations, either confined in cells with fixed boundaries, or free to grow in open space. In this article we study the Faraday instability triggered in a floating liquid lens. This is an intermediate situation in which a hydrodynamical instability develops in a domain with flexible boundaries. The instability is observed to be initially disordered with fluctuations of both the wave field and the lens boundaries. However, a slow dynamics takes place, leading to a mutual adaptation so that a steady regime is reached with a stable wave field in a stable lens contour. The most recurrent equilibrium lens shape is elongated with the Faraday wave vector along the main axis. In this self-organized situation an equilibrium is reached between the radiation pressure exerted by Faraday waves on the borders and their capillary response. The elongated shape is obtained theoretically as the exact solution of a Riccati equation with a unique control parameter and compared with the experiment.
DOI
17
Chemotaxis migration and morphogenesis of living colonies - Ben Amar, Martine
EUROPEAN PHYSICAL JOURNAL E 36 (2013) 
LPS


Abstract : Development of forms in living organisms is complex and fascinating. Morphogenetic theories that investigate these shapes range from discrete to continuous models, from the variational elasticity to time-dependent fluid approach. Here a mixture model is chosen to describe the mass transport in a morphogenetic gradient: it gives a mathematical description of a mixture involving several constituents in mechanical interactions. This model, which is highly flexible can incorporate many biological processes but also complex interactions between cells as well as between cells and their environment. We use this model to derive a free-boundary problem easier to handle analytically. We solve it in the simplest geometry: an infinite linear front advancing with a constant velocity. In all the cases investigated here as the 3D diffusion, the increase of mitotic activity at the border, nonlinear laws for the uptake of morphogens or for the mobility coefficient, a planar front exists above a critical threshold for the mobility coefficient but it becomes unstable just above the threshold at long wavelengths due to the existence of a Goldstone mode. This explains why sparsely bacteria exhibit dendritic patterns experimentally in opposition to other colonies such as biofilms and epithelia which are more compact. In the most unstable situation, where all the laws: diffusion, chemotaxis driving and chemoattractant uptake are linear, we show also that the system can recover a dynamic stability. A second threshold for the mobility exists which has a lower value as the ratio between diffusion coefficients decreases. Within the framework of this model where the biomass is treated mainly as a viscous and diffusive fluid, we show that the multiplicity of independent parameters in real biologic experimental set-up may explain varieties of observed patterns.
DOI
18
Anisotropic growth shapes intestinal tissues during embryogenesis - Ben Amar, Martine and Jia, Fei
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 11010525-10530 (2013) 
LPS


Abstract : Embryogenesis offers a real laboratory for pattern formation, buckling, and postbuckling induced by growth of soft tissues. Each part of our body is structured in multiple adjacent layers: the skin, the brain, and the interior of organs. Each layer has a complex biological composition presenting different elasticity. Generated during fetal life, these layers will experience growth and remodeling in the early postfertilization stages. Here, we focus on a herringbone pattern occurring in fetal intestinal tissues. Common to many mammalians, this instability is a precursor of the villi, finger-like projections into the lumen. For avians (chicks' and turkeys' embryos), it has been shown that, a few days after fertilization, the mucosal epithelium of the duodenum is smooth, and then folds emerge, which present 2 d later a pronounced zigzag instability. Many debates and biological studies are devoted to this specific morphology, which regulates the cell renewal in the intestine. After reviewing experimental results about duodenum morphogenesis, we show that a model based on simplified hypothesis for the growth of the mesenchyme can explain buckling and postbuckling instabilities. Being completely analytical, it is based on biaxial compressive stresses due to differential growth between layers and it predicts quantitatively the morphological changes. The growth anisotropy increasing with time, the competition between folds and zigzags, is proved to occur as a secondary instability. The model is compared with available experimental data on chick's duodenum and can be applied to other intestinal tissues, the zigzag being a common and spectacular microstructural pattern of intestine embryogenesis.
 
2012
DOI
19
Peristaltic patterns for swelling and shrinking of soft cylindrical gels - Ciarletta, Pasquale and Ben Amar, Martine
SOFT MATTER 81760-1763 (2012) 
LPS


Abstract : We propose a variational method for determining the surface patterns of cylindrical gels for both swelling and shrinking. Exact solutions are calculated for the initial stages of such peristaltic instabilities. The morphology and the formation mechanisms depend on a competition between bulk elastic energy and surface tension.
DOI
20
Mechanical Instabilities of Gels - Dervaux, Julien and Ben Amar, Martine
in ANNUAL REVIEW OF CONDENSED MATTER PHYSICS, VOL 3 edited by Langer, JS (2012) 
LPS


Abstract : Although the study of gels undoubtedly takes its roots within the field of physicochemistry, the interest in gels has flourished and they have progressively become an important object in the study of the mechanics of polymeric materials and volumetric growth, raising some fascinating problems, some of them remaining unsolved. Because gels are multiphase objects, their study represents an important step in the understanding of the mechanics of complex soft matter as well as for the process of shape generation in biological bodies. The scope of this article is to review the understanding we have of the mechanical behavior of gels, with a strong focus on the development of instabilities in swelling gels.