DOI

1

Shape and energy of a membrane bud induced by protein coats or viral protein assembly - Foret, Lionel

EUROPEAN PHYSICAL JOURNAL E 37, (2014)

Abstract : Intracellular transport vesicles and enveloped virus production is mediated by the polymerization of proteins that form bi-dimensional curved and rigid structures, or ``coats'', on a membrane. Using the classical framework of fluid membrane elasticity, we compute numerically the shape and the mechanical energy of the membrane deformation induced by a coat at different stage of growth. We furthermore derive analytical approximate expressions for the membrane shape and energy. They are found to be very accurate when compared to numerical calculations. These analytical expressions should be useful when building a relevant model of coat polymerization kinetics. We also discuss some consequences of the membrane energy features on the coat assembly process, showing that at high tension a kinetically arrested state of incomplete assembly could exist.

EUROPEAN PHYSICAL JOURNAL E 37, (2014)

Abstract : Intracellular transport vesicles and enveloped virus production is mediated by the polymerization of proteins that form bi-dimensional curved and rigid structures, or ``coats'', on a membrane. Using the classical framework of fluid membrane elasticity, we compute numerically the shape and the mechanical energy of the membrane deformation induced by a coat at different stage of growth. We furthermore derive analytical approximate expressions for the membrane shape and energy. They are found to be very accurate when compared to numerical calculations. These analytical expressions should be useful when building a relevant model of coat polymerization kinetics. We also discuss some consequences of the membrane energy features on the coat assembly process, showing that at high tension a kinetically arrested state of incomplete assembly could exist.

DOI

2

Chemotaxis migration and morphogenesis of living colonies - Ben Amar, Martine

EUROPEAN PHYSICAL JOURNAL E 36, (2013)

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.

EUROPEAN PHYSICAL JOURNAL E 36, (2013)

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

3

Aggregation on a membrane of particles undergoing active exchange with a reservoir - Foret, L.

EUROPEAN PHYSICAL JOURNAL E 35, (2012)

Abstract : We investigate the dynamics of clusters made of aggregating particles on a membrane which exchanges particles with a reservoir. Exchanges are driven by chemical reactions which supply energy to the system, leading to the establishment of a non-equilibrium steady state. We predict the distribution of cluster size at steady state. We show in particular that in a regime, that cannot exist at equilibrium, the distribution is bimodal: the membrane is mainly populated of single particles and finite-size clusters. This work is motivated by the observations that have revealed the existence of submicrometric clusters of proteins in biological membranes.

EUROPEAN PHYSICAL JOURNAL E 35, (2012)

Abstract : We investigate the dynamics of clusters made of aggregating particles on a membrane which exchanges particles with a reservoir. Exchanges are driven by chemical reactions which supply energy to the system, leading to the establishment of a non-equilibrium steady state. We predict the distribution of cluster size at steady state. We show in particular that in a regime, that cannot exist at equilibrium, the distribution is bimodal: the membrane is mainly populated of single particles and finite-size clusters. This work is motivated by the observations that have revealed the existence of submicrometric clusters of proteins in biological membranes.

DOI

4

Effective line tension and contact angles between membrane domains in biphasic vesicles - Trejo, M. and Ben Amar, M.

EUROPEAN PHYSICAL JOURNAL E 34, (2011)

Abstract : Inhomogeneities in membranes give rise to localized interactions at the interface between domains in two-component vesicles. The corresponding energy is expressed as a line tension between the two phases. In this paper we study the implications of the thickness mismatch between domains which has been experimentally reported to be of order 20-30\% and the conditions under which the induced line tension can destabilize the domains in inhomogeneous vesicles. For asymmetric lipidic membranes we prove an increase of the line tension and the existence of a contact angle. Adsorption of impurities is also examined, our scope being the extension of the Canham-Helfrich model to describe elastic deformations and chemical interactions arising at microscopic scales. This mismatch effect may have important consequences for the stability of very small domains.

EUROPEAN PHYSICAL JOURNAL E 34, (2011)

Abstract : Inhomogeneities in membranes give rise to localized interactions at the interface between domains in two-component vesicles. The corresponding energy is expressed as a line tension between the two phases. In this paper we study the implications of the thickness mismatch between domains which has been experimentally reported to be of order 20-30\% and the conditions under which the induced line tension can destabilize the domains in inhomogeneous vesicles. For asymmetric lipidic membranes we prove an increase of the line tension and the existence of a contact angle. Adsorption of impurities is also examined, our scope being the extension of the Canham-Helfrich model to describe elastic deformations and chemical interactions arising at microscopic scales. This mismatch effect may have important consequences for the stability of very small domains.

DOI

5

Non-spherical shapes of capsules within a fourth-order curvature model - Manyuhina, O. V. and Hetzel, J. J. and Katsnelson, M. I. and Fasolino, A.

EUROPEAN PHYSICAL JOURNAL E 32, 223-228 (2010)

Abstract : We minimize a discrete version of the fourth-order curvature-based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy minimizers. Our results suggest that the buckling and faceting transitions, usually associated with crystalline matter, can also be an intrinsic property of non-crystalline membranes.

EUROPEAN PHYSICAL JOURNAL E 32, 223-228 (2010)

Abstract : We minimize a discrete version of the fourth-order curvature-based Landau free energy by extending Brakke's Surface Evolver. This model predicts spherical as well as non-spherical shapes with dimples, bumps and ridges to be the energy minimizers. Our results suggest that the buckling and faceting transitions, usually associated with crystalline matter, can also be an intrinsic property of non-crystalline membranes.

DOI

6

Non-Newtonian thin films with normal stresses: dynamics and spreading - Boudaoud, A.

EUROPEAN PHYSICAL JOURNAL E 22, 107-109 (2007)

Abstract : The dynamics of a thin film on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line.

EUROPEAN PHYSICAL JOURNAL E 22, 107-109 (2007)

Abstract : The dynamics of a thin film on a horizontal solid substrate is investigated in the case of non-Newtonian fluids exhibiting normal stress differences, the rheology of which is strongly non-linear. Two coupled equations of evolution for the thickness of the film and the shear rate are proposed within the lubrication approximation. This framework is applied to the motion of an advancing contact line. The apparent dynamic contact angle is found to depend logarithmically on a lengthscale determined solely by the rheological properties of the fluid and the velocity of the contact line.

DOI

7

Statics and dynamics of adhesion between two soap bubbles - Besson, S. and Debregeas, G.

EUROPEAN PHYSICAL JOURNAL E 24, 109-117 (2007)

Abstract : An original set-up is used to study the adhesive properties of two hemispherical soap bubbles put into contact. The contact angle at the line connecting the three films is extracted by image analysis of the bubbles profiles. After the initial contact, the angle rapidly reaches a static value slightly larger than the standard 120 degrees angle expected from Plateau rule. This deviation is consistent with previous experimental and theoretical studies: it can be quantitatively predicted by taking into account the finite size of the Plateau border (the liquid volume trapped at the vertex) in the free energy minimization. The visco-elastic adhesion properties of the bubbles are further explored by measuring the deviation Delta theta(d)(t) of the contact angle from the static value as the distance between the two bubbles supports is sinusoidally modulated. It is found to linearly increase with Delta r(c)/r(c) , where r(c) is the radius of the central film and Delta r(c) the amplitude of modulation of this length induced by the displacement of the supports. The in-phase and out-of-phase components of Delta theta(d)(t) with the imposed modulation frequency are systematically probed, which reveals a transition from a viscous to an elastic response of the system with a crossover pulsation of the order 1 rad.s(-1). Independent interfacial rheological measurements, obtained from an oscillating bubble experiment, allow us to develop a model of dynamic adhesion which is confronted to our experimental results. The relevance of such adhesive dynamic properties to the rheology of foams is briefly discussed using a perturbative approach to the Princen 2D model of foams.

EUROPEAN PHYSICAL JOURNAL E 24, 109-117 (2007)

Abstract : An original set-up is used to study the adhesive properties of two hemispherical soap bubbles put into contact. The contact angle at the line connecting the three films is extracted by image analysis of the bubbles profiles. After the initial contact, the angle rapidly reaches a static value slightly larger than the standard 120 degrees angle expected from Plateau rule. This deviation is consistent with previous experimental and theoretical studies: it can be quantitatively predicted by taking into account the finite size of the Plateau border (the liquid volume trapped at the vertex) in the free energy minimization. The visco-elastic adhesion properties of the bubbles are further explored by measuring the deviation Delta theta(d)(t) of the contact angle from the static value as the distance between the two bubbles supports is sinusoidally modulated. It is found to linearly increase with Delta r(c)/r(c) , where r(c) is the radius of the central film and Delta r(c) the amplitude of modulation of this length induced by the displacement of the supports. The in-phase and out-of-phase components of Delta theta(d)(t) with the imposed modulation frequency are systematically probed, which reveals a transition from a viscous to an elastic response of the system with a crossover pulsation of the order 1 rad.s(-1). Independent interfacial rheological measurements, obtained from an oscillating bubble experiment, allow us to develop a model of dynamic adhesion which is confronted to our experimental results. The relevance of such adhesive dynamic properties to the rheology of foams is briefly discussed using a perturbative approach to the Princen 2D model of foams.

DOI

8

Life and death of a fakir droplet: Impalement transitions on superhydrophobic surfaces - Moulinet, S. and Bartolo, D.

EUROPEAN PHYSICAL JOURNAL E 24, 251-260 (2007)

Abstract : We show that the equilibrium state of a water drop deposited on a superhydrophobic surface cannot be solely determined by its macroscopic contact angle but also depends on the drop size. Following the evolution of the interface of evaporating droplets, we demonstrate that the liquid can explore a succession of equilibrium conformations which are neither of the usual fakir nor Wenzel types. A comprehensive description of the transition between these wetting states is provided. To do so, we have taken advantage of microfabrication techniques and interference microscopy which allows for the ``3D'' imaging of the liquid interface. In addition, we propose a simple theoretical description of the interface geometry which goes beyond the standard two-state picture for superhydrophobicity. This model accounts correctly for all our experimental observations. Finally, guided by potential microfluidic applications we propose an efficient design strategy to build robust liquid repellant surfaces.

EUROPEAN PHYSICAL JOURNAL E 24, 251-260 (2007)

Abstract : We show that the equilibrium state of a water drop deposited on a superhydrophobic surface cannot be solely determined by its macroscopic contact angle but also depends on the drop size. Following the evolution of the interface of evaporating droplets, we demonstrate that the liquid can explore a succession of equilibrium conformations which are neither of the usual fakir nor Wenzel types. A comprehensive description of the transition between these wetting states is provided. To do so, we have taken advantage of microfabrication techniques and interference microscopy which allows for the ``3D'' imaging of the liquid interface. In addition, we propose a simple theoretical description of the interface geometry which goes beyond the standard two-state picture for superhydrophobicity. This model accounts correctly for all our experimental observations. Finally, guided by potential microfluidic applications we propose an efficient design strategy to build robust liquid repellant surfaces.