Robustness of force and stress inference in an epithelial tissue

During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time ($\sim$minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.Comment: 4 pages, 4 figure

Co-transport-induced instability of membrane voltage in tip-growing cells

A salient feature of stationary patterns in tip-growing cells is the key role played by the symports and antiports, membrane proteins that translocate two ionic species at the same time. It is shown that these co-transporters destabilize generically the membrane voltage if the two translocated ions diffuse differently and carry a charge of opposite (same) sign for symports (antiports). Orders of magnitude obtained for the time and lengthscale are in agreement with experiments. A weakly nonlinear analysis characterizes the bifurcation

Polarity patterns of stress fibers

Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.Comment: 5 pages, 3 figure

Magnetic order in the Ising model with parallel dynamics

It is discussed how the equilibrium properties of the Ising model are described by an Hamiltonian with an antiferromagnetic low temperature behavior if only an heat bath dynamics, with the characteristics of a Probabilistic Cellular Automaton, is assumed to determine the temporal evolution of the system.Comment: 9 pages, 3 figure

Nouvelle stratégie antibiofilm par dépôt LBL d’un polyélectrolyte cationique sur la membrane de dialyse anionique AN69

Cette étude présente une stratégie antibiofilm appliquée à une membrane de dialyse, l’AN69; il s’agit de réaliser une modification initiale de la surface de la membrane par un polyélectrolyte cationique, le poly(diallyldiméthyl-ammonium), noté PDADMA, selon un protocole de type « layer-by-layer ». Les caractéristiques physico-chimiques des deux membranes, l’AN69 et l’AN69 modifiée par le PDADMA, sont suivies par la détermination de la modification de la charge de la membrane en mettant en oeuvre des mesures de potentiels d’écoulement et de nombres de transports de Li+, de perméabilité hydraulique et des analyses morphologiques et topographiques effectuées par les microscopies électroniques à balayage et à force atomique, respectivement avant et après exposition à E. coli et à un biofilm marin. Nos résultats montrent tout d’abord un rôle majeur joué par l’attraction électrostatique entre les microorganismes et l’AN69 modifiée par le PDADMA à l’origine d’une adhésion forte des bactéries.Par ailleurs, nous avons mis au point un protocole original d’élimination du biofilm marin. Ce protocole consiste à immerger la membrane modifiée par le PDADMA et encrassée, dans une solution de chlorure de sodium 2M afin d’écranter les charges électrostatiques à l’origine de l’accroche du polyélectrolyte et permettre le décrochage du PDADMA qui entraîne avec lui l’encrassement (constitué de bactéries et autres résidus de biofilm). La recharge d’un film frais de PDADMA permet alors une réutilisation à l’infini de la membrane AN69. La simplicité de ce protocole « de régénération » ouvre la possibilité d’une modification non permanente des membranes de dialyse, dans le but de limiter les problèmes récurrents de biocolmatage et d’augmenter les durées de vie des membranes en milieu marin.The harmful effects generated by biofilms have an extremely high cost. In this study, we were interested in the formation of marine biofilms forming on the wellknown anionic dialysis membrane AN69 used in the reduction of seawater salinity for the preparation of body-washing solutions. We focused our study on two membranes: AN69 and AN69 modified (denoted AN69 mod) by the sorption of poly(diallyldimethyl-ammonium), a cationic polyelectrolyte denoted by PDADMA. Physico-chemical characteristics (membrane charge from Li+ transport and streaming potential measurements, water flux from hydraulic permeability measurements and morphological/topographical measurements using SEM and AFM, respectively) were monitered during the exposure of both membranes to E. coli and natural marine biofouling solutions. Our results showed that the modification of the AN69 membrane by PDADMA its charge and increased its electrostatic affinity for bacteria. Electrostatics forces are, therefore, the main forces responsible for membrane biofouling. Furthermore we developed a simple antibiofilm protocol based on a one-step dipping operation applied to the fouled AN69 membrane which eliminates the PDADMA and associated bacteria. For the first time, all deposited marine bacteria were easily eliminated allowing for the regeneration and sustainable use of the AN69 membrane

Contraction of cross-linked actomyosin bundles

Cross-linked actomyosin bundles retract when severed in vivo by laser ablation, or when isolated from the cell and micromanipulated in vitro in the presence of ATP. We identify the time scale for contraction as a viscoelastic time tau, where the viscosity is due to (internal) protein friction. We obtain an estimate of the order of magnitude of the contraction time tau ~ 10-100 s, consistent with available experimental data for circumferential microfilament bundles and stress fibers. Our results are supported by an exactly solvable, hydrodynamic model of a retracting bundle as a cylinder of isotropic, active matter, from which the order of magnitude of the active stress is estimated.Comment: To be published in Physical Biolog

Stochastic analysis of different rough surfaces

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more details. In particular we show the evidence of Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in details advantages and disadvantages of these methods.Comment: Minor text changes to be identical with the published versio

Nonlinear oscillator with parametric colored noise: some analytical results

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit

Synchronization in coupled map lattices as an interface depinning

We study an SOS model whose dynamics is inspired by recent studies of the synchronization transition in coupled map lattices (CML). The synchronization of CML is thus related with a depinning of interface from a binding wall. Critical behaviour of our SOS model depends on a specific form of binding (i.e., transition rates of the dynamics). For an exponentially decaying binding the depinning belongs to the directed percolation universality class. Other types of depinning, including the one with a line of critical points, are observed for a power-law binding.Comment: 4 pages, Phys.Rev.E (in press

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows $1/f$ noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension.Comment: 7 pages, 6 figures (revised