Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes

A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electro-diffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive non-linear evolution equations near the transitions to stationary patterns.Comment: 10 pages, 7 figures, will be submitted to Phys. Rev.

Interfacial rheology of microcapsules and dynamics in flow

A capsule is a drop bounded by a thin solid membrane providing specific mechanical properties. It is used to control the spatio-temporal delivery of substances in numerous processes and also as a model system of cells. Its dynamics under flow depends on its membrane characteristics. Moreover, the delivery of encapsulated drugs is controlled by its deformation. The interfacial rheology of microcapsules can be tuned according to their formulation. We will focus on cross-linked membrane made with human serum albumin and chitosan assembled with a surfactant via electrostatic interactions. The interfacial rheological properties of these soft microparticles are deduced from their dynamics of deformation in elongation and shear flows. In elongation flow, the surface shear modulus of the membrane is measured and related to the kind of biopolymer used and to the main parameters of the process of fabrication. In the regime of large deformations, the microcapsules can present a non-linear elastic response or plastic deformations. Non-linear elastic constitutive law is deduced by comparison of the evolution of the shape of the microcapsule in the two main planes of deformation of the capsule with numerical simulations. In shear flow, the rotation of the membrane, i.e. the tank-treading, is visualised and quantified by decorating the membrane of microcapsules with particles. The tracking of the distance between two close microparticles showed membrane contraction at the tips and stretching on the sides. This dynamic of deformation induce viscous dissipation inside the membrane. The order of magnitude of membrane viscosity is determined by comparison with numerical simulations. Wrinkling instability is observed in extensional flow and studied by varying the interfacial properties of the microcapsules. In this way, the phase diagram of wrinkle instability for microcapsules has been deduced as the scaling law between the wrinkles wave-length and the membrane thickness. Finally, we have developed a set of tools to characterize the interfacial viscoelasticity of microcapsules, their bending modulus and their non-linear elastic properties. We conclude the talk with some results on break-up of microcapsules in flow. Please click Additional Files below to see the full abstract

Cycle de sensibilisation sur l’illettrisme

Quatre journées, pas moins, étalées sur l’année 2006, ont été nécessaires pour mieux comprendre les enjeux majeurs de la lutte contre l’illettrisme, et, à partir d’exemples concrets, passer du constat et de la détermination des responsabilité aux engagements et à l’action

Monodisperse microcapsules with controlled interfacial properties generated in microfluidic T-shape junction

Microcapsules are widely found in the nature (e.g. red blood cells and some bacteria), as well as in artificial products. They are generally well-considered as liquid drop bounded by an elastic membrane which is often used to protect the core materials from the external harsh environments. Capsules of biopolymers are exhibiting a large increase of promising applications in the encapsulation and release of medical drugs, food additives, and cosmetics[1-3]. Indeed, there is also a growing interest to model the dynamics of red blood cells (RBCs) motion in vessels or circulations using artificial microcapsules. Particularly, in some cases, it requires the homogeneous physic-chemical properties of capsules, such as uniform size, same shell structure and mechanical characteristics. Therefore, the most challenging work could be to develop a facile strategy to synthesis microcapsules with controlled properties-determined parameters. The preparation of monodisperse microcapsules involves emulsification of the disperse phase into the continuous phase which both are immiscible. There are several strategies been developed to fabricate capsules including batch methods (high-pressure valve homogenisers, static mixers, and rotor stator systems), electrospray techniques, and emulsification through membrane pores. These methods, however, require multistage emulsion processes, and capsules obtained with non-uniform properties and a largely wide distribution of sizes[4-5]. To overcome these problems, recently, microfluidic controlling techniques are introduced, by which monodisperse biopolymer capsules in micrometer size ranges are allowed to be generated in a single step. The main purpose of this study is to develop an approach of fabricating monodisperse biopolymer microcapsules with homogeneous properties on the base of microfluidic controlling components. Thereafter, the membrane properties of obtained capsules are proposed to be measured consisting of flowing a capsule suspension into an elongation flow. The deformation of capsules in the elongation flow can be divided into two regions: linear and non-linear zones. Surface shear elastic modulus of the shell in the linear region (small deformation) and membrane wrinkles instability or plastic deformation in the non-linear region are detected, respectively. Furthermore, thanks to the microfluidic techniques, the interfacial rheological properties of microcapsules are able to be modified via the synthetic procedures, such as the concentrations of chemicals and interfacial polymerization time. Results show that the physic-chemical properties of biopolymer capsules produced by the microfluidic route are very close for the same generating lot

Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow

We review modeling of astrocyte ion dynamics with a specific focus on the implications of so-called spatial potassium buffering, where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. We thus include the key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.Comment: 27 pages, 7 figure

Bioelectrical signals and ion channels in the modeling of multicellular patterns and cancer biophysics

Bioelectrical signals and ion channels are central to spatial patterns in cell ensembles, a problem of fundamental interest in positional information and cancer processes. We propose a model for electrically connected cells based on simple biological concepts: i) the membrane potential of a single cell characterizes its electrical state; ii) the long-range electrical coupling of the multicellular ensemble is realized by a network of gap junction channels between neighboring cells; and iii) the spatial distribution of an external biochemical agent can modify the conductances of the ion channels in a cell membrane and the multicellular electrical state. We focus on electrical effects in small multicellular ensembles, ignoring slow diffusional processes. The spatio-temporal patterns obtained for the local map of cell electric potentials illustrate the normalization of regions with abnormal cell electrical states. The effects of intercellular coupling and blocking of specific channels on the electrical patterns are described. These patterns can regulate the electrically-induced redistribution of charged nanoparticles over small regions of a model tissue. The inclusion of bioelectrical signals provides new insights for the modeling of cancer biophysics because collective multicellular states show electrical coupling mechanisms that are not readily deduced from biochemical descriptions at the individual cell level

On biomembrane electrodiffusive models

Two models are used in the literature, to study the electric behaviour of cellular membranes such as in protein aggregates, excitable media or ionic currents for examples. The first one is the Electroneutral Model based on Nernst-Planck and Poisson equations with a specific condition of microscopic electroneutrality. The second one is the Cable Model valid for long wavelengths based on an analogy between an electric cable and a cell. Convincing experiments have justified the Cable equation. First, we show that these two models are in contradiction. More precisely the assumption of electroneutrality is not considered in the Cable Model. The main difference between the two models is highlighted by the analysis of the well known voltage instability due to a negative differential conductance. Then, we derive a new semi-microscopic model (the Biomembrane Electrodiffusive Model, called BEM) valid for phenomena at any wavelength. The BEM is based on Nernst-Planck and Poisson equations but, doesn't imply microscopic electroneutrality. It reveals the capacitive behaviour of the membrane. In the limit of long wavelengths, one recovers the behaviour described within the Cable framework, as shown precisely in the study of the negative differential conductance analysis. Finally, we demonstrate the intimate link between the last models: the Cable Model appears as the limit of the BEM for large wavelengths with some prerequisites which are discussed. The effects of geometry and asymmetrical media are introduced