Stéphanie Portet

Ionic wave propagation along actin filaments.

We investigate the conditions enabling actin filaments to act as electrical transmission lines for ion flows along their lengths. We propose a model in which each actin monomer is an electric element with a capacitive, inductive, and resistive property due to the molecular structure of the actin filament and viscosity of the solution. Based on Kirchhoffs laws taken in the continuum limit, a nonlinear partial differential equation is derived for the propagation of ionic waves. We solve this equation in two different regimes. In the first, the maximum propagation velocity wave is found in terms of Jacobi elliptic functions. In the general case, we analyze the equation in terms of Fisher-Kolmogoroff modes with both localized and extended wave characteristics. We propose a new signaling mechanism in the cell, especially in neurons.

A Quantitative Kinetic Model for the in Vitro Assembly of Intermediate Filaments from Tetrameric Vimentin

In vitro assembly of intermediate filament proteins is a very rapid process. It starts without significant delay by lateral association of tetramer complexes into unit-length filaments (ULFs) after raising the ionic strength from low salt to physiological conditions (100 mm KCl). We employed electron and scanning force microscopy complemented by mathematical modeling to investigate the kinetics of in vitro assembly of human recombinant vimentin. From the average length distributions of the resulting filaments measured at increasing assembly times we simulated filament assembly and estimated specific reaction rate parameters. We modeled eight different potential pathways for vimentin filament elongation. Comparing the numerical with the experimental data we conclude that a two-step mechanism involving rapid formation of ULFs followed by ULF and filament annealing is the most robust scenario for vimentin assembly. These findings agree with the first two steps of the previously proposed three-step assembly model (Herrmann, H., and Aebi, U. (1998) Curr. Opin. Struct. Biol. 8, 177-185). In particular, our modeling clearly demonstrates that end-to-end annealing of ULFs and filaments is obligatory for forming long filaments, whereas tetramer addition to filament ends does not contribute significantly to filament elongation.

Elastic vibrations in seamless microtubules

Parameters characterizing elastic properties of microtubules, measured in several recent experiments, reflect an anisotropic character. We describe the microscopic dynamical properties of microtubules using a discrete model based on an appropriate lattice of dimers. Adopting a harmonic approximation for the dimer–dimer interactions and estimating the lattice elastic constants, we make predictions regarding vibration dispersion relations and vibration propagation velocities. Vibration frequencies and velocities are expressed as functions of the elastic constants and of the geometrical characteristics of the microtubules. We show that vibrations which propagate along the protofilament do so significantly faster than those along the helix.

Weightlessness acts on human breast cancer cell line MCF-7

Because cells are sensitive to mechanical forces, weightlessness might act on stress-dependent cell changes. Human breast cancer cells MCF-7, flown in space in a Photon capsule, were fixed after 1.5, 22 and 48 h in orbit. Cells subjected to weightlessness were compared to 1 g in-flight and ground controls. Post-flight, fluorescent labeling was performed to visualize cell proliferation (Ki-67), three cytoskeleton components and chromatin structure. Confocal microscopy and image analysis were used to quantify cycling cells and mitosis, modifications of the cytokeratin network and chromatin structure. Several main phenomena were observed in weightlessness: The perinuclear cytokeratin network and chromatin structure were looser; More cells were cycling and mitosis was prolonged. Finally, cell proliferation was reduced as a consequence of a cell-cycle blockade; Microtubules were altered in many cells. The results reported in the first point are in agreement with basic predictions of cellular tensegrity. The prolongation of mitosis can be explained by an alteration of microtubules. We discuss here the different mechanisms involved in weightlessness alteration of microtubules: i) alteration of their self-organization by reaction-diffusion processes, and a mathematical model is proposed, ii) activation or deactivation of microtubules stabilizing proteins, acting on both microtubule and microfilament networks in cell cortex.

Organization of the cytokeratin network in an epithelial cell.

The cytoskeleton is a dynamic three-dimensional structure mainly located in the cytoplasm. It is involved in many cell functions such as mechanical signal transduction and maintenance of cell integrity. Among the three cytoskeletal components, intermediate filaments (the cytokeratin in epithelial cells) are the best candidates for this mechanical role. A model of the establishment of the cytokeratin network of an epithelial cell is proposed to study the dependence of its structural organization on extracellular mechanical environment. To implicitly describe the latter and its effects on the intracellular domain, we use mechanically regulated protein synthesis. Our model is a hybrid of a partial differential equation of parabolic type, governing the evolution of the concentration of cytokeratin, and a set of stochastic differential equations describing the dynamics of filaments. Each filament is described by a stochastic differential equation that reflects both the local interactions with the environment and the non-local interactions via the past history of the filament. A three-dimensional simulation model is derived from this mathematical model. This simulation model is then used to obtain examples of cytokeratin network architectures under given mechanical conditions, and to study the influence of several parameters.

Epidemiological implications of mobility between a large urban centre and smaller satellite cities.

An SIR infectious disease propagation model is considered that incorporates mobility of individuals between a large urban centre and smaller satellite cities. Because of the difference in population sizes, the urban centre has standard incidence and satellite cities have mass action incidence. It is shown that the general basic reproduction number

Keratin dynamics: modeling the interplay between turnover and transport

{\mathcal {R}}_{0}

Gravitational symmetry breaking leads to a polar liquid crystal phase of microtubules in vitro.

R0 acts as a threshold between global asymptotic stability of the disease free equilibrium and disease persistence. The case of Winnipeg (MB, Canada) and some neighbouring satellite communities is then considered numerically to complement the mathematical analysis, highlighting the importance of taking into account not only