A mathematical derivation of size spectra in fish populations.

Taking into account a predator/prey size ratio in a size-structured population model leads to a partial derivative equation of which we study the properties. By expliciting the structure of the attractor of this equation, it is shown that a simple mechanism, size-based opportunistic predation, can explain the stability in the shape of size spectra observed in various marine ecosystems.

Phytoplankton dynamics.

We present a model of the phytoplankton dynamics. The distribution of the size of the phytoplankton aggregates is described by a non-linear transport equation that contains terms responsible for the growth of phytoplankton aggregates, their fragmentation and coagulation. We study asymptotic behaviour of moments of the solutions and we explain why phytoplankton tends to create large aggregates.

Intermediate filament networks: in vitro and in vivo assembly models.

We propose two systems of ordinary differential equations modeling the assembly of intermediate filament networks. The first one describes the in vitro intermediate filament assembly dynamics. The second one deals with the in vivo evolution of cytokeratin, which is the intermediate filament protein expressed by epithelial cells. The in vitro model is then briefly analyzed in a simplified case.

A mathematical study of a two-regional population growth model.

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.

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.