Bouchra Aylaj

Biological and mathematical modeling of melanocyte development.

We aim to evaluate environmental and genetic effects on the expansion/proliferation of committed single cells during embryonic development, using melanoblasts as a paradigm to model this phenomenon. Melanoblasts are a specific type of cell that display extensive cellular proliferation during development. However, the events controlling melanoblast expansion are still poorly understood due to insufficient knowledge concerning their number and distribution in the various skin compartments. We show that melanoblast expansion is tightly controlled both spatially and temporally, with little variation between embryos. We established a mathematical model reflecting the main cellular mechanisms involved in melanoblast expansion, including proliferation and migration from the dermis to epidermis. In association with biological information, the model allows the calculation of doubling times for melanoblasts, revealing that dermal and epidermal melanoblasts have short but different doubling times. Moreover, the number of trunk founder melanoblasts at E8.5 was estimated to be 16, a population impossible to count by classical biological approaches. We also assessed the importance of the genetic background by studying gain- and loss-of-function β-catenin mutants in the melanocyte lineage. We found that any alteration of β-catenin activity, whether positive or negative, reduced both dermal and epidermal melanoblast proliferation. Finally, we determined that the pool of dermal melanoblasts remains constant in wild-type and mutant embryos during development, implying that specific control mechanisms associated with cell division ensure half of the cells at each cell division to migrate from the dermis to the epidermis. Modeling melanoblast expansion revealed novel links between cell division, cell localization within the embryo and appropriate feedback control through β-catenin.

Melanoblast proliferation dynamics during mouse embryonic development. Modeling and validation

In this paper, we are looking for mathematical modeling of mouse embryonic melanoblast proliferation dynamics, taking into account, the expression level of β-catenin. This protein plays an important role into the whole signal pathway process. Different assumptions on some unobservable features lead to different candidate models. From real data measured, from biological experiments and from a priori biological knowledge, it was able to validate or invalidate some of the candidate models. Data assimilation and parameter identification allowed us to derive a mathematical model that is in very good agreement with biological data. As a result, the produced model can give tracks for biologists into their biological investigations and experimental evidence. Another interest is the use of this model for robust hidden parameter identification like double times or number of founder melanoblasts.

Asymptotic behaviour of state trajectories for a class of tubular reactor non-linear models

We prove the global existence of the state trajectories for a class of non-linear systems arising from convection-dispersion-reaction processes. It is also shown that there is at least one steady state in the set of physically feasible states for such systems. The uniqueness and the stability analysis of this steady-state solution are discussed. Our approach is based on the analysis of a non-linear set of partial differential equations, using the upper and lower solutions, dissipativity properties, a subtangential condition and the positivity of the related C0-semigroup.

Convergence of Numerical Schemes to a Nonlinear Kinetic Model of Population Dynamics with Nonlocal Boundary Conditions

We examine existence and uniqueness of a global solution and some basic mathematical issues associated with the development of a numerical scheme for a model of a tumor-immune system interaction. The system consists of nonlinear transport equations with a bilinear operator like a Boltzmann type and with a nonlocal boundary condition. We construct a numerical scheme as a combination of a

State Trajectories Analysis for a Class of Tubular Reactor Nonlinear Nonautonomous Models

S(t)

Equilibrium Profiles for a Class of Tubular Reactor Nonlinear Models

-operator semigroup associated with the continuous problem and

Direct contact and environmental contaminations are responsible for HEV transmission in pigs.

P^\Delta

Global weak solution for a multi-stage physiologically structured population model with resource interaction

projection operator on the discrete space. The three estimates, (1)

Trajectory analysis of nonlinear kinetic models of population dynamics of several species

L^\infty

New Results - Dynamics of active particles with application to immune cells

bound, (2) a uniform total variation bound, and (3)