Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation.

We propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data. The paper proposes efficient numerical tools for forthcoming optimized procedures of cell transfection.

Reclamation of river dredged sediments polluted by PAHs by co-composting with green waste.

Polluted dredged sediments are classified as waste and cannot be re-used in civil and environmental engineering nor in agriculture, posing serious logistical, economic and environmental problems for their management. We tested co-composting of sediments (S) slightly polluted by PAHs with urban green waste (GW), as a sustainable technique to both degrade the organic pollutants and lend to sediments suitable properties to be reused as technosol. Four treatments were tested: sediments only (S), GW only (GW), 1:1 w:w S:GW (SGW1:1), and 3:1 w:w S:GW (SGW3:1) for a co-composting period of one year. The co-composting materials underwent to an initial short and moderate thermophilic phase. However, at the end of the co-composting process, SGW3:1 and SGW1:1 achieved suitable physical and chemical properties as plant substrate in terms of organic C, N and humic substances contents, electrical conductivity and bulk density. In the first six months of treatment, the PAHs concentration in SGW3:1 and SGW1:1 was reduced by 26% and 57%, respectively, reaching values below under 1mgg(-1), whereas such a reduction in S alone was observed only after nine months. We concluded that co-composting with green waste can be a suitable approach for reclamation of dredged sediments opening opportunities for their use as technosol or as plant growing substrate.

A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity.

In this article, we study in detail the fluid dynamics system proposed in Clarelli et al. (2013, J. Math. Biol., 66, 1387-1408) to model the formation of cyanobacteria biofilms. After analysing the linear stability of the unique non-trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of a cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed. All these elements enable us to control and to validate the model we have already derived and to present some numerical simulations in the 2D and the 3D cases.

A hybrid mathematical model for self-organizing cell migration in the zebrafish lateral line.

In this paper we propose a discrete in continuous mathematical model for the morphogenesis of the posterior lateral line system in zebrafish. Our model follows closely the results obtained in recent biological experiments. We rely on a hybrid description: discrete for the cellular level and continuous for the molecular level. We prove the existence of steady solutions consistent with the formation of particular biological structure, the neuromasts. Dynamical numerical simulations are performed to show the behavior of the model and its qualitative and quantitative accuracy to describe the evolution of the cell aggregate.

A fluid dynamics model of the growth of phototrophic biofilms.

A system of nonlinear hyperbolic partial differential equations is derived using mixture theory to model the formation of biofilms. In contrast with most of the existing models, our equations have a finite speed of propagation, without using artificial free boundary conditions. Adapted numerical scheme will be described in detail and several simulations will be presented in one and more space dimensions in the particular case of cyanobacteria biofilms. Besides, the numerical scheme we present is able to deal in a natural and effective way with regions where one of the phases is vanishing.

A spatial model of cellular molecular trafficking including active transport along microtubules.

We consider models of Ran-driven nuclear transport of molecules such as proteins in living cells. The mathematical model presented is the first to take into account for the active transport of molecules along the cytoplasmic microtubules. All parameters entering the models are thoroughly discussed. The model is tested by numerical simulations based on discontinuous Galerkin finite element methods. The numerical experiments are compared to the behavior observed experimentally.