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.

Conducting and permeable states of cell membrane submitted to high voltage pulses: mathematical and numerical studies validated by the experiments.

The aim of this paper is to present a new model of in vitro cell electropermeabilization, which describes separately the conducting state and the permeable state of the membrane submitted to high voltage pulses. We first derive the model based on the experimental observations and we present the numerical methods to solve the non-linear partial differential equations. We then present numerical simulations that corroborate qualitatively the experimental data dealing with the uptake of propidium iodide (PI) after millipulses. This tends to justify the validity of our modeling. Forthcoming work will be to calibrate the parameters of the model for quantitative description of the uptake.