Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst-Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred experimentally. It is crucial to understand how the mathematical model (and resulting simulations) depend on specific values of these parameters. Here we develop a rigorous approach based on the sensitivity equation for the electrodiffusion model. To illustrate the proposed methodology, we investigate the sensitivity of the electrical response of a node of Ranvier with respect to ionic diffusion coefficients and the membrane dielectric permittivity.

U1 - https://www.ncbi.nlm.nih.gov/pubmed/30187223?dopt=Abstract ER - TY - JOUR T1 - Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation. JF - PLoS One Y1 - 2016 A1 - Dione, Ibrahima A1 - Deteix, Jean A1 - Briffard, Thomas A1 - Chamberland, Eric A1 - Nicolas Doyon AB -In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.

VL - 11 IS - 8 U1 - http://www.ncbi.nlm.nih.gov/pubmed/27548674?dopt=Abstract ER - TY - JOUR T1 - Inhibitory synaptic plasticity: spike timing-dependence and putative network function. JF - Front Neural Circuits Y1 - 2013 A1 - Vogels, T P A1 - Froemke, R C A1 - Nicolas Doyon A1 - Gilson, M A1 - Haas, J S A1 - Liu, R A1 - Maffei, A A1 - Miller, P A1 - Wierenga, C J A1 - Woodin, M A A1 - Zenke, F A1 - Sprekeler, H KW - Action Potentials KW - Animals KW - Humans KW - Inhibitory Postsynaptic Potentials KW - Nerve Net KW - Neural Inhibition KW - Neuronal Plasticity KW - Synapses KW - Time Factors AB -While the plasticity of excitatory synaptic connections in the brain has been widely studied, the plasticity of inhibitory connections is much less understood. Here, we present recent experimental and theoretical findings concerning the rules of spike timing-dependent inhibitory plasticity and their putative network function. This is a summary of a workshop at the COSYNE conference 2012.

VL - 7 U1 - http://www.ncbi.nlm.nih.gov/pubmed/23882186?dopt=Abstract ER -