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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. [ABSTRACT FROM AUTHOR]

Chloride homeostasis is a critical determinant of the strength and robustness of inhibition mediated by GABAA receptors (GABAARs). The impact of changes in steady state Cl- gradient is relatively straightforward to understand, but how dynamic interplay between Cl- influx, diffusion, extrusion and interaction with other ion species affects synaptic signaling remains uncertain. Here we used electrodiffusion modeling to investigate the nonlinear interactions between these processes. Results demonstrate that diffusion is crucial for redistributing intracellular Cl- load on a fast time scale, whereas Cl2extrusion controls steady state levels. Interaction between diffusion and extrusion can result in a somato-dendritic Cl- gradient even when KCC2 is distributed uniformly across the cell. Reducing KCC2 activity led to decreased efficacy of GABAAR-mediated inhibition, but increasing GABAAR input failed to fully compensate for this form of disinhibition because of activity-dependent accumulation of Cl-. Furthermore, if spiking persisted despite the presence of GABAAR input, Cl- accumulation became accelerated because of the large Cl- driving force that occurs during spikes. The resulting positive feedback loop caused catastrophic failure of inhibition. Simulations also revealed other feedback loops, such as competition between Cl- and pH regulation. Several model predictions were tested and confirmed by [Cl-]i imaging experiments. Our study has thus uncovered how Cl- regulation depends on a multiplicity of dynamically interacting mechanisms. Furthermore, the model revealed that enhancing KCC2 activity beyond normal levels did not negatively impact firing frequency or cause overt extracellular K- accumulation, demonstrating that enhancing KCC2 activity is a valid strategy for therapeutic intervention. [ABSTRACT FROM AUTHOR]