Sensitivity analysis of the Poisson Nernst-Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model.

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.

Allosteric modulation of metabotropic glutamate receptors by chloride ions.

Metabotropic glutamate receptors (mGluRs) play key roles in the modulation of many synapses. Chloride (Cl(-)) is known to directly bind and regulate the function of different actors of neuronal activity, and several studies have pointed to the possible modulation of mGluRs by Cl(-). Herein, we demonstrate that Cl(-) behaves as a positive allosteric modulator of mGluRs. For example, whereas glutamate potency was 3.08 ± 0.33 µM on metabotropic glutamate (mGlu) 4 receptors in high-Cl(-) buffer, signaling activity was almost abolished in low Cl(-) in cell-based assays. Cl(-) potency was 78.6 ± 3.5 mM. Cl(-) possesses a high positive cooperativity with glutamate (Hill slope ≈6 on mGlu4), meaning that small variations in [Cl(-)] lead to large variations in glutamate action. Using molecular modeling and mutagenesis, we have identified 2 well-conserved Cl(-) binding pockets in the extracellular domain of mGluRs. Moreover, modeling of activity-dependent Cl(-) variations at GABAergic synapses suggests that these variations may be compatible with a dynamic modulation of the most sensitive mGluRs present in these synapses. Taken together, these data reveal a necessary role of Cl(-) for the glutamate activation of many mGluRs. Exploiting Cl(-) binding pockets may yield to the development of innovative regulators of mGluR activity.

Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.

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.