The emerging technological revolution in genetically encoded molecular sensors and super-resolution imaging provides neuroscientists with a pass to the real-time nano-world. On this small scale, however, classical principles of electrophysiology do not always apply. This is in large part because the nanoscopic heterogeneities in ionic concentrations and the local electric fields associated with individual ions and their movement can no longer be ignored. Here, we review basic principles of molecular electrodiffusion in the cellular environment of organized brain tissue. We argue that accurate interpretation of physiological observations on the nanoscale requires a better understanding of the underlying electrodiffusion phenomena.

/pdf/electrodiffusion-phenomena-in-neuroscience-a-neglected-16xyemdjkx.pdf

Electrodiffusion phenomena in neuroscience: a neglected companion.

Fast responses to an external threat depend on the rapid transmission of signals through a plant. Action potentials (APs) are proposed as such signals. Plant APs share similarities with their animal counterparts; they are proposed to depend on the activity of voltage-gated ion channels. Nonetheless, despite their demonstrated role in (a)biotic stress responses, the identities of the associated voltage-gated channels and transporters remain undefined in higher plants. By demonstrating the role of two potassium-selective channels in Arabidopsis thaliana in AP generation and shaping, we show that the plant AP does depend on similar Kv-like transport systems to those of the animal signal. We demonstrate that the outward-rectifying potassium-selective channel GORK limits the AP amplitude and duration, while the weakly-rectifying channel AKT2 affects membrane excitability. By computational modelling of plant APs, we reveal that the GORK activity not only determines the length of an AP but also the steepness of its rise and the maximal amplitude. Thus, outward-rectifying potassium channels contribute to both the repolarisation phase and the initial depolarisation phase of the signal. Additionally, from modelling considerations we provide indications that plant APs might be accompanied by potassium waves, which prime the excitability of the green cable.

/pdf/the-role-of-potassium-channels-in-arabidopsis-thaliana-long-5gb733elm9.pdf

The Role of Potassium Channels in Arabidopsis thaliana Long Distance Electrical Signalling: AKT2 Modulates Tissue Excitability While GORK Shapes Action Potentials

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

/pdf/effect-of-ionic-diffusion-on-extracellular-potentials-in-1wyj01jrp1.pdf

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Two mathematical models are part of the foundation of Computational neurophysiology; a) the Cable equation is used to compute the membrane potential of neurons, and, b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models a) and b) by comparing them to these more accurate schemes. The main assumption of a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant – at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

/pdf/an-evaluation-of-the-accuracy-of-classical-models-for-a2tky71pea.pdf

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

https://www.cell.com/biophysj/pdf/S0006-3495(15)01176-5.pdf

Intracellular Impedance Measurements Reveal Non-ohmic Properties of the Extracellular Medium around Neurons.

https://www.cell.com/biophysj/pdf/S0006-3495(13)00628-0.pdf

Electrodiffusion Models of Neurons and Extracellular Space Using the Poisson-Nernst-Planck Equations—Numerical Simulation of the Intra- and Extracellular Potential for an Axon Model

The extracellular space has an ambiguous role in neuroscience. It is present in every physiologically relevant system and often used as a measurement site in experimental recordings, but it has received subordinate attention compared to the intracellular domain. In computational modeling, it is often regarded as a passive, homogeneous resistive medium with a constant conductivity, which greatly simplifies the computation of extracellular potentials. However, novel studies have shown that local ionic diffusion and capacitive effects of electrically active membranes can have a substantial impact on the extracellular potential. These effects can not be described by traditional models, and they have been subject to recent theoretical and experimental analyses. We strive to give an overview over current progress in modeling the extracellular space with special regard towards the concentration and potential dynamics on different temporal and spatial scales. Three models with distinct assumptions and levels of detail are compared both theoretically and by means of numerical simulations: the classical volume conductor (VC) model, which is most frequently used in form of the line source approximation (LSA); the biophysically detailed, but computationally intensive Poisson-Nernst-Planck model of electrodiffusion (PNP); and an intermediate model called the electroneutral model (EN). The results clearly show that there is no one model for all applications, as they show significantly different responses - especially close to neuronal membranes. Finally, we list some common use cases for model simulations and give recommendations on which model to use in each situation.

A comparison of computational models for the extracellular potential of neurons.

The extracellular space has an ambiguous role in neuroscience. It is present in every physiologically relevant system and often used as a measurement site in experimental recordings, but it has received subordinate attention compared to the intracellular domain. In computational modeling, it is often regarded as a passive, homogeneous resistive medium with a constant conductivity, which greatly simplifies the computation of extracellular potentials. However, recent studies have shown that local ionic diffusion and capacitive effects of electrically active membranes can have a substantial impact on the extracellular potential. These effects can not be described by traditional models, and they have been subject to theoretical and experimental analyses. We strive to give an overview over recent progress in modeling the extracellular space with special regard towards the concentration and potential dynamics on different temporal and spatial scales. Three models with distinct assumptions and levels of detail are compared both theoretically and by means of numerical simulations: the classical volume conductor (VC) model, which is most frequently used in form of the line source approximation (LSA); the very detailed, but computationally intensive Poisson-Nernst-Planck model of electrodiffusion (PNP); and an intermediate one called the electroneutral model (EN). The results clearly show that there is no one model for all applications, as they show significantly different responses especially close to neuronal membranes. Finally, we list some common use cases for model simulations and give recommendations on which model to use in each situation.

Jurgis Pods

Papers

Electrodiffusion Models of Neurons and Extracellular Space Using the Poisson-Nernst-Planck Equations—Numerical Simulation of the Intra- and Extracellular Potential for an Axon Model

A comparison of computational models for the extracellular potential of neurons.

A Comparison of Computational Models for the Extracellular Potential of Neurons