An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain

Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.publishedVersio

Uncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis in Computational Neuroscience

Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the “raw” model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator

Electrodiffusive model for astrocytic and neuronal ion concentration dynamics

Electrical neural signalling typically takes place at the time-scale of milliseconds, and is typically modeled using the cable equation. This is a good approximation for processes when ionic concentrations vary little during the time course of a simulation. During periods of intense neural signalling, however, the local extracellular K+ concentration may increase by several millimolars. Clearance of excess K+ likely depends partly on diffusion in the extracellular space, partly on local uptake by- and intracellular transport within astrocytes. This process takes place at the time scale of seconds, and can not be modeled accurately without accounting for the spatiotemporal variations in ion concentrations. The work presented here consists of two main parts: First, we developed a general electrodiffusive formalism for modeling ion concentration dynamics in a one-dimensional geometry, including both an intra- and extracellular domain. The formalism was based on the Nernst-Planck equations. It ensures (i) consistency between the membrane potential and ion concentrations, (ii) global particle/charge conservation, and (iii) accounts for diffusion and concentration dependent variations in resistivities. Second, we applied the formalism to model how astrocytes exchange ions with the ECS, and identified the key astrocytic mechanisms involved in K+ removal from high concentration regions. We found that a local increase in extracellular K\textsuperscript{+} evoked a local depolarization of the astrocyte membrane, which at the same time (i) increased the local astrocytic uptake of K\textsuperscript{+}, (ii) suppressed extracellular transport of K+, (iii) increased transport of K+ within astrocytes, and (iv) facilitated astrocytic relase of K+ in extracellular low concentration regions. In summary, these mechanisms seem optimal for shielding the extracellular space from excess K+.Comment: 19 pages, 5 figures, 1 table (Equations 37 & 38 and the two first equations in Figure 2 were corrected May 30th 2013

Functional effects of schizophrenia-linked genetic variants on intrinsic single-neuron excitability: A modeling study

Background: Recent genome-wide association studies (GWAS) have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cell and identify possible common alterations in behavior across SCZ-related genes. Methods: We applied a biophysically detailed multi-compartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ, and used changes in neuron model parameters to represent the effects of these variants. Results: We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and Ca2+ transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ- related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree. Conclusions: Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside with the previously proposed deficits in synaptic communication and network behavior

Responses in fast-spiking interneuron firing rates to parameter variations associated with degradation of perineuronal nets

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A stepwise neuron model fitting procedure designed for recordings with high spatial resolution : Application to layer 5 pyramidal cells

© 2017 The Author(s). Published by Elsevier B. V. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.Background Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level. New method In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca2+ imaging. Result We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model. Comparison with existing methods Our approach combines features from several previously applied model-fitting strategies. The reduced-morphology neuron model obtained using our approach reliably reproduces the membrane-potential dynamics across the dendrites as predicted by the full-morphology model. Conclusions The network models produced using our method are cost-efficient and predict that interconnected L5PCs are able to amplify delta-range oscillatory inputs across a large range of network sizes and topologies, largely due to the medium after hyperpolarization mediated by the Ca2+-activated SK current.Peer reviewedFinal Published versio

A multi-compartment model for interneurons in the dorsal lateral geniculate nucleus

GABAergic interneurons (INs) in the dorsal lateral geniculate nucleus (dLGN) shape the information flow from retina to cortex, presumably by controlling the number of visually evoked spikes in geniculate thalamocortical (TC) neurons, and refining their receptive field. The INs exhibit a rich variety of firing patterns: Depolarizing current injections to the soma may induce tonic firing, periodic bursting or an initial burst followed by tonic spiking, sometimes with prominent spike-time adaptation. When released from hyperpolarization, some INs elicit rebound bursts, while others return more passively to the resting potential. A full mechanistic understanding that explains the function of the dLGN on the basis of neuronal morphology, physiology and circuitry is currently lacking. One way to approach such an understanding is by developing a detailed mathematical model of the involved cells and their interactions. Limitations of the previous models for the INs of the dLGN region prevent an accurate representation of the conceptual framework needed to understand the computational properties of this region. We here present a detailed compartmental model of INs using, for the first time, a morphological reconstruction and a set of active dendritic conductances constrained by experimental somatic recordings from INs under several different current-clamp conditions. The model makes a number of experimentally testable predictions about the role of specific mechanisms for the firing properties observed in these neurons. In addition to accounting for the significant features of all experimental traces, it quantitatively reproduces the experimental recordings of the action-potential- firing frequency as a function of injected current. We show how and why relative differences in conductance values, rather than differences in ion channel composition, could account for the distinct differences between the responses observed in two different neurons, suggesting that INs may be individually tuned to optimize network operation under different input conditions