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

Mechanism of an Intrinsic Oscillation in Rat Geniculate Interneurons

Depolarizing current injections produced a rhythmic bursting of action potentials - a bursting oscillation - in a set of local interneurons in the lateral geniculate nucleus (LGN) of rats. The current dynamics underlying this firing pattern have not been determined, though this cell type constitutes an important cellular component of thalamocortical circuitry, and contributes to both pathologic and non-pathologic brain states. We thus investigated the source of the bursting oscillation using pharmacological manipulations in LGN slices in vitro and in silico. 1. Selective blockade of calcium channel subtypes revealed that high-threshold calcium currentsI L andI P contributed strongly to the oscillation. 2. Increased extracellular K+ concentration (decreased K+currents) eliminated the oscillation. 3. Selective blockade of K+ channel subtypes demonstrated that the calcium-sensitive potassium current (I A H P ) was of primary importance. A morphologically simplified, multicompartment model of the thalamic interneuron characterized the oscillation as follows: 1. The low-threshold calcium currentI T provided the strong initial burst characteristic of the oscillation. 2. Alternating fluxes through high-threshold calcium channels andI A H P then provided the continuing oscillation's burst and interburst periods respectively. This interplay betweenI L andI A H P contrasts with the current dynamics underlying oscillations in thalamocortical and reticularis neurons, which primarily involveI T andI H , orI T andI A H P respectively. These findings thus point to a novel electrophysiological mechanism for generating intrinsic oscillations in a major thalamic cell type. Because local interneurons can sculpt the behavior of thalamocortical circuits, these results suggest new targets for the manipulation of ascending thalamocortical network activity.

An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms

In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na⁺, K⁺, Ca²⁺, and Cl⁻), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.

Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.

Estimation of neural network model parameters from local field potentials (LFPs)

Most modeling in systems neuroscience has been descriptive where neural representations such as ‘receptive fields’, have been found by statistically correlating neural activity to sensory input. In the traditional physics approach to modelling, hypotheses are represented by mechanistic models based on the underlying building blocks of the system, and candidate models are validated by comparing with experiments. Until now validation of mechanistic cortical network models has been based on comparison with neuronal spikes, found from the high-frequency part of extracellular electrical potentials. In this computational study we investigated to what extent the low-frequency part of the signal, the local field potential (LFP), can be used to validate and infer properties of mechanistic cortical network models. In particular, we asked the question whether the LFP can be used to accurately estimate synaptic connection weights in the underlying network. We considered the thoroughly analysed Brunel network comprising an excitatory and an inhibitory population of recurrently connected integrate-and-fire (LIF) neurons. This model exhibits a high diversity of spiking network dynamics depending on the values of only three network parameters. The LFP generated by the network was computed using a hybrid scheme where spikes computed from the point-neuron network were replayed on biophysically detailed multicompartmental neurons. We assessed how accurately the three model parameters could be estimated from power spectra of stationary ‘background’ LFP signals by application of convolutional neural nets (CNNs). All network parameters could be very accurately estimated, suggesting that LFPs indeed can be used for network model validation.

Most of what we have learned about brain networks in vivo has come from the measurement of spikes (action potentials) recorded by extracellular electrodes. The low-frequency part of these signals, the local field potential (LFP), contains unique information about how dendrites in neuronal populations integrate synaptic inputs, but has so far played a lesser role. To investigate whether the LFP can be used to validate network models, we computed LFP signals for a recurrent network model (the Brunel network) for which the ground-truth parameters are known. By application of convolutional neural nets (CNNs) we found that the synaptic weights indeed could be accurately estimated from ‘background’ LFP signals, suggesting a future key role for LFP in development of network models.

An Individual Interneuron Participates in Many Kinds of Inhibition and Innervates Much of the Mouse Visual Thalamus

One way to assess a neuron's function is to describe all its inputs and outputs. With this goal in mind, we used serial section electron microscopy to map 899 synaptic inputs and 623 outputs in one inhibitory interneuron in a large volume of the mouse visual thalamus. This neuron innervated 256 thalamocortical cells spread across functionally distinct subregions of the visual thalamus. All but one of its neurites were bifunctional, innervating thalamocortical and local interneurons while also receiving synapses from the retina. We observed a wide variety of local synaptic motifs. While this neuron innervated many cells weakly, with single en passant synapses, it also deployed specialized branches that climbed along other dendrites to form strong multi-synaptic connections with a subset of partners. This neuron's diverse range of synaptic relationships allows it to participate in a mix of global and local processing but defies assigning it a single circuit function.

Scalable Digital Neuromorphic Architecture for Large-Scale Biophysically Meaningful Neural Network With Multi-Compartment Neurons

Multicompartment emulation is an essential step to enhance the biological realism of neuromorphic systems and to further understand the computational power of neurons. In this paper, we present a hardware efficient, scalable, and real-time computing strategy for the implementation of large-scale biologically meaningful neural networks with one million multi-compartment neurons (CMNs). The hardware platform uses four Altera Stratix III field-programmable gate arrays, and both the cellular and the network levels are considered, which provides an efficient implementation of a large-scale spiking neural network with biophysically plausible dynamics. At the cellular level, a cost-efficient multi-CMN model is presented, which can reproduce the detailed neuronal dynamics with representative neuronal morphology. A set of efficient neuromorphic techniques for single-CMN implementation are presented with all the hardware cost of memory and multiplier resources removed and with hardware performance of computational speed enhanced by 56.59% in comparison with the classical digital implementation method. At the network level, a scalable network-on-chip (NoC) architecture is proposed with a novel routing algorithm to enhance the NoC performance including throughput and computational latency, leading to higher computational efficiency and capability in comparison with state-of-the-art projects. The experimental results demonstrate that the proposed work can provide an efficient model and architecture for large-scale biologically meaningful networks, while the hardware synthesis results demonstrate low area utilization and high computational speed that supports the scalability of the approach.

A computational model for gonadotropin releasing cells in the teleost fish medaka

Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca²⁺ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na⁺ currents (I_Na), high-voltage activated Ca²⁺ currents (I_Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I_Na is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by I_Ca. Unlike in rats, spontaneous I_Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by I_Na, and (3) the first pituitary cell model where the kinetics of the depolarizing currents, I_Na and I_Ca, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire I_Ca-based APs. We put a particular focus on how the big conductance K⁺ current (I_BK) modulates the AP shape. Interestingly, we find that I_BK can prolong AP duration in models that fire I_Ca-based APs, while it consistently shortens the duration of the predominantly I_Na-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire I_Na-mediated APs.

Excitable cells elicit electrical pulses called action potentials (APs), which are generated and shaped by a combination of ion channels in the cell membrane. Since one type of ion channels is permeable to Ca²⁺ ions, there is typically an influx of Ca²⁺ during an AP. Pituitary cells therefore use AP firing to regulate their cytosolic Ca²⁺ concentration, which in turn controls their hormone secretion rate. The amount of Ca²⁺ that enters during an AP depends strongly on how long it lasts, and it is therefore important to understand the mechanisms that control this. Pituitary APs are generally mediated by a combination of Ca²⁺ channels and Na⁺ channels, and the relative contributions of from the two vary between cell types, animal species and biological conditions. Previous computer models have predominantly been adapted to data from pituitary cells which tend to fire Ca²⁺-based APs. Here we develop a new model, adapted to data from pituitary cells in the fish medaka, which APs that are predominantly Na⁺-based, and compare its dynamical properties to the previous models that fire Ca²⁺-based APs.

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.

Biophysical network modeling of the dLGN circuit: Effects of cortical feedback on spatial response properties of relay cells

Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the dorsal lateral geniculate nucleus (dLGN) in shaping the visual signals is not properly understood. Placed on route from retina to primary visual cortex in the early visual pathway, a striking feature of the dLGN circuit is that both the relay cells (RCs) and interneurons (INs) not only receive feedforward input from retinal ganglion cells, but also a prominent feedback from cells in layer 6 of visual cortex. This feedback has been proposed to affect synchronicity and other temporal properties of the RC firing. It has also been seen to affect spatial properties such as the center-surround antagonism of thalamic receptive fields, i.e., the suppression of the response to very large stimuli compared to smaller, more optimal stimuli. Here we explore the spatial effects of cortical feedback on the RC response by means of a a comprehensive network model with biophysically detailed, single-compartment and multicompartment neuron models of RCs, INs and a population of orientation-selective layer 6 simple cells, consisting of pyramidal cells (PY). We have considered two different arrangements of synaptic feedback from the ON and OFF zones in the visual cortex to the dLGN: phase-reversed (‘push-pull’) and phase-matched (‘push-push’), as well as different spatial extents of the corticothalamic projection pattern. Our simulation results support that a phase-reversed arrangement provides a more effective way for cortical feedback to provide the increased center-surround antagonism seen in experiments both for flashing spots and, even more prominently, for patch gratings. This implies that ON-center RCs receive direct excitation from OFF-dominated cortical cells and indirect inhibitory feedback from ON-dominated cortical cells. The increased center-surround antagonism in the model is accompanied by spatial focusing, i.e., the maximum RC response occurs for smaller stimuli when feedback is present.

The functional role of the dorsal lateral geniculate nucleus (dLGN), placed on route from retina to primary visual cortex in the early visual pathway, is still poorly understood. A striking feature of the dLGN circuit is that dLGN cells not only receive feedforward input from the retina, but also a prominent feedback from cells in the visual cortex. It has been seen in experiments that cortical feedback modifies the spatial properties of dLGN cells in response to visual stimuli. In particular, it has been shown to increase the center-surround antagonism for flashing-spot and patch-grating visual stimuli, i.e., the suppression of responses to very large stimuli compared to smaller stimuli. Here we investigate the putative mechanisms behind this feature by means of a comprehensive network model of biophysically detailed neuron models for RCs and INs in the dLGN and orientation-selective cortical cells providing the feedback. Our results support that the experimentally observed feedback effects may be due to a phase-reversed (‘push-pull’) arrangement of the cortical feedback where ON-symmetry RCs receive (indirect) inhibitory feedback from ON-dominated cortical cell and excitation from OFF-dominated cortical cells, and vice versa for OFF-symmetry RCs.

Acetylcholine-dependent upregulation of TASK-1 channels in thalamic interneurons by a smooth muscle-like signalling pathway

KEY POINTS

The ascending brainstem transmitter acetylcholine depolarizes thalamocortical relay neurons while it induces hyperpolarization in local circuit inhibitory interneurons. Sustained K⁺ currents are modulated in thalamic neurons to control their activity modes; for the interneurons the molecular nature of the underlying ion channels is as yet unknown. Activation of TASK-1 K⁺ channels results in hyperpolarization of interneurons and suppression of their action potential firing. The modulation cascade involves a non-receptor tyrosine kinase, c-Src. The present study identifies a novel pathway for the activation of TASK-1 channels in CNS neurons that resembles cholinergic signalling and TASK-1 current modulation during hypoxia in smooth muscle cells.

ABSTRACT

The dorsal part of the lateral geniculate nucleus (dLGN) is the main thalamic site for state-dependent transmission of visual information. Non-retinal inputs from the ascending arousal system and inhibition provided by γ-aminobutyric acid (GABA)ergic local circuit interneurons (INs) control neuronal activity within the dLGN. In particular, acetylcholine (ACh) depolarizes thalamocortical relay neurons by inhibiting two-pore domain potassium (K_2P ) channels. Conversely, ACh also hyperpolarizes INs via an as-yet-unknown mechanism. By using whole cell patch-clamp recordings in brain slices and appropriate pharmacological tools we here report that stimulation of type 2 muscarinic ACh receptors induces IN hyperpolarization by recruiting the G-protein βγ subunit (Gβγ), class-1A phosphatidylinositol-4,5-bisphosphate 3-kinase, and cellular and sarcoma (c-Src) tyrosine kinase, leading to activation of two-pore domain weakly inwardly rectifying K⁺ channel (TWIK)-related acid-sensitive K⁺ (TASK)-1 channels. The latter was confirmed by the use of TASK-1-deficient mice. Furthermore inhibition of phospholipase Cβ as well as an increase in the intracellular level of phosphatidylinositol-3,4,5-trisphosphate facilitated the muscarinic effect. Our results have uncovered a previously unknown role of c-Src tyrosine kinase in regulating IN function in the brain and identified a novel mechanism by which TASK-1 channels are activated in neurons.

Effects of Small-World Rewiring Probability and Noisy Synaptic Conductivity on Slow Waves: Cortical Network

Physiological rhythms play a critical role in the functional development of living beings. Many biological functions are executed with an interaction of rhythms produced by internal characteristics of scores of cells. While synchronized oscillations may be associated with normal brain functions, anomalies in these oscillations may cause or relate the emergence of some neurological or neuropsychological pathologies. This study was designed to investigate the effects of topological structure and synaptic conductivity noise on the spatial synchronization and temporal rhythmicity of the waves generated by cells in the network. Because of holding the ability of clustering and randomizing with change of parameters, small-world (SW) network topology was chosen. The oscillatory activity of network was tried out by manipulating an insulated SW, cortical network model whose morphology is very close to real world. According to the obtained results, it was observed that at the optimal probabilistic rates of conductivity noise and rewiring of SW, powerful synchronized oscillatory small waves are generated in relation to the internal dynamics of cells, which are in line with the network's input. These two parameters were observed to be quite effective on the excitation-inhibition balance of the network. Accordingly, it may be suggested that the topological dynamics of SW and noisy synaptic conductivity may be associated with the normal and abnormal development of neurobiological structure.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

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.

Biophysical Network Modelling of the dLGN Circuit: Different Effects of Triadic and Axonal Inhibition on Visual Responses of Relay Cells

Despite its prominent placement between the retina and primary visual cortex in the early visual pathway, the role of the dorsal lateral geniculate nucleus (dLGN) in molding and regulating the visual signals entering the brain is still poorly understood. A striking feature of the dLGN circuit is that relay cells (RCs) and interneurons (INs) form so-called triadic synapses, where an IN dendritic terminal can be simultaneously postsynaptic to a retinal ganglion cell (GC) input and presynaptic to an RC dendrite, allowing for so-called triadic inhibition. Taking advantage of a recently developed biophysically detailed multicompartmental model for an IN, we here investigate putative effects of these different inhibitory actions of INs, i.e., triadic inhibition and standard axonal inhibition, on the response properties of RCs. We compute and investigate so-called area-response curves, that is, trial-averaged visual spike responses vs. spot size, for circular flashing spots in a network of RCs and INs. The model parameters are grossly tuned to give results in qualitative accordance with previous in vivo data of responses to such stimuli for cat GCs and RCs. We particularly investigate how the model ingredients affect salient response properties such as the receptive-field center size of RCs and INs, maximal responses and center-surround antagonisms. For example, while triadic inhibition not involving firing of IN action potentials was found to provide only a non-linear gain control of the conversion of input spikes to output spikes by RCs, axonal inhibition was in contrast found to substantially affect the receptive-field center size: the larger the inhibition, the more the RC center size shrinks compared to the GC providing the feedforward excitation. Thus, a possible role of the different inhibitory actions from INs to RCs in the dLGN circuit is to provide separate mechanisms for overall gain control (direct triadic inhibition) and regulation of spatial resolution (axonal inhibition) of visual signals sent to cortex.

Two types of interneurons in the mouse lateral geniculate nucleus are characterized by different h-current density

Although hyperpolarization-activated cyclic nucleotide-gated cation (HCN) channels and the corresponding h-current (I_h) have been shown to fundamentally shape the activity pattern in the thalamocortical network, little is known about their function in local circuit GABAergic interneurons (IN) of the dorsal part of the lateral geniculate nucleus (dLGN). By combining electrophysiological, molecular biological, immunohistochemical and cluster analysis, we characterized the properties of I_h and the expression profile of HCN channels in IN. Passive and active electrophysiological properties of IN differed. Two subclasses of IN were resolved by unsupervised cluster analysis. Small cells were characterized by depolarized resting membrane potentials (RMP), stronger anomalous rectification, higher firing frequency of faster action potentials (APs), appearance of rebound bursting, and higher I_h current density compared to the large IN. The depolarization exerted by sustained HCN channel activity facilitated neuronal firing. In addition to cyclic nucleotides, I_h in IN was modulated by PIP₂ probably based on the abundant expression of the HCN3 isoform. Furthermore, only IN with larger cell diameters expressed neuronal nitric oxide synthase (nNOS). It is discussed that I_h in IN is modulated by neurotransmitters present in the thalamus and that the specific properties of I_h in these cells closely reflect their modulatory options.

Functional Effects of Schizophrenia-Linked Genetic Variants on Intrinsic Single-Neuron Excitability: A Modeling Study

BACKGROUND

Recent genome-wide association studies 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 cells and identified possible common alterations in behavior across SCZ-related genes.

METHODS

We applied a biophysically detailed multicompartmental 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 calcium 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 the previously proposed deficits in synaptic communication and network behavior.

The subcellular distribution of T-type Ca2+ channels in interneurons of the lateral geniculate nucleus

Inhibitory interneurons (INs) in the lateral geniculate nucleus (LGN) provide both axonal and dendritic GABA output to thalamocortical relay cells (TCs). Distal parts of the IN dendrites often enter into complex arrangements known as triadic synapses, where the IN dendrite plays a dual role as postsynaptic to retinal input and presynaptic to TC dendrites. Dendritic GABA release can be triggered by retinal input, in a highly localized process that is functionally isolated from the soma, but can also be triggered by somatically elicited Ca²⁺-spikes and possibly by backpropagating action potentials. Ca²⁺-spikes in INs are predominantly mediated by T-type Ca²⁺-channels (T-channels). Due to the complex nature of the dendritic signalling, the function of the IN is likely to depend critically on how T-channels are distributed over the somatodendritic membrane (T-distribution). To study the relationship between the T-distribution and several IN response properties, we here run a series of simulations where we vary the T-distribution in a multicompartmental IN model with a realistic morphology. We find that the somatic response to somatic current injection is facilitated by a high T-channel density in the soma-region. Conversely, a high T-channel density in the distal dendritic region is found to facilitate dendritic signalling in both the outward direction (increases the response in distal dendrites to somatic input) and the inward direction (the soma responds stronger to distal synaptic input). The real T-distribution is likely to reflect a compromise between several neural functions, involving somatic response patterns and dendritic signalling.

Electrodiffusive model for astrocytic and neuronal ion concentration dynamics

The cable equation is a proper framework for modeling electrical neural signalling that takes place at a timescale at which the ionic concentrations vary little. However, in neural tissue there are also key dynamic processes that occur at longer timescales. For example, endured periods of intense neural signaling may cause the local extracellular K⁺-concentration to increase by several millimolars. The clearance of this excess K⁺ depends partly on diffusion in the extracellular space, partly on local uptake by astrocytes, and partly on intracellular transport (spatial buffering) within astrocytes. These processes, that take place at the time scale of seconds, demand a mathematical description able to account for the spatiotemporal variations in ion concentrations as well as the subsequent effects of these variations on the membrane potential. Here, we present a general electrodiffusive formalism for modeling of ion concentration dynamics in a one-dimensional geometry, including both the intra- and extracellular domains. Based on the Nernst-Planck equations, this formalism ensures that the membrane potential and ion concentrations are in consistency, it ensures global particle/charge conservation and it accounts for diffusion and concentration dependent variations in resistivity. We apply the formalism to a model of astrocytes exchanging ions with the extracellular space. The simulations show that K⁺-removal from high-concentration regions is driven by a local depolarization of the astrocyte membrane, which concertedly (i) increases the local astrocytic uptake of K⁺, (ii) suppresses extracellular transport of K⁺, (iii) increases axial transport of K⁺ within astrocytes, and (iv) facilitates astrocytic relase of K⁺ in regions where the extracellular concentration is low. Together, these mechanisms seem to provide a robust regulatory scheme for shielding the extracellular space from excess K⁺.

When neurons generate electrical signals they release potassium ions (K⁺) into the extracellular space. During periods of intense neural activity, the local extracellular K⁺ may increase drastically. If it becomes too high, it can lead to neural dysfunction. Astrocytes (a kind of glial cells) are involved in preventing this from happening. Astrocytes can take up excess K⁺, transport it intracellularly, and release it in regions where the concentration is lower. This process is called spatial buffering, and a full mechanistic understanding of it is currently lacking. The aim of this work is twofold: First, we develop a formalism for modeling ion concentration dynamics in the intra- and extracellular space. The formalism is general, and could be used to simulate many cellular processes. It accounts for ion transports due to diffusion (along concentration gradients) as well as electrical migration (along voltage gradients). It extends previous, related formalisms, which have focused only on intracellular dynamics. Secondly, we apply the formalism to model how astrocytes exchange ions with the extracellular space. We conclude that the membrane mechanisms possessed by astrocytes seem optimal for shielding the extracellular space from excess K⁺, and provide a full mechanistic description of the spatial (K⁺) buffering process.

Reciprocal inhibition and slow calcium decay in perigeniculate interneurons explain changes of spontaneous firing of thalamic cells caused by cortical inactivation

The role of cortical feedback in the thalamocortical processing loop has been extensively investigated over the last decades. With an exception of several cases, these searches focused on the cortical feedback exerted onto thalamo-cortical relay (TC) cells of the dorsal lateral geniculate nucleus (LGN). In a previous, physiological study, we showed in the cat visual system that cessation of cortical input, despite decrease of spontaneous activity of TC cells, increased spontaneous firing of their recurrent inhibitory interneurons located in the perigeniculate nucleus (PGN). To identify mechanisms underlying such functional changes we conducted a modeling study in NEURON on several networks of point neurons with varied model parameters, such as membrane properties, synaptic weights and axonal delays. We considered six network topologies of the retino-geniculo-cortical system. All models were robust against changes of axonal delays except for the delay between the LGN feed-forward interneuron and the TC cell. The best representation of physiological results was obtained with models containing reciprocally connected PGN cells driven by the cortex and with relatively slow decay of intracellular calcium. This strongly indicates that the thalamic reticular nucleus plays an essential role in the cortical influence over thalamo-cortical relay cells while the thalamic feed-forward interneurons are not essential in this process. Further, we suggest that the dependence of the activity of PGN cells on the rate of calcium removal can be one of the key factors determining individual cell response to elimination of cortical input.

A novel phase portrait for neuronal excitability

Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained a core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of FitzHugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which calcium channels control the two distinct firing modes of thalamocortical neurons.