Biology subjects

Halnes, G.

Publications and source records attributed to Halnes, G..

11 recordsLinked to original sources

bioRxiv2026

Functional distinction between ionic and electric ephaptic effects on neuronal firing dynamics

Neuronal activity alters extracellular ion concentrations and electric potentials. Ephaptic effects refer to the feedback influence that these extracellular changes can have on neuronal activity. While electric ephaptic effects occur on a fast timescale due to extracellular potential perturbations, ionic ephaptic effects are driven by slower, accumulative changes in ion concentrations. Among the previous computational studies of ephaptic effects, the vast majority have focused exclusively on electric effects, while ionic ephaptic effects have largely been neglected. In this work, we present an electrodiffusive computational framework consisting of two-compartment neurons that interact via a shared extracellular space. By accounting for both electric potentials and ion-concentration dynamics in a self-consistent manner, our framework enables us to explore the relative roles of electric and ionic ephaptic effects. Through numerical experiments, we demonstrate that ionic and electric ephaptic interactions play very different roles. While ionic ephaptic interactions increase population firing rates, electric ephaptic interactions primarily drive subtle shifts in spike timing. Furthermore, we show that these spike shifts cause the phase difference (the distance in spike times between a small collection of neurons) to converge to a stable, unique phase difference, which we coin the ephaptic intrinsic phase preference. Author summaryNeurons predominantly communicate through synapses: specialized contact points where a brief electrical signal, known as a spike or action potential, in one neuron influences another. Neurons generate these spikes by exchanging ions with the surrounding extracellular space. This way, spiking neurons alter extracellular ion concentrations and electric potentials. Since neurons are sensitive to such changes in their environment, they can also influence one another indirectly through the shared extracellular medium. This form of non-synaptic interaction is known as ephaptic coupling. Most computational models of neuronal activity neglect ephaptic interactions, and those that include them typically consider only electric effects while ignoring ionic contributions. As a result, the relative roles of electric and ionic ephaptic effects remain poorly understood. Here, we introduce a computational framework that accounts for both mechanisms in a self-consistent way. Our results show a functional distinction: ionic ephaptic effects act slowly, regulating population firing rates, whereas electric ephaptic effects act on millisecond timescales and subtly shift spike timing. These shifts cause spike-time differences between neurons to converge to a stable value, a phenomenon we call ephaptic intrinsic phase preference.

neuroscience↗

bioRxiv2023

Interplay of CaHVA and Ca2+-activated K+ channels affecting firing rate in perineuronal net disruption

Perineuronal nets (PNNs) are extracellular matrix structures consisting of proteoglycans crosslinked to hyaluronan. They wrap around subgroups of individual neurons in the brain, primarily parvalbumin positive inhibitory neurons. The nets have been found to affect conductances and activation curves of certain ion channels, including Ca2+-activated K+ and high-voltage-activated Ca2+ channels. We studied how PNN related parameters affected the firing rate of one-compartment neuron models. We found that the direct effect of the CaHVA current on firing rate was small, while it had a much larger indirect effect on firing rate through initiation of the SK current. Upregulation of the SK conductance similarly had a pronounced effect on the firing rate. The SK currents therefore acted as the main determinant of firing rate out of these two mechanisms. We shifted the CaHVA channel activation by 14.5 mV and increased the SK conductance by a factor of 3.337, consistent with experimental findings on PNN breakdown in the literature. We studied this in nine different models and found a reduction in firing rate in some, but not all, of these models.

neuroscience↗

bioRxiv2022

Brain signal predictions from multi-scale networks using a linearized framework

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies ([lsim] 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models ({gtrsim} 106 neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials ( spikes) or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin. Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for. The work also constitutes a major advance in computational efficacy of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework. Author summaryUnderstanding the brains function and activity in healthy and pathological states across spatial scales and times spanning entire lives is one of humanitys great undertakings. In experimental and clinical work probing the brains activity, a variety of electric and magnetic measurement techniques are routinely applied. However interpreting the extracellularly measured signals remains arduous due to multiple factors, mainly the large number of neurons contributing to the signals and complex interactions occurring in recurrently connected neuronal circuits. To understand how neurons give rise to such signals, mechanistic modeling combined with forward models derived using volume conductor theory has proven to be successful, but this approach currently does not scale to the systems level (encompassing millions of neurons or more) where simplified or abstract neuron representations typically are used. Motivated by experimental findings implying approximately linear relationships between times of neuronal action potentials and extracellular population signals, we provide a biophysics-based method for computing causal filters relating spikes and extracellular signals that can be applied with spike times or rates of large-scale neuronal network models for predictions of population signals without relying on ad hoc approximations.

neuroscience↗

bioRxiv2021

Validating a computational framework for ionicelectrodiffusion with cortical spreading depression as a case study

Cortical spreading depression (CSD) is a wave of pronounced depolarization of brain tissue accompanied by substantial shifts in ionic concentrations and cellular swelling. Here, we validate a computational framework for modelling electrical potentials, ionic movement, and cellular swelling in brain tissue during CSD. We consider different model variations representing wild type or knock-out/knock-down mice and systematically compare the numerical results with reports from a selection of experimental studies. We find that the data for several CSD hallmarks obtained computationally, including wave propagation speed, direct current shift duration, peak in extracellular K+ concentration as well as a pronounced shrinkage of extracellular space, are well in line with what has previously been observed experimentally. Further, we assess how key model parameters including cellular diffusivity, structural ratios, membrane water and/or K+ permeabilities affect the set of CSD characteristics. Significance StatementMovement of ions and molecules in and between cellular compartments is fundamental for brain function. Cortical spreading depression (CSD) is associated with dramatic failure of brain ion homeostasis. Better understanding the sequence of events in CSD could thus provide new insight into physiological processes in the brain. Despite extensive experimental research over the last decades, even basic questions related to mechanisms underlying CSD remain unanswered. Computational modelling can play an important role going forward, since simulation studies can address hypotheses that are difficult to target experimentally. Here, we assess the physiological validity of a novel mathematical framework for detailed modelling of brain electrodiffusion and osmosis - and provide a platform for in silico studies of CSD and other cerebral electro-mechanical phenomena.

neuroscience↗

bioRxiv2020

An electrodiffusive neuron-extracellular-glia model with somatodendritic interactions

Computational modeling in neuroscience has largely focused on simulating the electrical activity of neurons, while ignoring other components of brain tissue, such as glial cells and the extracellular space. As such, most existing models can not be used to address pathological conditions, such as spreading depression, which involves dramatic changes in ion concentrations, large extracellular potential gradients, and glial buffering processes. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine multicompartmental 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 neuronal somatic action potentials, and dendritic calcium spikes, (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. We demonstrate that the edNEG model performs realistically as a local and closed system, i.e., that it maintains a steady state for moderate neural activity, but experiences concentration-dependent effects, such as altered firing patterns and homeostatic breakdown, when the activity level becomes too intense. Furthermore, we study the role of glia in making the neuron more tolerable to hyperactive firing and in limiting neuronal swelling. Finally, we discuss how the edNEG model can be integrated with previous spatial continuum models of spreading depression to account for effects of neuronal morphology, action potential generation, and dendritic Ca2+ spikes which are currently not included in these models. Author summaryNeurons communicate by electrical signals mediated by the movement of ions across the cell membranes. The ionic flow changes the ion concentrations on both sides of the cell membranes, but most modelers of neurons assume ion concentrations to remain constant. Since the neuronal membrane contains structures called ion pumps and cotransporters that work to maintain close-to baseline ion concentrations, and the brain contains a cell type called astrocytes that contribute in keeping an appropriate ionic environment for neurons, the assumption is justifiable in many scenarios. However, for several pathological conditions, such as epilepsy and spreading depression, the ion concentrations may vary dramatically. To study these scenarios, we need models that account for changes in ion concentrations. In this paper, we present what we call the electrodiffusive neuron-extracellular-glia model (edNEG), which keeps track of all ions in a closed system containing a neuron, the extracellular space surrounding it, and an astrocytic "domain". The edNEG model ensures a complete and consistent relationship between ion concentrations and charge conservation. We envision that the model can be used to study a range of pathological conditions such as spreading depression and, hence, be of great value for the field of neuroscience.

neuroscience↗

bioRxiv2020

Biophysical modeling of the neural origin of EEG and MEG signals

Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techniques for non-invasively studying cognition and disease in the human brain. These signals are known to originate from cortical neural activity, typically described in terms of current dipoles. While the link between cortical current dipoles and EEG/MEG signals is relatively well understood, surprisingly little is known about the link between different kinds of neural activity and the current dipoles themselves. Detailed biophysical modeling has played an important role in exploring the neural origin of intracranial electric signals, like extracellular spikes and local field potentials. However, this approach has not yet been taken full advantage of in the context of exploring the neural origin of the cortical current dipoles that are causing EEG/MEG signals. Here, we present a method for reducing arbitrary simulated neural activity to single current dipoles. We find that the method is applicable for calculating extracranial signals, but less suited for calculating intracranial electrocorticography (ECoG) signals. We demonstrate that this approach can serve as a powerful tool for investigating the neural origin of EEG/MEG signals. This is done through example studies of the single-neuron EEG contribution, the putative EEG contribution from calcium spikes, and from calculating EEG signals from large-scale neural network simulations. We also demonstrate how the simulated current dipoles can be used directly in combination with detailed head models, allowing for simulated EEG signals with an unprecedented level of biophysical details. In conclusion, this paper presents a framework for biophysically detailed modeling of EEG and MEG signals, which can be used to better our understanding of non-inasively measured neural activity in humans. Graphical abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=103 SRC="FIGDIR/small/181875v1_ufig1.gif" ALT="Figure 1"> View larger version (28K): org.highwire.dtl.DTLVardef@47f029org.highwire.dtl.DTLVardef@e8244dorg.highwire.dtl.DTLVardef@a765c1org.highwire.dtl.DTLVardef@96550_HPS_FORMAT_FIGEXP M_FIG C_FIG HighlightsO_LICurrent dipoles are computed from biophysically detailed simulated neuron and network activity C_LIO_LIExtracted current dipoles allow for accurate computation of EEG and MEG signals in simplified and detailed head models C_LIO_LICurrent-diplole approximation generally not suitable for accurate calculations of ECoG signals C_LIO_LIMethod provides biophysics-based link between detailed neural activity and systems-level signals C_LI

neuroscience↗

bioRxiv2020

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

Most neuronal models are based on the assumption that ion concentrations remain constant during the simulated period, and do not account for possible effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials. Here, we present what is, to our knowledge, 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 model, which we refer to as the electrodiffusive Pinsky-Rinzel (edPR) model, is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron, where we have included homeostatic mechanisms and ion-specific leakage currents. Whereas the main dynamical variable in the original PR model is the transmembrane potential, the edPR model in addition keeps track of all ion concentrations (Na+, K+, Ca2+, and Cl-), electrical potentials, and the electrical conductivities in the intra- as well as extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity, when the homeostatic mechanisms succeed in maintaining ion concentrations close to baseline. For higher activity levels, homeostasis becomes incomplete, and the edPR model diverges from the PR model, as it accounts for changes in neuronal firing properties due to deviations from baseline ion concentrations. Whereas the focus of this work is to present and analyze the edPR model, we envision that it will become useful for the field in two main ways. Firstly, as it relaxes a set of 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 is a supplement to the PR model and should replace it in simulations of scenarios in which ion concentrations vary over time. As it is applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy. Author summaryNeurons 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 in a biophysically consistent way does account for the effects of ion concentration variations. We here 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 use for simulating a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.

neuroscience↗

bioRxiv2018

BK channels have opposite effects on sodium versus calcium-mediated action potentials in endocrine pituitary cells.

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 (INa), high-voltage activated Ca2+ currents (ICa), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where INa is largely inactivated at the resting potential, and spontaneous APs are exclusively mediated by ICa. As a part of the previous modeling studies, a paradoxical role was identified for the big conductance K+ current (IBK), which was found to prolong the duration of ICa-mediated APs, and sometimes give rise to pseudo-plateau bursts, contrary to what one would expect from a hyperpolarizing current. Unlike in rats, spontaneous INa-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop the, to our knowledge, first computational model of a pituitary cell that fires INa-mediated APs. Although we constrain the model to experimental data from gonadotrope cells in the teleost fish medaka (Oryzias latipes), it may likely provide insights also into other pituitary cell types that fire INa-mediated APs. In the current work, we use the model to explore how the effect of IBK depends on the AP generating mechanisms of pituitary cells. We do this by comparing simulations on the medaka gonadotrope model (two versions thereof) with simulations on a previously developed model of a rat pituitary cell. Interestingly, we find that IBK has the opposite effect on APs in the two models, i.e. it reduces the duration of already fast INa-mediated APs in the medaka model, and prolongs the duration of already slow ICa-mediated APs in the rat model.\n\nAuthor summaryExcitable cells elicit electrical pulses called action potentials (APs), which are generated and shaped by a combination of ion channels in the cell membrane. While neurons use APs for interneuronal communication and heart cells use them to generate heart-beats, pituitary cells use APs to regulate their cytosolic Ca2+ concentration, which in turn controls their hormone secretion rate. The amount of Ca2+ that enters the pituitary cell during an AP depends strongly on how long it lasts, and it is therefore important to understand the mechanisms that control this. Depending on animal species and biological conditions, pituitary APs may be initiated either by Ca2+ channels or Na+ channels. Here, we explore the differences between the two scenarios by comparing simulations on two different computer models: (i) a previously developed model which fires Na+-based APs, adapted to data from pituitary cells in rats, and (ii) a novel model that fires Ca2+-based APs, adapted to data from pituitary cells in the fish medaka. Interestingly, we find that the role of big conductance K+ (BK) channels, which are known to affect the duration of the AP, are opposite in the two models, i.e., they act to prolong Ca2+-based APs while they act to shorten Na+-based APs.

cell biology↗

bioRxiv2018

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.\n\nHere we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it easy and quick 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.\n\nUncertainpy 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, mean 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.\n\nThe aim of the current paper is to present Uncertainpy for the neuroscience community in a user- oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis on 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.\n\nSIGNIFICANCE STATEMENTA major challenge in computational neuroscience is to specify the often large number of parameters that define the neuron and neural network models. Many of these parameters have an inherent variability, and some may even be actively regulated and change with time. It is important to know how the uncertainty in model parameters affects the model predictions. To address this need we here present Uncertainpy, an open-source Python toolbox tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models.

neuroscience↗

bioRxiv2018

A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons

1Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.\n\n2 Author summaryMany pathological conditions, such as epilepsy and cortical spreading depression, are linked to abnormal extracellular ion concentrations in the brain. Understanding the underlying principles of such conditions may prove important in developing treatments for these illnesses, which incur societal costs of tens of billions annually. In order to investigate the role of ion-concentration dynamics in the pathological conditions, one must measure the spatial distribution of all ion concentrations over time. This remains challenging experimentally, which makes computational modeling an attractive tool. We have previously introduced the Kirchhoff-Nernst-Planck framework, an efficient framework for modeling electrodiffusion. In this study, we introduce a 3-dimensional version of this framework and use it to model the electrodiffusion of ions surrounding a morphologically detailed neuron. The simulation covered a 1 mm3 cylinder of tissue for over a minute and was performed in less than a day on a standard desktop computer, demonstrating the frameworks efficiency. We believe this to be an important step on the way to understanding phenomena involving ion concentration shifts at the tissue level.

neuroscience↗

bioRxiv2018

Firing-Rate Based Network Modeling of the dLGN Circuit: Effects of Cortical Feedback on Spatiotemporal Response Properties of Relay Cells

Visual signals originating in the retina pass through the dorsal geniculate nucleus (dLGN), the visual part of thalamus, on the way to the visual cortex. This is however not a simple feedforward flow of information: there is a significant feedback from cortical cells back to both relay cells and interneurons in the dLGN. Despite four decades of experimental and theoretical studies, the functional role of this feedback is still debated. Here we use a firing-rate model, the extended difference-of-gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. For this model the responses are found by direct evaluation of two- or three-dimensional integrals allowing for fast and comprehensive studies of putative effects of different candidate organizations of the cortical feedback. Our analysis identifies a special mixed configuration of excitatory and inhibitory cortical feedback which seems to best account for available experimental data. This configuration consists of a slow (long-delay) and spatially widespread inhibitory feedback, combined with a fast (short-delayed) and spatially narrow excitatory feedback, where (iii) the excitatory/inhibitory ON-ON connections are accompanied respectively by inhibitory/excitatory OFF-ON connections, i.e. following a phase-reversed arrangement. The recent development of optogenetic and pharmacogenetic methods has provided new tools for more precise manipulation and investigation of the thalamocortical circuit, in particular for mice. Such data will expectedly allow the eDOG model to be better constrained by data from specific animal model systems than has been possible until now for cat. We have therefore made the Python tool pyLGN which allows for easy adaptation of the eDOG model to new situations.\n\nAuthor SummaryOn route from the retina to primary visual cortex, visually evoked signals have to pass through the dorsal lateral geniculate nucleus (dLGN). However, this is not an exclusive feed forward flow of information as feedback exists from neurons in the cortex back to both relay cells and interneurons in the dLGN. The functional role of this feedback remains mostly unresolved. Here, we use a firing-rate model, the extended difference-of-gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. Our analysis indicates that a particular mix of excitatory and inhibitory cortical feedback agrees best with available experimental observations. In this configuration ON-center relay cells receive both excitatory and (indirect) inhibitory feedback from ON-center cortical cells (ON-ON feedback) where the excitatory feedback is fast and spatially narrow while the inhibitory feedback is slow and spatially widespread. In addition to the ON-ON feedback, the connections are accompanied by OFF-ON connections following a so-called phase-reversed (push-pull) arrangement. To facilitate further applications of the model, we have made the Python tool pyLGN which allows for easy modification and evaluation of the a priori quite general eDOG model to new situations.

neuroscience↗