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Mechanisms behind initial bursts and regular spiking. All panels show responses to a 70 pA depolarizing current injections. As a reference, the responses in ( A ) use the original parameters for P1 and P2, and are the same as in Figureo ˆ 4. In P2, the initial burst and the regular spiking are separated by a pronounced afterhyperpolarization ( A1 ), while in P1 the transition between the initial burst and the regular spiking is more gradual ( A2 ). These characteristics were interchanged between P1 and P2 when g AHP was interchanged (i.e., multiplied/
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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 injectio...
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... morphology (b) gave rise to a I/O curve that was steeper and shifted in the negative direction along the current axis, whereas morphology (c) gave rise to an I/O curve that was flatter and shifted in the positive direction along the current axis compared to the cases (o) and (a) (Figure 5B). Although occurring at different current input levels, the characteristic responses of P1 and P2 did not change qualitatively with morphology. Depolarizing current injections of sufficient intensity gave rise to initial bursts followed by regular AP firing, and with the initial bursts being most pronounced for the parameterization P2. Furthermore, strong hyperpolarizing current injections (-150 pA in case of morphology (o), (a) or (b) and -200 pA in case of morphology (c)) were followed by rebound bursts when using parameter set P1 at a holding potential of -57 mV, but not when using the parameter set P2 at a holding potential of -58 mV. The essential firing patterns of P1 and P2 were thus preserved under changes of morphology, and the I/O curve was always steeper for parameterization P1 (Figure 5C). We have developed a compartmental IN model which stands out from previous models in several ways: Firstly, the model was constrained by a broader range of I/O data than previous models of INs. It was able to exhibit a range of the response patterns characteristic for INs, including (i) initial sags, (ii) rebound bursts, (iii) tonic AP-firing, (iv) initial bursts/spike-time adaptation, and (v) periodic bursting. The mechanisms that we used to model these features have been described earlier in different works (e.g. [36,63,64,83,84,86,87]. By constraining the conductances of the different ion channels to I/O data from single neurons under eight different experimental conditions, including quantitative data on firing frequency vs. stimulus amplitude for depolarizing stimuli (I/ O curves), we were able to make more specific predictions on the contributions of each mechanism. Secondly, we used a much more realistic morphology compared to earlier IN models that include active conductances, opening the way to future studies investigat- ing how different dendritic regions (that generally receive input from different sources [78]) process local I/O operations. Thirdly, dendritic signal propagation also depends on active dendritic properties. As the dendrites of INs are both pre- and postsynaptic, dendritic ion channels will shape both incoming and outgoing signals, and will have an important impact on the signaling between INs and other neurons. Unlike previous IN models [33– 36], our model includes a spatial distribution of ion channels over the somatodendritic membrane that is consistent with the available empirical data. The set of seven ionic conductances that we used to fit the experimental findings (Table 1) is the same as in the previous model by Zhu et al. [36], but with kinetics that were updated to account for recent findings for activation/inactivation kinetics and somatodendritic distributions, and with conductance values constrained by a broader range of I/O data. Although these seven channel types were successful in reproducing the observed spiking patterns, we cannot exclude the presence of additional mechanisms, either overlapping with an included conductance type in terms of their action on the firing properties, or with a minor or negligible effect on the somatic response observed in the current clamp experiments. Several of the included ion channels have well documented roles in INs, including the role of Ca T in burst generation [36,39,44], the role of I h in generating initial sags [41] and the role of Ca L in increasing the intracellular calcium concentration [51,53]. I CAN is involved in making the dendrites leakier in connection with cholinergic modulation [52]. Its influence on the somatic response pattern of INs is less clear, although a previous modeling study has suggested that I CAN may be involved in generating plateau potentials and prolong bursts [36]. Due to the high calcium sensitivity of this channel [36,88], we found that even small depolarizations of the membrane gave rise to a tonically active I CAN . In our model, the main function of I CAN was to reduce the magnitude of the depolarizing current required for the neuron to reach AP firing threshold. In comparison to somatic voltage recordings from rat INs [39,41], our recordings from mouse INs show more pronounced initial sags for strong hyperpolarizing current injections (see Figure 2A, -150 pA stimuli). This suggests that the kinetics of I h may differ between INs in rats and mice, as is the case in CA1 pyramidal neurons [89].This we confirmed by measuring the voltage dependence of I h in three mouse INs (Figure 3). Simulations with I h kinetics based on our own measurements not only agreed better with the sag-shape in the mouse INs, but also predicted that the impact of I h on rebound burst generation was comparable to that of Ca T (Figure 6). This differs from the situation in rat INs, where rebound responses are mainly due to Ca T , with no measurable contribution from I h [39]. Conversely, in CA1 pyramidal neurons it has been shown that rebound spiking can be generated by I h alone [86]. However, a joint involvement of Ca T and I h in burst generation, were found to underlie intrinsic rhythmic bursting in subpopulations of TCs during inattentiveness in guinea pigs [64,84]. Intrinsic rhythmic bursting was not observed in our neurons. The presence of Ca L -conductances in IN dendrites [51,53,54] makes it likely that also inhibitory, calcium-dependent mechanisms (such as I AHP ) are present. The role of I AHP in INs has not been previously documented. Our model predicted that the interplay between Ca L and I AHP conductances was sufficient for explaining the modulation of the I/O curves, although additional mechanisms could be involved. For example, a slowly activating potassium channel ( K M ) with a high threshold and no inactivation gave similar results to our Ca L and I AHP mechanism, but without any calcium dependence (simulations were made using K M kinetics taken from [90], results not shown). However, no clear functional role could be assigned to K M other than that covered by I AHP . We thus did not explore this issue further, since I AHP gave a better agreement than K M with the time course of the intra-spike membrane potential and, especially, with the afterhyperpolarization following the initial bursts in P2. However, the possibility that K M and I AHP have overlapping functions in regulating the spiking frequency cannot be excluded. This could be experimentally tested by blocking the respective channels. We presented two parameterizations of the model (P1 and P2), which reproduced the electrophysiological properties of two different INs (IN1 and IN2). Rebound bursts as those generally observed only in a small subset of INs [39] were elicited by P1 but not P2. On the other hand, P2 elicited more pronounced initial bursts than P1 when exposed to depolarizing stimuli. P2 also had a less steep I/O curve and required weaker depolarization than P1 in order to reach AP-firing threshold. Our simulations showed that differences between P1 and P2 in terms of response properties and preferred input conditions arose from relative differences in specific conductances. Our model thus supports the idea that conductances values (i.e. channel density) in different subgroups of INs may be tuned in such a way as to optimize network operation under different input conditions. Under in vivo conditions, changes in input conditions (e.g. in synaptic input and/or shifts in membrane potential) may be mediated by ...
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... In this study, we investigate the basis of intrinsic oscillatory firing in another major thalamic cell constituent: the local thalamic interneuron (TI). This cell type comprises up to 25%-30% of the cells in the thalamic sensory nuclei of primates, and can demonstrate tonic firing (Pape and McCormick, 1995;Halnes et al., 2011), burst firing (Zhu et al., 1999b;Halnes et al., 2011), and intrinsic oscillations (Zhu et al., 1999a;Halnes et al., 2011). The mechanisms underlying the periodic bursting (or intrinsic oscillation) in this cell type have not yet been fully characterized. ...
... In this study, we investigate the basis of intrinsic oscillatory firing in another major thalamic cell constituent: the local thalamic interneuron (TI). This cell type comprises up to 25%-30% of the cells in the thalamic sensory nuclei of primates, and can demonstrate tonic firing (Pape and McCormick, 1995;Halnes et al., 2011), burst firing (Zhu et al., 1999b;Halnes et al., 2011), and intrinsic oscillations (Zhu et al., 1999a;Halnes et al., 2011). The mechanisms underlying the periodic bursting (or intrinsic oscillation) in this cell type have not yet been fully characterized. ...
... In this study, we investigate the basis of intrinsic oscillatory firing in another major thalamic cell constituent: the local thalamic interneuron (TI). This cell type comprises up to 25%-30% of the cells in the thalamic sensory nuclei of primates, and can demonstrate tonic firing (Pape and McCormick, 1995;Halnes et al., 2011), burst firing (Zhu et al., 1999b;Halnes et al., 2011), and intrinsic oscillations (Zhu et al., 1999a;Halnes et al., 2011). The mechanisms underlying the periodic bursting (or intrinsic oscillation) in this cell type have not yet been fully characterized. ...
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 currents IL and IP 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 (IAHP ) was of primary importance. A morphologically simplified, multicompartment model of the thalamic interneuron characterized the oscillation as follows: 1. The low-threshold calcium current (IT ) provided the strong initial burst characteristic of the oscillation. 2. Alternating fluxes through high-threshold calcium channels and IAHP then provided the continuing burst oscillation and interburst periods respectively. This interplay between IL and IAHP contrasts with the current dynamics underlying oscillations in thalamocortical and reticularis neurons, which primarily involve IT and IH, or IT and IAHP 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.
... In many neuron types, inward depolarizing Ca 2+ currents trigger outward hyperpolarizing K + currents through Ca 2+ -activated K + channels (see e.g. Destexhe & Sejnowski (2003) or Halnes et al. (2011)). Hence, whether the overall effect of a Ca 2+ current leads to an increased or decreased firing rate generally depends on the neuron's ion channel composition. ...
The perineuronal nets (PNNs) are sugar coated protein structures that encapsulate certain neurons in the brain, such as parvalbumin positive (PV) inhibitory neurons. As PNNs are theorized to act as a barrier to ion transport, they may effectively increase the membrane charge-separation distance, thereby affecting the membrane capacitance. Tewari et al. (2018) found that degradation of PNNs induced a 25%-50% increase in membrane capacitance [Formula: see text] and a reduction in the firing rates of PV-cells. In the current work, we explore how changes in [Formula: see text] affects the firing rate in a selection of computational neuron models, ranging in complexity from a single compartment Hodgkin-Huxley model to morphologically detailed PV-neuron models. In all models, an increased [Formula: see text] lead to reduced firing, but the experimentally reported increase in [Formula: see text] was not alone sufficient to explain the experimentally reported reduction in firing rate. We therefore hypothesized that PNN degradation in the experiments affected not only [Formula: see text], but also ionic reversal potentials and ion channel conductances. In simulations, we explored how various model parameters affected the firing rate of the model neurons, and identified which parameter variations in addition to [Formula: see text] that are most likely candidates for explaining the experimentally reported reduction in firing rate.
... In the literature, the neurons have been modelled with different levels of abstraction and detail. Works such as [64][65][66][67][68] focus on the definition and use of so-called multi-compartment neuron models. These kind of models try to account for each compartment of a neuron (dendrites, axon and soma) individually to more closely replicate biological evidence. ...
Spiking neural networks (SNNs) are largely inspired by biology and neuroscience, and leverage ideas and theories to create fast and efficient learning systems. Spiking neuron models are adopted as core processing units in neuromorphic systems because they enable event-based processing. The integrate-and-fire (I\&F) models are often adopted as considered more suitable, with the simple Leaky I\&F (LIF) being the most used. The reason for adopting such models is their efficiency or biological plausibility. Nevertheless, rigorous justification for the adoption of LIF over other neuron models for use in artificial learning systems has not yet been studied. This work considers a variety of neuron models in the literature and then selects computational neuron models that are single-variable, efficient, and display different types of complexities. From this selection, we make a comparative study of three simple I\&F neuron models, namely the LIF, the Quadratic I\&F (QIF) and the Exponential I\&F (EIF), to understand whether the use of more complex models increases the performance of the system and whether the choice of a neuron model can be directed by the task to be completed. Neuron models are tested within an SNN trained with Spike-Timing Dependent Plasticity (STDP) on a classification task on the N-MNIST and DVS Gestures datasets. Experimental results reveal that more complex neurons manifest the same ability as simpler ones to achieve high levels of accuracy on a simple dataset (N-MNIST), albeit requiring comparably more hyper-parameter tuning. However, when the data possess richer spatio-temporal features, the QIF and EIF neuron models steadily achieve better results. This suggests that accurately selecting the model based on the richness of the feature spectrum of the data could improve the performance of the whole system. Finally, the code implementing the spiking neurons in the SpykeTorch framework is made publicly available.
... Despite (or maybe because of) their likely more complicated action, fewer models have been developed for INs than RCs. Some models have investigated signal propagation in the elaborate dendritic structure of INs in the case of passive (Bloomfield and Sherman 1989;Briska et al. 2003) (Halnes et al. 2011;Zhu et al. 1999), and the most comprehensive of these two also includes active dendritic conductances (Halnes et al. 2011). Some of the IN models include intracellular calcium dynamics (Allken et al. 2014;Halnes et al. 2011;Zhu et al. 1999). ...
... Despite (or maybe because of) their likely more complicated action, fewer models have been developed for INs than RCs. Some models have investigated signal propagation in the elaborate dendritic structure of INs in the case of passive (Bloomfield and Sherman 1989;Briska et al. 2003) (Halnes et al. 2011;Zhu et al. 1999), and the most comprehensive of these two also includes active dendritic conductances (Halnes et al. 2011). Some of the IN models include intracellular calcium dynamics (Allken et al. 2014;Halnes et al. 2011;Zhu et al. 1999). ...
... Some models have investigated signal propagation in the elaborate dendritic structure of INs in the case of passive (Bloomfield and Sherman 1989;Briska et al. 2003) (Halnes et al. 2011;Zhu et al. 1999), and the most comprehensive of these two also includes active dendritic conductances (Halnes et al. 2011). Some of the IN models include intracellular calcium dynamics (Allken et al. 2014;Halnes et al. 2011;Zhu et al. 1999). ...
... Computational modelling is essential in understanding the function of the triadic synapse within the LGN. Neuronal models that simulate RCs or INs independently are scarce [5], [11], [12]. Moreover, to our knowledge, only a single published study to date integrates both RCs and INs in a single model simulate the triadic synapse [13]. ...
... An initial model was created by building and connecting single IN and RC cells with excitatory inputs from a single RGC added using the 'NetStim'/'Exp2Syn' stimulus protocol outlined below. The IN model was built based on specifications from [13], with additional complexity from [12]. It consists of a cell body (diameter 17.4μm, length 15.3μm) connected to a single dendrite and a single axon with the same dimensions (proximal diameter 4μm tapering to 0.3μm over length 100μm, then consistent diameter 0.3μm for distal 400μm). ...
... Therefore, it might seem peculiar that most models of neuronal activity are based on the approximation that the concentrations of the main charge carriers (Na + , K + , and Cl − ) do not change over time. This approximation is, for example, incorporated in the celebrated Hodgkin-Huxley model [1], and a large number of later models based on a Hodgkin-Huxley type formalism (see, e.g., [2][3][4][5][6][7]). ...
... This assumption is implicit in the majority of morphologically explicit models of neurons, where the (spatial) signal propagation in dendrites and axons are computed using the cable equation (see, e.g., [10][11][12]). Cable-equation based, multicompartmental neuronal models are widely used within the field of neuroscience, both for understanding dendritic integration and neuronal response properties at the single neuron level (see, e.g., [3,4,6,7]) and for exploring the dynamics of large neuronal networks (see e.g., [13][14][15]). They are even used in the context of performing forward modeling of extracellular potentials, such as local field potentials (LFP), the electrocorticogram (ECoG), and electroencephalogram (EEG) (see, e.g., [16][17][18]), despite the evident inconsistency involved when first computing neurodynamics under the approximation that ϕ e = 0 (Fig 1A), and then in the next step using this dynamics to predict a nonzero ϕ e (Fig 1B). ...
... The goal of this work is to propose what we may refer to as "a minimal neuronal model that has it all". By "has it all", we mean that it (1) has a spatial extension, (2) considers both extracellular-and intracellular dynamics, (3) keeps track of all ion concentrations (Na + , K + , Ca 2+ , and Cl − ) in all compartments, (4) keeps track of all electrical potentials (ϕ m , ϕ e , and ϕ i -the latter being the intracellular potential) in all compartments, (5) has differential expression of ion channels in soma versus dendrites, and can fire somatic APs and dendritic calcium spikes, (6) contains the homeostatic machinery that ensures that it maintains a realistic dynamics in ϕ m and all ion concentrations during long-time activity, and (7) accounts for transmembrane, intracellular and extracellular ionic movements due to both diffusion and electrical migration, and thus ensures a consistent relationship between ion concentrations and electrical charge. Being based on a unified framework for intra-and extracellular dynamics (Fig 1C), the model thus accounts for possible ephaptic effects from extracellular dynamics, as neglected in standard feedforward models based on volume conductor theory (Fig 1A and 1B). ...
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.
... Starting with Hodgkin and Huxley's development of a mechanistic model for action-potential generation and propagation in squid giant axons [3], mechanistic modeling of neurons is now well established [1,4,5]. Numerous biophysically detailed neuron models tailored to model specific neuron types have been constructed, for example, for cells in mammalian sensory cortex [6,7], hippocampus [8] and thalamus [9,10]. Further, simplified mechanistic point-neuron models of the integrate-and-fire type excellently mimicking experimental data, have been constructed [11,12]. ...
... For single neurons, biophysics-based modeling is well established [1,4,5] and numerous biophysically detailed models with anatomically reconstructed dendrites have been made by fitting to experimental data, for example, [6][7][8]10]. These models have mainly been fitted to intracellular electrical recordings, but extracellular recordings [54] and calcium concentrations [55] can also be used. ...
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.
... LINs in the dLGN have been studied for decades in a range of species including cats, primates and rodents (Bickford et al., 1999(Bickford et al., , 2010Blitz and Regehr, 2005;Bloomfield and Sherman, 1989;Cox and Beatty, 2017;Cox, 2012, 2013;Dankowski and Bickford, 2003;Halnes et al., 2011;Hámori et al., 1974;Hamos et al., 1985;Hirsch et al., 2015;Lam et al., 2005;Pasik et al., 1973Pasik et al., , 1976Seabrook et al., 2013;Wilson, 1989). Our connectivity map of a LIN in the mouse dLGN is broadly consistent with the conclusions reached in this body of work. ...
... Glutamate uncaging at distal LIN dendrites can drive inhibition of nearby TCs without depolarizing the LIN cell body (Crandall and Cox, 2012). Modeling of signal attenuation in LINs predicts that inputs to distal dendrites should be attenuated at the soma from ~50% to 99% (Bloomfield et al., 1987;Briska et al., 2003;Halnes et al., 2011;Perreault and Raastad, 2006). The level of attenuation in these models varies depending on membrane resistance, process diameter, active conductances and the spatial and temporal pattern of the input. ...
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.
... Cable-equation based, multicompartmental neuronal models are widely used within the 29 field of neuroscience, both for understanding dendritic integration and neuronal 30 response properties at the single neuron level (see, e.g., [3,4,6,7]) and for exploring the 31 dynamics of large neuronal networks (see e.g., [13][14][15]). They are even used in the 32 context of performing forward modeling of extracellular potentials, such as local field 33 potentials (LFP), the electrocorticogram (ECoG), and electroencephalogram (EEG) 34 (see, e.g., [16-18]), despite the evident inconsistency involved when first computing 35 ...
... Hence, to our knowledge, no morphologically explicit neuron 76 model has so far been developed that ensures biophysically consistent dynamics in ion 77 concentrations and electrical potentials during long-time activity, although useful 78 mathematical framework for constructing such models are available [58][59][60][61][62]. 79 The goal of this work is to propose what we may refer to as "a minimal neuronal 80 model that has it all". By "has it all", we mean that it (1) has a spatial extension, (2) 81 considers both extracellular-and intracellular dynamics, (3) keeps track of all ion 82 concentrations (Na + , K + , Ca 2+ , and Cl − ) in all compartments, (4) keeps track of all 83 electrical potentials (φ m , φ e , and φ i -the latter being the intracellular potential) in all 84 compartments, (5) has differential expression of ion channels in soma versus dendrites, 85 and can fire somatic APs and dendritic calcium spikes, (6) conductor theory (Fig 1A-B). By "minimal" we simply mean that we reduce the number 94 of spatial compartments to the minimal, which in this case is four, i.e., two neuronal 95 compartments (a soma and a dendrite), plus two extracellular compartments (outside 96 soma and outside dendrite). ...
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 ⁺ , Ca ²⁺ , 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 summary
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 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.
... Computational modelling is essential in understanding the function of the triadic synapse within the LGN. Neuronal models that simulate RCs or INs independently are scarce [5], [11], [12]. Moreover, to our knowledge, only a single published study to date integrates both RCs and INs in a single model simulate the triadic synapse [13]. ...
... Stimulus Protocol. The IN model was built based on specifications from [13], with additional complexity from [12]. It consists of a cell body (diameter 17.4μm, length 15.3μm) connected to a single dendrite and a single axon with the same dimensions (proximal diameter 4μm tapering to 0.3μm over length 100μm, then consistent diameter 0.3μm for distal 400μm). ...
