Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and down-regulation, by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In the present investigation, we analyze how the impulse patterns are regulated by the density of voltage-gated channels in a model neuron, based on voltage clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf bifurcation threshold dynamics, respectively. Single strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The presently found relationship between channel densities and oscillatory behavior may be relevance for understanding principal spiking patterns of cortical neurons (regular firing and fast spiking). It may also be of relevance for understanding the action of pharmacological compounds on brain oscillatory activity.     

Ocellar interneurons in the honeybee

Summary Morphologically identified spiking ocellar interneurons (L_B and L_D-neurons) of the honeybee (Apis melliferd) were investigated by combined intracellular recording and staining techniques using multimodal stimulus programs.Response patterns containing both graded and action potentials (mixed response), and pure spiking responses were analysed. Mixed responses allow a comparison of information coded simultaneously by graded and action potentials in one neuron. In most cases the intensity dependence coded by spikes was found to be similar to the intensity dependence coded by one of two different parameters evaluated from the graded signal. Lneurons with mixed responses were unimodal, i.e. they reacted exclusively to stationary illumination of the ocelli, as do nonspiking L-neurons.In contrast, spiking L-neurons that lacked a graded response component could also respond to stimuli of other sensory modalities: moving patterns, compound eye illumination, airstreams, mechanical and gustatory stimulation. One L_D-neuron was also excited by the wing beat.Recordings from the same type of neuron in different individuals demonstrate that the input modalities and response patterns of L-neurons vary remarkably. Consequently many recordings are required to properly characterise the physiological properties of these neurons even though anatomically they are identified.The existence of graded and action potentials in the same cell and the fact that these two signals carry different information is discussed in the context of a possible role for information transmission from L-neurons to postsynaptic cells.Abbreviation R/I response/intensity     

Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron

Neurons show diverse firing patterns. Even neurons belonging to a single chemical or morphological class, or the same identified neuron, can display different types of electrical activity. For example, motor neuron MN5, which innervates a flight muscle of adult Drosophila, can show distinct firing patterns under the same recording conditions. We developed a two-dimensional biophysical model and show that a core complement of just two voltage-gated channels is sufficient to generate firing pattern diversity. We propose Shab and DmNa _v to be two candidate genes that could encode these core currents, and find that changes in Shab channel expression in the model can reproduce activity resembling the main firing patterns observed in MN5 recordings. We use bifurcation analysis to describe the different transitions between rest and spiking states that result from variations in Shab channel expression, exposing a connection between ion channel expression, bifurcation structure, and firing patterns in models of membrane potential dynamics.     

Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos

Responding to various stimuli, some neurons either remain resting or can fire several distinct patterns of action potentials, such as spiking, bursting, subthreshold oscillations, and chaotic firing. In particular, Wilson’s conductance-based neocortical neuron model, derived from the Hodgkin–Huxley model, is explored to understand underlying mechanisms of the firing patterns. Phase diagrams describing boundaries between the domains of different firing patterns are obtained via extensive numerical computations. The boundaries are further studied by standard instability analyses, which demonstrates that the chaotic neural firing could develop via period-doubling and/or period- adding cascades. Sequences of the firing patterns often observed in many neural experiments are also discussed in the phase diagram framework developed. Our results lay the groundwork for wider use of the model, especially for incorporating it into neural field modeling of the brain.     

Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model

The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to affect the collective properties of the whole ion channel cluster. For example, there exists an optimal size of the membrane patch for which the internal noise alone causes a regular spontaneous generation of action potentials. In addition to varying the size of ion channel clusters, living organisms may adapt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. The influence of a channel block on the excitability of a membrane patch of a certain size is twofold: first, a variation of ion channel densities primarily yields a change of the conductance level; second, a down-regulation of working ion channels always increases the channel noise. While the former effect dominates in the case of sodium channel block resulting in a reduced spiking activity, the latter enhances the generation of spontaneous action potentials in the case of a tailored potassium channel blocking. Moreover, by blocking some portion of either potassium or sodium ion channels, it is possible to either increase or decrease the regularity of the spike train.     

Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na⁺ and K⁺ channels, with generator potential and graded potential models lacking voltage-gated Na⁺ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na⁺ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ∼50% in generator potentials, to ∼3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation.     

Density dependent neurodynamics

The dynamics of a neural network depends on density parameters at (at least) two different levels: the subcellular density of ion channels in single neurons, and the density of cells and synapses at a network level. For the Frankenhaeuser-Huxley (FH) neural model, the density of sodium (Na) and potassium (K) channels determines the behaviour of a single neuron when exposed to an external stimulus. The features of the onset of single neuron oscillations vary qualitatively among different regions in the channel density plane. At a network level, the density of neurons is reflected in the global connectivity. We study the relation between the two density levels in a network of oscillatory FH neurons, by qualitatively distinguishing between three regions, where the mean network activity is (1) spiking, (2) oscillating with enveloped frequencies, and (3) bursting, respectively. We demonstrate that the global activity can be shifted between regions by changing either the density of ion channels at the subcellular level, or the connectivity at the network level, suggesting that different underlying mechanisms can explain similar global phenomena. Finally, we model a possible effect of anaesthesia by blocking specific inhibitory ion channels.     

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-I_stim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-I_stim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane.     

Alternative splicing regulates kv3.1 polarized targeting to adjust maximal spiking frequency

Synaptic inputs received at dendrites are converted into digital outputs encoded by action potentials generated at the axon initial segment in most neurons. Here, we report that alternative splicing regulates polarized targeting of Kv3.1 voltage-gated potassium (Kv) channels to adjust the input-output relationship. The spiking frequency of cultured hippocampal neurons correlated with the level of endogenous Kv3 channels. Expression of axonal Kv3.1b, the longer form of Kv3.1 splice variants, effectively converted slow-spiking young neurons to fast-spiking ones; this was not the case for Kv1.2 or Kv4.2 channel constructs. Despite having identical biophysical properties as Kv3.1b, dendritic Kv3.1a was significantly less effective at increasing the maximal firing frequency. This suggests a possible role of channel targeting in regulating spiking frequency. Mutagenesis studies suggest the electrostatic repulsion between the Kv3.1b N/C termini, created by its C-terminal splice domain, unmasks the Kv3.1b axonal targeting motif. Kv3.1b axonal targeting increased the maximal spiking frequency in response to prolonged depolarization. This finding was further supported by the results of local application of channel blockers and computer simulations. Taken together, our studies have demonstrated that alternative splicing controls neuronal firing rates by regulating the polarized targeting of Kv3.1 channels.     

Targeted Expression of Channelrhodopsin-2 to the Axon Initial Segment Alters the Temporal Firing Properties of Retinal Ganglion Cells

The axon initial segment (AIS) is essential for initiating action potentials and maintaining neuronal excitability in axon-bearing neurons in the CNS. There is increasing interest in the targeting of optogenetic tools to subcellular compartments, including the AIS, to gain precise control of neuronal activity for basic research and clinical applications. In particular, targeted expression of optogenetic tools in retinal ganglion cells (RGCs) has been explored as an approach for restoring vision after photoreceptor degeneration. Thus, understanding the effects of such targeting on spiking abilities and/or patterns is important. Here, we examined the effects of recombinant adeno-associated virus (rAAV)-mediated targeted expression of channelrhodopsin-2 (ChR2)-GFP with a Na_V channel motif in mouse RGCs. We found that this targeted expression disrupted Na_V channel clustering at the AIS and converted the spike firing patterns of RGCs from sustained to transient. Our results suggest that the clustering of membrane channels, including Na_V channels, at the AIS is important for the ability of RGCs to generate sustained spike firing. Additionally, the targeting of optogenetic tools to the AIS with the Na_V channel motif may offer a way to create transient light responses in RGCs for vision restoration.     

Contributions of T-type calcium channel isoforms to neuronal firing

Low voltage-activated (LVA) T-type calcium channels play critical roles in the excitability of many cell types and are a focus of research aimed both at understanding the physiological basis of calcium channel-dependent signaling and the underlying pathophysiology associated with hyperexcitability disorders such as epilepsy. These channels play a critical role towards neuronal firing in both conducting calcium ions during action potentials and also in switching neurons between distinct modes of firing. In this review the properties of the CaV3.1, CaV3.2 and CaV3.3 T-type channel isoforms is discussed in relation to their individual contributions to action potentials during burst and tonic firing states as well their roles in switching between firing states.     

Cav1.2 calcium channels modulate the spiking pattern of hippocampal pyramidal cells

Ca(v)1.2 L-type calcium channels support hippocampal synaptic plasticity, likely by facilitating dendritic Ca2+ influx evoked by action potentials (AP) back-propagated from the soma. Ca2+ influx into hippocampal neurons during somatic APs is sufficient to activate signalling pathways associated with late phase LTP. Thus, mechanisms controlling AP firing of hippocampal neurons are of major functional relevance. We examined the excitability of CA1 pyramidal cells using somatic current-clamp recordings in brain slices from control type mice and mice with the Ca(v)1.2 gene inactivated in principal hippocampal neurons. Lack of the Ca(v)1.2 protein did not affect either affect basic characteristics, such as resting membrane potential and input resistance, or parameters of single action potentials (AP) induced by 5 ms depolarising current pulses. However, CA1 hippocampal neurons from control and mutant mice differed in their patterns of AP firing during 500 ms depolarising current pulses: threshold voltage for repetitive firing was shifted significantly by about 5 mV to more depolarised potentials in the mutant mice (p<0.01), and the latency until firing of the first AP was prolonged (73.2+/-6.6 ms versus 48.1+/- 7.8 ms in control; p<0.05). CA1 pyramidal cells from the mutant mice also showed a lowered initial spiking frequency within an AP train. In control cells, isradipine had matching effects, while BayK 8644 facilitated spiking. Our data demonstrate that Ca(v)1.2 channels are involved in regulating the intrinsic excitability of CA1 pyramidal neurons. This cellular mechanism may contribute to the known function of Ca(v)1.2 channels in supporting synaptic plasticity and memory.     

State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment.During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the model's biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting.During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable.We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neuron's complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.     

A novel disease connection for TRPM2 channels

Low voltage-activated (LVA) T-type calcium channels play critical roles in the excitability of many cell types and are a focus of research aimed both at understanding the physiological basis of calcium channel-dependent signaling and the underlying pathophysiology associated with hyperexcitability disorders such as epilepsy. These channels play a critical role towards neuronal firing in both conducting calcium ions during action potentials and also in switching neurons between distinct modes of firing. In this review the properties of the Ca_V3.1, Ca_V3.2 and Ca_V3.3 T-type channel isoforms is discussed in relation to their individual contributions to action potentials during burst and tonic firing states as well their roles in switching between firing states.     

Intrinsic coherence resonance in excitable membrane patches

The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. There exists an optimal size of the membrane patch for which the internal noise alone can cause a nearly regular spontaneous generation of action potentials. We consider the influence of intrinsic channel noise in presence of a constant and an oscillatory current driving for both, the mean interspike interval and the phenomenon of coherence resonance for neuronal spiking. Given small membrane patches, implying that channel noise dominates the excitable dynamics, we find the phenomenon of intrinsic coherence resonance. In this case, the relatively regular spiking behavior becomes essentially independent of an applied stimulus. We observed, however, the occurrence of a skipping of supra-threshold input events due to channel noise for intermediate patch sizes. This effect consequently reduces the overall coherence of the spiking.     

Effects of active versus passive dendritic membranes on the transfer properties of a simulated neuron

In a simulated neuron with a dendritic tree, the relative effects of active and passive dendritic membranes on transfer properties were studied. The simulations were performed by means of a digital computer. The computations calculated the changes in transmembrane voltages of many compartments over time as a function of other biophysical variables. These variables were synaptic input intensity, critical firing threshold, rate of leakage of current across the membrane, and rate of longitudinal current spread between compartments. For both passive and active dendrites, the transfer properties of the soma studied for different rates of longitudinal current spread. With low rates of current spread, graded changes in firing threshold produced correspondingly graded changes in output discharge. With high rates of current spread, the neuron became a bistable operator where spiking was enhanced if the threshold was below a certain level and suppressed if the threshold was above that level. Since alterations in firing threshold were shown to have the same effect on firing rate as alterations in synaptic input intensity, the neuron can be said to change from graded to contrast-enhancing in its response to stimuli of different intensities. The presence or absence of dendritic spiking was found to have a significant effect on the integrative properties of the simulated neuron. In particular, contrast enhancement was considerably more pronounced in neurons with passive than with active dendrites in that somatic spike rates reached a higher maximum when dendrites were passive. With active dendrites, a less intense input was needed to initiate somatic spiking than with passive dendrites because a distal dendritic spike could easily propagate by means of longitudinal current spread to the soma. Once somatic spiking was initiated, though, spike rates tended to be lower with active than with passive dendrites because the soma recovered more slowly from its post-spike refractory period if it was also influenced by refractory periods in the dendrites. The experiment of comparing neurons with active and passive dendrites was repeated at a different, higher value of synaptic input. The same differences in transfer properties between the active and passive cases emerged as before. Spiking patterns in neurons with active dendrites were also affected by the time distribution of synaptic inputs. In a previous study, inputs had been random over both space and time, varying about a predetermined mean, whereas in the present study, inputs were random over space but uniform over time. When inputs were made uniform over time, spiking became more difficult to initiate and the transition from graded to bistable response became less sharp.     

Different roles attributed to Cav1 channel subtypes in spontaneous action potential firing and fine tuning of exocytosis in mouse chromaffin cells

This study examines the Cav1 isoforms expressed in mouse chromaffin cells and compares their biophysical properties and roles played in cell excitability and exocytosis. Using immunocytochemical and electrophysiological techniques in mice lacking the Cav1.3α1 subunit (Cav1.3(-/-) ) or the high sensitivity of Cav1.2α1 subunits to dihydropyridines, Cav1.2 and Cav1.3 channels were identified as the only Cav1 channel subtypes expressed in mouse chromaffin cells. Cav1.3 channels were activated at more negative membrane potentials and inactivated more slowly than Cav1.2 channels. Cav1 channels, mainly Cav1.2, control cell excitability by functional coupling to BK channels, revealed by nifedipine blockade of BK channels in wild type (WT) and Cav1.3(-/-) cells (53% and 35%, respectively), and by the identical change in the shape of the spontaneous action potentials elicited by the dihydropyridine in both strains of mice. Cav1.2 channels also play a major role in spontaneous action potential firing, supported by the following evidence: (i) a similar percentage of WT and Cav1.3(-/-) cells fired spontaneous action potentials; (ii) firing frequency did not vary between WT and Cav1.3(-/-) cells; (iii) mostly Cav1.2 channels contributed to the inward current preceding the action potential threshold; and (iv) in the presence of tetrodotoxin, WT or Cav1.3(-/-) cells exhibited spontaneous oscillatory activity, which was fully abolished by nifedipine perfusion. Finally, Cav1.2 and Cav1.3 channels were essential for controlling the exocytotic process at potentials above and below -10 mV, respectively. Our data reveal the key yet differential roles of Cav1.2 and Cav1.3 channels in mediating action potential firing and exocytotic events in the neuroendocrine chromaffin cell.     

Channelrhodopsin-2 localised to the axon initial segment

The light-gated cation channel Channelrhodopsin-2 (ChR2) is a powerful and versatile tool for controlling neuronal activity. Currently available versions of ChR2 either distribute uniformly throughout the plasma membrane or are localised specifically to somatodendritic or synaptic domains. Localising ChR2 instead to the axon initial segment (AIS) could prove an extremely useful addition to the optogenetic repertoire, targeting the channel directly to the site of action potential initiation, and limiting depolarisation and associated calcium entry elsewhere in the neuron. Here, we describe a ChR2 construct that we localised specifically to the AIS by adding the ankyrinG-binding loop of voltage-gated sodium channels (Na(v)II-III) to its intracellular terminus. Expression of ChR2-YFP-Na(v)II-III did not significantly affect the passive or active electrical properties of cultured rat hippocampal neurons. However, the tiny ChR2 currents and small membrane depolarisations resulting from AIS targeting meant that optogenetic control of action potential firing with ChR2-YFP-Na(v)II-III was unsuccessful in baseline conditions. We did succeed in stimulating action potentials with light in some ChR2-YFP-Na(v)II-III-expressing neurons, but only when blocking KCNQ voltage-gated potassium channels. We discuss possible alternative approaches to obtaining precise control of neuronal spiking with AIS-targeted optogenetic constructs and propose potential uses for our ChR2-YFP-Na(v)II-III probe where subthreshold modulation of action potential initiation is desirable.     

Mechanisms of Gain Control by Voltage-Gated Channels in Intrinsically-Firing Neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.     

How modeling can reconcile apparently discrepant experimental results: the case of pacemaking in dopaminergic neurons

Midbrain dopaminergic neurons are endowed with endogenous slow pacemaking properties. In recent years, many different groups have studied the basis for this phenomenon, often with conflicting conclusions. In particular, the role of a slowly-inactivating L-type calcium channel in the depolarizing phase between spikes is controversial, and the analysis of slow oscillatory potential (SOP) recordings during the blockade of sodium channels has led to conflicting conclusions. Based on a minimal model of a dopaminergic neuron, our analysis suggests that the same experimental protocol may lead to drastically different observations in almost identical neurons. For example, complete L-type calcium channel blockade eliminates spontaneous firing or has almost no effect in two neurons differing by less than 1% in their maximal sodium conductance. The same prediction can be reproduced in a state of the art detailed model of a dopaminergic neuron. Some of these predictions are confirmed experimentally using single-cell recordings in brain slices. Our minimal model exhibits SOPs when sodium channels are blocked, these SOPs being uncorrelated with the spiking activity, as has been shown experimentally. We also show that block of a specific conductance (in this case, the SK conductance) can have a different effect on these two oscillatory behaviors (pacemaking and SOPs), despite the fact that they have the same initiating mechanism. These results highlight the fact that computational approaches, besides their well known confirmatory and predictive interests in neurophysiology, may also be useful to resolve apparent discrepancies between experimental results.