Increase in sodium conductance decreases firing rate and gain in model neurons

The enigmatic HCN channels: A cellular neurophysiology perspective

What physiological role does a slow hyperpolarization-activated ion channel with mixed cation selectivity play in the fast world of neuronal action potentials that are driven by depolarization? That puzzling question has piqued the curiosity of physiology enthusiasts about the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are widely expressed across the body and especially in neurons. In this review, we emphasize the need to assess HCN channels from the perspective of how they respond to time-varying signals, while also accounting for their interactions with other co-expressing channels and receptors. First, we illustrate how the unique structural and functional characteristics of HCN channels allow them to mediate a slow negative feedback loop in the neurons that they express in. We present the several physiological implications of this negative feedback loop to neuronal response characteristics including neuronal gain, voltage sag and rebound, temporal summation, membrane potential resonance, inductive phase lead, spike triggered average, and coincidence detection. Next, we argue that the overall impact of HCN channels on neuronal physiology critically relies on their interactions with other co-expressing channels and receptors. Interactions with other channels allow HCN channels to mediate intrinsic oscillations, earning them the "pacemaker channel" moniker, and to regulate spike frequency adaptation, plateau potentials, neurotransmitter release from presynaptic terminals, and spike initiation at the axonal initial segment. We also explore the impact of spatially non-homogeneous subcellular distributions of HCN channels in different neuronal subtypes and their interactions with other channels and receptors. Finally, we discuss how plasticity in HCN channels is widely prevalent and can mediate different encoding, homeostatic, and neuroprotective functions in a neuron. In summary, we argue that HCN channels form an important class of channels that mediate a diversity of neuronal functions owing to their unique gating kinetics that made them a puzzle in the first place.

Activity-dependent ectopic action potentials in regular-spiking neurons of the neocortex

Introduction

Action potentials usually travel orthodromically along a neuron's axon, from the axon initial segment (AIS) toward the presynaptic terminals. Under some circumstances action potentials also travel in the opposite direction, antidromically, after being initiated at a distal location. Given their initiation at an atypical site, we refer to these events as "ectopic action potentials." Ectopic action potentials (EAPs) were initially observed in pathological conditions including seizures and nerve injury. Several studies have described regular-spiking (RS) pyramidal neurons firing EAPs in seizure models. Under nonpathological conditions, EAPs were reported in a few populations of neurons, and our group has found that EAPs can be induced in a large proportion of parvalbumin-expressing interneurons in the neocortex. Nevertheless, to our knowledge there have been no prior reports of ectopic firing in the largest population of neurons in the neocortex, pyramidal neurons, under nonpathological conditions.

Methods

We performed in vitro recordings utilizing the whole-cell patch clamp technique. To elicit EAPs, we triggered orthodromic action potentialswith either long, progressively increasing current steps, or with trains of brief pulses at 30, 60, or 100 Hz delivered in 3 different ways, varying in stimulus and resting period duration.

Results

We found that a large proportion (72.7%) of neocortical RS cells from mice can fire EAPs after a specific stimulus in vitro, and that most RS cells (56.1%) are capable of firing EAPs across a broad range of stimulus conditions. Of the 37 RS neurons in which we were able to elicit EAPs, it took an average of 863.8 orthodromic action potentials delivered over the course of an average of ~81.4 s before the first EAP was seen. We observed that some cells responded to specific stimulus frequencies while less selective, suggesting frequency tuning in a subset of the cells.

Discussion

Our findings suggest that pyramidal cells can integrate information over long time-scales before briefly entering a mode of self-generated firing that originates in distal axons. The surprising ubiquity of EAP generation in RS cells raises interesting questions about the potential roles of ectopic spiking in information processing, cortical oscillations, and seizure susceptibility.

Loss or gain of function? Effects of ion channel mutations on neuronal firing depend on the neuron type

Introduction

Clinically relevant mutations to voltage-gated ion channels, called channelopathies, alter ion channel function, properties of ionic currents, and neuronal firing. The effects of ion channel mutations are routinely assessed and characterized as loss of function (LOF) or gain of function (GOF) at the level of ionic currents. However, emerging personalized medicine approaches based on LOF/GOF characterization have limited therapeutic success. Potential reasons are among others that the translation from this binary characterization to neuronal firing is currently not well-understood-especially when considering different neuronal cell types. In this study, we investigate the impact of neuronal cell type on the firing outcome of ion channel mutations.

Methods

To this end, we simulated a diverse collection of single-compartment, conductance-based neuron models that differed in their composition of ionic currents. We systematically analyzed the effects of changes in ion current properties on firing in different neuronal types. Additionally, we simulated the effects of known mutations in KCNA1 gene encoding the K_V1.1 potassium channel subtype associated with episodic ataxia type 1 (EA1).

Results

These simulations revealed that the outcome of a given change in ion channel properties on neuronal excitability depends on neuron type, i.e., the properties and expression levels of the unaffected ionic currents.

Discussion

Consequently, neuron-type specific effects are vital to a full understanding of the effects of channelopathies on neuronal excitability and are an important step toward improving the efficacy and precision of personalized medicine approaches.

Degeneracy in epilepsy: multiple routes to hyperexcitable brain circuits and their repair

Due to its complex and multifaceted nature, developing effective treatments for epilepsy is still a major challenge. To deal with this complexity we introduce the concept of degeneracy to the field of epilepsy research: the ability of disparate elements to cause an analogous function or malfunction. Here, we review examples of epilepsy-related degeneracy at multiple levels of brain organisation, ranging from the cellular to the network and systems level. Based on these insights, we outline new multiscale and population modelling approaches to disentangle the complex web of interactions underlying epilepsy and to design personalised multitarget therapies.

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

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.

The effect of urethane and MS-222 anesthesia on the electric organ discharge of the weakly electric fish Apteronotus leptorhynchus

Urethane and MS-222 are agents widely employed for general anesthesia, yet, besides inducing a state of unconsciousness, little is known about their neurophysiological effects. To investigate these effects, we developed an in vivo assay using the electric organ discharge (EOD) of the weakly electric fish Apteronotus leptorhynchus as a proxy for the neural output of the pacemaker nucleus. The oscillatory neural activity of this brainstem nucleus drives the fish's EOD in a one-to-one fashion. Anesthesia induced by urethane or MS-222 resulted in pronounced decreases of the EOD frequency, which lasted for up to 3 h. In addition, each of the two agents caused a manifold increase in the generation of transient modulations of the EOD known as chirps. The reduction in EOD frequency can be explained by the modulatory effect of urethane on neurotransmission, and by the blocking of voltage-gated sodium channels by MS-222, both within the circuitry controlling the neural oscillations of the pacemaker nucleus. The present study demonstrates a marked effect of urethane and MS-222 on neural activity within the central nervous system and on the associated animal's behavior. This calls for caution when conducting neurophysiological experiments under general anesthesia and interpreting their results.

Long-Term Functional and Cytoarchitectonic Effects of the Systemic Administration of the Histamine H1 Receptor Antagonist/Inverse Agonist Chlorpheniramine During Gestation in the Rat Offspring Primary Motor Cortex

The transient histaminergic system is among the first neurotransmitter systems to appear during brain development in the rat mesencephalon/rhombencephalon. Histamine increases FOXP2-positive deep-layer neuron differentiation of cortical neural stem cells through H₁ receptor activation in vitro. The in utero or systemic administration of chlorpheniramine (H₁ receptor antagonist/inverse agonist) during deep-layer cortical neurogenesis decreases FOXP2 neurons in the developing cortex, and H₁R- or histidine decarboxylase-knockout mice show impairment in learning and memory, wakefulness and nociception, functions modulated by the cerebral cortex. Due to the role of H₁R in cortical neural stem cell neurogenesis, the purpose of this study was to evaluate the postnatal impact of the systemic administration of chlorpheniramine during deep-layer cortical neuron differentiation (E12–14) in the primary motor cortex (M1) of neonates (P0) and 21-day-old pups (P21). Chlorpheniramine or vehicle were systemically administered (5 mg/kg, i.p.) to pregnant Wistar rats at gestational days 12–14, and the expression and distribution of deep- (FOXP2 and TBR1) and superficial-layer (SATB2) neuronal cortical markers were analyzed in neonates from both groups. The qRT-PCR analysis revealed a reduction in the expression of Satb2 and FoxP2. However, Western blot and immunofluorescence showed increased protein levels in the chlorpheniramine-treated group. In P21 pups, the three markers showed impaired distribution and increased immunofluorescence in the experimental group. The Sholl analysis evidenced altered dendritic arborization of deep-layer neurons, with lower excitability in response to histamine, as evaluated by whole-cell patch-clamp recording, as well as diminished depolarization-evoked [³H]-glutamate release from striatal slices. Overall, these results suggest long-lasting effects of blocking H₁Rs during early neurogenesis that may impact the pathways involved in voluntary motor activity and cognition.

Histone Deacetylase Inhibitor Improves the Dysfunction of Hippocampal Gamma Oscillations and Fast Spiking Interneurons in Alzheimer's Disease Model Mice

The hippocampal gamma oscillation is important for cognitive function, and its deficit is related to cognitive impairment in Alzheimer’s disease (AD). Recently, it has been recognized that post-translational modification via histone acetylation is a fundamental molecular mechanism for regulating synaptic plasticity and cognitive function. However, little is known regarding the regulation of hippocampal gamma oscillation by histone acetylation. We investigated whether histone acetylation regulated kainate-induced gamma oscillations and their important regulator, fast-spiking interneurons, using acute hippocampal slices of AD model mice (PSAPP transgenic mice). We found a decrease in kainate-induced gamma oscillations in slices from PSAPP mice, accompanied with the increased activity of fast spiking interneurons in basal state and the decreased activity in activated state. The histone deacetylase (HDAC) inhibitor (SAHA, named vorinostat) restored deficits of gamma oscillation in PSAPP mice, accompanied with rescue of activity of fast spiking interneurons in basal and activated state. The effect of SAHA was different from that of the clinical AD drug donepezil, which rescued only function of fast spiking interneurons in basal state. Besides, activator of nuclear receptor family 4a (NR4a) receptor (cytosporone B), as one of the epigenetic modification related to HDAC inhibition, rescued the deficits in gamma oscillations in PSAPP mice. These results suggested a novel mechanism in which HDAC inhibition improved impairment of gamma oscillations in PSAPP mice by restoring the activity of fast spiking interneurons both in basal and activated state. The reversal of gamma oscillation deficits by HDAC inhibition and/or NR4a activation appears to be a potential therapeutic target for treating cognitive impairment in AD patients.

Reduced Dopamine Signaling Impacts Pyramidal Neuron Excitability in Mouse Motor Cortex

Dopaminergic modulation is essential for the control of voluntary movement; however, the role of dopamine in regulating the neural excitability of the primary motor cortex (M1) is not well understood. Here, we investigated two modes by which dopamine influences the input/output function of M1 neurons. To test the direct regulation of M1 neurons by dopamine, we performed whole-cell recordings of excitatory neurons and measured excitability before and after local, acute dopamine receptor blockade. We then determined whether chronic depletion of dopaminergic input to the entire motor circuit, via a mouse model of Parkinson's disease, was sufficient to shift M1 neuron excitability. We show that D1 receptor (D1R) and D2R antagonism altered subthreshold and suprathreshold properties of M1 pyramidal neurons in a layer-specific fashion. The effects of D1R antagonism were primarily driven by changes to intrinsic properties, while the excitability shifts following D2R antagonism relied on synaptic transmission. In contrast, chronic depletion of dopamine to the motor circuit with 6-hydroxydopamine induced layer-specific synaptic transmission-dependent shifts in M1 neuron excitability that only partially overlapped with the effects of acute D1R antagonism. These results suggest that while acute and chronic changes in dopamine modulate the input/output function of M1 neurons, the mechanisms engaged are distinct depending on the duration and origin of the manipulation. Our study highlights the broad influence of dopamine on M1 excitability by demonstrating the consequences of local and global dopamine depletion on neuronal input/output function.

Ion-channel regulation of response decorrelation in a heterogeneous multi-scale model of the dentate gyrus

Heterogeneities in biological neural circuits manifest in afferent connectivity as well as in local-circuit components such as neuronal excitability, neural structure and local synaptic strengths. The expression of adult neurogenesis in the dentate gyrus (DG) amplifies local-circuit heterogeneities and guides heterogeneities in afferent connectivity. How do neurons and their networks endowed with these distinct forms of heterogeneities respond to perturbations to individual ion channels, which are known to change under several physiological and pathophysiological conditions? We sequentially traversed the ion channels-neurons-network scales and assessed the impact of eliminating individual ion channels on conductance-based neuronal and network models endowed with disparate local-circuit and afferent heterogeneities. We found that many ion channels differentially contributed to specific neuronal or network measurements, and the elimination of any given ion channel altered several functional measurements. We then quantified the impact of ion-channel elimination on response decorrelation, a well-established metric to assess the ability of neurons in a network to convey complementary information, in DG networks endowed with different forms of heterogeneities. Notably, we found that networks constructed with structurally immature neurons exhibited functional robustness, manifesting as minimal changes in response decorrelation in the face of ion-channel elimination. Importantly, the average change in output correlation was dependent on the eliminated ion channel but invariant to input correlation. Our analyses suggest that neurogenesis-driven structural heterogeneities could assist the DG network in providing functional resilience to molecular perturbations.

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Perturbations at one scale result in a cascading impact on physiology across scales.

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Heterogeneous multi-scale models used to assess the impact of ion-channel deletion.

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Mapping of structural components to functional outcomes is many-to-many.

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Differential & variable impact of ion channel deletion on response decorrelation.

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Neurogenesis-induced structural heterogeneity confers resilience to perturbations.

The Input-Output Relation of Primary Nociceptive Neurons is Determined by the Morphology of the Peripheral Nociceptive Terminals

The output from the peripheral terminals of primary nociceptive neurons, which detect and encode the information regarding noxious stimuli, is crucial in determining pain sensation. The nociceptive terminal endings are morphologically complex structures assembled from multiple branches of different geometry, which converge in a variety of forms to create the terminal tree. The output of a single terminal is defined by the properties of the transducer channels producing the generation potentials and voltage-gated channels, translating the generation potentials into action potential (AP) firing. However, in the majority of cases, noxious stimuli activate multiple terminals; thus, the output of the nociceptive neuron is defined by the integration and computation of the inputs of the individual terminals. Here, we used a computational model of nociceptive terminal tree to study how the architecture of the terminal tree affects the input-output relation of the primary nociceptive neurons. We show that the input-output properties of the nociceptive neurons depend on the length, the axial resistance (Ra), and location of individual terminals. Moreover, we show that activation of multiple terminals by a capsaicin-like current allows summation of the responses from individual terminals, thus leading to increased nociceptive output. Stimulation of the terminals in simulated models of inflammatory or neuropathic hyperexcitability led to a change in the temporal pattern of AP firing, emphasizing the role of temporal code in conveying key information about changes in nociceptive output in pathologic conditions, leading to pain hypersensitivity.SIGNIFICANCE STATEMENT Noxious stimuli are detected by terminal endings of primary nociceptive neurons, which are organized into morphologically complex terminal trees. The information from multiple terminals is integrated along the terminal tree, computing the neuronal output, which propagates toward the CNS, thus shaping the pain sensation. Here, we revealed that the structure of the nociceptive terminal tree determines the output of nociceptive neurons. We show that the integration of noxious information depends on the morphology of the terminal trees and how this integration and, consequently, the neuronal output change under pathologic conditions. Our findings help to predict how nociceptive neurons encode noxious stimuli and how this encoding changes in pathologic conditions, leading to pain.

Influence of Delayed Conductance on Neuronal Synchronization

In the brain, the excitation-inhibition balance prevents abnormal synchronous behavior. However, known synaptic conductance intensity can be insufficient to account for the undesired synchronization. Due to this fact, we consider time delay in excitatory and inhibitory conductances and study its effect on the neuronal synchronization. In this work, we build a neuronal network composed of adaptive integrate-and-fire neurons coupled by means of delayed conductances. We observe that the time delay in the excitatory and inhibitory conductivities can alter both the state of the collective behavior (synchronous or desynchronous) and its type (spike or burst). For the weak coupling regime, we find that synchronization appears associated with neurons behaving with extremes highest and lowest mean firing frequency, in contrast to when desynchronization is present when neurons do not exhibit extreme values for the firing frequency. Synchronization can also be characterized by neurons presenting either the highest or the lowest levels in the mean synaptic current. For the strong coupling, synchronous burst activities can occur for delays in the inhibitory conductivity. For approximately equal-length delays in the excitatory and inhibitory conductances, desynchronous spikes activities are identified for both weak and strong coupling regimes. Therefore, our results show that not only the conductance intensity, but also short delays in the inhibitory conductance are relevant to avoid abnormal neuronal synchronization.

PRRT2 controls neuronal excitability by negatively modulating Na+ channel 1.2/1.6 activity

See Lerche (doi:10.1093/brain/awy073) for a scientific commentary on this article.

Proline-rich transmembrane protein 2 (PRRT2) is the causative gene for a heterogeneous group of familial paroxysmal neurological disorders that include seizures with onset in the first year of life (benign familial infantile seizures), paroxysmal kinesigenic dyskinesia or a combination of both. Most of the PRRT2 mutations are loss-of-function leading to haploinsufficiency and 80% of the patients carry the same frameshift mutation (c.649dupC; p.Arg217Profs*8), which leads to a premature stop codon. To model the disease and dissect the physiological role of PRRT2, we studied the phenotype of neurons differentiated from induced pluripotent stem cells from previously described heterozygous and homozygous siblings carrying the c.649dupC mutation. Single-cell patch-clamp experiments on induced pluripotent stem cell-derived neurons from homozygous patients showed increased Na⁺ currents that were fully rescued by expression of wild-type PRRT2. Closely similar electrophysiological features were observed in primary neurons obtained from the recently characterized PRRT2 knockout mouse. This phenotype was associated with an increased length of the axon initial segment and with markedly augmented spontaneous and evoked firing and bursting activities evaluated, at the network level, by multi-electrode array electrophysiology. Using HEK-293 cells stably expressing Na_v channel subtypes, we demonstrated that the expression of PRRT2 decreases the membrane exposure and Na⁺ current of Na_v1.2/Na_v1.6, but not Na_v1.1, channels. Moreover, PRRT2 directly interacted with Na_v1.2/Na_v1.6 channels and induced a negative shift in the voltage-dependence of inactivation and a slow-down in the recovery from inactivation. In addition, by co-immunoprecipitation assays, we showed that the PRRT2-Na_v interaction also occurs in brain tissue. The study demonstrates that the lack of PRRT2 leads to a hyperactivity of voltage-dependent Na⁺ channels in homozygous PRRT2 knockout human and mouse neurons and that, in addition to the reported synaptic functions, PRRT2 is an important negative modulator of Na_v1.2 and Na_v1.6 channels. Given the predominant paroxysmal character of PRRT2-linked diseases, the disturbance in cellular excitability by lack of negative modulation of Na⁺ channels appears as the key pathogenetic mechanism.

Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.

Tune it in: mechanisms and computational significance of neuron-autonomous plasticity

The activity of a neural network is a result of synaptic signals that convey the communication between neurons and neuron-based intrinsic currents that determine the neuron’s input-output transfer function. Ample studies have demonstrated that cell-based excitability, and in particular intrinsic excitability, is modulated by learning and that these modifications play a key role in learning-related behavioral changes. The field of cell-based plasticity is largely growing, and it entails numerous experimental findings that demonstrate a large diversity of currents that are affected by learning. The diverse effect of learning on the neuron’s excitability emphasizes the need for a framework under which cell-based plasticity can be categorized to enable the assessment of the computational roles of the intrinsic modifications. We divide the domain of cell-based plasticity into three main categories, where the first category entails the currents that mediate the passive properties and single-spike generation, the second category entails the currents that mediate spike frequency adaptation, and the third category entails a novel learning-induced mechanism where all excitatory and inhibitory synapses double their strength. Curiously, this elementary division enables a natural categorization of the computational roles of these learning-induced plasticities. The computational roles are diverse and include modification of the neuronal mode of action, such as bursting, prolonged, and fast responsive; attention-like effect where the signal detection is improved; transfer of the network into an active state; biasing the competition for memory allocation; and transforming an environmental cue into a dominant cue and enabling a quicker formation of new memories.

Effects of Metabolic Energy on Synaptic Transmission and Dendritic Integration in Pyramidal Neurons

As a sophisticated computing unit, the pyramidal neuron requires sufficient metabolic energy to fuel its powerful computational capabilities. However, the majority of previous works focus on nonlinear integration and energy consumption in individual pyramidal neurons but seldom on the effects of metabolic energy on synaptic transmission and dendritic integration. Here, we developed biologically plausible models to simulate the synaptic transmission and dendritic integration of pyramidal neurons, exploring the relations between synaptic transmission and metabolic energy and between dendritic integration and metabolic energy. We find that synaptic energy not only drives synaptic vesicle cycle, but also participates in the regulation of this cycle. Release probability of synapses adapts to synaptic energy levels by regulating the speed of synaptic vesicle cycle. Besides, we also find that to match neural energy levels, only a part of the synapses receive presynaptic signals during a given period so that neurons have a low action potential frequency. That is, the number of simultaneously active synapses over a period of time should be adapted to neural energy levels.

Degeneracy in the regulation of short-term plasticity and synaptic filtering by presynaptic mechanisms

KEY POINTS

We develop a new biophysically rooted, physiologically constrained conductance-based synaptic model to mechanistically account for short-term facilitation and depression, respectively through residual calcium and transmitter depletion kinetics. We address the specific question of how presynaptic components (including voltage-gated ion channels, pumps, buffers and release-handling mechanisms) and interactions among them define synaptic filtering and short-term plasticity profiles. Employing global sensitivity analyses (GSAs), we show that near-identical synaptic filters and short-term plasticity profiles could emerge from disparate presynaptic parametric combinations with weak pairwise correlations. Using virtual knockout models, a technique to address the question of channel-specific contributions within the GSA framework, we unveil the differential and variable impact of each ion channel on synaptic physiology. Our conclusions strengthen the argument that parametric and interactional complexity in biological systems should not be viewed from the limited curse-of-dimensionality standpoint, but from the evolutionarily advantageous perspective of providing functional robustness through degeneracy.

ABSTRACT

Information processing in neurons is known to emerge as a gestalt of pre- and post-synaptic filtering. However, the impact of presynaptic mechanisms on synaptic filters has not been quantitatively assessed. Here, we developed a biophysically rooted, conductance-based model synapse that was endowed with six different voltage-gated ion channels, calcium pumps, calcium buffer and neurotransmitter-replenishment mechanisms in the presynaptic terminal. We tuned our model to match the short-term plasticity profile and band-pass structure of Schaffer collateral synapses, and performed sensitivity analyses to demonstrate that presynaptic voltage-gated ion channels regulated synaptic filters through changes in excitability and associated calcium influx. These sensitivity analyses also revealed that calcium- and release-control mechanisms were effective regulators of synaptic filters, but accomplished this without changes in terminal excitability or calcium influx. Next, to perform global sensitivity analysis, we generated 7000 randomized models spanning 15 presynaptic parameters, and computed eight different physiological measurements in each of these models. We validated these models by applying experimentally obtained bounds on their measurements, and found 104 (∼1.5%) models to match the validation criteria for all eight measurements. Analysing these valid models, we demonstrate that analogous synaptic filters emerge from disparate combinations of presynaptic parameters exhibiting weak pairwise correlations. Finally, using virtual knockout models, we establish the variable and differential impact of different presynaptic channels on synaptic filters, underlining the critical importance of interactions among different presynaptic components in defining synaptic physiology. Our results have significant implications for protein-localization strategies required for physiological robustness and for degeneracy in long-term synaptic plasticity profiles.

Purkinje cell intrinsic excitability increases after synaptic long term depression

Coding in cerebellar Purkinje cells not only depends on synaptic plasticity but also on their intrinsic membrane excitability. We performed whole cell patch-clamp recordings of Purkinje cells in sagittal cerebellar slices in mice. We found that inducing long-term depression (LTD) in the parallel fiber to Purkinje cell synapses results in an increase in the gain of the firing rate response. This increase in excitability is accompanied by an increase in the input resistance and a decrease in the amplitude of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel-mediated voltage sag. Application of a HCN channel blocker prevents the increase in input resistance and excitability without blocking the expression of synaptic LTD. We conclude that the induction of parallel fiber-Purkinje cell LTD is accompanied by an increase in excitability of Purkinje cells through downregulation of the HCN-mediated h current. We suggest that HCN downregulation is linked to the biochemical pathway that sustains synaptic LTD. Given the diversity of information carried by the parallel fiber system, we suggest that changes in intrinsic excitability enhance the coding capacity of the Purkinje cell to specific input sources.

From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability

Models of electrical activity in excitable cells involve nonlinear interactions between many ionic currents. Changing parameters in these models can produce a variety of activity patterns with sometimes unexpected effects. Further more, introducing new currents will have different effects depending on the initial parameter set. In this study we combined global sampling of parameter space and local analysis of representative parameter sets in a pituitary cell model to understand the effects of adding K (+) conductances, which mediate some effects of hormone action on these cells. Global sampling ensured that the effects of introducing K (+) conductances were captured across a wide variety of contexts of model parameters. For each type of K (+) conductance we determined the types of behavioral transition that it evoked. Some transitions were counterintuitive, and may have been missed without the use of global sampling. In general, the wide range of transitions that occurred when the same current was applied to the model cell at different locations in parameter space highlight the challenge of making accurate model predictions in light of cell-to-cell heterogeneity. Finally, we used bifurcation analysis and fast/slow analysis to investigate why specific transitions occur in representative individual models. This approach relies on the use of a graphics processing unit (GPU) to quickly map parameter space to model behavior and identify parameter sets for further analysis. Acceleration with modern low-cost GPUs is particularly well suited to exploring the moderate-sized (5-20) parameter spaces of excitable cell and signaling models.

Molecular variability elicits a tunable switch with discrete neuromodulatory response phenotypes

Recent single cell studies show extensive molecular variability underlying cellular responses. We evaluated the impact of molecular variability in the expression of cell signaling components and ion channels on electrophysiological excitability and neuromodulation. We employed a computational approach that integrated neuropeptide receptor-mediated signaling with electrophysiology. We simulated a population of neurons in which expression levels of a neuropeptide receptor and multiple ion channels were simultaneously varied within a physiological range. We analyzed the effects of variation on the electrophysiological response to a neuropeptide stimulus. Our results revealed distinct response patterns associated with low versus high receptor levels. Neurons with low receptor levels showed increased excitability and neurons with high receptor levels showed reduced excitability. These response patterns were separated by a narrow receptor level range forming a separatrix. The position of this separatrix was dependent on the expression levels of multiple ion channels. To assess the relative contributions of receptor and ion channel levels to the response profiles, we categorized the responses into six phenotypes based on response kinetics and magnitude. We applied several multivariate statistical approaches and found that receptor and channel expression levels influence the neuromodulation response phenotype through a complex though systematic mapping. Our analyses extended our understanding of how cellular responses to neuromodulation vary as a function of molecular expression. Our study showed that receptor expression and biophysical state interact with distinct relative contributions to neuronal excitability.

Variability in cardiac electrophysiology: Using experimentally-calibrated populations of models to move beyond the single virtual physiological human paradigm

Physiological variability manifests itself via differences in physiological function between individuals of the same species, and has crucial implications in disease progression and treatment. Despite its importance, physiological variability has traditionally been ignored in experimental and computational investigations due to averaging over samples from multiple individuals. Recently, modelling frameworks have been devised for studying mechanisms underlying physiological variability in cardiac electrophysiology and pro-arrhythmic risk under a variety of conditions and for several animal species as well as human. One such methodology exploits populations of cardiac cell models constrained with experimental data, or experimentally-calibrated populations of models. In this review, we outline the considerations behind constructing an experimentally-calibrated population of models and review the studies that have employed this approach to investigate variability in cardiac electrophysiology in physiological and pathological conditions, as well as under drug action. We also describe the methodology and compare it with alternative approaches for studying variability in cardiac electrophysiology, including cell-specific modelling approaches, sensitivity-analysis based methods, and populations-of-models frameworks that do not consider the experimental calibration step. We conclude with an outlook for the future, predicting the potential of new methodologies for patient-specific modelling extending beyond the single virtual physiological human paradigm.

Post-translational modifications of voltage-gated sodium channels in chronic pain syndromes

In the peripheral sensory nervous system the neuronal expression of voltage-gated sodium channels (Navs) is very important for the transmission of nociceptive information since they give rise to the upstroke of the action potential (AP). Navs are composed of nine different isoforms with distinct biophysical properties. Studying the mutations associated with the increase or absence of pain sensitivity in humans, as well as other expression studies, have highlighted Nav1.7, Nav1.8, and Nav1.9 as being the most important contributors to the control of nociceptive neuronal electrogenesis. Modulating their expression and/or function can impact the shape of the AP and consequently modify nociceptive transmission, a process that is observed in persistent pain conditions. Post-translational modification (PTM) of Navs is a well-known process that modifies their expression and function. In chronic pain syndromes, the release of inflammatory molecules into the direct environment of dorsal root ganglia (DRG) sensory neurons leads to an abnormal activation of enzymes that induce Navs PTM. The addition of small molecules, i.e., peptides, phosphoryl groups, ubiquitin moieties and/or carbohydrates, can modify the function of Navs in two different ways: via direct physical interference with Nav gating, or via the control of Nav trafficking. Both mechanisms have a profound impact on neuronal excitability. In this review we will discuss the role of Protein Kinase A, B, and C, Mitogen Activated Protein Kinases and Ca++/Calmodulin-dependent Kinase II in peripheral chronic pain syndromes. We will also discuss more recent findings that the ubiquitination of Nav1.7 by Nedd4-2 and the effect of methylglyoxal on Nav1.8 are also implicated in the development of experimental neuropathic pain. We will address the potential roles of other PTMs in chronic pain and highlight the need for further investigation of PTMs of Navs in order to develop new pharmacological tools to alleviate pain.

The domain of neuronal firing on a plane of input current and conductance

The activation of neurotransmitter receptors increases the current flow and membrane conductance and thus controls the firing rate of a neuron. In the present work, we justified the two-dimensional representation of a neuronal input by voltage-independent current and conductance and obtained experimentally and numerically a complete input-output (I/O) function. The dependence of the steady-state firing rate on the input current and conductance was studied as a two-parameter I/O function. We employed the dynamic patch clamp technique in slices to get this dependence for the whole domain of two input signals that evoke stationary spike trains in a single neuron (Ω-domain). As found, the Ω-domain is finite and an additional conductance decreases the range of spike-evoking currents. The I/O function has been reproduced in a Hodgkin-Huxley-like model. Among the simulated effects of different factors on the I/O function, including passive and active membrane properties, external conditions and input signal properties, the most interesting were: the shift of the right boundary of the Ω-domain (corresponding to the exCitation block) leftwards due to the decrease of the maximal potassium conductance; and the reduction of the Ω-domain by the decrease of the maximal sodium concentration. As found in experiments and simulations, the Ω-domain is reduced by the decrease of extracellular sodium concentration, by cooling, and by adding slow potassium currents providing interspike interval adaptation; the Ω-domain height is increased by adding color noise. Our modeling data provided a generalization of I/O dependencies that is consistent with previous studies and our experiments. Our results suggest that both current flow and membrane conductance should be taken into account when determining neuronal firing activity.

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.

The role of slow and persistent TTX-resistant sodium currents in acute tumor necrosis factor-α-mediated increase in nociceptors excitability

Tetrodotoxin-resistant (TTX-r) sodium channels are key players in determining the input-output properties of peripheral nociceptive neurons. Changes in gating kinetics or in expression levels of these channels by proinflammatory mediators are likely to cause the hyperexcitability of nociceptive neurons and pain hypersensitivity observed during inflammation. Proinflammatory mediator, tumor necrosis factor-α (TNF-α), is secreted during inflammation and is associated with the early onset, as well as long-lasting, inflammation-mediated increase in excitability of peripheral nociceptive neurons. Here we studied the underlying mechanisms of the rapid component of TNF-α-mediated nociceptive hyperexcitability and acute pain hypersensitivity. We showed that TNF-α leads to rapid onset, cyclooxygenase-independent pain hypersensitivity in adult rats. Furthermore, TNF-α rapidly and substantially increases nociceptive excitability in vitro, by decreasing action potential threshold, increasing neuronal gain and decreasing accommodation. We extended on previous studies entailing p38 MAPK-dependent increase in TTX-r sodium currents by showing that TNF-α via p38 MAPK leads to increased availability of TTX-r sodium channels by partial relief of voltage dependence of their slow inactivation, thereby contributing to increase in neuronal gain. Moreover, we showed that TNF-α also in a p38 MAPK-dependent manner increases persistent TTX-r current by shifting the voltage dependence of activation to a hyperpolarized direction, thus producing an increase in inward current at functionally critical subthreshold voltages. Our results suggest that rapid modulation of the gating of TTX-r sodium channels plays a major role in the mediated nociceptive hyperexcitability of TNF-α during acute inflammation and may lead to development of effective treatments for inflammatory pain, without modulating the inflammation-induced healing processes.

Differential effects of static and dynamic inputs on neuronal excitability

The intrinsic excitability of neurons is known to be dynamically regulated by activity-dependent plasticity and homeostatic mechanisms. Such processes are commonly analyzed in the context of input-output functions that describe how neurons fire in response to constant levels of current. However, it is not well understood how changes of excitability as observed under static inputs translate to the function of the same neurons in their natural synaptic environment. Here we performed a computational study and hybrid experiments on rat bed nucleus of stria terminalis neurons to compare the two scenarios. The inward rectifying Kir current (IKir) and the hyperpolarization-activated cation current (Ih) were found to be considerably more effective in regulating the firing under synaptic inputs than under static stimuli. This prediction was experimentally confirmed by dynamic-clamp insertion of a synthetic inwardly rectifying Kir current into the biological neurons. At the same time, ionic currents that activate with depolarization were more effective regulating the firing under static inputs. When two intrinsic currents are concurrently altered such as those under homeostatic regulation, the effects in firing responses under static vs. dynamic inputs can be even more contrasting. Our results show that plastic or homeostatic changes of intrinsic membrane currents can shape the current step responses of neurons and their firing under synaptic inputs in a differential manner.

Cell-intrinsic mechanisms of temperature compensation in a grasshopper sensory receptor neuron

Changes in temperature affect biochemical reaction rates and, consequently, neural processing. The nervous systems of poikilothermic animals must have evolved mechanisms enabling them to retain their functionality under varying temperatures. Auditory receptor neurons of grasshoppers respond to sound in a surprisingly temperature-compensated manner: firing rates depend moderately on temperature, with average Q10 values around 1.5. Analysis of conductance-based neuron models reveals that temperature compensation of spike generation can be achieved solely relying on cell-intrinsic processes and despite a strong dependence of ion conductances on temperature. Remarkably, this type of temperature compensation need not come at an additional metabolic cost of spike generation. Firing rate-based information transfer is likely to increase with temperature and we derive predictions for an optimal temperature dependence of the tympanal transduction process fostering temperature compensation. The example of auditory receptor neurons demonstrates how neurons may exploit single-cell mechanisms to cope with multiple constraints in parallel.DOI: http://dx.doi.org/10.7554/eLife.02078.001.

Pumilio-2 regulates translation of Nav1.6 to mediate homeostasis of membrane excitability

The ability to regulate intrinsic membrane excitability, to maintain consistency of action potential firing, is critical for stable neural circuit activity. Without such mechanisms, Hebbian-based synaptic plasticity could push circuits toward activity saturation or, alternatively, quiescence. Although now well documented, the underlying molecular components of these homeostatic mechanisms remain poorly understood. Recent work in the fruit fly, Drosophila melanogaster, has identified Pumilio (Pum), a translational repressor, as an essential component of one such mechanism. In response to changing synaptic excitation, Pum regulates the translation of the voltage-gated sodium conductance, leading to a concomitant adjustment in action potential firing. Although similar homeostatic mechanisms are operational in mammalian neurons, it is unknown whether Pum is similarly involved. In this study, we report that Pum2 is indeed central to the homeostatic mechanism regulating membrane excitability in rat visual cortical pyramidal neurons. Using RNA interference, we observed that loss of Pum2 leads to increased sodium current (I(Na)) and action potential firing, mimicking the response by these neurons to being deprived of synaptic depolarization. In contrast, increased synaptic depolarization results in increased Pum2 expression and subsequent reduction in INa and membrane excitability. We further show that Pum2 is able to directly bind the predominant voltage-gated sodium channel transcript (NaV1.6) expressed in these neurons and, through doing so, regulates translation of this key determinant of membrane excitability. Together, our results show that Pum2 forms part of a homeostatic mechanism that matches membrane excitability to synaptic depolarization in mammalian neurons.