Criticality and degeneracy in injury-induced changes in primary afferent excitability and the implications for neuropathic pain

Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells

Complex systems are neither fully determined nor completely random. Biological complex systems, including single neurons, manifest intermediate regimes of randomness that recruit integration of specific combinations of functionally specialized subsystems. Such emergence of biological function provides the substrate for the expression of degeneracy, the ability of disparate combinations of subsystems to yield similar function. Here, we present evidence for the expression of degeneracy in morphologically realistic models of dentate gyrus granule cells (GCs) through functional integration of disparate ion-channel combinations. We performed a 45-parameter randomized search spanning 16 active and passive ion channels, each biophysically constrained by their gating kinetics and localization profiles, to search for valid GC models. Valid models were those that satisfied 17 sub- and suprathreshold cellular-scale electrophysiological measurements from rat GCs. A vast majority (>99%) of the 15,000 random models were not electrophysiologically valid, demonstrating that arbitrarily random ion-channel combinations would not yield GC functions. The 141 valid models (0.94% of 15,000) manifested heterogeneities in and cross-dependencies across local and propagating electrophysiological measurements, which matched with their respective biological counterparts. Importantly, these valid models were widespread throughout the parametric space and manifested weak cross-dependencies across different parameters. These observations together showed that GC physiology could neither be obtained by entirely random ion-channel combinations nor is there an entirely determined single parametric combination that satisfied all constraints. The complexity, the heterogeneities in measurement and parametric spaces, and degeneracy associated with GC physiology should be rigorously accounted for while assessing GCs and their robustness under physiological and pathological conditions.NEW & NOTEWORTHY A recent study from our laboratory had demonstrated pronounced heterogeneities in a set of 17 electrophysiological measurements obtained from a large population of rat hippocampal granule cells. Here, we demonstrate the manifestation of ion-channel degeneracy in a heterogeneous population of morphologically realistic conductance-based granule cell models that were validated against these measurements and their cross-dependencies. Our analyses show that single neurons are complex entities whose functions emerge through intricate interactions among several functionally specialized subsystems.

Diversity-induced trivialization and resilience of neural dynamics

Heterogeneity is omnipresent across all living systems. Diversity enriches the dynamical repertoire of these systems but remains challenging to reconcile with their manifest robustness and dynamical persistence over time, a fundamental feature called resilience. To better understand the mechanism underlying resilience in neural circuits, we considered a nonlinear network model, extracting the relationship between excitability heterogeneity and resilience. To measure resilience, we quantified the number of stationary states of this network, and how they are affected by various control parameters. We analyzed both analytically and numerically gradient and non-gradient systems modeled as non-linear sparse neural networks evolving over long time scales. Our analysis shows that neuronal heterogeneity quenches the number of stationary states while decreasing the susceptibility to bifurcations: a phenomenon known as trivialization. Heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in network size and connection probability by quenching the system's dynamic volatility.

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.

Short-term plasticity in the spinal nociceptive system

ABSTRACT

Somatosensory information is delivered to neuronal networks of the dorsal horn (DH) of the spinal cord by the axons of primary afferent neurons that encode the intensity of peripheral sensory stimuli under the form of a code based on the frequency of action potential firing. The efficient processing of these messages within the DH involves frequency-tuned synapses, a phenomenon linked to their ability to display activity-dependent forms of short-term plasticity (STP). By affecting differently excitatory and inhibitory synaptic transmissions, these STP properties allow a powerful gain control in DH neuronal networks that may be critical for the integration of nociceptive messages before they are forwarded to the brain, where they may be ultimately interpreted as pain. Moreover, these STPs can be finely modulated by endogenous signaling molecules, such as neurosteroids, adenosine, or GABA. The STP properties of DH inhibitory synapses might also, at least in part, participate in the pain-relieving effect of nonpharmacological analgesic procedures, such as transcutaneous electrical nerve stimulation, electroacupuncture, or spinal cord stimulation. The properties of target-specific STP at inhibitory DH synapses and their possible contribution to electrical stimulation-induced reduction of hyperalgesic and allodynic states in chronic pain will be reviewed and discussed.

Deep RNA-seq of male and female murine sensory neuron subtypes after nerve injury

ABSTRACT

Dorsal root ganglia (DRG) neurons have been well described for their role in driving both acute and chronic pain. Although nerve injury is known to cause transcriptional dysregulation, how this differs across neuronal subtypes and the impact of sex is unclear. Here, we study the deep transcriptional profiles of multiple murine DRG populations in early and late pain states while considering sex. We have exploited currently available transgenics to label numerous subpopulations for fluorescent-activated cell sorting and subsequent transcriptomic analysis. Using bulk tissue samples, we are able to circumvent the issues of low transcript coverage and drop-outs seen with single-cell data sets. This increases our power to detect novel and even subtle changes in gene expression within neuronal subtypes and discuss sexual dimorphism at the neuronal subtype level. We have curated this resource into an accessible database for other researchers ( https://livedataoxford.shinyapps.io/drg-directory/ ). We see both stereotyped and unique subtype signatures in injured states after nerve injury at both an early and late timepoint. Although all populations contribute to a general injury signature, subtype enrichment changes can also be seen. Within populations, there is not a strong intersection of sex and injury, but previously unknown sex differences in naïve states-particularly in Aβ-RA + Aδ-low threshold mechanoreceptors-still contribute to differences in injured neurons.

Intrinsic neural diversity quenches the dynamic volatility of neural networks

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical diversity enriches neural systems' dynamical repertoire, it remains challenging to reconcile with the robustness and persistence of brain function over time (resilience). To better understand the relationship between excitability heterogeneity (variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations-signs of instability-in response to a slowly varying modulatory fluctuation. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell heterogeneity in the robustness of brain function in the face of change.

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.

Electrophysiological Alterations Driving Pain-Associated Spontaneous Activity in Human Sensory Neuron Somata Parallel Alterations Described in Spontaneously Active Rodent Nociceptors

Neuropathic pain in rodents can be driven by ectopic spontaneous activity (SA) generated by sensory neurons in dorsal root ganglia (DRG). The recent demonstration that SA in dissociated human DRG neurons is associated with reported neuropathic pain in patients enables a detailed comparison of pain-linked electrophysiological alterations driving SA in human DRG neurons to alterations that distinguish SA in nociceptors from SA in low-threshold mechanoreceptors (LTMRs) in rodent neuropathy models. Analysis of recordings from dissociated somata of patient-derived DRG neurons showed that SA and corresponding pain in both sexes were significantly associated with the three functional electrophysiological alterations sufficient to generate SA in the absence of extrinsic depolarizing inputs. These include enhancement of depolarizing spontaneous fluctuations of membrane potential (DSFs), which were analyzed quantitatively for the first time in human DRG neurons. The functional alterations were indistinguishable from SA-driving alterations reported for nociceptors in rodent chronic pain models. Irregular, low-frequency DSFs in human DRG neurons closely resemble DSFs described in rodent nociceptors while differing substantially from the high-frequency sinusoidal oscillations described in rodent LTMRs. These findings suggest that conserved physiological mechanisms of SA in human nociceptor somata can drive neuropathic pain despite documented cellular differences between human and rodent DRG neurons. PERSPECTIVE: Electrophysiological alterations in human sensory neurons associated with patient-reported neuropathic pain include all three of the functional alterations that logically can promote spontaneous activity. The similarity of distinctively altered spontaneous depolarizations in human DRG neurons and rodent nociceptors suggests that spontaneously active human nociceptors can persistently promote neuropathic pain in patients.

Multiscale Computer Model of the Spinal Dorsal Horn Reveals Changes in Network Processing Associated with Chronic Pain

Pain-related sensory input is processed in the spinal dorsal horn (SDH) before being relayed to the brain. That processing profoundly influences whether stimuli are correctly or incorrectly perceived as painful. Significant advances have been made in identifying the types of excitatory and inhibitory neurons that comprise the SDH, and there is some information about how neuron types are connected, but it remains unclear how the overall circuit processes sensory input or how that processing is disrupted under chronic pain conditions. To explore SDH function, we developed a computational model of the circuit that is tightly constrained by experimental data. Our model comprises conductance-based neuron models that reproduce the characteristic firing patterns of spinal neurons. Excitatory and inhibitory neuron populations, defined by their expression of genetic markers, spiking pattern, or morphology, were synaptically connected according to available qualitative data. Using a genetic algorithm, synaptic weights were tuned to reproduce projection neuron firing rates (model output) based on primary afferent firing rates (model input) across a range of mechanical stimulus intensities. Disparate synaptic weight combinations could produce equivalent circuit function, revealing degeneracy that may underlie heterogeneous responses of different circuits to perturbations or pathologic insults. To validate our model, we verified that it responded to the reduction of inhibition (i.e., disinhibition) and ablation of specific neuron types in a manner consistent with experiments. Thus validated, our model offers a valuable resource for interpreting experimental results and testing hypotheses in silico to plan experiments for examining normal and pathologic SDH circuit function.SIGNIFICANCE STATEMENT We developed a multiscale computer model of the posterior part of spinal cord gray matter (spinal dorsal horn), which is involved in perceiving touch and pain. The model reproduces several experimental observations and makes predictions about how specific types of spinal neurons and synapses influence projection neurons that send information to the brain. Misfiring of these projection neurons can produce anomalous sensations associated with chronic pain. Our computer model will not only assist in planning future experiments, but will also be useful for developing new pharmacotherapy for chronic pain disorders, connecting the effect of drugs acting at the molecular scale with emergent properties of neurons and circuits that shape the pain experience.

Minimal requirements for a neuron to co-regulate many properties and the implications for ion channel correlations and robustness

Neurons regulate their excitability by adjusting their ion channel levels. Degeneracy – achieving equivalent outcomes (excitability) using different solutions (channel combinations) – facilitates this regulation by enabling a disruptive change in one channel to be offset by compensatory changes in other channels. But neurons must coregulate many properties. Pleiotropy – the impact of one channel on more than one property – complicates regulation because a compensatory ion channel change that restores one property to its target value often disrupts other properties. How then does a neuron simultaneously regulate multiple properties? Here, we demonstrate that of the many channel combinations producing the target value for one property (the single-output solution set), few combinations produce the target value for other properties. Combinations producing the target value for two or more properties (the multioutput solution set) correspond to the intersection between single-output solution sets. Properties can be effectively coregulated only if the number of adjustable channels (n_in) exceeds the number of regulated properties (n_out). Ion channel correlations emerge during homeostatic regulation when the dimensionality of solution space (n_in − n_out) is low. Even if each property can be regulated to its target value when considered in isolation, regulation as a whole fails if single-output solution sets do not intersect. Our results also highlight that ion channels must be coadjusted with different ratios to regulate different properties, which suggests that each error signal drives modulatory changes independently, despite those changes ultimately affecting the same ion channels.

Degenerate brainstem circuitry after combined physiochemical exposure to jet fuel and noise

Degenerate neural circuits exhibit "different" circuit properties yet produce similar circuit outcomes (many-to-one) which ensures circuit robustness and complexity. However, neuropathies may hijack degeneracy to yield robust and complex pathological circuits. The aim of the current study was to test the hypothesis that physiochemical exposure to combined jet fuel and noise might induce degeneracy in the brainstem. The auditory brainstem of pigmented rats was used as a model system. The animals were randomized into the following experimental groups: Fuel+Noise, fuel-only, noise-only, and control. Ascending volume conductance from various auditory brainstem regions were evaluated simultaneously with peripheral nervous system (PNS) input to brainstem circuitry. Data demonstrated normal PNS inputs for all groups. However, the Fuel+Noise exposure group produced different caudal brainstem circuit properties while rostral brainstem circuitry initiated outputs that were similar to that of control. This degenerative effect was specific to Fuel+Noise exposure, since neither noise-alone or fuel-alone produced the same result. Degeneracy in the auditory brainstem is consistent with perceptual abnormalities, such as poor speech discrimination (hear but not understand), tinnitus (ringing in the ear), hyperacusis (hypersensitivity to even low-level sound), and loudness intolerance. Therefore, a potential consequence of Fuel+Noise exposure among military and civilian populations may be evidenced as increased rates of super-threshold auditory perceptual abnormalities. This is particularly important because to date, the ototoxic profile of Fuel+Noise exposure has remained unresolved.

A functional subdivision within the somatosensory system and its implications for pain research

Somatosensory afferents are traditionally classified by soma size, myelination, and their response specificity to external and internal stimuli. Here, we propose the functional subdivision of the nociceptive somatosensory system into two branches. The exteroceptive branch detects external threats and drives reflexive-defensive reactions to prevent or limit injury. The interoceptive branch senses the disruption of body integrity, produces tonic pain with strong aversive emotional components, and drives self-caring responses toward to the injured region to reduce suffering. The central thesis behind this functional subdivision comes from a reflection on the dilemma faced by the pain research field, namely, the use of reflexive-defensive behaviors as surrogate assays for interoceptive tonic pain. The interpretation of these assays is now being challenged by the discovery of distinct but interwoven circuits that drive exteroceptive versus interoceptive types of behaviors, with the conflation of these two components contributing partially to the poor translation of therapies from preclinical studies.

A population of in silico models identifies the interplay between Nav 1.8 conductance and potassium currents as key in regulating human dorsal root ganglion neuron excitability

Background: The Nav 1.8 sodium channel has a key role in generating repetitive action potentials in nociceptive human dorsal root ganglion neurons. Nav 1.8 is differentiated from other voltage-gated sodium channels by its unusually slow inactivation kinetics and depolarised voltage-dependence of activation. These features are particularly pronounced in the human Nav 1.8 channel and allow the channel to remain active during repolarisation. Gain-of-function mutations in Nav 1.8 have been linked to neuropathic pain and selective blockers of Nav 1.8 have been developed as potential new analgesics. However, it is not well understood how modulating the Nav 1.8 conductance alters neuronal excitability and how this depends on the balance of other ion channels expressed by nociceptive neurons. Methods: To investigate this, we developed a novel computational model of the human dorsal root ganglion neuron and used it to construct a population of models that mimicked inter-neuronal heterogeneity in ionic conductances and action potential morphology Results: By simulating changes to the Nav 1.8 conductance in the population of models, we found that moderately increasing the Nav 1.8 conductance led to increased firing rate, as expected, but increasing Nav 1.8 conductance beyond an inflection point caused firing rate to decrease. We found that the delayed rectifier and M-type potassium conductances were also critical for determining neuronal excitability. In particular, altering the delayed rectifier potassium conductance shifted the position of the Nav 1.8 inflection point and therefore the relationship between Nav 1.8 conductance and firing rate. Conclusions: Our results suggest that the effects of modulating Nav 1.8 in a nociceptive neuron can depend significantly on other conductances, particularly potassium conductances.

Degeneracy in the nervous system: from neuronal excitability to neural coding

Degeneracy is ubiquitous across biological systems where structurally different elements can yield a similar outcome. Degeneracy is of particular interest in neuroscience too. On the one hand, degeneracy confers robustness to the nervous system and facilitates evolvability: Different elements provide a backup plan for the system in response to any perturbation or disturbance. On the other, a difficulty in the treatment of some neurological disorders such as chronic pain is explained in light of different elements all of which contribute to the pathological behavior of the system. Under these circumstances, targeting a specific element is ineffective because other elements can compensate for this modulation. Understanding degeneracy in the physiological context explains its beneficial role in the robustness of neural circuits. Likewise, understanding degeneracy in the pathological context opens new avenues of discovery to find more effective therapies.

Ion-channel degeneracy: Multiple ion channels heterogeneously regulate intrinsic physiology of rat hippocampal granule cells

Degeneracy, the ability of multiple structural components to elicit the same characteristic functional properties, constitutes an elegant mechanism for achieving biological robustness. In this study, we sought electrophysiological signatures for the expression of ion-channel degeneracy in the emergence of intrinsic properties of rat hippocampal granule cells. We measured the impact of four different ion-channel subtypes-hyperpolarization-activated cyclic-nucleotide-gated (HCN), barium-sensitive inward rectifier potassium (Kir ), tertiapin-Q-sensitive inward rectifier potassium, and persistent sodium (NaP) channels-on 21 functional measurements employing pharmacological agents, and report electrophysiological data on two characteristic signatures for the expression of ion-channel degeneracy in granule cells. First, the blockade of a specific ion-channel subtype altered several, but not all, functional measurements. Furthermore, any given functional measurement was altered by the blockade of many, but not all, ion-channel subtypes. Second, the impact of blocking each ion-channel subtype manifested neuron-to-neuron variability in the quantum of changes in the electrophysiological measurements. Specifically, we found that blocking HCN or Ba-sensitive Kir channels enhanced action potential firing rate, but blockade of NaP channels reduced firing rate of granule cells. Subthreshold measures of granule cell intrinsic excitability (input resistance, temporal summation, and impedance amplitude) were enhanced by blockade of HCN or Ba-sensitive Kir channels, but were not significantly altered by NaP channel blockade. We confirmed that the HCN and Ba-sensitive Kir channels independently altered sub- and suprathreshold properties of granule cells through sequential application of pharmacological agents that blocked these channels. Finally, we found that none of the sub- or suprathreshold measurements of granule cells were significantly altered upon treatment with tertiapin-Q. Together, the heterogeneous many-to-many mapping between ion channels and single-neuron intrinsic properties emphasizes the need to account for ion-channel degeneracy in cellular- and network-scale physiology.

Effects of Several Classes of Voltage-Gated Ion Channel Conductances on Gamma and Theta Oscillations in a Hippocampal Microcircuit Model

Gamma and theta oscillations have been functionally associated with cognitive processes, such as learning and memory. Synaptic conductances play an important role in the generation of intrinsic network rhythmicity, but few studies have examined the effects of voltage-gated ion channels (VGICs) on these rhythms. In this report, we have used a pyramidal-interneuron-gamma (PING) network consisting of excitatory pyramidal cells and two types of inhibitory interneurons. We have constructed a conductance-based neural network incorporating a persistent sodium current (I_NaP), a delayed rectifier potassium current (I_KDR), a inactivating potassium current (I_A) and a hyperpolarization-activated current (I_H). We have investigated the effects of several conductances on network theta and gamma frequency oscillations. Variation of all conductances of interest changed network rhythmicity. Theta power was altered by all conductances tested. Gamma rhythmogenesis was dependent on I_A and I_H. The I_KDR currents in excitatory pyramidal cells as well as both types of inhibitory interneurons were essential for theta rhythmogenesis and altered gamma rhythm properties. Increasing I_NaP suppressed both gamma and theta rhythms. Addition of noise did not alter these patterns. Our findings suggest that VGICs strongly affect brain network rhythms. Further investigations in vivo will be of great interest, including potential effects on neural function and cognition.

Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience

The large number of ion channels found in all nervous systems poses fundamental questions concerning how the characteristic intrinsic properties of single neurons are determined by the specific subsets of channels they express. All neurons display many different ion channels with overlapping voltage- and time-dependent properties. We speculate that these overlapping properties promote resilience in neuronal function. Individual neurons of the same cell type show variability in ion channel conductance densities even though they can generate reliable and similar behavior. This complicates a simple assignment of function to any conductance and is associated with variable responses of neurons of the same cell type to perturbations, deletions, and pharmacological manipulation. Ion channel genes often show strong positively correlated expression, which may result from the molecular and developmental rules that determine which ion channels are expressed in a given cell type.

Computational analysis of a 9D model for a small DRG neuron

Small dorsal root ganglion (DRG) neurons are primary nociceptors which are responsible for sensing pain. Elucidation of their dynamics is essential for understanding and controlling pain. To this end, we present a numerical bifurcation analysis of a small DRG neuron model in this paper. The model is of Hodgkin-Huxley type and has 9 state variables. It consists of a Na_v1.7 and a Na_v1.8 sodium channel, a leak channel, a delayed rectifier potassium, and an A-type transient potassium channel. The dynamics of this model strongly depend on the maximal conductances of the voltage-gated ion channels and the external current, which can be adjusted experimentally. We show that the neuron dynamics are most sensitive to the Na_v1.8 channel maximal conductance ([Formula: see text]). Numerical bifurcation analysis shows that depending on [Formula: see text] and the external current, different parameter regions can be identified with stable steady states, periodic firing of action potentials, mixed-mode oscillations (MMOs), and bistability between stable steady states and stable periodic firing of action potentials. We illustrate and discuss the transitions between these different regimes. We further analyze the behavior of MMOs. As the external current is decreased, we find that MMOs appear after a cyclic limit point. Within this region, bifurcation analysis shows a sequence of isolated periodic solution branches with one large action potential and a number of small amplitude peaks per period. For decreasing external current, the number of small amplitude peaks is increasing and the distance between the large amplitude action potentials is growing, finally tending to infinity and thereby leading to a stable steady state. A closer inspection reveals more complex concatenated MMOs in between these periodic MMO branches, forming Farey sequences. Lastly, we also find small solution windows with aperiodic oscillations which seem to be chaotic. The dynamical patterns found here-as consequences of bifurcation points regulated by different parameters-have potential translational significance as repetitive firing of action potentials imply pain of some form and intensity; manipulating these patterns by regulating the different parameters could aid in investigating pain dynamics.

Circuit Stability to Perturbations Reveals Hidden Variability in the Balance of Intrinsic and Synaptic Conductances

Neurons and circuits each with a distinct balance of intrinsic and synaptic conductances can generate similar behavior but sometimes respond very differently to perturbation. Examining a large family of circuit models with non-identical neurons and synapses underlying rhythmic behavior, we analyzed the circuits' response to modifications in single and multiple intrinsic conductances in the individual neurons. To summarize these changes over the entire range of perturbed parameters, we quantified circuit output by defining a global stability measure. Using this measure, we identified specific subsets of conductances that when perturbed generate similar behavior in diverse individuals of the population. Our unbiased clustering analysis enabled us to quantify circuit stability when simultaneously perturbing multiple conductances as a nonlinear combination of single conductance perturbations. This revealed surprising conductance combinations that can predict the response to specific perturbations, even when the remaining intrinsic and synaptic conductances are unknown. Therefore, our approach can expose hidden variability in the balance of intrinsic and synaptic conductances of the same neurons across different versions of the same circuit solely from the circuit response to perturbations. Developed for a specific family of model circuits, our quantitative approach to characterizing high-dimensional degenerate systems provides a conceptual and analytic framework to guide future theoretical and experimental studies on degeneracy and robustness.

SIGNIFICANCE STATEMENT Neural circuits can generate nearly identical behavior despite neuronal and synaptic parameters varying several-fold between individual instantiations. Yet, when these parameters are perturbed through channel deletions and mutations or environmental disturbances, seemingly identical circuits can respond very differently. What distinguishes inconsequential perturbations that barely alter circuit behavior from disruptive perturbations that drastically disturb circuit output remains unclear. Focusing on a family of rhythmic circuits, we propose a computational approach to reveal hidden variability in the intrinsic and synaptic conductances in seemingly identical circuits based solely on circuit output to different perturbations. We uncover specific conductance combinations that work similarly to maintain stability and predict the effect of changing multiple conductances simultaneously, which often results from neuromodulation or injury.

Intermittent Failure of Spike Propagation in Primary Afferent Neurons during Tactile Stimulation

Primary afferent neurons convey somatosensory information to the CNS. Low-threshold mechanoreceptors are classified as slow-adapting (SA) or rapid-adapting (RA) based on whether or not they spike repetitively during sustained tactile stimulation; the former are subclassified as Type 1 or 2 based on the regularity of their spiking. Recording in vivo from DRGs of mice, we observed irregular- and regular-spiking units consistent with SA1 and SA2 low-threshold mechanoreceptors, but some units, which we labeled "semiregular," did not fit cleanly into the existing classification scheme. Analysis of their spiking revealed integer-multiple patterning in which spike trains comprised a fundamental interspike interval and multiples thereof. Integer-multiple-patterned spiking was reproduced by randomly removing spikes from an otherwise regular spike train, suggesting that semiregular units represent SA2 units in which some spikes are "missing." We hypothesized that missing spikes arose from intermittent failure of spikes to initiate or to propagate. Intermittent failure of spike initiation was ruled out by several observations: integer-multiple-patterned spiking was not induced by intradermal lidocaine, was independent of stimulus modality (mechanical vs optogenetic), and could not be reproduced in a conductance-based model neuron given constant input. On the other hand, integer-multiple-patterned spiking was induced by application of lidocaine to the DRG, thus pinpointing intermittent failure of spike propagation as the basis for integer-multiple-patterned spiking. Indeed, half of all SA2 units exhibited some missing spikes, mostly at low rate (<5%), which suggests that axons are efficient in using the lowest safety factor capable of producing near-perfect propagation reliability.SIGNIFICANCE STATEMENT The impedance mismatch at axon branch points can impede spike propagation. Reliability of spike propagation across branch points remains an open question and is especially important for primary afferents whose spikes must cross a T-junction to reach the CNS. Past research on propagation reliability has relied almost entirely on simulations and in vitro experiments. Here, recording in vivo, we linked a distinctive pattern of spiking to the intermittent failure of spike propagation at the T-junction. The rarity of failures argues that safety factor is high under physiological conditions, yet the occurrence of such failures argues that safety factor is just high enough to ensure near-perfect reliability, consistent with a good balance between propagation reliability and energy efficiency.

Lysozyme elicits pain during nerve injury by neuronal Toll-like receptor 4 activation and has therapeutic potential in neuropathic pain

The role of neuronal Toll-like receptor 4 (TLR4) in nerve injury is being pursued actively. However, the endogenous activation of neuronal TLR4 during neuroinflammation, in absence of the participation of glial TLR4, remains elusive. Here, we identified lysozyme as an endogenous activator of neuronal TLR4 signaling during nerve injury. Upon nerve injury, enhanced expression of lysozyme promoted neuronal hyperexcitability and neuropathic pain. Injections of lysozyme in healthy rats increased their mechanical and thermal pain sensitivity. Likewise, infusion of spinal cord slices with lysozyme increased neuronal excitability typical of neuropathic pain. Our results also showed that lysozyme activated excitability of both Aδ- and C-fibers. Thus, in addition to the discovery of lysozyme as an endogenous ligand for regulating neuronal TLR4 signaling, this study also lays the foundation of our understanding of its role in nervous system pathologies, providing multiple avenues for treating neuroinflammation.

Software piracy and bundling in the cloud-based software era

Purpose

In the cloud computing era, three merging developments in software industry are: cloud and on-premises software may offer complementary value to each other; cloud software service requires the support of significant information technology infrastructure; and software piracy problems can be better managed in the cloud. However, how these developments together impact a vendor’s bundling strategy has not yet been investigated. The paper aims to discuss this issue.

Design/methodology/approach

Drawing on the product bundling framework, this research establishes stylized models to study a software vendor’s bundling decision in the cloud-based era with special consideration on the issue of software piracy.

Findings

The authors find different key parameters associated with the cloud era exert different effects on the bundling decision. When on-premises software and cloud software generate additional value by complementing each other, software vendors can make greater profits under the pure components (PC) strategy. Regarding a low infrastructure cost, software vendors should favor pure bundling (PB). The impact of piracy deterrence effectiveness is less straightforward – it favors PC when piracy deterrence effectiveness is low, but PB when piracy deterrence effectiveness is high.

Originality/value

This study makes key contributions to theory and practice. First, this is the first study to examine software bundling strategies in the cloud computing era, whereby the three factors relevant to the cloud phenomenon have been considered. Second, this paper contributes to the literature of bundling and software piracy by examining the intersection of these two streams of literature. Third, this paper sheds light on a vendor’s bundling decision when facing piracy problems in the emerging cloud software era.

TRESK K+ Channel Activity Regulates Trigeminal Nociception and Headache

Although TWIK-related spinal cord K⁺ (TRESK) channel is expressed in all primary afferent neurons in trigeminal ganglia (TG) and dorsal root ganglia (DRG), whether TRESK activity regulates trigeminal pain processing is still not established. Dominant-negative TRESK mutations are associated with migraine but not with other types of pain in humans, suggesting that genetic TRESK dysfunction preferentially affects the generation of trigeminal pain, especially headache. Using TRESK global knock-out mice as a model system, we found that loss of TRESK in all TG neurons selectively increased the intrinsic excitability of small-diameter nociceptors, especially those that do not bind to isolectin B4 (IB4^-). Similarly, loss of TRESK resulted in hyper-excitation of the small IB4^- dural afferent neurons but not those that bind to IB4 (IB4⁺). Compared with wild-type littermates, both male and female TRESK knock-out mice exhibited more robust trigeminal nociceptive behaviors, including headache-related behaviors, whereas their body and visceral pain responses were normal. Interestingly, neither the total persistent outward current nor the intrinsic excitability was altered in adult TRESK knock-out DRG neurons, which may explain why genetic TRESK dysfunction is not associated with body and/or visceral pain in humans. We reveal for the first time that, among all primary afferent neurons, TG nociceptors are the most vulnerable to the genetic loss of TRESK. Our findings indicate that endogenous TRESK activity regulates trigeminal nociception, likely through controlling the intrinsic excitability of TG nociceptors. Importantly, we provide evidence that genetic loss of TRESK significantly increases the likelihood of developing headache.

Chloride Dysregulation through Downregulation of KCC2 Mediates Neuropathic Pain in Both Sexes

The behavioral features of neuropathic pain are not sexually dimorphic despite sex differences in the underlying neuroimmune signaling. This raises questions about whether neural processing is comparably altered. Here, we test whether the K+-Cl- co-transporter KCC2, which regulates synaptic inhibition, plays an equally important role in development of neuropathic pain in male and female rodents. Past studies on KCC2 tested only males. We find that inhibiting KCC2 in uninjured animals reproduces behavioral and electrophysiological features of neuropathic pain in both sexes and, consistent with equivalent injury-induced downregulation of KCC2, that counteracting chloride dysregulation reverses injury-induced behavioral and electrophysiological changes in both sexes. These findings demonstrate that KCC2 downregulation contributes equally to pain hypersensitivity in males and females. Whereas diverse (and sexually dimorphic) mechanisms regulate KCC2, regulation of intracellular chloride relies almost exclusively on KCC2. Directly targeting KCC2 thus remains a promising strategy for treatment of neuropathic pain in both sexes.

Isolated nociceptors reveal multiple specializations for generating irregular ongoing activity associated with ongoing pain

Ongoing pain has been linked to ongoing activity (OA) in human C-fiber nociceptors, but rodent models of pain-related OA have concentrated on allodynia rather than ongoing pain, and on OA generated in non-nociceptive Aβ fibers rather than C-fiber nociceptors. Little is known about how ongoing pain or nociceptor OA is generated. To define neurophysiological alterations underlying nociceptor OA, we have used isolated dorsal root ganglion neurons that continue to generate OA after removal from animals displaying ongoing pain. We subclassify OA as either spontaneous activity generated solely by alterations intrinsic to the active neuron or as extrinsically driven OA. Both types of OA were implicated previously in nociceptors in vivo and after isolation following spinal cord injury, which produces chronic ongoing pain. Using novel automated algorithms to analyze irregular changes in membrane potential, we have found, in a distinctive, nonaccommodating type of probable nociceptor, induction by spinal cord injury of 3 alterations that promote OA: (1) prolonged depolarization of resting membrane potential, (2) a hyperpolarizing shift in the voltage threshold for action potential generation, and (3) an increase in the incidence of large depolarizing spontaneous fluctuations (DSFs). Can DSFs also be enhanced acutely to promote OA in neurons from uninjured animals? A low dose of serotonin failed to change resting membrane potential but lowered action potential threshold. When combined with artificial depolarization to model inflammation, serotonin also strongly potentiated DSFs and OA. These findings reveal nociceptor specializations for generating OA that may promote ongoing pain in chronic and acute conditions.

Using dynamic clamp to quantify pathological changes in the excitability of primary somatosensory neurons

KEY POINTS

Primary somatosensory neurons normally respond to somatic depolarization with transient spiking but can switch to repetitive spiking under pathological conditions. This switch in spiking pattern reflects a qualitative change in spike initiation dynamics and contributes to the hyperexcitability associated with chronic pain. Neurons can be converted to repetitive spiking by adding a virtual conductance using dynamic clamp. By titrating the conductance to determine how much must be added to cause repetitive spiking, we found that small cells are more susceptible to switching (i.e. required less added conductance) than medium-large cells. By measuring how much less conductance is required to cause repetitive spiking when dynamic clamp was combined with other pathomimetic manipulations (e.g. application of inflammatory mediators), we measured how much each manipulation facilitated repetitive spiking. Our results suggest that many pathological factors facilitate repetitive spiking but that the switch to repetitive spiking requires the cumulative effect of many co-occurring factors.

ABSTRACT

Primary somatosensory neurons become hyperexcitable in many chronic pain conditions. Hyperexcitability can include a switch from transient to repetitive spiking during sustained somatic depolarization. This switch results from diverse pathological processes that impact ion channel expression or function. Because multiple pathological processes co-occur, isolating how much each contributes to switching the spiking pattern is difficult. Our approach to this challenge involves adding a virtual sodium conductance via dynamic clamp. The magnitude of that conductance was titrated to determine the minimum required to enable rheobasic stimulation to evoke repetitive spiking. The minimum required conductance, termed g¯ Na ∗, was re-measured before and during manipulations designed to model various pathological processes in vitro. The reduction in g¯ Na ∗ caused by each pathomimetic manipulation reflects how much the modelled process contributes to switching the spiking pattern. We found that elevating extracellular potassium or applying inflammatory mediators reduced g¯ Na ∗ whereas direct hyperpolarization had no effect. Inflammatory mediators reduced g¯ Na ∗ more in medium-large (>30 μm diameter) neurons than in small (⩽30 μm diameter) neurons, but had equivalent effects in cutaneous and muscle afferents. The repetitive spiking induced by dynamic clamp was also found to differ between small and medium-large neurons, thus revealing latent differences in adaptation. Our study demonstrates a novel way to determine to what extent individual pathological factors facilitate repetitive spiking. Our results suggest that most factors facilitate but do not cause repetitive spiking on their own, and, therefore, that a switch to repetitive spiking results from the cumulative effect of many co-occurring factors.

Using an engineered glutamate-gated chloride channel to silence sensory neurons and treat neuropathic pain at the source

See Basbaum (doi:10.1093/brain/awx227) for a scientific commentary on this article. Peripheral neuropathic pain arises as a consequence of injury to sensory neurons; the development of ectopic activity in these neurons is thought to be critical for the induction and maintenance of such pain. Local anaesthetics and anti-epileptic drugs can suppress hyperexcitability; however, these drugs are complicated by unwanted effects on motor, central nervous system and cardiac function, and alternative more selective treatments to suppress hyperexcitability are therefore required. Here we show that a glutamate-gated chloride channel modified to be activated by low doses of ivermectin (but not glutamate) is highly effective in silencing sensory neurons and reversing neuropathic pain-related hypersensitivity. Activation of the glutamate-gated chloride channel expressed in either rodent or human induced pluripotent stem cell-derived sensory neurons in vitro potently inhibited their response to both electrical and algogenic stimuli. We have shown that silencing is achieved both at nerve terminals and the soma and is independent of membrane hyperpolarization and instead likely mediated by lowering of the membrane resistance. Using intrathecal adeno-associated virus serotype 9-based delivery, the glutamate-gated chloride channel was successfully targeted to mouse sensory neurons in vivo, resulting in high level and long-lasting expression of the channel selectively in sensory neurons. This enabled reproducible and reversible modulation of thermal and mechanical pain thresholds in vivo; analgesia was observed for 3 days after a single systemic dose of ivermectin. We did not observe any motor or proprioceptive deficits and noted no reduction in cutaneous afferent innervation or upregulation of the injury marker ATF3 following prolonged glutamate-gated chloride channel expression. Established mechanical and cold pain-related hypersensitivity generated by the spared nerve injury model of neuropathic pain was reversed by ivermectin treatment. The efficacy of ivermectin in ameliorating behavioural hypersensitivity was mirrored at the cellular level by a cessation of ectopic activity in sensory neurons. These findings demonstrate the importance of aberrant afferent input in the maintenance of neuropathic pain and the potential for targeted chemogenetic silencing as a new treatment modality in neuropathic pain.

Combined Changes in Chloride Regulation and Neuronal Excitability Enable Primary Afferent Depolarization to Elicit Spiking without Compromising its Inhibitory Effects

The central terminals of primary afferent fibers experience depolarization upon activation of GABAA receptors (GABAAR) because their intracellular chloride concentration is maintained above electrochemical equilibrium. Primary afferent depolarization (PAD) normally mediates inhibition via sodium channel inactivation and shunting but can evoke spikes under certain conditions. Antidromic (centrifugal) conduction of these spikes may contribute to neurogenic inflammation while orthodromic (centripetal) conduction could contribute to pain in the case of nociceptive fibers. PAD-induced spiking is assumed to override presynaptic inhibition. Using computer simulations and dynamic clamp experiments, we sought to identify which biophysical changes are required to enable PAD-induced spiking and whether those changes necessarily compromise PAD-mediated inhibition. According to computational modeling, a depolarizing shift in GABA reversal potential (EGABA) and increased intrinsic excitability (manifest as altered spike initiation properties) were necessary for PAD-induced spiking, whereas increased GABAAR conductance density (ḡGABA) had mixed effects. We tested our predictions experimentally by using dynamic clamp to insert virtual GABAAR conductances with different EGABA and kinetics into acutely dissociated dorsal root ganglion (DRG) neuron somata. Comparable experiments in central axon terminals are prohibitively difficult but the biophysical requirements for PAD-induced spiking are arguably similar in soma and axon. Neurons from naïve (i.e. uninjured) rats were compared before and after pharmacological manipulation of intrinsic excitability, and against neurons from nerve-injured rats. Experimental data confirmed that, in most neurons, both predicted changes were necessary to yield PAD-induced spiking. Importantly, such changes did not prevent PAD from inhibiting other spiking or from blocking spike propagation. In fact, since the high value of ḡGABA required for PAD-induced spiking still mediates strong inhibition, we conclude that PAD-induced spiking does not represent failure of presynaptic inhibition. Instead, diminished PAD caused by reduction of ḡGABA poses a greater risk to presynaptic inhibition and the sensory processing that relies upon it.

Enhanced excitability and suppression of A-type K(+) currents in joint sensory neurons in a murine model of antigen-induced arthritis

Pain is a dominant symptom of rheumatoid arthritis (RA) and its adequate treatment represents a major unmet need. However, the cellular mechanisms that drive arthritis pain are largely unexplored. Here, we examined the changes in the activity of joint sensory neurons and the associated ionic mechanisms using an animal model of antigen-induced arthritis (AIA). Methylated-bovine serum albumin (mBSA), but not vehicle challenge, in the ankle of previously immunized mice produced time-dependent symptoms of arthritis, including joint inflammation, primary mechanical hyperalgesia in the ipsilateral ankle, and secondary mechanical and heat hyperalgesia in the ipsilateral hindpaw. In vivo electrophysiological recordings revealed that Dil-labeled joint sensory neurons in AIA mice exhibited a greater incidence of spontaneous activity, mechanically evoked after-discharges, and/or increased responses to mechanical stimulation of their receptive fields, compared to control animals. Whole-cell recordings in vitro showed that AIA enhanced the excitability of joint sensory neurons. These signs of neuronal hyperexcitability were associated with a significant reduction in the density of A-type K⁺ currents. Thus, our data suggest that neuronal hyperexcitability, brought about in part by reduced A-type K⁺ currents, may contribute to pain-related behaviors that accompany antigen-induced arthritis and/or other antigen-mediated diseases.

A Probabilistic Model for Estimating the Depth and Threshold Temperature of C-fiber Nociceptors

The subjective experience of thermal pain follows the detection and encoding of noxious stimuli by primary afferent neurons called nociceptors. However, nociceptor morphology has been hard to access and the mechanisms of signal transduction remain unresolved. In order to understand how heat transducers in nociceptors are activated in vivo, it is important to estimate the temperatures that directly activate the skin-embedded nociceptor membrane. Hence, the nociceptor's temperature threshold must be estimated, which in turn will depend on the depth at which transduction happens in the skin. Since the temperature at the receptor cannot be accessed experimentally, such an estimation can currently only be achieved through modeling. However, the current state-of-the-art model to estimate temperature at the receptor suffers from the fact that it cannot account for the natural stochastic variability of neuronal responses. We improve this model using a probabilistic approach which accounts for uncertainties and potential noise in system. Using a data set of 24 C-fibers recorded in vitro, we show that, even without detailed knowledge of the bio-thermal properties of the system, the probabilistic model that we propose here is capable of providing estimates of threshold and depth in cases where the classical method fails.

Ion channel degeneracy enables robust and tunable neuronal firing rates

Firing rate is an important means of encoding information in the nervous system. To reliably encode a wide range of signals, neurons need to achieve a broad range of firing frequencies and to move smoothly between low and high firing rates. This can be achieved with specific ionic currents, such as A-type potassium currents, which can linearize the frequency-input current curve. By applying recently developed mathematical tools to a number of biophysical neuron models, we show how currents that are classically thought to permit low firing rates can paradoxically cause a jump to a high minimum firing rate when expressed at higher levels. Consequently, achieving and maintaining a low firing rate is surprisingly difficult and fragile in a biological context. This difficulty can be overcome via interactions between multiple currents, implying a need for ion channel degeneracy in the tuning of neuronal properties.

Physiological Dynamics in Demyelinating Diseases: Unraveling Complex Relationships through Computer Modeling

Despite intense research, few treatments are available for most neurological disorders. Demyelinating diseases are no exception. This is perhaps not surprising considering the multifactorial nature of these diseases, which involve complex interactions between immune system cells, glia and neurons. In the case of multiple sclerosis, for example, there is no unanimity among researchers about the cause or even which system or cell type could be ground zero. This situation precludes the development and strategic application of mechanism-based therapies. We will discuss how computational modeling applied to questions at different biological levels can help link together disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism. By making testable predictions and revealing critical gaps in existing knowledge, such models can help direct research and will provide a rigorous framework in which to integrate new data as they are collected. Nowadays, there is no shortage of data; the challenge is to make sense of it all. In that respect, computational modeling is an invaluable tool that could, ultimately, transform how we understand, diagnose, and treat demyelinating diseases.

Noise-induced plasticity of KCNQ2/3 and HCN channels underlies vulnerability and resilience to tinnitus

Vulnerability to noise-induced tinnitus is associated with increased spontaneous firing rate in dorsal cochlear nucleus principal neurons, fusiform cells. This hyperactivity is caused, at least in part, by decreased Kv7.2/3 (KCNQ2/3) potassium currents. However, the biophysical mechanisms underlying resilience to tinnitus, which is observed in noise-exposed mice that do not develop tinnitus (non-tinnitus mice), remain unknown. Our results show that noise exposure induces, on average, a reduction in KCNQ2/3 channel activity in fusiform cells in noise-exposed mice by 4 days after exposure. Tinnitus is developed in mice that do not compensate for this reduction within the next 3 days. Resilience to tinnitus is developed in mice that show a re-emergence of KCNQ2/3 channel activity and a reduction in HCN channel activity. Our results highlight KCNQ2/3 and HCN channels as potential targets for designing novel therapeutics that may promote resilience to tinnitus.

Sensory neuron subpopulation-specific dysregulation of intracellular calcium in a rat model of chemotherapy-induced peripheral neuropathy

The purpose of the present study was to test the prediction that the unique manifestation of chemotherapeutic-induced peripheral neuropathy (CIPN) would be reflected in a specific pattern of changes in the regulation of the intracellular Ca(2+) concentration ([Ca(2+)]i) in subpopulations of cutaneous neurons. To test this prediction, we characterized the pattern of changes in mechanical nociceptive threshold associated with paclitaxel administration (2mg/kg, iv, every other day for four days), as well as the impact of target of innervation and paclitaxel treatment on the regulation of [Ca(2+)]i in subpopulations of putative nociceptive and non-nociceptive neurons. Neurons innervating the glabrous and hairy skin of the hindpaw as well as the thigh were identified with retrograde tracers, and fura-2 was used to assess changes in [Ca(2+)]i. Paclitaxel was associated with a persistent decrease in mechanical nociceptive threshold in response to stimuli applied to the glabrous skin of the hindpaw, but not the hairy skin of the hindpaw or the thigh. However, in both putative nociceptive and non-nociceptive neurons, resting [Ca(2+)]i was significantly lower in neurons innervating the thigh after treatment. The magnitude of the depolarization-evoked Ca(2+) transient was also lower in putative non-nociceptive thigh neurons. More interestingly, while paclitaxel had no detectable influence on either resting or depolarization-evoked Ca(2+) transients in putative non-nociceptive neurons, in putative nociceptive neurons there was a subpopulation-specific decrease in the duration of the evoked Ca(2+) transient that was largely restricted to neurons innervating the glabrous skin. These results suggest that peripheral nerve length alone, does not account for the selective distribution of CIPN symptoms. Rather, they suggest the symptoms of CIPN reflect an interaction between the toxic actions of the therapeutic and unique properties of the neurons deleteriously impacted.

Cooperativity between remote sites of ectopic spiking allows afterdischarge to be initiated and maintained at different locations

Many symptoms of nerve damage arise from ectopic spiking caused by hyperexcitability. Ectopic spiking can originate at the site of axonal damage and elsewhere within affected neurons. This raises the question of whether localized damage elicits cell-wide changes in excitability and/or if localized changes in excitability can drive abnormal spiking at remote locations. Computer modeling revealed an example of the latter involving afterdischarge (AD)--stimulus-evoked spiking that outlasts stimulation. We found that AD originating in a hyperexcitable region of axon could shift to the soma where it was maintained. This repositioning of ectopic spike initiation was independent of distance between the two sites but relied on the rate and number of ectopic spikes originating from the first site. Nonlinear dynamical analysis of a reduced model demonstrated that properties which rendered the axonal site prone to initiating AD discouraged it from maintaining AD, whereas the soma had the inverse properties thus enabling the two sites to interact cooperatively. A first phase of AD originating in the axon could, by providing sufficient drive to trigger somatic AD, give way to a second phase of AD originating in the soma such that spiking continued when axonal AD failed. Ectopic spikes originating from the soma during phase 2 AD propagated successfully through the defunct site of axonal spike initiation. This novel mechanism whereby ectopic spiking at one site facilitates ectopic spiking at another site is likely to contribute to the chronification of hyperexcitability in conditions such as neuropathic pain.

Local knockdown of the NaV1.6 sodium channel reduces pain behaviors, sensory neuron excitability, and sympathetic sprouting in rat models of neuropathic pain

In the spinal nerve ligation (SNL) model of neuropathic pain, as in other pain models, abnormal spontaneous activity of myelinated sensory neurons occurs early and is essential for establishing pain behaviors and other pathologies. Sympathetic sprouting into the dorsal root ganglion (DRG) is observed after SNL, and sympathectomy reduces pain behavior. Sprouting and spontaneous activity may be mutually reinforcing: blocking neuronal activity reduces sympathetic sprouting, and sympathetic spouts functionally increase spontaneous activity in vitro. However, most studies in this field have used nonspecific methods to block spontaneous activity, methods that also block evoked and normal activity. In this study, we injected small inhibitory (si) RNA directed against the NaV1.6 sodium channel isoform into the DRG before SNL. This isoform can mediate high-frequency repetitive firing, like that seen in spontaneously active neurons. Local knockdown of NaV1.6 markedly reduced mechanical pain behaviors induced by SNL, reduced sympathetic sprouting into the ligated sensory ganglion, and blocked abnormal spontaneous activity and other measures of hyperexcitability in myelinated neurons in the ligated sensory ganglion. Immunohistochemical experiments showed that sympathetic sprouting preferentially targeted NaV1.6-positive neurons. Under these experimental conditions, NaV1.6 knockdown did not prevent or strongly alter single evoked action potentials, unlike previous less specific methods used to block spontaneous activity. NaV1.6 knockdown also reduced pain behaviors in another pain model, chronic constriction of the sciatic nerve, provided the model was modified so that the lesion site was relatively close to the siRNA-injected lumbar DRGs. The results highlight the relative importance of abnormal spontaneous activity in establishing both pain behaviors and sympathetic sprouting, and suggest that the NaV1.6 isoform may have value as a therapeutic target.

Novel method to assess axonal excitability using channelrhodopsin-based photoactivation

Measuring the excitability of individual axons is complicated by the prohibitive difficulty in obtaining intracellular recordings. Here, we present an innovative methodology that enables local excitability to be measured anywhere in a channelrhodopsin (ChR2)-expressing neuron. The approach hinges on activating ChR2 in a spatially and temporally precise manner while recording the resulting spike train from a remote site. We validated this approach in primary afferent neurons (PANs). Initial encoding of somatosensory stimuli relies on transduction of the physical stimulus into a receptor potential and transformation of the receptor potential into a spike train; the transformation process depends on the excitability of the most distal PAN endings but, as explained above, is extraordinarily difficult to study in situ using traditional methods. Using ChR2-based photoactivation, we show 1) that excitability differs between the distal endings and more proximal portions of PAN axons, 2) that the transformation process differs between PANs, and 3) that the transformation process is directly affected by inflammation. Beyond presenting an innovative method by which to study axonal excitability, this study has validated its utility in helping to decipher the earliest stages of somatosensory encoding.

Subthreshold membrane currents confer distinct tuning properties that enable neurons to encode the integral or derivative of their input

Neurons rely on action potentials, or spikes, to encode information. But spikes can encode different stimulus features in different neurons. We show here through simulations and experiments how neurons encode the integral or derivative of their input based on the distinct tuning properties conferred upon them by subthreshold currents. Slow-activating subthreshold inward (depolarizing) current mediates positive feedback control of subthreshold voltage, sustaining depolarization and allowing the neuron to spike on the basis of its integrated stimulus waveform. Slow-activating subthreshold outward (hyperpolarizing) current mediates negative feedback control of subthreshold voltage, truncating depolarization and forcing the neuron to spike on the basis of its differentiated stimulus waveform. Depending on its direction, slow-activating subthreshold current cooperates or competes with fast-activating inward current during spike initiation. This explanation predicts that sensitivity to the rate of change of stimulus intensity differs qualitatively between integrators and differentiators. This was confirmed experimentally in spinal sensory neurons that naturally behave as specialized integrators or differentiators. Predicted sensitivity to different stimulus features was confirmed by covariance analysis. Integration and differentiation, which are themselves inverse operations, are thus shown to be implemented by the slow feedback mediated by oppositely directed subthreshold currents expressed in different neurons.

The pros and cons of degeneracy

Drugs could treat neuropathic pain more effectively if they simultaneously targeted two or more types of ion channel.