Integration time in a subset of spinal lamina I neurons is lengthened by sodium and calcium currents acting synergistically to prolong subthreshold depolarization

Noise or signal? Spontaneous activity of dorsal horn neurons: patterns and function in health and disease

Spontaneous activity refers to the firing of action potentials by neurons in the absence of external stimulation. Initially considered an artifact or "noise" in the nervous system, it is now recognized as a potential feature of neural function. Spontaneous activity has been observed in various brain areas, in experimental preparations from different animal species, and in live animals and humans using non-invasive imaging techniques. In this review, we specifically focus on the spontaneous activity of dorsal horn neurons of the spinal cord. We use a historical perspective to set the basis for a novel classification of the different patterns of spontaneous activity exhibited by dorsal horn neurons. Then we examine the origins of this activity and propose a model circuit to explain how the activity is generated and transmitted to the dorsal horn. Finally, we discuss possible roles of this activity during development and during signal processing under physiological conditions and pain states. By analyzing recent studies on the spontaneous activity of dorsal horn neurons, we aim to shed light on its significance in sensory processing. Understanding the different patterns of activity, the origins of this activity, and the potential roles it may play, will contribute to our knowledge of sensory mechanisms, including pain, to facilitate the modeling of spinal circuits and hopefully to explore novel strategies for pain treatment.

Novel aspects of signal processing in lamina I

The most superficial layer of the spinal dorsal horn, lamina I, is a key element of the nociceptive processing system. It contains different types of projection neurons (PNs) and local-circuit neurons (LCNs) whose functional roles in the signal processing are poorly understood. This article reviews recent progress in elucidating novel anatomical features and physiological properties of lamina I PNs and LCNs revealed by whole-cell recordings in ex vivo spinal cord. This article is part of the Special Issue on "Ukrainian Neuroscience".

Synapse-specific diversity of distinct postsynaptic GluN2 subtypes defines transmission strength in spinal lamina I

The unitary postsynaptic response to presynaptic quantal glutamate release is the fundamental basis of excitatory information transfer between neurons. The view, however, of individual glutamatergic synaptic connections in a population as homogenous, fixed-strength units of neural communication is becoming increasingly scrutinized. Here, we used minimal stimulation of individual glutamatergic afferent axons to evoke single synapse resolution postsynaptic responses from central sensory lamina I neurons in an ex vivo adult rat spinal slice preparation. We detected unitary events exhibiting a NMDA receptor component with distinct kinetic properties across synapses conferred by specific GluN2 subunit composition, indicative of GluN2 subtype-based postsynaptic heterogeneity. GluN2A, 2A and 2B, or 2B and 2D synaptic predominance functioned on distinct lamina I neuron types to narrowly, intermediately, or widely tune, respectively, the duration of evoked unitary depolarization events from resting membrane potential, which enabled individual synapses to grade differentially depolarizing steps during temporally patterned afferent input. Our results lead to a model wherein a core locus of proteomic complexity prevails at this central glutamatergic sensory synapse that involves distinct GluN2 subtype configurations. These findings have major implications for subthreshold integrative capacity and transmission strength in spinal lamina I and other CNS regions.

Intrinsic and synaptic properties of adult mouse spinoperiaqueductal gray neurons and the influence of neonatal tissue damage

ABSTRACT

The periaqueductal gray (PAG) represents a key target of projection neurons residing in the spinal dorsal horn. In comparison to lamina I spinoparabrachial neurons, little is known about the intrinsic and synaptic properties governing the firing of spino-PAG neurons, or whether such activity is modulated by neonatal injury. In this study, this issue was addressed using ex vivo whole-cell patch clamp recordings from lamina I spino-PAG neurons in adult male and female FVB mice after hindpaw incision at postnatal day (P)3. Spino-PAG neurons were classified as high output, medium output, or low output based on their action potential discharge after dorsal root stimulation. The high-output subgroup exhibited prevalent spontaneous burst firing and displayed initial burst or tonic patterns of intrinsic firing, whereas low-output neurons showed little spontaneous activity. Interestingly, the level of dorsal root-evoked firing significantly correlated with the resting potential and membrane resistance but not with the strength of primary afferent-mediated glutamatergic drive. Neonatal incision failed to alter the pattern of monosynaptic sensory input, with most spino-PAG neurons receiving direct connections from low-threshold C-fibers. Furthermore, primary afferent-evoked glutamatergic input and action potential discharge in adult spino-PAG neurons were unaltered by neonatal surgical injury. Finally, Hebbian long-term potentiation at sensory synapses, which significantly increased afferent-evoked firing, was similar between P3-incised and naive littermates. Collectively, these data suggest that the functional response of lamina I spino-PAG neurons to sensory input is largely governed by their intrinsic membrane properties and appears resistant to the persistent influence of neonatal tissue damage.

Central and peripheral contributions of T-type calcium channels in pain

Chronic pain is a severely debilitating condition that reflects a long-term sensitization of signal transduction in the afferent pain pathway. Among the key players in this pathway are T-type calcium channels, in particular the Cav3.2 isoform. Because of their biophysical characteristics, these channels are ideally suited towards regulating neuronal excitability. Recent evidence suggests that T-type channels contribute to excitability of neurons all along the ascending and descending pain pathways, within primary afferent neurons, spinal dorsal horn neurons, and within pain-processing neurons in the midbrain and cortex. Here we review the contribution of T-type channels to neuronal excitability and function in each of these neuronal populations and how they are dysregulated in chronic pain conditions. Finally, we discuss their molecular pharmacology and the potential role of these channels as therapeutic targets for chronic pain.

Excitatory neurons are more disinhibited than inhibitory neurons by chloride dysregulation in the spinal dorsal horn

Neuropathic pain is a debilitating condition caused by the abnormal processing of somatosensory input. Synaptic inhibition in the spinal dorsal horn plays a key role in that processing. Mechanical allodynia - the misperception of light touch as painful - occurs when inhibition is compromised. Disinhibition is due primarily to chloride dysregulation caused by hypofunction of the potassium-chloride co-transporter KCC2. Here we show, in rats, that excitatory neurons are disproportionately affected. This is not because chloride is differentially dysregulated in excitatory and inhibitory neurons, but, rather, because excitatory neurons rely more heavily on inhibition to counterbalance strong excitation. Receptive fields in both cell types have a center-surround organization but disinhibition unmasks more excitatory input to excitatory neurons. Differences in intrinsic excitability also affect how chloride dysregulation affects spiking. These results deepen understanding of how excitation and inhibition are normally balanced in the spinal dorsal horn, and how their imbalance disrupts somatosensory processing.

Weakly electric fish distinguish between envelope stimuli arising from different behavioral contexts

Understanding how sensory information is processed by the brain in order to give rise to behavior remains poorly understood in general. Here, we investigated the behavioral responses of the weakly electric fish Apteronotus albifrons to stimuli arising from different contexts, by measuring changes in the electric organ discharge (EOD) frequency. Specifically, we focused on envelopes, which can arise either because of movement (i.e. motion envelopes) or because of interactions between the electric fields of three of more fish (i.e. social envelopes). Overall, we found that the animal's EOD frequency effectively tracked the detailed time course of both motion and social envelopes. In general, behavioral sensitivity (i.e. gain) decreased while phase lag increased with increasing envelope and carrier frequency. However, changes in gain and phase lag as a function of changes in carrier frequency were more prominent for motion than for social envelopes in general. Importantly, we compared behavioral responses to motion and social envelopes with similar characteristics. Although behavioral sensitivities were similar, we observed an increased response lag for social envelopes, primarily for low carrier frequencies. Thus, our results imply that the organism can, based on behavioral responses, distinguish envelope stimuli resulting from movement from those that instead result from social interactions. We discuss the implications of our results for neural coding of envelopes and propose that behavioral responses to motion and social envelopes are mediated by different neural circuits in the brain.

Origin and classification of spontaneous discharges in mouse superficial dorsal horn neurons

Superficial laminae of the spinal cord possess a considerable number of neurons with spontaneous activity as reported in vivo and in vitro preparations of several species. Such neurons may play a role in the development of the nociceptive system and/or in the spinal coding of somatosensory signals. We have used electrophysiological techniques in a horizontal spinal cord slice preparation from adult mice to investigate how this activity is generated and what are the main patterns of activity that can be found. The results show the existence of neurons that fire regularly and irregularly. Within each of these main types, it was possible to distinguish patterns of spontaneous activity formed by single action potentials and different types of bursts according to intra-burst firing frequency. Activity in neurons with irregular patterns was blocked by a mixture of antagonists of the main neurotransmitter receptors present in the cord. Approximately 82% of neurons with a regular firing pattern were insensitive to synaptic antagonists but their activity was inhibited by specific ion channel blockers. It is suggested that these neurons generate endogenous activity due to the functional expression of hyperpolarisation-activated and persistent sodium currents driving the activity of irregular neurons.

Origin of heterogeneous spiking patterns from continuously distributed ion channel densities: a computational study in spinal dorsal horn neurons

KEY POINTS

Distinct spiking patterns may arise from qualitative differences in ion channel expression (i.e. when different neurons express distinct ion channels) and/or when quantitative differences in expression levels qualitatively alter the spike generation process. We hypothesized that spiking patterns in neurons of the superficial dorsal horn (SDH) of spinal cord reflect both mechanisms. We reproduced SDH neuron spiking patterns by varying densities of KV 1- and A-type potassium conductances. Plotting the spiking patterns that emerge from different density combinations revealed spiking-pattern regions separated by boundaries (bifurcations). This map suggests that certain spiking pattern combinations occur when the distribution of potassium channel densities straddle boundaries, whereas other spiking patterns reflect distinct patterns of ion channel expression. The former mechanism may explain why certain spiking patterns co-occur in genetically identified neuron types. We also present algorithms to predict spiking pattern proportions from ion channel density distributions, and vice versa.

ABSTRACT

Neurons are often classified by spiking pattern. Yet, some neurons exhibit distinct patterns under subtly different test conditions, which suggests that they operate near an abrupt transition, or bifurcation. A set of such neurons may exhibit heterogeneous spiking patterns not because of qualitative differences in which ion channels they express, but rather because quantitative differences in expression levels cause neurons to operate on opposite sides of a bifurcation. Neurons in the spinal dorsal horn, for example, respond to somatic current injection with patterns that include tonic, single, gap, delayed and reluctant spiking. It is unclear whether these patterns reflect five cell populations (defined by distinct ion channel expression patterns), heterogeneity within a single population, or some combination thereof. We reproduced all five spiking patterns in a computational model by varying the densities of a low-threshold (KV 1-type) potassium conductance and an inactivating (A-type) potassium conductance and found that single, gap, delayed and reluctant spiking arise when the joint probability distribution of those channel densities spans two intersecting bifurcations that divide the parameter space into quadrants, each associated with a different spiking pattern. Tonic spiking likely arises from a separate distribution of potassium channel densities. These results argue in favour of two cell populations, one characterized by tonic spiking and the other by heterogeneous spiking patterns. We present algorithms to predict spiking pattern proportions based on ion channel density distributions and, conversely, to estimate ion channel density distributions based on spiking pattern proportions. The implications for classifying cells based on spiking pattern are discussed.

Non-Decaying postsynaptics potentials and delayed spikes in hippocampal pyramidal neurons generated by a zero slope conductance created by the persistent Na+ current

The negative slope conductance created by the persistent sodium current (I_NaP) prolongs the decay phase of excitatory postsynaptic potentials (EPSPs). In a recent study, we demonstrated that this effect was due to an increase of the membrane time constant. When the negative slope conductance opposes completely the positive slope conductances of the other currents it creates a zero slope conductance region. In this region the membrane time constant is infinite and the decay phase of the EPSPs is virtually absent. Here we show that non-decaying EPSPs are present in CA1 hippocampal pyramidal cells in the zero slope conductance region, in the suprathreshold range of membrane potential. Na⁺ channel block with tetrodotoxin abolishes the non-decaying EPSPs. Interestingly, the non-decaying EPSPs are observed only in response to artificial excitatory postsynaptic currents (aEPSCs) of small amplitude, and not in response to aEPSCs of big amplitude. We also observed concomitantly delayed spikes with long latencies and high variability only in response to small amplitude aEPSCs. Our results showed that in CA1 pyramidal neurons I_NaP creates non-decaying EPSPs and delayed spikes in the subthreshold range of membrane potentials, which could potentiate synaptic integration of synaptic potentials coming from distal regions of the dendritic tree.

Sign and magnitude scaling properties of heart rate variability in patients with end-stage renal failure: Are these properties useful to identify pathophysiological adaptations?

The scaling properties of heart rate variability data are reliable dynamical features to predict mortality and for the assessment of cardiovascular risk. The aim of this manuscript was to determine if the scaling properties, as provided by the sign and magnitude analysis, can be used to differentiate between pathological changes and those adaptations basically introduced by modifications of the mean heart rate in distinct manoeuvres (active standing or hemodialysis treatment, HD), as well as clinical conditions (end stage renal disease, ESRD). We found that in response to active standing, the short-term scaling index (α₁) increased in healthy subjects and in ESRD patients only after HD. The sign short-term scaling exponent (α_1sign) increased in healthy subjects and ESRD patients, showing a less anticorrelated behavior in active standing. Both α₁ and α_1sign did show covariance with the mean heart rate in healthy subjects, while in ESRD patients, this covariance was observed only after HD. A reliable estimation of the magnitude short-term scaling exponent (α_1magn) required the analysis of time series with a large number of samples (>3000 data points). This exponent was similar for both groups and conditions and did not show covariance with the mean heart rate. A surrogate analysis confirmed the presence of multifractal properties (α_1magn > 0.5) in the time series of healthy subjects and ESDR patients. In conclusion, α₁ and α_1sign provided insights into the physiological adaptations during active standing, which revealed a transitory impairment before HD in ESRD patients. The presence of multifractal properties indicated that a reduced short-term variability does not necessarily imply a declined regulatory complexity in these patients.

The role of negative conductances in neuronal subthreshold properties and synaptic integration

Based on passive cable theory, an increase in membrane conductance produces a decrease in the membrane time constant and input resistance. Unlike the classical leak currents, voltage-dependent currents have a nonlinear behavior which can create regions of negative conductance, despite the increase in membrane conductance (permeability). This negative conductance opposes the effects of the passive membrane conductance on the membrane input resistance and time constant, increasing their values and thereby substantially affecting the amplitude and time course of postsynaptic potentials at the voltage range of the negative conductance. This paradoxical effect has been described for three types of voltage-dependent inward currents: persistent sodium currents, L- and T-type calcium currents and ligand-gated glutamatergic N-methyl-D-aspartate currents. In this review, we describe the impact of the creation of a negative conductance region by these currents on neuronal membrane properties and synaptic integration. We also discuss recent contributions of the quasi-active cable approximation, an extension of the passive cable theory that includes voltage-dependent currents, and its effects on neuronal subthreshold properties.

A Negative Slope Conductance of the Persistent Sodium Current Prolongs Subthreshold Depolarizations

Neuronal subthreshold voltage-dependent currents determine membrane properties such as the input resistance (R_in) and the membrane time constant (τ_m) in the subthreshold range. In contrast with classical cable theory predictions, the persistent sodium current (I_NaP), a non-inactivating mode of the voltage-dependent sodium current, paradoxically increases R_in and τ_m when activated. Furthermore, this current amplifies and prolongs synaptic currents in the subthreshold range. Here, using a computational neuronal model, we showed that the creation of a region of negative slope conductance by I_NaP activation is responsible for these effects and the ability of the negative slope conductance to amplify and prolong R_in and τ_m relies on the fast activation of I_NaP. Using dynamic clamp in hippocampal CA1 pyramidal neurons in brain slices, we showed that the effects of I_NaP on R_in and τ_m can be recovered by applying an artificial I_NaP after blocking endogenous I_NaP with tetrodotoxin. Furthermore, we showed that injection of a pure negative conductance is enough to reproduce the effects of I_NaP on R_in and τ_m and is also able to prolong artificial excitatory post synaptic currents. Since both the negative slope conductance and the almost instantaneous activation are critical for producing these effects, the I_NaP is an ideal current for boosting the amplitude and duration of excitatory post synaptic currents near the action potential threshold.

Stimulus background influences phase invariant coding by correlated neural activity

Previously we reported that correlations between the activities of peripheral afferents mediate a phase invariant representation of natural communication stimuli that is refined across successive processing stages thereby leading to perception and behavior in the weakly electric fish Apteronotus leptorhynchus (Metzen et al., 2016). Here, we explore how phase invariant coding and perception of natural communication stimuli are affected by changes in the sinusoidal background over which they occur. We found that increasing background frequency led to phase locking, which decreased both detectability and phase invariant coding. Correlated afferent activity was a much better predictor of behavior as assessed from both invariance and detectability than single neuron activity. Thus, our results provide not only further evidence that correlated activity likely determines perception of natural communication signals, but also a novel explanation as to why these preferentially occur on top of low frequency as well as low-intensity sinusoidal backgrounds.

Near-Perfect Synaptic Integration by Nav1.7 in Hypothalamic Neurons Regulates Body Weight

Neurons are well suited for computations on millisecond timescales, but some neuronal circuits set behavioral states over long time periods, such as those involved in energy homeostasis. We found that multiple types of hypothalamic neurons, including those that oppositely regulate body weight, are specialized as near-perfect synaptic integrators that summate inputs over extended timescales. Excitatory postsynaptic potentials (EPSPs) are greatly prolonged, outlasting the neuronal membrane time-constant up to 10-fold. This is due to the voltage-gated sodium channel Na_v1.7 (Scn9a), previously associated with pain-sensation but not synaptic integration. Scn9a deletion in AGRP, POMC, or paraventricular hypothalamic neurons reduced EPSP duration, synaptic integration, and altered body weight in mice. In vivo whole-cell recordings in the hypothalamus confirmed near-perfect synaptic integration. These experiments show that integration of synaptic inputs over time by Na_v1.7 is critical for body weight regulation and reveal a mechanism for synaptic control of circuits regulating long term homeostatic functions.

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Hypothalamic neurons that regulate body weight are near-perfect synaptic integrators

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Near-perfect synaptic integration is observed in hypothalamic neurons in vivo

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Near-perfect synaptic integration depends on the voltage-gated sodium channel Na_v1.7

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Loss of Na_v1.7 in hypothalamic neurons disrupts regulation of body weight

Slowly Building Excitement

While some neurons are tuned to integrate fast and precisely timed inputs, others set behavioral states on much slower timescales. In this issue of Cell, Branco et al. demonstrate that body weight is regulated by hypothalamic neurons using a highly effective form of slow synaptic integration, which is mediated by the voltage gated sodium channel Nav1.7.

Motor Cortex Excitability and BDNF Levels in Chronic Musculoskeletal Pain According to Structural Pathology

The central sensitization syndrome (CSS) encompasses disorders with overlapping symptoms in a structural pathology spectrum ranging from persistent nociception [e.g., osteoarthritis (OA)] to an absence of tissue injuries such as the one presented in fibromyalgia (FM) and myofascial pain syndrome (MPS). First, we hypothesized that these syndromes present differences in their cortical excitability parameters assessed by transcranial magnetic stimulation (TMS), namely motor evoked potential (MEP), cortical silent period (CSP), short intracortical inhibition (SICI) and short intracortical facilitation (SICF). Second, considering that the presence of tissue injury could be detected by serum neurotrophins, we hypothesized that the spectrum of structural pathology (i.e., from persistent nociception like in OA, to the absence of tissue injury like in FM and MPS), could be detected by differential efficiency of their descending pain inhibitory system, as assessed by the conditioned pain modulation (CPM) paradigm. Third, we explored whether brain-derived neurotrophic factor (BDNF) had an influence on the relationship between motor cortex excitability and structural pathology. This cross-sectional study pooled baseline data from three randomized clinical trials. We included females (n = 114), aged 19-65 years old with disability by chronic pain syndromes (CPS): FM (n = 19), MPS (n = 54), OA (n = 27) and healthy subjects (n = 14). We assessed the serum BDNF, the motor cortex excitability by parameters the TMS measures and the change on numerical pain scale [NPS (0-10)] during CPM-task. The adjusted mean (SD) on the SICI observed in the absence of tissue injury was 56.36% lower than with persistent nociceptive input [0.31(0.18) vs. 0.55 (0.32)], respectively. The BDNF was inversely correlated with the SICI and with the change on NPS (0-10)during CPM-task. These findings suggest greater disinhibition in the motor cortex and the descending pain inhibitory system in FM and MPS than in OA and healthy subjects. Likewise, the inter-hemispheric disinhibition as well as the dysfunction in the descending pain modulatory system is higher in chronic pain without tissue injury compared to a structural lesion. In addition, they suggest that a greater level of serum BDNF may be involved in the processes that mediate the disinhibition of motor cortex excitability, as well as the function of descending inhibitory pain modulation system, independently of the physiopathology mechanism of musculoskeletal pain syndromes.

Activation of Ih and TTX-sensitive sodium current at subthreshold voltages during CA1 pyramidal neuron firing

We used dynamic clamp and action potential clamp techniques to explore how currents carried by tetrodotoxin-sensitive sodium channels and HCN channels (Ih) regulate the behavior of CA1 pyramidal neurons at resting and subthreshold voltages. Recording from rat CA1 pyramidal neurons in hippocampal slices, we found that the apparent input resistance and membrane time constant were strongly affected by both conductances, with Ih acting to decrease apparent input resistance and time constant and sodium current acting to increase both. We found that both Ih and sodium current were active during subthreshold summation of artificial excitatory postsynaptic potentials (EPSPs) generated by dynamic clamp, with Ih dominating at less depolarized voltages and sodium current at more depolarized voltages. Subthreshold sodium current-which amplifies EPSPs-was most effectively recruited by rapid voltage changes, while Ih-which blunts EPSPs-was maximal for slow voltage changes. The combined effect is to selectively amplify rapid EPSPs. We did similar experiments in mouse CA1 pyramidal neurons, doing voltage-clamp experiments using experimental records of action potential firing of CA1 neurons previously recorded in awake, behaving animals as command voltages to quantify flow of Ih and sodium current at subthreshold voltages. Subthreshold sodium current was larger and subthreshold Ih was smaller in mouse neurons than in rat neurons. Overall, the results show opposing effects of subthreshold sodium current and Ih in regulating subthreshold behavior of CA1 neurons, with subthreshold sodium current prominent in both rat and mouse CA1 pyramidal neurons and additional regulation by Ih in rat neurons.

Spinal sensory projection neuron responses to spinal cord stimulation are mediated by circuits beyond gate control

Spinal cord stimulation (SCS) is a therapy used to treat intractable pain with a putative mechanism of action based on the Gate Control Theory. We hypothesized that sensory projection neuron responses to SCS would follow a single stereotyped response curve as a function of SCS frequency, as predicted by the Gate Control circuit. We recorded the responses of antidromically identified sensory projection neurons in the lumbar spinal cord during 1- to 150-Hz SCS in both healthy rats and neuropathic rats following chronic constriction injury (CCI). The relationship between SCS frequency and projection neuron activity predicted by the Gate Control circuit accounted for a subset of neuronal responses to SCS but could not account for the full range of observed responses. Heterogeneous responses were classifiable into three additional groups and were reproduced using computational models of spinal microcircuits representing other interactions between nociceptive and nonnociceptive sensory inputs. Intrathecal administration of bicuculline, a GABAA receptor antagonist, increased spontaneous and evoked activity in projection neurons, enhanced excitatory responses to SCS, and reduced inhibitory responses to SCS, suggesting that GABAA neurotransmission plays a broad role in regulating projection neuron activity. These in vivo and computational results challenge the Gate Control Theory as the only mechanism underlying SCS and refine our understanding of the effects of SCS on spinal sensory neurons within the framework of contemporary understanding of dorsal horn circuitry.

Coding of envelopes by correlated but not single-neuron activity requires neural variability

Understanding how the brain processes sensory information is often complicated by the fact that neurons exhibit trial-to-trial variability in their responses to stimuli. Indeed, the role of variability in sensory coding is still highly debated. Here, we examined how variability influences neural responses to naturalistic stimuli consisting of a fast time-varying waveform (i.e., carrier or first order) whose amplitude (i.e., envelope or second order) varies more slowly. Recordings were made from fish electrosensory and monkey vestibular sensory neurons. In both systems, we show that correlated but not single-neuron activity can provide detailed information about second-order stimulus features. Using a simple mathematical model, we made the strong prediction that such correlation-based coding of envelopes requires neural variability. Strikingly, the performance of correlated activity at predicting the envelope was similarly optimally tuned to a nonzero level of variability in both systems, thereby confirming this prediction. Finally, we show that second-order sensory information can only be decoded if one takes into account joint statistics when combining neural activities. Our results thus show that correlated but not single-neural activity can transmit information about the envelope, that such transmission requires neural variability, and that this information can be decoded. We suggest that envelope coding by correlated activity is a general feature of sensory processing that will be found across species and systems.

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.

Modeling effects of spinal cord stimulation on wide-dynamic range dorsal horn neurons: influence of stimulation frequency and GABAergic inhibition

Spinal cord stimulation (SCS) is a clinical therapy for chronic, neuropathic pain, but an incomplete understanding of the mechanisms underlying SCS contributes to the lack of improvement in SCS efficacy over time. To study the mechanisms underlying SCS, we constructed a biophysically based network model of the dorsal horn circuit consisting of interconnected dorsal horn interneurons and a wide-dynamic range (WDR) projection neuron and representations of both local and surround receptive field inhibition. We validated the network model by reproducing cellular and network responses relevant to pain processing including wind-up, A fiber-mediated inhibition, and surround receptive field inhibition. We then simulated the effects of SCS on the activity of the WDR projection neuron and found that the response of the model WDR neuron to SCS depends on the SCS frequency; SCS frequencies of 30–100 Hz maximally inhibited the model WDR neuron, while frequencies under 30 Hz and over 100 Hz excited the model WDR neuron. We also studied the impacts on the effects of SCS of loss of inhibition due to the loss of either GABA or KCC2 function. Reducing the influence of local and surround GABAergic interneurons by weakening their inputs or their connections to the WDR neuron and shifting the anionic reversal potential of the WDR neurons upward each reduced the range of optimal SCS frequencies and changed the frequency at which SCS had a maximal effect. The results of this study provide insights into the mechanisms of SCS and pave the way for improved SCS parameter selection.

Mechanisms and models of spinal cord stimulation for the treatment of neuropathic pain

Spinal cord stimulation (SCS) is an established and cost-effective therapy for treating severe chronic pain. However, despite over 40 years of clinical practice and the development of novel electrode designs and treatment protocols, increases in clinical success, defined as the proportion of patients that experience 50% or greater self-reported pain relief, have stalled. An incomplete knowledge of the neural circuits and systems underlying chronic pain and the interaction of SCS with these circuits may underlie this plateau in clinical efficacy. This review summarizes prior work and identifies gaps in our knowledge regarding the neural circuits related to pain and SCS in the dorsal horn, supraspinal structures, and the Pain Matrix. In addition, this review discusses and critiques current experimental and computational models used to investigate and optimize SCS. Further research into the interactions between SCS and pain pathways in the nervous system using animal and computational models is a fruitful approach to improve this promising therapy.

Pacemaker Neurons and the Development of Nociception

Spontaneous activity is known to be essential for the proper formation of sensory networks in the developing CNS. This activity can be produced by a variety of mechanisms including the presence of "pacemaker" neurons, which can be defined by their intrinsic ability to generate rhythmic bursts of action potential discharge. Recent work has identified pacemaker activity within lamina I of the neonatal rodent spinal cord that emerges from a complex interaction between voltage-dependent and voltage-independent ("leak") ionic conductances, including an important modulatory role for the inward-rectifying K(+) (Kir) channels. The available evidence suggests that lamina I pacemakers are glutamatergic and project extensively throughout the dorsal-ventral axis of the spinal cord, although the identity of their postsynaptic targets has yet to be elucidated. A better understanding of this connectivity could yield valuable insight into the role of the lamina I pacemaker population in the maturation of spinal circuitry underlying nociceptive processing and/or sensorimotor integration.

Impact of neuronal properties on network coding: roles of spike initiation dynamics and robust synchrony transfer

Neural networks are more than the sum of their parts, but the properties of those parts are nonetheless important. For instance, neuronal properties affect the degree to which neurons receiving common input will spike synchronously, and whether that synchrony will propagate through the network. Stimulus-evoked synchrony can help or hinder network coding depending on the type of code. In this Perspective, we describe how spike initiation dynamics influence neuronal input-output properties, how those properties affect synchronization, and how synchronization affects network coding. We propose that synchronous and asynchronous spiking can be used to multiplex temporal (synchrony) and rate coding and discuss how pyramidal neurons would be well suited for that task.

Transcriptional expression of voltage-gated Na⁺ and voltage-independent K⁺ channels in the developing rat superficial dorsal horn

Neurons within the superficial dorsal horn (SDH) of the rodent spinal cord exhibit distinct firing properties during early life. While this may reflect a unique combination of voltage-gated Na(+) (Na(v)) and voltage-independent (i.e. "leak'') K(+) channels which strongly influence neuronal excitability across the CNS, surprisingly little is known about which genes encoding for Na(v) and leak K(+) channels are expressed within developing spinal pain circuits. The goal of the present study was therefore to characterize the transcriptional expression of these channels within the rat SDH at postnatal days (P) 3, 10, 21 or adulthood using quantitative real-time polymerase chain reaction. The results demonstrate that Na(v) isoforms are developmentally regulated at the mRNA level in a subtype-specific manner, as Na(v)1.2 and Na(v)1.3 decreased significantly from P3 to adulthood, while Na(v)1.1 was up-regulated during this period. The data also indicate selective, age-dependent changes in the mRNA expression of two-pore domain (K(2P)) K(+) channels, as TWIK-related acid-sensitive K(+) channels TASK-1 (KCNK3) and TASK-3 (KCNK9) were down-regulated during postnatal development in the absence of any changes in the tandem of pore domains in a weak inward rectifying K(+) channel (TWIK) isoforms examined (KCNK1 and KCNK6). In addition, a developmental shift occurred within the TREK subfamily due to decreased TREK-2 (KCNK10) mRNA within the mature SDH. Meanwhile, G-protein-coupled inward rectifying K(+) channels (K(ir)3.1 and K(ir)3.2) were expressed in the SDH at mature levels from birth. Overall, the results suggest that the transcription of ion channel genes occurs in a highly age-dependent manner within the SDH, raising the possibility that manipulating the expression or function of ion channels which are preferentially expressed within immature nociceptive networks could yield novel approaches to relieving pain in infants and children.

In vivo voltage-dependent influences on summation of synaptic potentials in neurons of the lateral nucleus of the amygdala

The amygdala has a fundamental role in driving affective behaviors in response to sensory cues. To accomplish this, neurons of the lateral nucleus (LAT) must integrate a large number of synaptic inputs. A wide range of factors influence synaptic integration, including membrane potential, voltage-gated ion channels and GABAergic inhibition. However, little is known about how these factors modulate integration of synaptic inputs in LAT neurons in vivo. The purpose of this study was to determine the voltage-dependent factors that modify in vivo integration of synaptic inputs in the soma of LAT neurons. In vivo intracellular recordings from anesthetized rats were used to measure post-synaptic potentials (PSPs) and clusters of PSPs across a range of membrane potentials. These studies found that the relationship between membrane potential and PSP clusters was sublinear, due to a reduction of cluster amplitude and area at depolarized membrane potentials. In combination with intracellular delivery of pharmacological agents, it was found that the voltage-dependent suppression of PSP clusters was sensitive to tetraethylammonium (TEA), but not cesium or a blocker of fast GABAergic inhibition. These findings indicate that integration of PSPs in LAT neurons in vivo is strongly modified by somatic membrane potential, likely through voltage-dependent TEA-sensitive potassium channels. Conditions that lead to a shift in membrane potential, or a modulation of the number or function of these ion channels will lead to a more uniform capacity for integration across voltages, and perhaps greatly facilitate amygdala-dependent behaviors.

THE PAST AND PRESENT OF HUMAN MOVEMENT RESEARCH: TOWARDS THE DESIGN OF HUMAN-LIKE ROBOTS

The Journal of Mechanics in Medicine and Biology(JMMB) has retracted the above paper from its April 2012 issue. The Publisher of JMMB was alerted to the fact that the conference paper was previously published in IEEE in 2011. The authors indicated that this manuscript was suggested by the conference organizers for journal publication. As stated clearly in the journal’s guidelines, only original manuscripts will be considered. Once a manuscript is accepted, the author is assumed to cede full copyright of their manuscript over to the publisher - World Scientific Publishing Co.

Bursting activity in myelinated sensory neurons plays a key role in pain behavior induced by localized inflammation of the rat sensory ganglion

Abnormal spontaneous activity of sensory neurons is observed in many different preclinical pain models, but its basis is not well understood. In this study mechanical and cold hypersensitivity were induced in rats after inflammation of the L5 dorsal root ganglion (DRG), initiated by local application of the immune stimulator zymosan in incomplete Freund's adjuvant. Mechanical hypersensitivity was evident by day 1 and maintained for 2 months. The model also showed reduction of rearing behavior in a novel environment. Microelectrode recordings made in isolated whole DRG on day 3 after inflammation showed a marked increase of spontaneous activity, predominantly with a bursting pattern. The incidence was especially high (44%) in Aαβ cells. Spontaneous activity and subthreshold membrane potential oscillations were completely blocked by tetrodotoxin (500 nM) and by riluzole (10 μM), a blocker of persistent sodium currents. In vivo, local perfusion of the inflamed DRG for the first 7 days with riluzole gave long-lasting, dose-dependent reduction in mechanical pain behaviors. Riluzole perfusion did not affect mechanical sensitivity in normal animals. Unmyelinated C cells had a very low incidence of spontaneous activity and were much less affected by riluzole in vitro. Taken together these results suggest that high-frequency and/or bursting spontaneous activity in Aαβ sensory neurons may play important roles in initiating pain behaviors resulting from inflammatory irritation of the DRG.

Pain processing by spinal microcircuits: afferent combinatorics

Pain, itch, heat, cold, and touch represent different percepts arising from somatosensory input. How stimuli give rise to these percepts has been debated for over a century. Recent work supports the view that primary afferents are highly specialized to transduce and encode specific stimulus modalities. However, cross-modal interactions (e.g. inhibition or exacerbation of pain by touch) support convergence rather than specificity in central circuits. We outline how peripheral specialization together with central convergence could enable spinal microcircuits to combine inputs from distinctly specialized, co-activated afferents and to modulate the output signals thus formed through computations like normalization. These issues will be discussed alongside recent advances in our understanding of microcircuitry in the superficial dorsal horn.

Pacemaker neurons within newborn spinal pain circuits

Spontaneous activity driven by "pacemaker" neurons, defined by their intrinsic ability to generate rhythmic burst firing, contributes to the development of sensory circuits in many regions of the immature CNS. However, it is unknown whether pacemaker-like neurons are present within central pain pathways in the neonate. Here, we provide evidence that a subpopulation of glutamatergic interneurons within lamina I of the rat spinal cord exhibits oscillatory burst firing during early life, which occurs independently of fast synaptic transmission. Pacemaker neurons were distinguished by a higher ratio of persistent, voltage-gated Na(+) conductance to leak membrane conductance (g(Na,P)/g(leak)) compared with adjacent, nonbursting lamina I neurons. The activation of high-threshold (N-type and L-type) voltage-gated Ca(2+) channels also facilitated rhythmic burst firing by triggering intracellular Ca(2+) signaling. Bursting neurons received direct projections from high-threshold sensory afferents but transmitted nociceptive signals with poor fidelity while in the bursting mode. The observation that pacemaker neurons send axon collaterals throughout the neonatal spinal cord raises the possibility that intrinsic burst firing could provide an endogenous drive to the developing sensorimotor networks that mediate spinal pain reflexes.

Multiple T-type Ca2+ current subtypes in electrophysiologically characterized hamster dorsal horn neurons: possible role in spinal sensory integration

Whole cell patch-clamp recordings were used to investigate the contribution of transient, low-threshold calcium currents (I(T)) to firing properties of hamster spinal dorsal horn neurons. I(T) was widely, though not uniformly, expressed by cells in Rexed's laminae I-IV and correlated with the pattern of action potential discharge evoked under current-clamp conditions: I(T) in neurons responding to constant membrane depolarization with one or two action potentials was nearly threefold larger than I(T) in cells responding to the same activation with continuous firing. I(T) was evoked by depolarizing voltage ramps exceeding 46 mV/s and increased with ramp slope (240-2,400 mV/s). Bath application of 200 μM Ni(2+) depressed ramp-activated I(T). Phasic firing recorded in current clamp could only be activated by membrane depolarizations exceeding ∼43-46 mV/s and was blocked by Ni(2+) and mibefradil, suggesting I(T) as an underlying mechanism. Two components of I(T), "fast" and "slow," were isolated based on a difference in time constant of inactivation (12 ms and 177 ms, respectively). The amplitude of the fast subtype depended on the slope of membrane depolarization and was twice as great in burst-firing cells than in cells having a tonic discharge. Post hoc single-cell RT-PCR analyses suggested that the fast component is associated with the Ca(V)3.1 channel subtype. I(T) may enhance responses of phasic-firing dorsal horn neurons to rapid membrane depolarizations and contribute to an ability to discriminate between afferent sensory inputs that encode high- and low-frequency stimulus information.

Riluzole decreases flexion withdrawal reflex but not voluntary ankle torque in human chronic spinal cord injury

The objectives of this study were to probe the contribution of spinal neuron persistent sodium conductances to reflex hyperexcitability in human chronic spinal cord injury. The intrinsic excitability of spinal neurons provides a novel target for medical intervention. Studies in animal models have shown that persistent inward currents, such as persistent sodium currents, profoundly influence neuronal excitability, and recovery of persistent inward currents in spinal neurons of animals with spinal cord injury routinely coincides with the appearance of spastic reflexes. Pharmacologically, this neuronal excitability can be decreased by agents that reduce persistent inward currents, such as the selective persistent sodium current inhibitor riluzole. We were able to recruit seven subjects with chronic incomplete spinal cord injury who were not concurrently taking antispasticity medications into the study. Reflex responses (flexion withdrawal and H-reflexes) and volitional strength (isometric maximum voluntary contractions) were tested at the ankle before and after placebo-controlled, double-blinded oral administration of riluzole (50 mg). Riluzole significantly decreased the peak ankle dorsiflexion torque component of the flexion withdrawal reflex. Peak maximum voluntary torque in both dorsiflexion and plantarflexion directions was not significantly changed. Average dorsiflexion torque sustained during the 5-s isometric maximum voluntary contraction, however, increased significantly. There was no effect, however, on the monosynaptic plantar and dorsiflexor H-reflex responses. Overall, these results demonstrate a contribution of persistent sodium conductances to polysynaptic reflex excitability in human chronic spinal cord injury without a significant role in maximum strength production. These results suggest that intrinsic spinal cellular excitability could be a target for managing chronic spinal cord injury hyperreflexia impairments without causing a significant loss in volitional strength.

A novel slow-inactivation-specific ion channel modulator attenuates neuropathic pain

Voltage-gated ion channels are implicated in pain sensation and transmission signaling mechanisms within both peripheral nociceptors and the spinal cord. Genetic knockdown and knockout experiments have shown that specific channel isoforms, including Na(V)1.7 and Na(V)1.8 sodium channels and Ca(V)3.2 T-type calcium channels, play distinct pronociceptive roles. We have rationally designed and synthesized a novel small organic compound (Z123212) that modulates both recombinant and native sodium and calcium channel currents by selectively stabilizing channels in their slow-inactivated state. Slow inactivation of voltage-gated channels can function as a brake during periods of neuronal hyperexcitability, and Z123212 was found to reduce the excitability of both peripheral nociceptors and lamina I/II spinal cord neurons in a state-dependent manner. In vivo experiments demonstrate that oral administration of Z123212 is efficacious in reversing thermal hyperalgesia and tactile allodynia in the rat spinal nerve ligation model of neuropathic pain and also produces acute antinociception in the hot-plate test. At therapeutically relevant concentrations, Z123212 did not cause significant motor or cardiovascular adverse effects. Taken together, the state-dependent inhibition of sodium and calcium channels in both the peripheral and central pain signaling pathways may provide a synergistic mechanism toward the development of a novel class of pain therapeutics.

GAD67-GFP+ neurons in the Nucleus of Roller: a possible source of inhibitory input to hypoglossal motoneurons. I. Morphology and firing properties

In this study we examined the electrophysiological and morphological properties of inhibitory neurons located just ventrolateral to the hypoglossal motor (XII) nucleus in the Nucleus of Roller (NR). In vitro experiments were performed on medullary slices derived from postnatal day 5 (P5) to P15 GAD67-GFP knock-in mouse pups. on cell recordings from GFP+ cells in NR in rhythmic slices revealed that these neurons are spontaneously active, although their spiking activity does not exhibit inspiratory phase modulation. Morphologically, GFP+ cells were bi- or multipolar cells with small- to medium-sized cell bodies and small dendritic trees that were often oriented parallel to the border of the XII nucleus. GFP+ cells were classified as either tonic or phasic based on their firing responses to depolarizing step current stimulation in whole cell current clamp. Tonic GFP+ cells fired a regular train of action potentials (APs) throughout the duration of the pulse and often showed rebound spikes after a hyperpolarizing step. In contrast, phasic GFP+ neurons did not fire throughout the depolarizing current step but instead fired fewer than four APs at the onset of the pulse or fired multiple APs, but only after a marked delay. Phasic cells had a significantly smaller input resistance and shorter membrane time constant than tonic GFP+ cells. In addition, phasic GFP+ cells differed from tonic cells in the shape and time course of their spike afterpotentials, the minimum firing frequency at threshold current amplitude, and the slope of their current-frequency relationship. These results suggest that GABAergic neurons in the NR are morphologically and electrophysiologically heterogeneous cells that could provide tonic inhibitory synaptic input to HMs.

Sensory input drives multiple intracellular information streams in somatosensory cortex

Stable perception arises from the interaction between sensory inputs and internal activity fluctuations in cortex. Here we analyzed how different types of activity contribute to cortical sensory processing at the cellular scale. We performed whole-cell recordings in the barrel cortex of anesthetized rats while applying ongoing whisker stimulation and measured the information conveyed about the time-varying stimulus by different types of input (membrane potential) and output (spiking) signals. We found that substantial, comparable amounts of incoming information are carried by two types of membrane potential signal: slow, large (up-down state) fluctuations, and faster (>20 Hz), smaller-amplitude synaptic activity. Both types of activity fluctuation are therefore significantly driven by the stimulus on an ongoing basis. Each stream conveys essentially independent information. Output (spiking) information is contained in spike timing not just relative to the stimulus but also relative to membrane potential fluctuations. Information transfer is favored in up states relative to down states. Thus, slow, ongoing activity fluctuations and finer-scale synaptic activity generate multiple channels for incoming and outgoing information within barrel cortex neurons during ongoing stimulation.

NMDA Channels Together With L-Type Calcium Currents and Calcium-Activated Nonspecific Cationic Currents Are Sufficient to Generate Windup in WDR Neurons

Windup is characterized as a frequency-dependent increase in the number of evoked action potentials in dorsal horn neurons in response to electrical stimulation of afferent C-fibers. This phenomenon was first described in the mid-60s, but the core mechanisms behind it still remain elusive. Several factors affecting its dynamics have been identified, but the distinction between modulating mechanisms from generating mechanisms is not always clear. Several mechanisms contribute to the excitation of dorsal horn neurons exhibiting windup, and one of our main aims was to help making this distinction. The approach presented here relies on mathematical and computational analysis to study the mechanism(s) underlying windup. From experimentally obtained windup profiles, we extract the time scale of the facilitation mechanisms that may support the characteristics of windup. Guided by these values and using simulations of a biologically realistic compartmental model of a wide dynamic range (WDR) neuron, we are able to assess the contribution of each mechanism for the generation of action potentials windup. We show that the key mechanisms giving rise to windup is the temporal summation of N-methyl-d-aspartate (NMDA) long-lasting postsynaptic responses taking place on top of a membrane potential cumulative depolarization. Calcium-activated nonspecific cationic currents driven by calcium influx from L-type calcium channels and synaptic currents support this cumulative depolarization and plateau formation in WDR neuron membrane potential. The effects of different nonhomogeneous stimulation protocols are explored, and their important role in clarifying many aspects of the windup generation is shown. The models are used to produce several predictions that can be tested experimentally.

Biophysical basis for three distinct dynamical mechanisms of action potential initiation

Transduction of graded synaptic input into trains of all-or-none action potentials (spikes) is a crucial step in neural coding. Hodgkin identified three classes of neurons with qualitatively different analog-to-digital transduction properties. Despite widespread use of this classification scheme, a generalizable explanation of its biophysical basis has not been described. We recorded from spinal sensory neurons representing each class and reproduced their transduction properties in a minimal model. With phase plane and bifurcation analysis, each class of excitability was shown to derive from distinct spike initiating dynamics. Excitability could be converted between all three classes by varying single parameters; moreover, several parameters, when varied one at a time, had functionally equivalent effects on excitability. From this, we conclude that the spike-initiating dynamics associated with each of Hodgkin's classes represent different outcomes in a nonlinear competition between oppositely directed, kinetically mismatched currents. Class 1 excitability occurs through a saddle node on invariant circle bifurcation when net current at perithreshold potentials is inward (depolarizing) at steady state. Class 2 excitability occurs through a Hopf bifurcation when, despite net current being outward (hyperpolarizing) at steady state, spike initiation occurs because inward current activates faster than outward current. Class 3 excitability occurs through a quasi-separatrix crossing when fast-activating inward current overpowers slow-activating outward current during a stimulus transient, although slow-activating outward current dominates during constant stimulation. Experiments confirmed that different classes of spinal lamina I neurons express the subthreshold currents predicted by our simulations and, further, that those currents are necessary for the excitability in each cell class. Thus, our results demonstrate that all three classes of excitability arise from a continuum in the direction and magnitude of subthreshold currents. Through detailed analysis of the spike-initiating process, we have explained a fundamental link between biophysical properties and qualitative differences in how neurons encode sensory input.

Information is transmitted through the nervous system in the form of action potentials or spikes. Contrary to popular belief, a spike is not generated instantaneously when membrane potential crosses some preordained threshold. In fact, different neurons employ different rules to determine when and why they spike. These different rules translate into diverse spiking patterns that have been observed experimentally and replicated time and again in computational models. In this study, our aim was not simply to replicate different spiking patterns; instead, we sought to provide deeper insight into the connection between biophysics and neural coding by relating each to the process of spike initiation. We show that Hodgkin's three classes of excitability result from a nonlinear competition between oppositely directed, kinetically mismatched currents; the outcome of that competition is manifested as dynamically distinct spike-initiating mechanisms. Our results highlight the benefits of forward engineering minimal models capable of reproducing phenomena of interest and then dissecting those models in order to identify general explanations of how those phenomena arise. Furthermore, understanding nonlinear dynamical processes such as spike initiation is crucial for definitively explaining how biophysical properties impact neural coding.

Spinal cord injury causes plasticity in a subpopulation of lamina I GABAergic interneurons

Dysfunction of the spinal GABAergic system has been implicated in pain syndromes following spinal cord injury (SCI). Since lamina I is involved in nociceptive and thermal signaling, we characterized the effects of chronic SCI on the cellular properties of its GABAergic neurons fluorescently identified in spinal slices from GAD67-GFP transgenic mice. Whole cell recordings were obtained from the lumbar cord of 13- to 17-day-old mice, including those having had a thoracic segment (T8-11) removed 6-9 days prior to experiments. Following chronic SCI, the distribution, incidence, and firing classes of GFP+ cells remained similar to controls, and there were minimal changes in membrane properties in cells that responded to current injection with a single spike. In contrast, cells displaying tonic/initial burst firing had more depolarized membrane potentials, increased steady-state outward currents, and increased spike heights. Moreover, higher firing frequencies and spontaneous plateau potentials were much more prevalent after chronic SCI, and these changes occurred predominantly in cells displaying a tonic firing pattern. Persistent inward currents (PICs) were observed in a similar fraction of cells from spinal transects and may have contributed to these plateaus. Persistent Na+ and L-type Ca2+ channels likely contributed to the currents as both were identified pharmacologically. In conclusion, chronic SCI induces a plastic response in a subpopulation of lamina I GABAergic interneurons. Alterations are directed toward amplifying neuronal responsiveness. How these changes alter spinal sensory integration and whether they contribute to sensory dysfunction remains to be elucidated.

Simulation of networks of spiking neurons: a review of tools and strategies

We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.

Persistent inward currents in rat ventral horn neurones

Throughout the mammalian spinal cord, interneurones have been shown to exhibit distinct firing patterns in response to a step of injected current. In this study of ventral horn interneurones in a thick slice preparation of the lumbar cord of 11-19-day-old-rats, four distinct firing patterns were observed and classified as repetitive-firing, repetitive/burst, initial-burst or single-spiking. The hypothesis that a persistent sodium current was the predominant determinant of cell firing behaviour was investigated. A slow voltage ramp was used to assess persistent inward currents (PICs). Cells with repetitive-firing patterns had significantly larger PICs than cells displaying repetitive/burst, initial-burst or single-spiking patterns. Repetitive-firing, repetitive/burst and initial-burst-firing cells were reduced to a single-spiking pattern with the application of riluzole, which also markedly reduced the persistent sodium current. Persistent sodium current was found to account for most of the PIC with only a small contribution from L-type calcium current. These results suggest that the persistent sodium current plays a major role in determining firing patterns in these cells.

Pinch-current injection defines two discharge profiles in mouse superficial dorsal horn neurones, in vitro

Neurones in the superficial dorsal horn (SDH) are a major target for nociceptive afferents and play an important role in pain processing. One approach to understanding the role of SDH neurones has been to study their action potential (AP) discharge in spinal cord slices during injection of depolarizing step-currents. Four or five neurone subpopulations are typically identified based on AP discharge, with various roles proposed for each in pain processing. During noxious peripheral stimulation in vivo, however, SDH neurones are activated via synaptic inputs. This produces a conductance change with different somato-dendritic distributions and temporal characteristics to that provided by a somatic step-current injection. Here we introduce an alternative approach to studying SDH neurone discharge under in vitro conditions. We recorded voltage-clamp responses in SDH neurones, in vivo, during noxious mechanical stimulation of the hindpaw (1 s pinch, approximately 100 g mm(-2)). From these recordings a representative 'pinch-current' was selected and subsequently injected into SDH neurones in spinal cord slices (recording temperature 32 degrees C). Pinch-current-evoked discharge was compared to that evoked by rectangular step-current injections. Pinch- and step-current-evoked AP discharge frequency was highly correlated (r2 = 0.61). This was also true for rheobase current comparisons (r2 = 0.61). Conversely, latency to discharge and discharge duration were not correlated when step- and pinch-current responses were compared. When neurones were grouped according to step-current-evoked discharge, five distinct patterns were apparent (tonic firing, initial bursting, delayed firing, single spiking, and reluctant firing). In contrast, pinch-current responses separated into two clear patterns of activity (robust and resistant firing). During pinch-current injection, tonic-firing and initial-bursting neurones exhibited robust AP discharge with similar characteristics. In contrast, single-spiking and reluctant-firing neurones were resistant to AP discharge. Delayed-firing neurones exhibited pinch-current responses that were transitional between those of tonic-firing/initial-bursting and single-spiking/reluctant-firing neurones. Injection of digitally filtered pinch-currents indicated that transient current fluctuations are necessary for robust repetitive discharge in initial-bursting neurones. These data suggest the functional significance of the diverse step-current-evoked firing patterns, previously reported in SDH neurones remains to be fully understood. When a 'facsimile' current profile or pinch-current is used in place of step-currents, AP discharge diversity is much reduced.

Developmental changes in two voltage-dependent sodium currents in utricular hair cells

Two kinds of sodium current (I(Na)) have been separately reported in hair cells of the immature rodent utricle, a vestibular organ. We show that rat utricular hair cells express one or the other current depending on age (between postnatal days 0 and 22, P0-P22), hair cell type (I, II, or immature), and epithelial zone (striola vs. extrastriola). The properties of these two currents, or a mix, can account for descriptions of I(Na) in hair cells from other reports. The patterns of Na channel expression during development suggest a role in establishing the distinct synapses of vestibular hair cells of different type and epithelial zone. All type I hair cells expressed I(Na,1), a TTX-insensitive current with a very negative voltage range of inactivation (midpoint: -94 mV). I(Na,2) was TTX sensitive and had less negative voltage ranges of activation and inactivation (inactivation midpoint: -72 mV). I(Na,1) dominated in the striola at all ages, but current density fell by two-thirds after the first postnatal week. I(Na,2) was expressed by 60% of hair cells in the extrastriola in the first week, then disappeared. In the third week, all type I cells and about half of type II cells had I(Na,1); the remaining cells lacked sodium current. I(Na,1) is probably carried by Na(V)1.5 subunits based on biophysical and pharmacological properties, mRNA expression, and immunoreactivity. Na(V)1.5 was also localized to calyx endings on type I hair cells. Several TTX-sensitive subunits are candidates for I(Na,2).

Reduction of anion reversal potential subverts the inhibitory control of firing rate in spinal lamina I neurons: towards a biophysical basis for neuropathic pain

Background

Reduction of the transmembrane chloride gradient in spinal lamina I neurons contributes to the cellular hyperexcitability producing allodynia and hyperalgesia after peripheral nerve injury. The resultant decrease in anion reversal potential (i.e. shift in E_anion to less negative potentials) reduces glycine/GABA_A receptor-mediated hyperpolarization, but the large increase in membrane conductance caused by inhibitory input can nonetheless shunt concurrent excitatory input. Without knowing the relative contribution of hyperpolarization and shunting to inhibition's modulation of firing rate, it is difficult to predict how much net disinhibition results from reduction of E_anion. We therefore used a biophysically accurate lamina I neuron model to investigate quantitatively how changes in E_anion affect firing rate modulation.

Results

Simulations reveal that even a small reduction of E_anion compromises inhibitory control of firing rate because reduction of E_anion not only decreases glycine/GABA_A receptor-mediated hyperpolarization, but can also indirectly compromise the capacity of shunting to reduce spiking. The latter effect occurs because shunting-mediated modulation of firing rate depends on a competition between two biophysical phenomena: shunting reduces depolarization, which translates into reduced spiking, but shunting also shortens the membrane time constant, which translates into faster membrane charging and increased spiking; the latter effect predominates when average depolarization is suprathreshold. Disinhibition therefore occurs as both hyperpolarization- and shunting-mediated modulation of firing rate are subverted by reduction of E_anion. Small reductions may be compensated for by increased glycine/GABA_A receptor-mediated input, but the system decompensates (i.e. compensation fails) as reduction of E_anion exceeds a critical value. Hyperexcitability necessarily develops once disinhibition becomes incompensable. Furthermore, compensation by increased glycine/GABA_A receptor-mediated input introduces instability into the system, rendering it increasingly prone to abrupt decompensation and even paradoxical excitation.

Conclusion

Reduction of E_anion dramatically compromises the inhibitory control of firing rate and, if compensation fails, is likely to contribute to the allodynia and hyperalgesia associated with neuropathic pain. These data help explain the relative intractability of neuropathic pain and illustrate how it is important to choose therapies not only based on disease mechanism, but based on quantitative understanding of that mechanism.

Two types of GABAergic miniature inhibitory postsynaptic currents in mouse substantia gelatinosa neurons

The physiological and pharmacological properties of gamma-aminobutyric acid (GABA)ergic miniature inhibitory postsynaptic currents (mIPSCs) were investigated in substantia gelatinosa neurons of mouse spinal cord using whole-cell patch clamp recordings. Two cell populations were pharmacologically identified based on the effect of propofol (10 muM) on the mIPSC decay kinetics: those exhibiting propofol-sensitive mIPSCs, with a slow decay kinetic (mIPSC(SLOW)), and those exhibiting propofol-resistant mIPSCs, with a fast decay kinetic (mIPSC(FAST)) (decay time constants of 14.2+/-0.7 and 7.4+/-0.8 ms, respectively). The frequency and amplitude of both types of mIPSCs were not affected by propofol. Miniature IPSC(FAST) showed midazolam insensitivity, while midazolam prolonged the decay phase of mIPSC(SLOW) without modulation of the frequency and amplitude. Exogenous GABA-evoked responses in the neurons with mIPSC(SLOW) were potentiated by propofol, while those in neurons with mIPSC(FAST) were unaffected by propofol. Furthermore, non-stationary noise analysis of the two kinetically and pharmacologically distinct mIPSCs revealed different conductance of GABA(A) receptor channels underlying the synaptic events. Pharmacological responses to propofol and midazolam suggested that mIPSC(FAST) and mIPSC(SLOW) in substantia gelatinosa neurons can be mediated by GABA(A) receptors with different subunit compositions.

Essential role of the persistent sodium current in spike initiation during slowly rising inputs in mouse spinal neurones

Spinal motoneurons, like many neurons, respond with repetitive spiking to sustained inputs. The afterhyperpolarization (AHP) that follows each spike, however, decays relatively slowly in motoneurons. The slow depolarization during this decay should allow sodium (Na+) channel inactivation to keep up with its activation and thus should prevent initiation of the next spike. We hypothesized that the persistent component of the total Na+ current provides the mechanism that generates a rate of rise sufficiently rapid to generate a spike. In large cultured spinal neurons, presumed to be primarily motoneurons, inhibition of persistent sodium current (NaP) by the drug riluzole at low concentrations resulted in a loss of repetitive firing. However, cells remained fully capable of producing spikes to transient inputs. These effects of riluzole were not due to insufficient depolarization, enhancement of the AHP, or sustained Na+ channel inactivation. To further test this hypothesis, computer simulations were performed with a kinetic Na+ channel model that provided greater independent control of NaP relative to transient Na+ current (NaT) than that provided by riluzole administration. The model was tuned to generate substantial NaP and exhibited good repetitive firing to slowly rising inputs. When NaP was sharply reduced without significantly altering NaT, the model reproduced the effects of riluzole administration, inducing failure of repetitive firing but allowing single spikes in response to sharp transients. These results strongly support the essential role of NaP in spike initiation to slow inputs in spinal neurons. NaP may play a fundamental role in determining how a neuron responds to sustained inputs.

Upregulation of persistent and ramp sodium current in dorsal horn neurons after spinal cord injury

Traumatic spinal cord injury (SCI) results not only in motor impairment, but also in chronic central neuropathic pain, which often is refractory to conventional treatment approaches. Upregulated expression of sodium channel Nav1.3 has been observed within the spinal dorsal horn neurons after SCI, and appears to contribute to neuronal hyperresponsiveness and pain-related behaviors. In this study we characterized the changes in sodium current properties within dorsal horn neurons after contusive SCI. Four weeks after adult male Sprague-Dawley rats underwent T9 spinal cord contusion injury, when behavioral nociceptive thresholds were decreased to both mechanical and thermal stimuli, whole-cell patch-clamp recordings were performed on acutely dissociated lumbar dorsal horn neurons. The cells demonstrated characteristic fast-activating and fast-inactivating sodium currents. SCI led to a shift of the steady-state activation and inactivation of the sodium current towards more depolarized potentials. The shifted steady-state inactivation shows similarities to that obtained from axotomized dorsal root ganglions, which were shown to upregulate Nav1.3. Small slow depolarizations below action potential threshold produced ramp currents, which were markedly enhanced by SCI (from 182 +/- 41 to 338 +/- 55 pA). The density of the noninactivating persistent sodium current was also significantly enhanced in neurons from SCI animals (from 17.4 +/- 3.2 to 27.7 +/- 4.4 pA/pF at 50-70 ms of depolarization). The increased persistent sodium current and ramp current, which are consistent with upregulation of Nav1.3 within dorsal horn neurons, suggest a basis for the hyperresponsiveness of these neurons following SCI.