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

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.

The century-old picture of a nerve spike is wrong: filaments fire, before membrane

In 1907, Lapicque proposed that an electric field passes through the neuronal membrane and transmits a signal. Subsequently, a “snake curve” or spike was used to depict the means by which a linear flat current undergoes a sudden Gaussian or Laplacian peak. This concept has been the accepted scenario for more than 115 years even appearing in textbooks on the subject. It was not noted that the membrane spike should have a cylindrical shape. A nerve spike having a dot shape on membrane surface cannot propagate through a cylindrical surface since it would dissipate instantaneously. A nerve spike should have the appearance of a ring, encompassing the diameter of a cylindrical axon or dendron. However, this subtle change has remarkable implications. Maintaining a circular form of an electric field is not easy, especially at the surface of an organic object. Here, we suggest that neuroscience could redefine itself if we accept that a nerve spike is not a localized 3D Gaussian or Laplacian wave packet, rather it is a 3D ring encompassing the diameter of a neural branch.

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.

Imbalanced Subthreshold Currents Following Sepsis and Chemotherapy: A Shared Mechanism Offering a New Therapeutic Target?

Both sepsis and treatment of cancer with chemotherapy are known to cause neurologic dysfunction. The primary defects seen in both groups of patients are neuropathy and encephalopathy; the underlying mechanisms are poorly understood. Analysis of preclinical models of these disparate conditions reveal similar defects in ion channel function contributing to peripheral neuropathy. The defects in ion channel function extend to the central nervous system where lower motoneurons are affected. In motoneurons the defect involves ion channels responsible for subthreshold currents that convert steady depolarization into repetitive firing. The inability to correctly translate depolarization into steady, repetitive firing has profound effects on motor function, and could be an important contributor to weakness and fatigue experienced by both groups of patients. The possibility that disruption of function, either instead of, or in addition to neurodegeneration, may underlie weakness and fatigue leads to a novel approach to therapy. Activation of serotonin (5HT) receptors in a rat model of sepsis restores the normal balance of subthreshold currents and normal motoneuron firing. If an imbalance of subthreshold currents also occurs in other central nervous system neurons, it could contribute to encephalopathy. We hypothesize that pharmacologically restoring the proper balance of subthreshold currents might provide effective therapy for both neuropathy and encephalopathy in patients recovering from sepsis or treatment with chemotherapy.

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.

Kv1 channels regulate variations in spike patterning and temporal reliability in the avian cochlear nucleus angularis

Diverse physiological phenotypes in a neuronal population can broaden the range of computational capabilities within a brain region. The avian cochlear nucleus angularis (NA) contains a heterogeneous population of neurons whose variation in intrinsic properties results in electrophysiological phenotypes with a range of sensitivities to temporally modulated input. The low-threshold potassium conductance (G_KLT) is a key feature of neurons involved in fine temporal structure coding for sound localization, but a role for these channels in intensity or spectrotemporal coding has not been established. To determine whether G_KLT affects the phenotypical variation and temporal properties of NA neurons, we applied dendrotoxin-I (DTX), a potent antagonist of Kv1-type potassium channels, to chick brain stem slices in vitro during whole cell patch-clamp recordings. We found a cell-type specific subset of NA neurons that was sensitive to DTX: single-spiking NA neurons were most profoundly affected, as well as a subset of tonic-firing neurons. Both tonic I (phasic onset bursting) and tonic II (delayed firing) neurons showed DTX sensitivity in their firing rate and phenotypical firing pattern. Tonic III neurons were unaffected. Spike time reliability and fluctuation sensitivity measured in DTX-sensitive NA neurons was also reduced with DTX. Finally, DTX reduced spike threshold adaptation in these neurons, suggesting that G_KLT contributes to the temporal properties that allow coding of rapid changes in the inputs to NA neurons. These results suggest that variation in Kv1 channel expression may be a key factor in functional diversity in the avian cochlear nucleus.NEW & NOTEWORTHY The dendrotoxin-sensitive voltage-gated potassium conductance typically associated with neuronal coincidence detection in the timing pathway for sound localization is demonstrated to affect spiking patterns and temporal input sensitivity in the intensity pathway in the avian auditory brain stem. The Kv1-family channels appear to be present in a subset of cochlear nucleus angularis neurons, regulate spike threshold dynamics underlying high-pass membrane filtering, and contribute to intrinsic firing diversity.

Cytoskeletal Filaments Deep Inside a Neuron Are not Silent: They Regulate the Precise Timing of Nerve Spikes Using a Pair of Vortices

Hodgkin and Huxley showed that even if the filaments are dissolved, a neuron’s membrane alone can generate and transmit the nerve spike. Regulating the time gap between spikes is the brain’s cognitive key. However, the time modula-tion mechanism is still a mystery. By inserting a coaxial probe deep inside a neuron, we have re-peatedly shown that the filaments transmit electromagnetic signals ~200 μs before an ionic nerve spike sets in. To understand its origin, here, we mapped the electromagnetic vortex produced by a filamentary bundle deep inside a neuron, regulating the nerve spike’s electrical-ionic vortex. We used monochromatic polarized light to measure the transmitted signals beating from the internal components of a cultured neuron. A nerve spike is a 3D ring of the electric field encompassing the perimeter of a neural branch. Several such vortices flow sequentially to keep precise timing for the brain’s cognition. The filaments hold millisecond order time gaps between membrane spikes with microsecond order signaling of electromagnetic vortices. Dielectric resonance images revealed that ordered filaments inside neural branches instruct the ordered grid-like network of actin–beta-spectrin just below the membrane. That layer builds a pair of electric field vortices, which coherently activates all ion-channels in a circular area of the membrane lipid bilayer when a nerve spike propagates. When biomaterials vibrate resonantly with microwave and radio-wave, simultaneous quantum optics capture ultra-fast events in a non-demolition mode, revealing multiple correlated time-domain operations beyond the Hodgkin–Huxley paradigm. Neuron holograms pave the way to understanding the filamentary circuits of a neural network in addition to membrane circuits.

Electrophysiology using coaxial atom probe array: live imaging reveals hidden circuits of a hippocampal neural network

Since the 1960s, it is held that when a neuron fires, a nerve spike passes only through the selective branches, the calculated choice is a key to learning by rewiring. It is argued by chemically estimating the membrane's ion channel density that different axonal branches get active to pass the spike-branches blink at firing at different time domains. Here, using a new time-lapse dielectric imaging, we visualize the classic branch selection process; thenceforth, hidden circuits operating at different time domains become visible. The fractal grid of coaxial probes captures wireless snapshots of material's vibration at various depths below the membrane by setting a suitable frequency. Thus far, branch selection observed emitted energy or particle but never the emitters, what they do. As each dielectric material transmits and reflects signals of different frequencies, we image live how filaments search for many branch-made circuits, choose a unique pathway 10³ times faster than a single nerve spike. It reveals that neural branches and circuit visible in a microscope are not absolute, there coexist many circuits each operating in different dime domains, operating at a time.NEW & NOTEWORTHY Using dielectric resonance scanner, we show electromagnetic field connections between physically separated neurons. Electromagnetic field creates field lines that pass through gap junctions, connect Axon initial segment with the dendrites through Soma, and connect axonal or dendritic branches even if there is no synaptic junction. Consequently, many distinct loops connecting various branches form coexisting circuits. Our discovery suggests that physically appearing neural circuit is a fractional view of many simultaneously operating circuits in different time domains in a neural network.

From Topological Analyses to Functional Modeling: The Case of Hippocampus

Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

A spiking neural program for sensorimotor control during foraging in flying insects

Foraging is a vital behavioral task for living organisms. Behavioral strategies and abstract mathematical models thereof have been described in detail for various species. To explore the link between underlying neural circuits and computational principles, we present how a biologically detailed neural circuit model of the insect mushroom body implements sensory processing, learning, and motor control. We focus on cast and surge strategies employed by flying insects when foraging within turbulent odor plumes. Using a spike-based plasticity rule, the model rapidly learns to associate individual olfactory sensory cues paired with food in a classical conditioning paradigm. We show that, without retraining, the system dynamically recalls memories to detect relevant cues in complex sensory scenes. Accumulation of this sensory evidence on short time scales generates cast-and-surge motor commands. Our generic systems approach predicts that population sparseness facilitates learning, while temporal sparseness is required for dynamic memory recall and precise behavioral control. Our work successfully combines biological computational principles with spike-based machine learning. It shows how knowledge transfer from static to arbitrary complex dynamic conditions can be achieved by foraging insects and may serve as inspiration for agent-based machine learning.

Simulations reveal how M-currents and memory-based inputs from CA3 enable single neuron mismatch detection for EC3 inputs to the CA1 subfield of hippocampus

Significant evidence has accumulated to support the hypothesis that hippocampal region CA1 operates as an associative mismatch detector (e.g., Hasselmo ME, Schnell E, Barkai E. J Neurosci 15: 5249-5262, 1995; Duncan K, Curtis C, Davachi L. J Neurosci 29: 131-139, 2009; Kumaran D, Maguire EA. J Neurosci 27: 8517-8524, 2007; Lisman JE, Grace AA. Neuron 46: 703-713, 2005; Lisman JE, Otmakhova NA. Hippocampus 11: 551-568 2001; Lörincz A, Buzsáki G. Ann N Y Acad Sci 911: 83-111, 2000; Meeter M, Murre JMJ, Talamini LM. Hippocampus 14: 722-741, 2004; Schiffer AM, Ahlheim C, Wurm MF, Schubotz RI. PLoS One 7: e36445, 2012; Vinogradova OS. Hippocampus 11: 578-598 2001). CA1 compares predictive synaptic signals from CA3 with synaptic signals from EC3, which reflect actual sensory inputs. The new CA1 pyramidal model presented here shows that the distal-proximal segregation of synaptic inputs from EC3 versus CA3, along with other biophysical features, enable such pyramids to serve as comparators that switch output encoding from a brief burst, for a match, to prolonged tonic spiking, for a mismatch. By including often-overlooked features of CA1 pyramidal neurons, this new model allows simulation of pharmacological effects that can eliminate either the match (phasic mode) response or the mismatch (tonic mode) response. These simulations reveal that dysfunctions can arise from either too much or too little ACh stimulation of the muscarinic receptors that control KCNQ channels. Additionally, a dysfunction caused by administration of an N-methyl-d-aspartate antagonist could be rescued by simultaneous administration of a KCNQ channel agonist, such as retigabine.NEW & NOTEWORTHY Hippocampal region CA1 operates as an associative mismatch detector, comparing predictive signals from CA3 with signals from EC3 reflecting sensory inputs. This new CA1 pyramidal model shows that biophysical features enable these comparators to switch output between brief bursts for matches and tonic spiking for mismatches. This suggests that cognitive learning models (e.g., predictive coding) may require much less match/mismatch circuitry than commonly assumed. Additional simulations illuminate deficits seen in psychiatric disorders and drug-induced states.

Propriospinal Neurons of L3-L4 Segments Involved in Control of the Rat External Urethral Sphincter

Coordination of activity of external urethral sphincter (EUS) striated muscle and bladder (BL) smooth muscle is essential for efficient voiding. In this study we examined the morphological and electrophysiological properties of neurons in the L3/L4 spinal cord (SC) that are likely to have an important role in EUS-BL coordination in rats. EUS-related SC neurons were identified by retrograde transsynaptic tracing following injection of pseudorabies virus (PRV) co-expressing fluorescent markers into the EUS of P18-P20 male rats. Tracing revealed not only EUS motoneurons in L6/S1 but also interneurons in lamina X of the L6/S1 and L3/L4 SC. Physiological properties of fluorescently labeled neurons were assessed during whole-cell recordings in SC slices followed by reconstruction of biocytin-filled neurons. Reconstructions of neuronal processes from transverse or longitudinal slices showed that some L3/L4 neurons have axons projecting toward and into the ventro-medial funiculus (VMf) where axons extended caudally. Other neurons had axons projecting within laminae X and VII. Dendrites of L3/L4 neurons were distributed within laminae X and VII. The majority of L3/L4 neurons exhibited tonic firing in response to depolarizing currents. In transverse slices focal electrical stimulation (FES) in the VMf or in laminae X and VII elicited antidromic axonal spikes and/or excitatory synaptic responses in L3/L4 neurons; while in longitudinal slices FES elicited excitatory synaptic inputs from sites up to 400 μm along the central canal. Inhibitory inputs were rarely observed. These data suggest that L3/L4 EUS-related circuitry consists of at least two neuronal populations: segmental interneurons and propriospinal neurons projecting to L6/S1.

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.

Selective attenuation of Ether-a-go-go related K+ currents by endogenous acetylcholine reduces spike-frequency adaptation and network correlation

Most neurons do not simply convert inputs into firing rates. Instead, moment-to-moment firing rates reflect interactions between synaptic inputs and intrinsic currents. Few studies investigated how intrinsic currents function together to modulate output discharges and which of the currents attenuated by synthetic cholinergic ligands are actually modulated by endogenous acetylcholine (ACh). In this study we optogenetically stimulated cholinergic fibers in rat neocortex and find that ACh enhances excitability by reducing Ether-à-go-go Related Gene (ERG) K+ current. We find ERG mediates the late phase of spike-frequency adaptation in pyramidal cells and is recruited later than both SK and M currents. Attenuation of ERG during coincident depolarization and ACh release leads to reduced late phase spike-frequency adaptation and persistent firing. In neuronal ensembles, attenuating ERG enhanced signal-to-noise ratios and reduced signal correlation, suggesting that these two hallmarks of cholinergic function in vivo may result from modulation of intrinsic properties.

Differentially synchronized spiking enables multiplexed neural coding

The nervous system processes phenomenal amounts of information. This processing must be conducted efficiently. In telecommunications systems, efficiency is increased by transmitting multiple signals through a single communication channel, or multiplexing. Neurons also multiplex. Here, we demonstrate a strategy for multiplexing different features of aperiodic stimuli: Cortical neurons use the rate of asynchronous spiking to encode stimulus intensity while using the timing of synchronous spikes to encode abrupt changes in stimulus intensity. This is possible because high-contrast features (e.g., edges) evoke spikes that transiently synchronize across neurons, whereas low-contrast features evoke sustained asynchronous spiking whose rate is proportional to stimulus intensity. Differentially synchronized spiking evoked in the same neurons by different stimulus features enables the formation of multiplexed representations.

Multiplexing refers to the simultaneous encoding of two or more signals. Neurons have been shown to multiplex, but different stimuli require different multiplexing strategies. Whereas the frequency and amplitude of periodic stimuli can be encoded by the timing and rate of the same spikes, natural scenes, which comprise areas over which intensity varies gradually and sparse edges where intensity changes abruptly, require a different multiplexing strategy. Recording in vivo from neurons in primary somatosensory cortex during tactile stimulation, we found that stimulus onset and offset (edges) evoked highly synchronized spiking, whereas other spikes in the same neurons occurred asynchronously. Stimulus intensity modulated the rate of asynchronous spiking, but did not affect the timing of synchronous spikes. From this, we hypothesized that spikes driven by high- and low-contrast stimulus features can be distinguished on the basis of their synchronization, and that differentially synchronized spiking can thus be used to form multiplexed representations. Applying a Bayesian decoding method, we verified that information about high- and low-contrast features can be recovered from an ensemble of model neurons receiving common input. Equally good decoding was achieved by distinguishing synchronous from asynchronous spikes and applying reverse correlation methods separately to each spike type. This result, which we verified with patch clamp recordings in vitro, demonstrates that neurons receiving common input can use the rate of asynchronous spiking to encode the intensity of low-contrast features while using the timing of synchronous spikes to encode the occurrence of high-contrast features. We refer to this strategy as synchrony-division multiplexing.

Cav3.2 T-type calcium channels shape electrical firing in mouse Lamina II neurons

The T-type calcium channel, Cav3.2, is necessary for acute pain perception, as well as mechanical and cold allodynia in mice. Being found throughout sensory pathways, from excitatory primary afferent neurons up to pain matrix structures, it is a promising target for analgesics. In our study, Cav3.2 was detected in ~60% of the lamina II (LII) neurons of the spinal cord, a site for integration of sensory processing. It was co-expressed with Tlx3 and Pax2, markers of excitatory and inhibitory interneurons, as well as nNOS, calretinin, calbindin, PKCγ and not parvalbumin. Non-selective T-type channel blockers slowed the inhibitory but not the excitatory transmission in LII neurons. Furthermore, T-type channel blockers modified the intrinsic properties of LII neurons, abolishing low-threshold activated currents, rebound depolarizations, and blunting excitability. The recording of Cav3.2-positive LII neurons, after intraspinal injection of AAV-DJ-Cav3.2-mcherry, showed that their intrinsic properties resembled those of the global population. However, Cav3.2 ablation in the dorsal horn of Cav3.2^GFP-Flox KI mice after intraspinal injection of AAV-DJ-Cav3.2-Cre-IRES-mcherry, had drastic effects. Indeed, it (1) blunted the likelihood of transient firing patterns; (2) blunted the likelihood and the amplitude of rebound depolarizations, (3) eliminated action potential pairing, and (4) remodeled the kinetics of the action potentials. In contrast, the properties of Cav3.2-positive neurons were only marginally modified in Cav3.1 knockout mice. Overall, in addition to their previously established roles in the superficial spinal cord and in primary afferent neurons, Cav3.2 channel appear to be necessary for specific, significant and multiple controls of LII neuron excitability.

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.

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.

Active Mechanisms of Vibration Encoding and Frequency Filtering in Central Mechanosensory Neurons

To better understand biophysical mechanisms of mechanosensory processing, we investigated two cell types in the Drosophila brain (A2 and B1 cells) that are postsynaptic to antennal vibration receptors. A2 cells receive excitatory synaptic currents in response to both directions of movement: thus, twice per vibration cycle. The membrane acts as a low-pass filter, so that voltage and spiking mainly track the vibration envelope rather than individual cycles. By contrast, B1 cells are excited by only forward or backward movement, meaning they are sensitive to vibration phase. They receive oscillatory synaptic currents at the stimulus frequency, and they bandpass filter these inputs to favor specific frequencies. Different cells prefer different frequencies, due to differences in their voltage-gated conductances. Both Na⁺ and K⁺ conductances suppress low-frequency synaptic inputs, so cells with larger voltage-gated conductances prefer higher frequencies. These results illustrate how membrane properties and voltage-gated conductances can extract distinct stimulus features into parallel channels.

Transient cell assembly networks encode stable spatial memories

One of the mysteries of memory is that it can last despite changes in the underlying synaptic architecture. How can we, for example, maintain an internal spatial map of an environment over months or years when the underlying network is full of transient connections? In the following, we propose a computational model for describing the emergence of the hippocampal cognitive map in a network of transient place cell assemblies and demonstrate, using methods of algebraic topology, how such a network can maintain spatial memory over time.

Noise-enhanced coding in phasic neuron spike trains

The stochastic nature of neuronal response has lead to conjectures about the impact of input fluctuations on the neural coding. For the most part, low pass membrane integration and spike threshold dynamics have been the primary features assumed in the transfer from synaptic input to output spiking. Phasic neurons are a common, but understudied, neuron class that are characterized by a subthreshold negative feedback that suppresses spike train responses to low frequency signals. Past work has shown that when a low frequency signal is accompanied by moderate intensity broadband noise, phasic neurons spike trains are well locked to the signal. We extend these results with a simple, reduced model of phasic activity that demonstrates that a non-Markovian spike train structure caused by the negative feedback produces a noise-enhanced coding. Further, this enhancement is sensitive to the timescales, as opposed to the intensity, of a driving signal. Reduced hazard function models show that noise-enhanced phasic codes are both novel and separate from classical stochastic resonance reported in non-phasic neurons. The general features of our theory suggest that noise-enhanced codes in excitable systems with subthreshold negative feedback are a particularly rich framework to study.

Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both

Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary temporal precision for phase locking and coincidence detection. Exemplars are found in the auditory brain stem where precise timing is used in sound localization. Phasicness at the cellular level arises from a dynamic, voltage-gated, negative feedback that can be recruited subthreshold, preventing the neuron from reaching spike threshold if the voltage does not rise fast enough. We consider two mechanisms for phasicness: a low threshold potassium current (subtractive mechanism) and a sodium current with subthreshold inactivation (divisive mechanism). We develop and analyze three reduced models with either divisive or subtractive mechanisms or both to gain insight into the dynamical mechanisms for the potentially high temporal precision of type III-excitable neurons. We compare their firing properties and performance for a range of stimuli. The models have characteristic non-monotonic input-output relations, firing rate vs. input intensity, for either stochastic current injection or Poisson-timed excitatory synaptic conductance trains. We assess performance according to precision of phase-locking and coincidence detection by the models' responses to repetitive packets of unitary excitatory synaptic inputs with more or less temporal coherence. We find that each mechanism contributes features but best performance is attained if both are present. The subtractive mechanism confers extraordinary precision for phase locking and coincidence detection but only within a restricted parameter range when the divisive mechanism of sodium inactivation is inoperative. The divisive mechanism guarantees robustness of phasic properties, without compromising excitability, although with somewhat less precision. Finally, we demonstrate that brief transient inhibition if properly timed can enhance the reliability of firing.

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.

Integrator or Coincidence Detector: A Novel Measure Based on the Discrete Reverse Correlation to Determine a Neuron’s Operational Mode

In this letter, we propose a definition of the operational mode of a neuron, that is, whether a neuron integrates over its input or detects coincidences. We complete the range of possible operational modes by a new mode we call gap detection, which means that a neuron responds to gaps in its stimulus. We propose a measure consisting of two scalar values, both ranging from −1 to +1: the neural drive, which indicates whether its stimulus excites the neuron, serves as background noise, or inhibits it; the neural mode, which indicates whether the neuron’s response is the result of integration over its input, of coincidence detection, or of gap detection; with all three modes possible for all neural drive values. This is a pure spike-based measure and can be applied to measure the influence of either all or subset of a neuron’s stimulus. We derive the measure by decomposing the reverse correlation, test it in several artificial and biological settings, and compare it to other measures, finding little or no correlation between them. We relate the results of the measure to neural parameters and investigate the effect of time delay during spike generation. Our results suggest that a neuron can use several different modes simultaneously on different subsets of its stimulus to enable it to respond to its stimulus in a complex manner.

Gamma Synchronization Influences Map Formation Time in a Topological Model of Spatial Learning

The mammalian hippocampus plays a crucial role in producing a cognitive map of space-an internalized representation of the animal's environment. We have previously shown that it is possible to model this map formation using a topological framework, in which information about the environment is transmitted through the temporal organization of neuronal spiking activity, particularly those occasions in which the firing of different place cells overlaps. In this paper, we discuss how gamma rhythm, one of the main components of the extracellular electrical field potential affects the efficiency of place cell map formation. Using methods of algebraic topology and the maximal entropy principle, we demonstrate that gamma modulation synchronizes the spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales.

High-Degree Neurons Feed Cortical Computations

Recent work has shown that functional connectivity among cortical neurons is highly varied, with a small percentage of neurons having many more connections than others. Also, recent theoretical developments now make it possible to quantify how neurons modify information from the connections they receive. Therefore, it is now possible to investigate how information modification, or computation, depends on the number of connections a neuron receives (in-degree) or sends out (out-degree). To do this, we recorded the simultaneous spiking activity of hundreds of neurons in cortico-hippocampal slice cultures using a high-density 512-electrode array. This preparation and recording method combination produced large numbers of neurons recorded at temporal and spatial resolutions that are not currently available in any in vivo recording system. We utilized transfer entropy (a well-established method for detecting linear and nonlinear interactions in time series) and the partial information decomposition (a powerful, recently developed tool for dissecting multivariate information processing into distinct parts) to quantify computation between neurons where information flows converged. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to receive connections from high out-degree neurons. However, the in-degree of a neuron was not related to the amount of information it computed. To gain insight into these findings, we developed a simple feedforward network model. We found that a degree-modified Hebbian wiring rule best reproduced the pattern of computation and degree correlation results seen in the real data. Interestingly, this rule also maximized signal propagation in the presence of network-wide correlations, suggesting a mechanism by which cortex could deal with common random background input. These are the first results to show that the extent to which a neuron modifies incoming information streams depends on its topological location in the surrounding functional network.

We recorded the electrical activity of hundreds of neurons simultaneously in brain tissue from mice and we analyzed these signals using state-of-the-art tools from information theory. These tools allowed us to ascertain which neurons were transmitting information to other neurons and to characterize the computations performed by neurons using the inputs they received from two or more other neurons. We found that computations did not occur equally in all neurons throughout the networks. Surprisingly, neurons that computed large amounts of information tended to be recipients of information from neurons with a large number of outgoing connections. Interestingly, the number of incoming connections to a neuron was not related to the amount of information that neuron computed. To better understand these results, we built a network model to match the data. Unexpectedly, the model also maximized information transfer in the presence of network-wide correlations. This suggested a way that networks of cortical neurons could deal with common random background input. These results are the first to show that the amount of information computed by a neuron depends on where it is located in the surrounding network.

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na⁺-channel inactivation regulate the sensitivity to rapid input fluctuations.

Over the last decades, a variety of simplified spiking models have been shown to achieve a surprisingly high performance in predicting the neuronal responses to in vitro somatic current injections. Because of the complex adaptive behavior featured by cortical neurons, this success is however restricted to limited stimulus ranges: model parameters optimized for a specific input regime are often inappropriate to describe the response to input currents with different statistical properties. In the present study, a new spiking neuron model is introduced that captures single-neuron computation over a wide range of input statistics and explains different aspects of the neuronal dynamics within a single framework. Our results indicate that complex forms of single neuron adaptation are mediated by the nonlinear dynamics of the firing threshold and that the input-output transformation performed by cortical pyramidal neurons can be intuitively understood in terms of an enhanced Generalized Linear Model in which both the input filter and the spike-history filter adapt to the input statistics.

Convergence, Divergence, and Reconvergence in a Feedforward Network Improves Neural Speed and Accuracy

One of the proposed canonical circuit motifs employed by the brain is a feedforward network where parallel signals converge, diverge, and reconverge. Here we investigate a network with this architecture in the Drosophila olfactory system. We focus on a glomerulus whose receptor neurons converge in an all-to-all manner onto six projection neurons that then reconverge onto higher-order neurons. We find that both convergence and reconvergence improve the ability of a decoder to detect a stimulus based on a single neuron's spike train. The first transformation implements averaging, and it improves peak detection accuracy but not speed; the second transformation implements coincidence detection, and it improves speed but not peak accuracy. In each case, the integration time and threshold of the postsynaptic cell are matched to the statistics of convergent spike trains.

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.