Nonlinear interaction between shunting and adaptation controls a switch between integration and coincidence detection in pyramidal neurons

The enigmatic HCN channels: A cellular neurophysiology perspective

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

Spike-frequency adaptation inhibits the pairwise spike correlation

Introduction

The spike train output correlation with pairwise neurons determines the neural population coding, which depends on the average firing rate of individual neurons. Spike frequency adaptation (SFA), which serves as an essential cellular encoding strategy, modulates the firing rates of individual neurons. However, the mechanism by which the SFA modulates the output correlation of the spike trains remains unclear.

Methods

We introduce a pairwise neuron model that receives correlated inputs to generate spike trains, and the output correlation is qualified using Pearson correlation coefficient. The SFA is modeled using adaptation currents to examine its effect on the output correlation. Moreover, we use dynamic thresholds to explore the effect of SFA on output correlation. Furthermore, a simple phenomenological neuron model with a threshold-linear transfer function is utilized to confirm the effect of SFA on decreasing the output correlation.

Results

The results show that the adaptation currents decreased the output correlation by reducing the firing rate of a single neuron. At the onset of a correlated input, a transient process shows a decrease in interspike intervals (ISIs), resulting in a temporary increase in the correlation. When the adaptation current is sufficiently activated, the correlation reached a steady state, and the ISIs are maintained at higher values. The enhanced adaptation current achieved by increasing the adaptation conductance further reduces the pairwise correlation. While the time and slide windows influence the correlation, they make no difference in the effect of SFA on decreasing the output correlation. Moreover, SFA simulated by dynamic thresholds also decreases the output correlation. Furthermore, the simple phenomenological neuron model with a threshold-linear transfer function confirms the effect of SFA on decreasing the output correlation. The strength of the signal input and the slope of the linear component of the transfer function, the latter of which can be decreased by SFA, could together modulate the strength of the output correlation. Stronger SFA will decrease the slope and hence decrease the output correlation.

Conclusions

The results reveal that the SFA reduces the output correlation with pairwise neurons in the network by reducing the firing rate of individual neurons. This study provides a link between cellular non-linear mechanisms and network coding strategies.

Neural synchrony in cortical networks: mechanisms and implications for neural information processing and coding

Synchronization of neuronal discharges on the millisecond scale has long been recognized as a prevalent and functionally important attribute of neural activity. In this article, I review classical concepts and corresponding evidence of the mechanisms that govern the synchronization of distributed discharges in cortical networks and relate those mechanisms to their possible roles in coding and cognitive functions. To accommodate the need for a selective, directed synchronization of cells, I propose that synchronous firing of distributed neurons is a natural consequence of spike-timing-dependent plasticity (STDP) that associates cells repetitively receiving temporally coherent input: the “synchrony through synaptic plasticity” hypothesis. Neurons that are excited by a repeated sequence of synaptic inputs may learn to selectively respond to the onset of this sequence through synaptic plasticity. Multiple neurons receiving coherent input could thus actively synchronize their firing by learning to selectively respond at corresponding temporal positions. The hypothesis makes several predictions: first, the position of the cells in the network, as well as the source of their input signals, would be irrelevant as long as their input signals arrive simultaneously; second, repeating discharge patterns should get compressed until all or some part of the signals are synchronized; and third, this compression should be accompanied by a sparsening of signals. In this way, selective groups of cells could emerge that would respond to some recurring event with synchronous firing. Such a learned response pattern could further be modulated by synchronous network oscillations that provide a dynamic, flexible context for the synaptic integration of distributed signals. I conclude by suggesting experimental approaches to further test this new hypothesis.

Physiological noise facilitates multiplexed coding of vibrotactile-like signals in somatosensory cortex

Neurons can use different aspects of their spiking to simultaneously represent (multiplex) different features of a stimulus. For example, some pyramidal neurons in primary somatosensory cortex (S1) use the rate and timing of their spikes to, respectively, encode the intensity and frequency of vibrotactile stimuli. Doing so has several requirements. Because they fire at low rates, pyramidal neurons cannot entrain 1:1 with high-frequency (100 to 600 Hz) inputs and, instead, must skip (i.e., not respond to) some stimulus cycles. The proportion of skipped cycles must vary inversely with stimulus intensity for firing rate to encode stimulus intensity. Spikes must phase-lock to the stimulus for spike times (intervals) to encode stimulus frequency, but, in addition, skipping must occur irregularly to avoid aliasing. Using simulations and in vitro experiments in which mouse S1 pyramidal neurons were stimulated with inputs emulating those induced by vibrotactile stimuli, we show that fewer cycles are skipped as stimulus intensity increases, as required for rate coding, and that intrinsic or synaptic noise can induce irregular skipping without disrupting phase locking, as required for temporal coding. This occurs because noise can modulate the reliability without disrupting the precision of spikes evoked by small-amplitude, fast-onset signals. Specifically, in the fluctuation-driven regime associated with sparse spiking, rate and temporal coding are both paradoxically improved by the strong synaptic noise characteristic of the intact cortex. Our results demonstrate that multiplexed coding by S1 pyramidal neurons is not only feasible under in vivo conditions, but that background synaptic noise is actually beneficial.

Distinct neuronal types contribute to hybrid temporal encoding strategies in primate auditory cortex

Studies of the encoding of sensory stimuli by the brain often consider recorded neurons as a pool of identical units. Here, we report divergence in stimulus-encoding properties between subpopulations of cortical neurons that are classified based on spike timing and waveform features. Neurons in auditory cortex of the awake marmoset (Callithrix jacchus) encode temporal information with either stimulus-synchronized or nonsynchronized responses. When we classified single-unit recordings using either a criteria-based or an unsupervised classification method into regular-spiking, fast-spiking, and bursting units, a subset of intrinsically bursting neurons formed the most highly synchronized group, with strong phase-locking to sinusoidal amplitude modulation (SAM) that extended well above 20 Hz. In contrast with other unit types, these bursting neurons fired primarily on the rising phase of SAM or the onset of unmodulated stimuli, and preferred rapid stimulus onset rates. Such differentiating behavior has been previously reported in bursting neuron models and may reflect specializations for detection of acoustic edges. These units responded to natural stimuli (vocalizations) with brief and precise spiking at particular time points that could be decoded with high temporal stringency. Regular-spiking units better reflected the shape of slow modulations and responded more selectively to vocalizations with overall firing rate increases. Population decoding using time-binned neural activity found that decoding behavior differed substantially between regular-spiking and bursting units. A relatively small pool of bursting units was sufficient to identify the stimulus with high accuracy in a manner that relied on the temporal pattern of responses. These unit type differences may contribute to parallel and complementary neural codes.

Neurons in auditory cortex show highly diverse responses to sounds. This study suggests that neuronal type inferred from baseline firing properties accounts for much of this diversity, with a subpopulation of bursting units being specialized for precise temporal encoding.

M-current induced Bogdanov-Takens bifurcation and switching of neuron excitability class

In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current [Formula: see text], the maximal conductance of the M-current [Formula: see text] and the conductance of the leak current [Formula: see text]. We give precise conditions for the model that ensure the existence of a Bogdanov-Takens (BT) point and show that such a point can occur by varying [Formula: see text] and [Formula: see text]. We discuss the case when the BT point becomes a Bogdanov-Takens-cusp (BTC) point and show that such a point can occur in the three-dimensional parameter space. The results of the bifurcation analysis are applied to different neuronal models and are verified and supplemented by numerical bifurcation diagrams generated using the package MATCONT. We conclude that there is a transition in the neuronal excitability type organised by the BT point and the neuron switches from Class-I to Class-II as conductance of the M-current increases.

Extracellular GABA waves regulate coincidence detection in excitatory circuits

KEY POINTS

Rapid changes in neuronal network activity trigger widespread waves of extracellular GABA in hippocampal neuropil. Elevations of extracellular GABA narrow the coincidence detection window for excitatory inputs to CA1 pyramidal cells. GABA transporters control the effect of extracellular GABA on coincidence detection. Small changes in the kinetics of dendritic excitatory currents amplify when reaching the soma.

ABSTRACT

Coincidence detection of excitatory inputs by principal neurons underpins the rules of signal integration and Hebbian plasticity in the brain. In the hippocampal circuitry, detection fidelity is thought to depend on the GABAergic synaptic input through a feedforward inhibitory circuit also involving the hyperpolarisation-activated Ih current. However, afferent connections often bypass feedforward circuitry, suggesting that a different GABAergic mechanism might control coincidence detection in such cases. To test whether fluctuations in the extracellular GABA concentration [GABA] could play a regulatory role here, we use a GABA 'sniffer' patch in acute hippocampal slices of the rat and document strong dependence of [GABA] on network activity. We find that blocking GABAergic signalling strongly widens the coincidence detection window of direct excitatory inputs to pyramidal cells whereas increasing [GABA] through GABA uptake blockade shortens it. The underlying mechanism involves membrane-shunting tonic GABAA receptor current; it does not have to rely on Ih but depends strongly on the neuronal GABA transporter GAT-1. We use dendrite-soma dual patch-clamp recordings to show that the strong effect of membrane shunting on coincidence detection relies on nonlinear amplification of changes in the decay of dendritic synaptic currents when they reach the soma. Our results suggest that, by dynamically regulating extracellular GABA, brain network activity can optimise signal integration rules in local excitatory circuits.

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.

Heterogeneities in intrinsic excitability and frequency-dependent response properties of granule cells across the blades of the rat dentate gyrus

The dentate gyrus (DG), the input gate to the hippocampus proper, is anatomically segregated into three different sectors, namely, the suprapyramidal blade, the crest region, and the infrapyramidal blade. Although there are well-established differences between these sectors in terms of neuronal morphology, connectivity patterns, and activity levels, differences in electrophysiological properties of granule cells within these sectors have remained unexplored. Here, employing somatic whole cell patch-clamp recordings from the rat DG, we demonstrate that granule cells in these sectors manifest considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, these neurons showed positive temporal summation of their responses to inputs mimicking excitatory postsynaptic currents and showed little to no sag in their voltage responses to pulse currents. Consistently, the impedance amplitude profile manifested low-pass characteristics and the impedance phase profile lacked positive phase values at all measured frequencies and voltages and for all sectors. Granule cells in all sectors exhibited class I excitability, with broadly linear firing rate profiles, and granule cells in the crest region fired significantly fewer action potentials compared with those in the infrapyramidal blade. Finally, we found weak pairwise correlations across the 18 different measurements obtained individually from each of the three sectors, providing evidence that these measurements are indeed reporting distinct aspects of neuronal physiology. Together, our analyses show that granule cells act as integrators of afferent information and emphasize the need to account for the considerable physiological heterogeneities in assessing their roles in information encoding and processing.NEW & NOTEWORTHY We employed whole cell patch-clamp recordings from granule cells in the three subregions of the rat dentate gyrus to demonstrate considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, granule cells did not express membrane potential resonance, and their impedance profiles lacked inductive phase leads at all measured frequencies. Our analyses also show that granule cells manifest class I excitability characteristics, categorizing them as integrators of afferent information.

Dramatically Amplified Thoracic Sympathetic Postganglionic Excitability and Integrative Capacity Revealed with Whole-Cell Patch-Clamp Recordings

Thoracic paravertebral sympathetic postganglionic neurons (tSPNs) comprise the final integrative output of the distributed sympathetic nervous system controlling vascular and thermoregulatory systems. Considered a non-integrating relay, what little is known of tSPN intrinsic excitability has been determined by sharp microelectrodes with presumed impalement injury. We thus undertook the first electrophysiological characterization of tSPN cellular properties using whole-cell recordings and coupled results with a conductance-based model to explore the principles governing their excitability in adult mice of both sexes. Recorded membrane resistance and time constant values were an order of magnitude greater than values previously obtained, leading to a demonstrable capacity for synaptic integration in driving recruitment. Variation in membrane resistivity was the primary determinant controlling cell excitability with vastly lower currents required for tSPN recruitment. Unlike previous microelectrode recordings in mouse which observed inability to sustain firing, all tSPNs were capable of repetitive firing. Computational modeling demonstrated that observed differences are explained by introduction of a microelectrode impalement injury conductance. Overall, tSPNs largely linearly encoded injected current magnitudes over a broad frequency range with distinct subpopulations differentiable based on repetitive firing signatures. Thus, whole-cell recordings reveal tSPNs have more dramatically amplified excitability than previously thought, with greater intrinsic capacity for synaptic integration and with the ability for maintained firing to support sustained actions on vasomotor tone and thermoregulatory function. Rather than acting as a relay, these studies support a more responsive role and possible intrinsic capacity for tSPNs to drive sympathetic autonomic function.

The Changes of Intrinsic Excitability of Pyramidal Neurons in Anterior Cingulate Cortex in Neuropathic Pain

To find satisfactory treatment strategies for neuropathic pain syndromes, the cellular mechanisms should be illuminated. Central sensitization is a generator of pain hypersensitivity, and is mainly reflected in neuronal hyperexcitability in pain pathway. Neuronal excitability depends on two components, the synaptic inputs and the intrinsic excitability. Previous studies have focused on the synaptic plasticity in different forms of pain. But little is known about the changes of neuronal intrinsic excitability in neuropathic pain. To address this question, whole-cell patch clamp recordings were performed to study the synaptic transmission and neuronal intrinsic excitability 1 week after spared nerve injury (SNI) or sham operation in male C57BL/6J mice. We found increased spontaneous excitatory postsynaptic currents (sEPSC) frequency in layer II/III pyramidal neurons of anterior cingulate cortex (ACC) from mice with neuropathic pain. Elevated intrinsic excitability of these neurons after nerve injury was also picked up, which was reflected in gain of input-output curve, inter-spike interval (ISI), spike threshold and Refractory period (RP). Besides firing rate related to neuronal intrinsic excitability, spike timing also plays an important role in neural information processing. The precision of spike timing measured by standard deviation of spike timing (SDST) was decreased in neuropathic pain state. The electrophysiological studies revealed the elevated intrinsic excitation in layer II/III pyramidal neurons of ACC in mice with neuropathic pain, which might contribute to central excitation.

Differences in the Electrophysiological Properties of Mouse Somatosensory Layer 2/3 Neurons In Vivo and Slice Stem from Intrinsic Sources Rather than a Network-Generated High Conductance State

Synaptic activity in vivo can potentially alter the integration properties of neurons. Using recordings in awake mice, we targeted somatosensory layer 2/3 pyramidal neurons and compared neuronal properties with those from slices. Pyramidal cells in vivo had lower resistance and gain values, as well as broader spikes and increased spike frequency adaptation compared to the same cells in slices. Increasing conductance in neurons using dynamic clamp to levels observed in vivo, however, did not lessen the differences between in vivo and slice conditions. Further, local application of tetrodotoxin (TTX) in vivo blocked synaptic-mediated membrane voltage fluctuations but had little impact on pyramidal cell membrane input resistance and time constant values. Differences in electrophysiological properties of layer 2/3 neurons in mouse somatosensory cortex, therefore, stem from intrinsic sources separate from synaptic-mediated membrane voltage fluctuations.

Nonlinear Relationship Between Spike-Dependent Calcium Influx and TRPC Channel Activation Enables Robust Persistent Spiking in Neurons of the Anterior Cingulate Cortex

Continuation of spiking after a stimulus ends (i.e. persistent spiking) is thought to support working memory. Muscarinic receptor activation enables persistent spiking among synaptically isolated pyramidal neurons in anterior cingulate cortex (ACC), but a detailed characterization of that spiking is lacking and the underlying mechanisms remain unclear. Here, we show that the rate of persistent spiking in ACC neurons is insensitive to the intensity and number of triggers, but can be modulated by injected current, and that persistent spiking can resume after several seconds of hyperpolarization-imposed quiescence. Using electrophysiology and calcium imaging in brain slices from male rats, we determined that canonical transient receptor potential (TRPC) channels are necessary for persistent spiking and that TRPC-activating calcium enters in a spike-dependent manner via voltage-gated calcium channels. Constrained by these biophysical details, we built a computational model that reproduced the observed pattern of persistent spiking. Nonlinear dynamical analysis of that model revealed that TRPC channels become fully activated by the small rise in intracellular calcium caused by evoked spikes. Calcium continues to rise during persistent spiking, but because TRPC channel activation saturates, firing rate stabilizes. By calcium rising higher than required for maximal TRPC channel activation, TRPC channels are able to remain active during periods of hyperpolarization-imposed quiescence (until calcium drops below saturating levels) such that persistent spiking can resume when hyperpolarization is discontinued. Our results thus reveal that the robust intrinsic bistability exhibited by ACC neurons emerges from the nonlinear positive feedback relationship between spike-dependent calcium influx and TRPC channel activation.SIGNIFICANCE STATEMENT Neurons use action potentials, or spikes, to encode information. Some neurons can store information for short periods (seconds to minutes) by continuing to spike after a stimulus ends, thus enabling working memory. This so-called "persistent" spiking occurs in many brain areas and has been linked to activation of canonical transient receptor potential (TRPC) channels. However, TRPC activation alone is insufficient to explain many aspects of persistent spiking such as resumption of spiking after periods of imposed quiescence. Using experiments and simulations, we show that calcium influx caused by spiking is necessary and sufficient to activate TRPC channels and that the ensuing positive feedback interaction between intracellular calcium and TRPC channel activation can account for many hitherto unexplained aspects of persistent spiking.

Dopamine terminals from the ventral tegmental area gate intrinsic inhibition in the prefrontal cortex

Spike frequency adaptation (SFA or accommodation) and calcium‐activated potassium channels that underlie after‐hyperpolarization potentials (AHP) regulate repetitive firing of neurons. Precisely how neuromodulators such as dopamine from the ventral tegmental area (VTA) regulate SFA and AHP (together referred to as intrinsic inhibition) in the prefrontal cortex (PFC) remains unclear. Using whole cell electrophysiology, we measured intrinsic inhibition in prelimbic (PL) layer 5 pyramidal cells of male adult rats. Results demonstrate that bath application of dopamine reduced intrinsic inhibition (EC₅₀: 25.0 μmol/L). This dopamine action was facilitated by coapplication of cocaine (1 μmol/L), a blocker of dopamine reuptake. To evaluate VTA dopamine terminals in PFC slices, we transfected VTA dopamine cells of TH::Cre rats in vivo with Cre‐dependent AAVs to express channelrhodopsin‐2 (ChR2) or designer receptors exclusively activated by designer drugs (DREADDS). In PFC slices from these animals, stimulation of VTA terminals with either blue light to activate ChR2 or bath application of clozapine‐N‐oxide (CNO) to activate Gq‐DREADDs produced a similar reduction in intrinsic inhibition in PL neurons. Electrophysiological recordings from cells expressing retrograde fluorescent tracers showed that this plasticity occurs in PL neurons projecting to the accumbens core. Collectively, these data highlight an ability of VTA terminals to gate intrinsic inhibition in the PFC, and under appropriate circumstances, enhance PL neuronal firing. These cellular actions of dopamine may be important for dopamine‐dependent behaviors involving cocaine and cue‐reward associations within cortical–striatal circuits.

Spike threshold dynamics in spinal motoneurons during scratching and swimming

KEY POINTS

Action potential threshold can vary depending on firing history and synaptic inputs. We used an ex vivo carapace-spinal cord preparation from adult turtles to study spike threshold dynamics in motoneurons during two distinct types of functional motor behaviour - fictive scratching and fictive swimming. The threshold potential depolarizes by about 10 mV within each burst of spikes generated during scratch and swim network activity and recovers between bursts to a slightly depolarized level. Slow synaptic integration resulting in a wave of membrane potential depolarization is the factor influencing the threshold potential within firing bursts during motor behaviours. Depolarization of the threshold potential decreases the excitability of motoneurons and may provide a mechanism for stabilization of the response of a motoneuron to intense synaptic inputs to maintain the motor commands within an optimal range for muscle activation.

ABSTRACT

During functional spinal neural network activity motoneurons receive intense synaptic input, and this could modulate the threshold for action potential generation, providing the ability to dynamically adjust the excitability and recruitment order for functional needs. In the present study we investigated the dynamics of action potential threshold during motor network activity. Intracellular recordings from spinal motoneurons in an ex vivo carapace-spinal cord preparation from adult turtles were performed during two distinct types of motor behaviour - fictive scratching and fictive swimming. We found that the threshold of the first spike in episodes of scratching and swimming was the lowest. The threshold potential depolarizes by about 10 mV within each burst of spikes generated during scratch and swim network activity and recovers between bursts to a slightly depolarized level. Depolarization of the threshold potential results in decreased excitability of motoneurons. Synaptic inputs do not modulate the threshold of the first action potential during episodes of scratching or of swimming. There is no correlation between changes in spike threshold and interspike intervals within bursts. Slow synaptic integration that results in a wave of membrane potential depolarization rather than fast synaptic events preceding each spike is the factor influencing the threshold potential within firing bursts during motor behaviours.

Dendritic Properties Control Energy Efficiency of Action Potentials in Cortical Pyramidal Cells

Neural computation is performed by transforming input signals into sequences of action potentials (APs), which is metabolically expensive and limited by the energy available to the brain. The metabolic efficiency of single AP has important consequences for the computational power of the cell, which is determined by its biophysical properties and morphologies. Here we adopt biophysically-based two-compartment models to investigate how dendrites affect energy efficiency of APs in cortical pyramidal neurons. We measure the Na⁺ entry during the spike and examine how it is efficiently used for generating AP depolarization. We show that increasing the proportion of dendritic area or coupling conductance between two chambers decreases Na⁺ entry efficiency of somatic AP. Activating inward Ca²⁺ current in dendrites results in dendritic spike, which increases AP efficiency. Activating Ca²⁺-activated outward K⁺ current in dendrites, however, decreases Na⁺ entry efficiency. We demonstrate that the active and passive dendrites take effects by altering the overlap between Na⁺ influx and internal current flowing from soma to dendrite. We explain a fundamental link between dendritic properties and AP efficiency, which is essential to interpret how neural computation consumes metabolic energy and how biophysics and morphologies contribute to such consumption.

Theta-frequency selectivity in the somatic spike-triggered average of rat hippocampal pyramidal neurons is dependent on HCN channels

The ability to distill specific frequencies from complex spatiotemporal patterns of afferent inputs is a pivotal functional requirement for neurons residing in networks receiving frequency-multiplexed inputs. Although the expression of theta-frequency subthreshold resonance is established in hippocampal pyramidal neurons, it is not known if their spike initiation dynamics manifest spectral selectivity, or if their intrinsic properties are tuned to process gamma-frequency inputs. Here, we measured the spike-triggered average (STA) of rat hippocampal pyramidal neurons through electrophysiological recordings and quantified spectral selectivity in their spike initiation dynamics and their coincidence detection window (CDW). Our results revealed strong theta-frequency selectivity in the STA, which was also endowed with gamma-range CDW, with prominent neuron-to-neuron variability that manifested distinct pairwise dissociations and correlations with different intrinsic measurements. Furthermore, we demonstrate that the STA and its measurements substantially adapted to the state of the neuron defined by its membrane potential and to the statistics of its afferent inputs. Finally, we tested the effect of pharmacologically blocking the hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels on the STA and found that the STA characteristic frequency reduced significantly to the delta-frequency band after HCN channel blockade. This delta-frequency selectivity in the STA emerged in the absence of subthreshold resonance, which was abolished by HCN channel blockade, thereby confirming computational predictions on the dissociation between these two forms of spectral selectivity. Our results expand the roles of HCN channels to theta-frequency selectivity in the spike initiation dynamics, apart from underscoring the critical role of interactions among different ion channels in regulating neuronal physiology.NEW & NOTEWORTHY We had previously predicted, using computational analyses, that the spike-triggered average (STA) of hippocampal neurons would exhibit theta-frequency (4-10 Hz) spectral selectivity and would manifest coincidence detection capabilities for inputs in the gamma-frequency band (25-150 Hz). Here, we confirmed these predictions through direct electrophysiological recordings of STA from rat CA1 pyramidal neurons and demonstrate that blocking HCN channels reduces the frequency of STA spectral selectivity to the delta-frequency range (0.5-4 Hz).

Extracellular Linkers Completely Transplant the Voltage Dependence from Kv1.2 Ion Channels to Kv2.1

The transmembrane voltage needed to open different voltage-gated K (Kv) channels differs by up to 50 mV from each other. In this study we test the hypothesis that the channels' voltage dependences to a large extent are set by charged amino-acid residues of the extracellular linkers of the Kv channels, which electrostatically affect the charged amino-acid residues of the voltage sensor S4. Extracellular cations shift the conductance-versus-voltage curve, G(V), by interfering with these extracellular charges. We have explored these issues by analyzing the effects of the divalent strontium ion (Sr²⁺) on the voltage dependence of the G(V) curves of wild-type and chimeric Kv channels expressed in Xenopus oocytes, using the voltage-clamp technique. Out of seven Kv channels, Kv1.2 was found to be most sensitive to Sr²⁺ (50 mM shifted G(V) by +21.7 mV), and Kv2.1 to be the least sensitive (+7.8 mV). Experiments on 25 chimeras, constructed from Kv1.2 and Kv2.1, showed that the large Sr²⁺-induced G(V) shift of Kv1.2 can be transferred to Kv2.1 by exchanging the extracellular linker between S3 and S4 (L3/4) in combination with either the extracellular linker between S5 and the pore (L5/P) or that between the pore and S6 (LP/6). The effects of the linker substitutions were nonadditive, suggesting specific structural interactions. The free energy of these interactions was ∼20 kJ/mol, suggesting involvement of hydrophobic interactions and/or hydrogen bonds. Using principles from double-layer theory we derived an approximate linear equation (relating the voltage shifts to altered ionic strength), which proved to well match experimental data, suggesting that Sr²⁺ acts on these channels mainly by screening surface charges. Taken together, these results highlight the extracellular surface potential at the voltage sensor as an important determinant of the channels' voltage dependence, making the extracellular linkers essential targets for evolutionary selection.

Morphology controls how hippocampal CA1 pyramidal neuron responds to uniform electric fields: a biophysical modeling study

Responses of different neurons to electric field (EF) are highly variable, which depends on intrinsic properties of cell type. Here we use multi-compartmental biophysical models to investigate how morphologic features affect EF-induced responses in hippocampal CA1 pyramidal neurons. We find that the basic morphologies of neuronal elements, including diameter, length, bend, branch, and axon terminals, are all correlated with somatic depolarization through altering the current sources or sinks created by applied field. Varying them alters the EF threshold for triggering action potentials (APs), and then determines cell sensitivity to suprathreshold field. Introducing excitatory postsynaptic potential increases cell excitability and reduces morphology-dependent EF firing threshold. It is also shown that applying identical subthreshold EF results in distinct polarizations on cell membrane with different realistic morphologies. These findings shed light on the crucial role of morphologies in determining field-induced neural response from the point of view of biophysical models. The predictions are conducive to better understanding the variability in modulatory effects of EF stimulation at the cellular level, which could also aid the interpretations of how applied fields activate central nervous system neurons and affect relevant circuits.

Persistent irregular activity is a result of rebound and coincident detection mechanisms: A computational study

Persistent irregular activity is defined as elevated irregular neural discharges in the brain in such a way that while the average network activity displays high frequency oscillations, the participating neurons display irregular and low frequency oscillations. This type of activity is observed in many brain regions like prefrontal cortex that plays a role in working memory. Previous studies have shown that large networks with sparse connections, networks with strong noise and persistent inhibition and networks with structured synaptic connections display persistent-irregular activity. However, experimental studies show that, not all brain regions obey these assumptions. In this study we show that a small network of excitatory-inhibitory neurons with random synaptic connections can reproduce persistent-irregular activity. In particular, the model shows that less than perfect rebound pattern in excitatory cells, coincident-sensitive inhibitory cells and sparse synaptic inhibition can account for persistent-irregular activity in an excitatory-inhibitory neural network with randomly assigned synaptic connections.

Real Time Multiplicative Memory Amplification Mediated by Whole-Cell Scaling of Synaptic Response in Key Neurons

Intense spiking response of a memory-pattern is believed to play a crucial role both in normal learning and pathology, where it can create biased behavior. We recently proposed a novel model for memory amplification where the simultaneous two-fold increase of all excitatory (AMPAR-mediated) and inhibitory (GABA_AR-mediated) synapses in a sub-group of cells that constitutes a memory-pattern selectively amplifies this memory. Here we confirm the cellular basis of this model by validating its major predictions in four sets of experiments, and demonstrate its induction via a whole-cell transduction mechanism. Subsequently, using theory and simulations, we show that this whole-cell two-fold increase of all inhibitory and excitatory synapses functions as an instantaneous and multiplicative amplifier of the neurons’ spiking. The amplification mechanism acts through multiplication of the net synaptic current, where it scales both the average and the standard deviation of the current. In the excitation-inhibition balance regime, this scaling creates a linear multiplicative amplifier of the cell’s spiking response. Moreover, the direct scaling of the synaptic input enables the amplification of the spiking response to be synchronized with rapid changes in synaptic input, and to be independent of previous spiking activity. These traits enable instantaneous real-time amplification during brief elevations of excitatory synaptic input. Furthermore, the multiplicative nature of the amplifier ensures that the net effect of the amplification is large mainly when the synaptic input is mostly excitatory. When induced on all cells that comprise a memory-pattern, these whole-cell modifications enable a substantial instantaneous amplification of the memory-pattern when the memory is activated. The amplification mechanism is induced by CaMKII dependent phosphorylation that doubles the conductance of all GABA_A and AMPA receptors in a subset of neurons. This whole-cell transduction mechanism enables both long-term induction of memory amplification when necessary and extinction when not further required.

Amplifying the strength of a neuronal assembly that underlies a behavioral choice can lead to a particularly long lasting dominant memory. We report experimental and theoretical evidence for a long-term mechanism that amplifies the response of a neuronal assembly which we termed “memory amplification mechanism”. The amplification mechanism is mediated by doubling the strength of all inhibitory and all excitatory synapses in the cell and is induced by whole-cell phosphorylation of all inhibitory and excitatory synaptic receptors in a subset of cells, via a process that is distinct from memory formation. Computationally, the inherent scaling of both excitation and inhibition yields a robust and stable amplifier of the neuron’s response. When such an amplifier is induced in a set of cells that compose a memory-pattern, it can selectively amplify the response of this memory. The memory amplification mechanism is independent from associative learning. Thus, while associative learning forms a memory that encodes new associations, the amplification mechanism can promote an already formed memory to a dominant memory.

Metabolic Energy of Action Potentials Modulated by Spike Frequency Adaptation

Spike frequency adaptation (SFA) exists in many types of neurons, which has been demonstrated to improve their abilities to process incoming information by synapses. The major carrier used by a neuron to convey synaptic signals is the sequences of action potentials (APs), which have to consume substantial metabolic energies to initiate and propagate. Here we use conductance-based models to investigate how SFA modulates the AP-related energy of neurons. The SFA is attributed to either calcium-activated K⁺ (I_AHP) or voltage-activated K⁺ (I_M) current. We observe that the activation of I_AHP or I_M increases the Na⁺ load used for depolarizing membrane, while produces few effects on the falling phase of AP. Then, the metabolic energy involved in Na⁺ current significantly increases from one AP to the next, while for K⁺ current it is less affected. As a consequence, the total energy cost by each AP gets larger as firing rate decays down. It is also shown that the minimum Na⁺ charge needed for the depolarization of each AP is unaffected during the course of SFA. This indicates that the activation of either adaptation current makes APs become less efficient to use Na⁺ influx for their depolarization. Further, our simulations demonstrate that the different biophysical properties of I_M and I_AHP result in distinct modulations of metabolic energy usage for APs. These investigations provide a fundamental link between adaptation currents and neuronal energetics, which could facilitate to interpret how SFA participates in neuronal information processing.

The influence of increased membrane conductance on response properties of spinal motoneurons

During functional spinal neural network activity motoneurons receive massive synaptic excitation and inhibition, and their membrane conductance increases considerably - they are switched to a high-conductance state. High-conductance states can substantially alter response properties of motoneurons. In the present study we investigated how an increase in membrane conductance affects spike frequency adaptation, the gain (i.e., the slope of the frequency-current relationship) and the threshold for action potential generation. We used intracellular recordings from adult turtle motoneurons in spinal cord slices. Membrane conductance was increased pharmacologically by extracellular application of the GABAA receptor agonist muscimol. Our findings suggest that an increase in membrane conductance of about 40-50% increases the magnitude of spike frequency adaptation, but does not change the threshold for action potential generation. Increased conductance causes a subtractive rather than a divisive effect on the initial and the early frequency-current relationships and may have not only a subtractive but also a divisive effect on the steady-state frequency-current relationship.

Theoretical Analysis of Transcranial Magneto-Acoustical Stimulation with Hodgkin-Huxley Neuron Model

Transcranial magneto-acoustical stimulation (TMAS) is a novel stimulation technology in which an ultrasonic wave within a magnetostatic field generates an electric current in an area of interest in the brain to modulate neuronal activities. As a key part of the neural network, neurons transmit information in the nervous system. However, the effect of TMAS on the neuronal firing pattern remains unknown. To address this problem, we investigated the stimulatory mechanism of TMAS on neurons, by using a Hodgkin-Huxley neuron model. The simulation results indicated that the magnetostatic field intensity and ultrasonic power affect the amplitude and interspike interval of neuronal action potential under a continuous wave ultrasound. The simulation results also showed that the ultrasonic power, duty cycle and repetition frequency can alter the firing pattern of neural action potential under pulsed wave ultrasound. This study may help to reveal and explain the biological mechanism of TMAS and to provide a theoretical basis for TMAS in the treatment or rehabilitation of neuropsychiatric disorders.

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.

Protective role of Kv7 channels in oxygen and glucose deprivation-induced damage in rat caudate brain slices

Ischemic stroke can cause striatal dopamine efflux that contributes to cell death. Since Kv7 potassium channels regulate dopamine release, we investigated the effects of their pharmacological modulation on dopamine efflux, measured by fast cyclic voltammetry (FCV), and neurotoxicity, in Wistar rat caudate brain slices undergoing oxygen and glucose deprivation (OGD). The Kv7 activators retigabine and ICA27243 delayed the onset, and decreased the peak level of dopamine efflux induced by OGD; and also decreased OGD-induced damage measured by 2,3,5-triphenyltetrazolium chloride (TTC) staining. Retigabine also reduced OGD-induced necrotic cell death evaluated by lactate dehydrogenase activity assay. The Kv7 blocker linopirdine increased OGD-evoked dopamine efflux and OGD-induced damage, and attenuated the effects of retigabine. Quantitative-PCR experiments showed that OGD caused an ~6-fold decrease in Kv7.2 transcript, while levels of mRNAs encoding for other Kv7 subunits were unaffected; western blot experiments showed a parallel reduction in Kv7.2 protein levels. Retigabine also decreased the peak level of dopamine efflux induced by L-glutamate, and attenuated the loss of TTC staining induced by the excitotoxin. These results suggest a role for Kv7.2 in modulating ischemia-evoked caudate damage.

Postnatal development attunes olfactory bulb mitral cells to high-frequency signaling

Mitral cells (MCs) are a major class of principal neurons in the vertebrate olfactory bulb, conveying odor-evoked activity from the peripheral sensory neurons to olfactory cortex. Previous work has described the development of MC morphology and connectivity during the first few weeks of postnatal development. However, little is known about the postnatal development of MC intrinsic biophysical properties. To understand stimulus encoding in the developing olfactory bulb, we have therefore examined the development of MC intrinsic biophysical properties in acute slices from postnatal day (P)7-P35 mice. Across development, we observed systematic changes in passive membrane properties and action potential waveforms consistent with a developmental increase in sodium and potassium conductances. We further observed developmental decreases in hyperpolarization-evoked membrane potential sag and firing regularity, extending recent links between MC sag heterogeneity and firing patterns. We then applied a novel combination of statistical analyses to examine how the evolution of these intrinsic biophysical properties specifically influenced the representation of fluctuating stimuli by MCs. We found that immature MCs responded to frozen fluctuating stimuli with lower firing rates, lower spike-time reliability, and lower between-cell spike-time correlations than more mature MCs. Analysis of spike-triggered averages revealed that these changes in spike timing were driven by a developmental shift from broad integration of inputs to more selective detection of coincident inputs. Consistent with this shift, generalized linear model fits to MC firing responses demonstrated an enhanced encoding of high-frequency stimulus features by mature MCs.

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

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

Regulation of Cortical Dynamic Range by Background Synaptic Noise and Feedforward Inhibition

The cortex encodes a broad range of inputs. This breadth of operation requires sensitivity to weak inputs yet non-saturating responses to strong inputs. If individual pyramidal neurons were to have a narrow dynamic range, as previously claimed, then staggered all-or-none recruitment of those neurons would be necessary for the population to achieve a broad dynamic range. Contrary to this explanation, we show here through dynamic clamp experiments in vitro and computer simulations that pyramidal neurons have a broad dynamic range under the noisy conditions that exist in the intact brain due to background synaptic input. Feedforward inhibition capitalizes on those noise effects to control neuronal gain and thereby regulates the population dynamic range. Importantly, noise allows neurons to be recruited gradually and occludes the staggered recruitment previously attributed to heterogeneous excitation. Feedforward inhibition protects spike timing against the disruptive effects of noise, meaning noise can enable the gain control required for rate coding without compromising the precise spike timing required for temporal coding.

Active dendrites mediate stratified gamma-range coincidence detection in hippocampal model neurons

KEY POINTS

Quantitative metrics for the temporal window of integration/coincidence detection, based on the spike-triggered average, were employed to assess the emergence and dependence of gamma-range coincidence detection in hippocampal pyramidal neurons on various ion channel combinations. The presence of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels decreased the coincidence detection window (CDW) of the neuronal compartment to the gamma frequency range. Interaction of HCN channels with T-type calcium channels and persistent sodium channels further reduced the CDW, whereas interaction with A-type potassium channels broadened the CDW. When multiple channel gradients were co-expressed, the high density of resonating conductances in the distal dendrites led to a slow gamma CDW in the proximal dendrites and a fast-gamma CDW in the distal dendrites. The presence of resonating and spike-generating conductances serve as a mechanism underlying the emergence of stratified gamma-range coincidence detection in the dendrites of CA1 pyramidal neurons, enabling them to perform behaviour- and state-dependent gamma frequency multiplexing.

ABSTRACT

Hippocampal pyramidal neurons exhibit gamma-phase preference in their spikes, selectively route inputs through gamma frequency multiplexing and are considered part of gamma-bound cell assemblies. How do these neurons exhibit gamma-frequency coincidence detection capabilities, a feature that is essential for the expression of these physiological observations, despite their slow membrane time constant? In this conductance-based modelling study, we developed quantitative metrics for the temporal window of integration/coincidence detection based on the spike-triggered average (STA) of the neuronal compartment. We employed these metrics in conjunction with quantitative measures for spike initiation dynamics to assess the emergence and dependence of coincidence detection and STA spectral selectivity on various ion channel combinations. We found that the presence of resonating conductances (hyperpolarization-activated cyclic nucleotide-gated or T-type calcium), either independently or synergistically when expressed together, led to the emergence of spectral selectivity in the spike initiation dynamics and a significant reduction in the coincidence detection window (CDW). The presence of A-type potassium channels, along with resonating conductances, reduced the STA characteristic frequency and broadened the CDW, but persistent sodium channels sharpened the CDW by strengthening the spectral selectivity in the STA. Finally, in a morphologically precise model endowed with experimentally constrained channel gradients, we found that somatodendritic compartments expressed functional maps of strong theta-frequency selectivity in spike initiation dynamics and gamma-range CDW. Our results reveal the heavy expression of resonating and spike-generating conductances as the mechanism underlying the robust emergence of stratified gamma-range coincidence detection in the dendrites of hippocampal and cortical pyramidal neurons.

Spike-frequency adaptation of a two-compartment neuron modulated by extracellular electric fields

Spike-frequency adaptation has been shown to play an important role in neural coding. Based on a reduced two-compartment model, here we investigate how two common adaptation currents, i.e., voltage-sensitive potassium current (I(M)) and calcium-sensitive potassium current (I(AHP)), modulate neuronal responses to extracellular electric fields. It is shown that two adaptation mechanisms lead to distinct effects on the dynamical behavior of the neuron to electric fields. These effects depend on a neuronal morphological parameter that characterizes the ratio of soma area to total membrane area and internal coupling conductance. In the case of I(AHP) current, changing the morphological parameter switches spike initiation dynamics between saddle-node on invariant cycle bifurcation and supercritical Hopf bifurcation, whereas it only switches between subcritical and supercritical Hopf bifurcations for I(M) current. Unlike the morphological parameter, internal coupling conductance is unable to alter the bifurcation scenario for both adaptation currents. We also find that the electric field threshold for triggering neuronal steady-state firing is determined by two parameters, especially by the morphological parameter. Furthermore, the neuron with I(AHP) current generates mixed-mode oscillations through the canard phenomenon for some small values of the morphological parameter. All these results suggest that morphological properties play a critical role in field-induced effects on neuronal dynamics, which could qualitatively alter the outcome of adaptation by modulating internal current between soma and dendrite. The findings are readily testable in experiments, which could help to reveal the mechanisms underlying how the neuron responds to electric field stimulus.

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na⁺ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances.

The membrane voltage of neurons in vivo is dominated by noisy “background” fluctuations generated by network-based synaptic activity from nearby cells. It has been speculated that membrane voltage fluctuations in neurons play an important role in scaling the relationship between input amplitude and spike rate response. For this to be true, neuronal spike input-output behavior must be sensitive to physiological membrane voltage fluctuations. Using a combination of single cell recordings and modeling, we investigated the mechanisms through which voltage fluctuations modulate neuronal input-output responses. We find that neurons that express an increase in membrane input resistance with depolarization show low levels of noise-mediated modulation of input-output responses due, in part, to voltage trajectories that suppress the likelihood of generating a spike in response to random current input fluctuations. Hence, non-linear membrane properties arising from certain types of voltage-gated conductances limit noise-based modulation of neuronal input-output responses.

Critical slowing down governs the transition to neuron spiking

Many complex systems have been found to exhibit critical transitions, or so-called tipping points, which are sudden changes to a qualitatively different system state. These changes can profoundly impact the functioning of a system ranging from controlled state switching to a catastrophic break-down; signals that predict critical transitions are therefore highly desirable. To this end, research efforts have focused on utilizing qualitative changes in markers related to a system’s tendency to recover more slowly from a perturbation the closer it gets to the transition—a phenomenon called critical slowing down. The recently studied scaling of critical slowing down offers a refined path to understand critical transitions: to identify the transition mechanism and improve transition prediction using scaling laws.

Here, we outline and apply this strategy for the first time in a real-world system by studying the transition to spiking in neurons of the mammalian cortex. The dynamical system approach has identified two robust mechanisms for the transition from subthreshold activity to spiking, saddle-node and Hopf bifurcation. Although theory provides precise predictions on signatures of critical slowing down near the bifurcation to spiking, quantitative experimental evidence has been lacking. Using whole-cell patch-clamp recordings from pyramidal neurons and fast-spiking interneurons, we show that 1) the transition to spiking dynamically corresponds to a critical transition exhibiting slowing down, 2) the scaling laws suggest a saddle-node bifurcation governing slowing down, and 3) these precise scaling laws can be used to predict the bifurcation point from a limited window of observation. To our knowledge this is the first report of scaling laws of critical slowing down in an experiment. They present a missing link for a broad class of neuroscience modeling and suggest improved estimation of tipping points by incorporating scaling laws of critical slowing down as a strategy applicable to other complex systems.

Neurons efficiently convey information by being able to switch rapidly between two different states: quiescence and spiking. Such sudden shifts to a qualitatively different state are observed in many complex systems; the often dramatic consequences of these tipping points for diverse fields such as economics, ecology, and the brain have spurred interest to better understand their transition mechanisms and predict their sudden occurrences. By studying the transition from neuronal quiescence to spiking, we show that the quantitative scaling laws for critical slowing down, i.e., a system’s tendency to recover more slowly from perturbations upon approaching its transition point, inform about the underlying bifurcation mechanism and can be used to improve the prediction of a system’s tipping point.

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.

Intrinsic neuronal properties switch the mode of information transmission in networks

Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.

Differences in ion channel composition endow different neuronal types with distinct computational properties. Understanding how these biophysical differences affect network-level computation is an important frontier. We focus on a set of biophysical properties, experimentally observed in developing cortical neurons, that allow these neurons to efficiently encode their inputs despite time-varying changes in the statistical context. Large-scale propagating waves are autonomously generated by the developing brain even before the onset of sensory experience. Using multi-layered feedforward networks, we examine how changes in intrinsic properties can lead to changes in the network's ability to represent and transmit information on multiple timescales. We demonstrate that measured changes in the computational properties of immature single neurons enable the propagation of slow-varying wave-like inputs. In contrast, neurons with more mature properties are more sensitive to fast fluctuations, which modulate the slow-varying information. While slow events are transmitted with high fidelity in initial network layers, noise degrades transmission in downstream network layers. Our results show how short-term adaptation and modulation of the neurons' input-output firing curves by background synaptic noise determine the ability of neural networks to transmit information on multiple timescales.

Density of voltage-gated potassium channels is a bifurcation parameter in pyramidal neurons

Several types of intrinsic dynamics have been identified in brain neurons. Type 1 excitability is characterized by a continuous frequency-stimulus relationship and, thus, an arbitrarily low frequency at threshold current. Conversely, Type 2 excitability is characterized by a discontinuous frequency-stimulus relationship and a nonzero threshold frequency. In previous theoretical work we showed that the density of Kv channels is a bifurcation parameter, such that increasing the Kv channel density in a neuron model transforms Type 1 excitability into Type 2 excitability. Here we test this finding experimentally, using the dynamic clamp technique on Type 1 pyramidal cells in rat cortex. We found that increasing the density of slow Kv channels leads to a shift from Type 1 to Type 2 threshold dynamics, i.e., a distinct onset frequency, subthreshold oscillations, and reduced latency to first spike. In addition, the action potential was resculptured, with a narrower spike width and more pronounced afterhyperpolarization. All changes could be captured with a two-dimensional model. It may seem paradoxical that an increase in slow K channel density can lead to a higher threshold firing frequency; however, this can be explained in terms of bifurcation theory. In contrast to previous work, we argue that an increased outward current leads to a change in dynamics in these neurons without a rectification of the current-voltage curve. These results demonstrate that the behavior of neurons is determined by the global interactions of their dynamical elements and not necessarily simply by individual types of ion channels.

Neuronal spike initiation modulated by extracellular electric fields

Based on a reduced two-compartment model, the dynamical and biophysical mechanism underlying the spike initiation of the neuron to extracellular electric fields is investigated in this paper. With stability and phase plane analysis, we first investigate in detail the dynamical properties of neuronal spike initiation induced by geometric parameter and internal coupling conductance. The geometric parameter is the ratio between soma area and total membrane area, which describes the proportion of area occupied by somatic chamber. It is found that varying it could qualitatively alter the bifurcation structures of equilibrium as well as neuronal phase portraits, which remain unchanged when varying internal coupling conductance. By analyzing the activating properties of somatic membrane currents at subthreshold potentials, we explore the relevant biophysical basis of spike initiation dynamics induced by these two parameters. It is observed that increasing geometric parameter could greatly decrease the intensity of the internal current flowing from soma to dendrite, which switches spike initiation dynamics from Hopf bifurcation to SNIC bifurcation; increasing internal coupling conductance could lead to the increase of this outward internal current, whereas the increasing range is so small that it could not qualitatively alter the spike initiation dynamics. These results highlight that neuronal geometric parameter is a crucial factor in determining the spike initiation dynamics to electric fields. The finding is useful to interpret the functional significance of neuronal biophysical properties in their encoding dynamics, which could contribute to uncovering how neuron encodes electric field signals.

Neuronal adaptation involves rapid expansion of the action potential initiation site

Action potential (AP) generation is the key to information-processing in the brain. Although APs are normally initiated in the axonal initial segment, developmental adaptation or prolonged network activity may alter the initiation site geometry thus affecting cell excitability. Here we find that hippocampal dentate granule cells adapt their spiking threshold to the kinetics of the ongoing dendrosomatic excitatory input by expanding the AP-initiation area away from the soma while also decelerating local axonal spikes. Dual-patch soma–axon recordings combined with axonal Na⁺ and Ca²⁺ imaging and biophysical modelling show that the underlying mechanism involves distance-dependent inactivation of axonal Na⁺ channels due to somatic depolarization propagating into the axon. Thus, the ensuing changes in the AP-initiation zone and local AP propagation could provide activity-dependent control of cell excitability and spiking on a relatively rapid timescale.

Neuronal adaptation to repetitive stimuli is required for the correct functioning of neuronal networks. Here, the authors show that rapid expansion of the axonal spike-initiation site accompanied by local spike deceleration is the cell adaptation mechanism that responds to repetitive excitatory inputs.

Effects of extremely low-frequency magnetic fields on the response of a conductance-based neuron model

To provide insights into the modulation of neuronal activity by extremely low-frequency (ELF) magnetic field (MF), we present a conductance-based neuron model and introduce ELF sinusoidal MF as an additive voltage input. By analyzing spike times and spiking frequency, it is observed that neuron with distinct spiking patterns exhibits different response properties in the presence of MF exposure. For tonic spiking neuron, the perturbations of MF exposure on spike times is maximized at the harmonics of neuronal intrinsic spiking frequency, while it is maximized at the harmonics of bursting frequency for burst spiking neuron. As MF intensity increases, the perturbations also increase. Compared with tonic spiking, bursting dynamics are less sensitive to the perturbations of ELF MF exposure. Further, ELF MF exposure is more prone to perturb neuronal spike times relative to spiking frequency. Our finding suggests that the resonance may be one of the neural mechanisms underlying the modulatory effects of the low-intensity ELF MFs on neuronal activities. The results highlight the impacts of ELF MFs exposure on neuronal activity from the single cell level, and demonstrate various factors including ELF MF properties and neuronal spiking characteristics could determine the outcome of exposure. These insights into the mechanism of MF exposure may be relevant for the design of multi-intensity magnetic stimulus protocols, and may even contribute to the interpretation of MF effects on the central nervous systems.

Activity-dependent hyperpolarization of EGABA is absent in cutaneous DRG neurons from inflamed rats

A shift in GABA(A) signaling from inhibition to excitation in primary afferent neurons appears to contribute to the inflammation-induced increase in afferent input to the CNS. An activity-dependent depolarization of the GABA(A) current equilibrium potential (E(GABA)) has been described in CNS neurons which drives a shift in GABA(A) signaling from inhibition to excitation. The purpose of the present study was to determine if such an activity-dependent depolarization of E(GABA) occurs in primary afferents and whether the depolarization is amplified with persistent inflammation. Acutely dissociated retrogradely labeled cutaneous dorsal root ganglion (DRG) neurons from naïve and inflamed rats were studied with gramicidin perforated patch recording. Rather than a depolarization, 200 action potentials delivered at 2 Hz resulted in a ∼10 mV hyperpolarization of E(GABA) in cutaneous neurons from naïve rats. No such hyperpolarization was observed in neurons from inflamed rats. The shift in E(GABA) was not blocked by 10 μM bumetanide. Furthermore, because activity-dependent hyperpolarization of E(GABA) was fully manifest in the absence of HCO₃⁻ in the bath solution, this shift was not dependent on a change in HCO₃⁻-Cl⁻ exchanger activity, despite evidence of HCO₃⁻-Cl⁻ exchangers in DRG neurons that may contribute to the establishment of E(GABA) in the presence of HCO₃⁻. While the mechanism underlying the activity-dependent hyperpolarization of E(GABA) has yet to be identified, because this mechanism appears to function as a form of feedback inhibition, facilitating GABA-mediated inhibition of afferent activity, it may serve as a novel target for the treatment of inflammatory pain.

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.

Reliability of spike and burst firing in thalamocortical relay cells

The reliability and precision of the timing of spikes in a spike train is an important aspect of neuronal coding. We investigated reliability in thalamocortical relay (TCR) cells in the acute slice and also in a Morris-Lecar model with several extensions. A frozen Gaussian noise current, superimposed on a DC current, was injected into the TCR cell soma. The neuron responded with spike trains that showed trial-to-trial variability, due to amongst others slow changes in its internal state and the experimental setup. The DC current allowed to bring the neuron in different states, characterized by a well defined membrane voltage (between -80 and -50 mV) and by a specific firing regime that on depolarization gradually shifted from a predominantly bursting regime to a tonic spiking regime. The filtered frozen white noise generated a spike pattern output with a broad spike interval distribution. The coincidence factor and the Hunter and Milton measure were used as reliability measures of the output spike train. In the experimental TCR cell as well as the Morris-Lecar model cell the reliability depends on the shape (steepness) of the current input versus spike frequency output curve. The model also allowed to study the contribution of three relevant ionic membrane currents to reliability: a T-type calcium current, a cation selective h-current and a calcium dependent potassium current in order to allow bursting, investigate the consequences of a more complex current-frequency relation and produce realistic firing rates. The reliability of the output of the TCR cell increases with depolarization. In hyperpolarized states bursts are more reliable than single spikes. The analytically derived relations were capable to predict several of the experimentally recorded spike features.

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

We studied the effects of increased sodium conductance on firing rate and gain in two populations of conductance-based, single-compartment model neurons. The first population consisted of 1000 model neurons with differing values of seven voltage-dependent conductances. In many of these models, increasing the sodium conductance threefold unexpectedly reduced the firing rate and divisively scaled the gain at high input current. In the second population, consisting of 1000 simplified model neurons, we found that enhanced sodium conductance changed the frequency-current (FI) curve in two computationally distinct ways, depending on the firing rate. In these models, increased sodium conductance produced a subtractive shift in the FI curve at low firing rates because the additional sodium conductance allowed the neuron to respond more strongly to equivalent input current. In contrast, at high input current, the increase in sodium conductance resulted in a divisive change in the gain because the increased conductance produced a proportionally larger activation of the delayed rectifier potassium conductance. The control and sodium-enhanced FI curves intersect at a point that delimits two regions in which the same biophysical manipulation produces two fundamentally different changes to the model neuron's computational properties. This suggests a potentially difficult problem for homeostatic regulation of intrinsic excitability.

Spike phase locking in CA1 pyramidal neurons depends on background conductance and firing rate

Oscillatory activity in neuronal networks correlates with different behavioral states throughout the nervous system, and the frequency-response characteristics of individual neurons are believed to be critical for network oscillations. Recent in vivo studies suggest that neurons experience periods of high membrane conductance, and that action potentials are often driven by membrane potential fluctuations in the living animal. To investigate the frequency-response characteristics of CA1 pyramidal neurons in the presence of high conductance and voltage fluctuations, we performed dynamic-clamp experiments in rat hippocampal brain slices. We drove neurons with noisy stimuli that included a sinusoidal component ranging, in different trials, from 0.1 to 500 Hz. In subsequent data analysis, we determined action potential phase-locking profiles with respect to background conductance, average firing rate, and frequency of the sinusoidal component. We found that background conductance and firing rate qualitatively change the phase-locking profiles of CA1 pyramidal neurons versus frequency. In particular, higher average spiking rates promoted bandpass profiles, and the high-conductance state promoted phase-locking at frequencies well above what would be predicted from changes in the membrane time constant. Mechanistically, spike rate adaptation and frequency resonance in the spike-generating mechanism are implicated in shaping the different phase-locking profiles. Our results demonstrate that CA1 pyramidal cells can actively change their synchronization properties in response to global changes in activity associated with different behavioral states.

Robustness, variability, phase dependence, and longevity of individual synaptic input effects on spike timing during fluctuating synaptic backgrounds: a modeling study of globus pallidus neuron phase response properties

A neuron's phase response curve (PRC) shows how inputs arriving at different times during the spike cycle differentially affect the timing of subsequent spikes. Using a full morphological model of a globus pallidus (GP) neuron, we previously demonstrated that dendritic conductances shape the PRC in a spike frequency-dependent manner, suggesting different functional roles of perisomatic and distal dendritic synapses in the control of patterned network activity. In the present study we extend this analysis to examine the impact of physiologically realistic high conductance states on somatic and dendritic PRCs and the time course of spike train perturbations. First, we found that average somatic and dendritic PRCs preserved their shapes and spike frequency dependence when the model was driven by spatially-distributed, stochastic conductance inputs rather than tonic somatic current. However, responses to inputs during specific synaptic backgrounds often deviated substantially from the average PRC. Therefore, we analyzed the interactions of PRC stimuli with transient fluctuations in the synaptic background on a trial-by-trial basis. We found that the variability in responses to PRC stimuli and the incidence of stimulus-evoked added or skipped spikes were stimulus-phase-dependent and reflected the profile of the average PRC, suggesting commonality in the underlying mechanisms. Clear differences in the relation between the phase of input and variability of spike response between dendritic and somatic inputs indicate that these regions generally represent distinct dynamical subsystems of synaptic integration with respect to influencing the stability of spike time attractors generated by the overall synaptic conductance.

Single neuron firing properties impact correlation-based population coding

Correlated spiking has been widely observed, but its impact on neural coding remains controversial. Correlation arising from comodulation of rates across neurons has been shown to vary with the firing rates of individual neurons. This translates into rate and correlation being equivalently tuned to the stimulus; under those conditions, correlated spiking does not provide information beyond that already available from individual neuron firing rates. Such correlations are irrelevant and can reduce coding efficiency by introducing redundancy. Using simulations and experiments in rat hippocampal neurons, we show here that pairs of neurons receiving correlated input also exhibit correlations arising from precise spike-time synchronization. Contrary to rate comodulation, spike-time synchronization is unaffected by firing rate, thus enabling synchrony- and rate-based coding to operate independently. The type of output correlation depends on whether intrinsic neuron properties promote integration or coincidence detection: "ideal" integrators (with spike generation sensitive to stimulus mean) exhibit rate comodulation, whereas ideal coincidence detectors (with spike generation sensitive to stimulus variance) exhibit precise spike-time synchronization. Pyramidal neurons are sensitive to both stimulus mean and variance, and thus exhibit both types of output correlation proportioned according to which operating mode is dominant. Our results explain how different types of correlations arise based on how individual neurons generate spikes, and why spike-time synchronization and rate comodulation can encode different stimulus properties. Our results also highlight the importance of neuronal properties for population-level coding insofar as neural networks can employ different coding schemes depending on the dominant operating mode of their constituent neurons.