Mechanisms of Gain Control by Voltage-Gated Channels in Intrinsically-Firing Neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.     

Shunting inhibition controls the gain modulation mediated by asynchronous neurotransmitter release in early development

The sensitivity of a neuron to its input can be modulated in several ways. Changes in the slope of the neuronal input-output curve depend on factors such as shunting inhibition, background noise, frequency-dependent synaptic excitation, and balanced excitation and inhibition. However, in early development GABAergic interneurons are excitatory and other mechanisms such as asynchronous transmitter release might contribute to regulating neuronal sensitivity. We modeled both phasic and asynchronous synaptic transmission in early development to study the impact of activity-dependent noise and short-term plasticity on the synaptic gain. Asynchronous release decreased or increased the gain depending on the membrane conductance. In the high shunt regime, excitatory input due to asynchronous release was divisive, whereas in the low shunt regime it had a nearly multiplicative effect on the firing rate. In addition, sensitivity to correlated inputs was influenced by shunting and asynchronous release in opposite ways. Thus, asynchronous release can regulate the information flow at synapses and its impact can be flexibly modulated by the membrane conductance.     

Synaptic integration in motoneurons with hyper-excitable dendrites

Motoneurons have extensive dendritic trees that receive the numerous inputs required to produce movement. These dendrites are highly active, containing voltage-sensitive channels that generate persistent inward currents (PICs) that can enhance synaptic input 5-fold or more. However, this enhancement is proportional to the level of activity of monoaminergic inputs from the brainstem that release serotonin and noradrenalin. The higher this activity, the larger the dendritic PIC and the higher the firing rate evoked by a given amount of excitatory synaptic input. This brainstem control of motoneuron input-output gain translates directly into control of system gain of a motor pool and its muscle. Because large dendritic PICs are probably necessary for motoneurons to have sufficient gain to generate large forces, it is possible that descending monoaminergic inputs scale in proportion to voluntary force. Inhibition from sensory inputs has a strong suppressive effect on dendritic PICs: the stronger the inhibition, the smaller the PIC. Thus, local inhibitory inputs within the cord may oppose the descending monoaminergic control of PICs. Most motor behaviors evoke a mixture of excitation and inhibition (e.g., the reciprocal inhibition between antagonists). Therefore, normal joint movements may involve constant adjustment of PIC amplitude.     

Static and dynamic input-output relations of the feline medial gastrocnemius motoneuron-muscle system subjected to recurrent inhibition: a model study

The physiological function of spinal recurrent inhibition is still a matter of debate because of the experimental difficulty or impossibility of observing recurrent inhibition at work in normally behaving animals. The purpose of this study was to investigate, by computer simulation, the role of recurrent inhibition in shaping the input-output (I/O) relationships between descending command signals (DCS) as inputs and motoneuron (MN) and Renshaw cell (RC) firing rates and muscle force as outputs. Changing the spatial (topographical) distribution of recurrent inhibition from nonhomogeneous (as in the standard model) to homogeneous did not alter the I/O relationships significantly, while changing the functional distribution related to MN types did. Altering the global gain of recurrent inhibition, as happens naturally in various motor acts, changes the slopes and positions (at high inputs) of the I/O relationships, making recurrent inhibition a suitable means of gain control. Coupling a decrease in recurrent inhibitory gain with an increase in DCS input, as could occur during slow dynamic contractions, would increase the MN and force gains during the act. Short dynamic ramp-and-hold DCS inputs generate MN firing patterns, to which recurrent inhibition contributes interspike-interval variability and damped oscillations, which are related to issues of tremor and its control.     

Feedforward excitation and inhibition evoke dual modes of firing in the cat's visual thalamus during naturalistic viewing

Thalamic relay cells transmit information from retina to cortex by firing either rapid bursts or tonic trains of spikes. Bursts occur when the membrane voltage is low, as during sleep, because they depend on channels that cannot respond to excitatory input unless they are primed by strong hyperpolarization. Cells fire tonically when depolarized, as during waking. Thus, mode of firing is usually associated with behavioral state. Growing evidence, however, suggests that sensory processing involves both burst and tonic spikes. To ask if visually evoked synaptic responses induce each type of firing, we recorded intracellular responses to natural movies from relay cells and developed methods to map the receptive fields of the excitation and inhibition that the images evoked. In addition to tonic spikes, the movies routinely elicited lasting inhibition from the center of the receptive field that permitted bursts to fire. Therefore, naturally evoked patterns of synaptic input engage dual modes of firing.     

Coexistence of lateral and co-tuned inhibitory configurations in cortical networks

The responses of neurons in sensory cortex depend on the summation of excitatory and inhibitory synaptic inputs. How the excitatory and inhibitory inputs scale with stimulus depends on the network architecture, which ranges from the lateral inhibitory configuration where excitatory inputs are more narrowly tuned than inhibitory inputs, to the co-tuned configuration where both are tuned equally. The underlying circuitry that gives rise to lateral inhibition and co-tuning is yet unclear. Using large-scale network simulations with experimentally determined connectivity patterns and simulations with rate models, we show that the spatial extent of the input determined the configuration: there was a smooth transition from lateral inhibition with narrow input to co-tuning with broad input. The transition from lateral inhibition to co-tuning was accompanied by shifts in overall gain (reduced), output firing pattern (from tonic to phasic) and rate-level functions (from non-monotonic to monotonically increasing). The results suggest that a single cortical network architecture could account for the extended range of experimentally observed response types between the extremes of lateral inhibitory versus co-tuned configurations.     

Mechanisms of firing patterns in fast-spiking cortical interneurons

Cortical fast-spiking (FS) interneurons display highly variable electrophysiological properties. Their spike responses to step currents occur almost immediately following the step onset or after a substantial delay, during which subthreshold oscillations are frequently observed. Their firing patterns include high-frequency tonic firing and rhythmic or irregular bursting (stuttering). What is the origin of this variability? In the present paper, we hypothesize that it emerges naturally if one assumes a continuous distribution of properties in a small set of active channels. To test this hypothesis, we construct a minimal, single-compartment conductance-based model of FS cells that includes transient Na(+), delayed-rectifier K(+), and slowly inactivating d-type K(+) conductances. The model is analyzed using nonlinear dynamical system theory. For small Na(+) window current, the neuron exhibits high-frequency tonic firing. At current threshold, the spike response is almost instantaneous for small d-current conductance, gd, and it is delayed for larger gd. As gd further increases, the neuron stutters. Noise substantially reduces the delay duration and induces subthreshold oscillations. In contrast, when the Na(+) window current is large, the neuron always fires tonically. Near threshold, the firing rates are low, and the delay to firing is only weakly sensitive to noise; subthreshold oscillations are not observed. We propose that the variability in the response of cortical FS neurons is a consequence of heterogeneities in their gd and in the strength of their Na(+) window current. We predict the existence of two types of firing patterns in FS neurons, differing in the sensitivity of the delay duration to noise, in the minimal firing rate of the tonic discharge, and in the existence of subthreshold oscillations. We report experimental results from intracellular recordings supporting this prediction.     

Target-Specific Expression of Presynaptic NMDA Receptors in Neocortical Microcircuits

Traditionally, NMDA receptors are located postsynaptically; yet, putatively presynaptic NMDA receptors (preNMDARs) have been reported. Although implicated in controlling synaptic plasticity, their function is not well understood and their expression patterns are debated. We demonstrate that, in layer 5 of developing mouse visual cortex, preNMDARs specifically control synaptic transmission at pyramidal cell inputs to other pyramidal cells and to Martinotti cells, while leaving those to basket cells unaffected. We also reveal a type of interneuron that mediates ascending inhibition. In agreement with synapse-specific expression, we find preNMDAR-mediated calcium signals in a subset of pyramidal cell terminals. A tuned network model predicts that preNMDARs specifically reroute information flow in local circuits during high-frequency firing, in particular by impacting frequency-dependent disynaptic inhibition mediated by Martinotti cells, a finding that we experimentally verify. We conclude that postsynaptic cell type determines presynaptic terminal molecular identity and that preNMDARs govern information processing in neocortical columns.     

Ionic mechanisms underlying excitation-to-frequency transduction: studies by voltage clamp methods

The transduction of synaptic activity to impulse generation is controlled by the active and passive properties of neurons. The voltage dependent conductances of cat motoneurons, as we understand them, are presented and related to repetitive firing behavior. Both outward potassium and inward calcium currents are activated in the subthreshold region. Accomodation of the initial segment allows tonic activation of these currents during repetitive firing and the response properties of the neuron depend upon the balance of inward and outward currents. The effects of putative neurotransmitters and changes in ionic concentration upon the active ionic currents and upon the response properties of neurons are also discussed.     

Homeostatic plasticity and excitation-inhibition balance: The good,the bad,and the ugly

In this review, we discuss the significance of the synaptic excitation/inhibition (E/I) balance in the context of homeostatic plasticity, whose primary goal is thought to maintain neuronal firing rates at a set point. We first provide an overview of the processes through which patterned input activity drives synaptic E/I tuning and maturation of circuits during development. Next, we emphasize the importance of the E/I balance at the synaptic level (homeostatic control of message reception) as a means to achieve the goal (homeostatic control of information transmission) at the network level and consider how compromised homeostatic plasticity associated with neurological diseases leads to hyperactivity, network instability, and ultimately improper information processing. Lastly, we highlight several pathological conditions related to sensory deafferentation and describe how, in some cases, homeostatic compensation without appropriate sensory inputs can result in phantom perceptions.     

Properties of human motoneurones and their synaptic noise deduced from motor unit recordings with the aid of computer modelling.

This paper reviews two new facets of the behaviour of human motoneurones; these were demonstrated by modelling combined with analysis of long periods of low-frequency tonic motor unit firing (sub-primary range). 1) A novel transformation of the interval histogram has shown that the effective part of the membrane's post-spike voltage trajectory is a segment of an exponential (rather than linear), with most spikes being triggered by synaptic noise before the mean potential reaches threshold. The curvature of the motoneurone's trajectory affects virtually all measures of its behaviour and response to stimulation. The 'trajectory' is measured from threshold, and so includes any changes in threshold during the interspike interval. 2) A novel rhythmic stimulus (amplitude-modulated pulsed vibration) has been used to show that the motoneurone produces appreciable phase-advance during sinusoidal excitation. At low frequencies, the advance increases with rising stimulus frequency but then, slightly below the motoneurones mean firing rate, it suddenly becomes smaller. The gain has a maximum for stimuli at the mean firing rate (the 'carrier'). Such behaviour is functionally important since it affects the motoneurone's response to any rhythmic input, whether generated peripherally by the receptors (as in tremor) or by the CNS (as with cortical oscillations). Low mean firing rates favour tremor, since the high gain and reduced phase advance at the 'carrier' reduce the stability of the stretch reflex.     

Less means more: inhibition of spontaneous firing triggers persistent increases in excitability

Modulation of intrinsic excitability is an alternative to classical synaptic plasticity for implementing activity-dependent changes in neuronal networks. In this issue of Neuron, Nelson et al. reveal a new form of plasticity of intrinsic excitability that can be triggered rapidly when synaptic inhibition reduces spontaneous firing, resulting in persistent enhancement of firing rate and neuronal gain.     

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.     

Retrograde inhibition of presynaptic calcium influx by endogenous cannabinoids at excitatory synapses onto Purkinje cells

Brief depolarization of cerebellar Purkinje cells was found to inhibit parallel fiber and climbing fiber EPSCs for tens of seconds. This depolarization-induced suppression of excitation (DSE) is accompanied by altered paired-pulse plasticity, suggesting a presynaptic locus. Fluorometric imaging revealed that postsynaptic depolarization also reduces presynaptic calcium influx. The inhibition of both presynaptic calcium influx and EPSCs is eliminated by buffering postsynaptic calcium with BAPTA. The cannabinoid CB1 receptor antagonist AM251 prevents DSE, and the agonist WIN 55,212-2 occludes DSE. These findings suggest that Purkinje cells release endogenous cannabinoids in response to elevated calcium, thereby inhibiting presynaptic calcium entry and suppressing transmitter release. DSE may provide a way for cells to use their firing rate to dynamically regulate synaptic inputs. Together with previous studies, these findings suggest a widespread role for endogenous cannabinoids in retrograde synaptic inhibition.     

Stochastic properties of motoneuron activity and the effect of muscular length

The activity of single motor units contributing to small tonic isometric contractions in human muscle at different muscular lengths was analyzed. The form of motor unit firing patterns shows that the interspike intervals compose independent sequences with about a 10% coefficient of variation and have a gamma distribution. The variability and the distribution shape curves show that as the mean interval decreases the variance also decreases and the interval density function becomes more symmetric. More significant is the fact that the form of the firing pattern remains unchanged when a motor unit has the same mean interval but with the muscle at different lengths. Comparison of these facts with experimental data from neuron models and cat motoneurons indicates that in the human the only relevant input-output relationship in motoneurons is that the net excitation adjusts the firing rate.     

Amplification of trial-to-trial response variability by neurons in visual cortex

The visual cortex responds to repeated presentations of the same stimulus with high variability. Because the firing mechanism is remarkably noiseless, the source of this variability is thought to lie in the membrane potential fluctuations that result from summated synaptic input. Here this hypothesis is tested through measurements of membrane potential during visual stimulation. Surprisingly, trial-to-trial variability of membrane potential is found to be low. The ratio of variance to mean is much lower for membrane potential than for firing rate. The high variability of firing rate is explained by the threshold present in the function that converts inputs into firing rates. Given an input with small, constant noise, this function produces a firing rate with a large variance that grows with the mean. This model is validated on responses recorded both intracellularly and extracellularly. In neurons of visual cortex, thus, a simple deterministic mechanism amplifies the low variability of summated synaptic inputs into the large variability of firing rate. The computational advantages provided by this amplification are not known.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Maturation of GABAergic Inhibition Promotes Strengthening of Temporally Coherent Inputs among Convergent Pathways

Spike-timing-dependent plasticity (STDP), a form of Hebbian plasticity, is inherently stabilizing. Whether and how GABAergic inhibition influences STDP is not well understood. Using a model neuron driven by converging inputs modifiable by STDP, we determined that a sufficient level of inhibition was critical to ensure that temporal coherence (correlation among presynaptic spike times) of synaptic inputs, rather than initial strength or number of inputs within a pathway, controlled postsynaptic spike timing. Inhibition exerted this effect by preferentially reducing synaptic efficacy, the ability of inputs to evoke postsynaptic action potentials, of the less coherent inputs. In visual cortical slices, inhibition potently reduced synaptic efficacy at ages during but not before the critical period of ocular dominance (OD) plasticity. Whole-cell recordings revealed that the amplitude of unitary IPSCs from parvalbumin positive (Pv+) interneurons to pyramidal neurons increased during the critical period, while the synaptic decay time-constant decreased. In addition, intrinsic properties of Pv+ interneurons matured, resulting in an increase in instantaneous firing rate. Our results suggest that maturation of inhibition in visual cortex ensures that the temporally coherent inputs (e.g. those from the open eye during monocular deprivation) control postsynaptic spike times of binocular neurons, a prerequisite for Hebbian mechanisms to induce OD plasticity.