Neuronal arithmetic

Glutamate-bound NMDARs arising from in vivo-like network activity extend spatio-temporal integration in a L5 cortical pyramidal cell model

In vivo, cortical pyramidal cells are bombarded by asynchronous synaptic input arising from ongoing network activity. However, little is known about how such 'background' synaptic input interacts with nonlinear dendritic mechanisms. We have modified an existing model of a layer 5 (L5) pyramidal cell to explore how dendritic integration in the apical dendritic tuft could be altered by the levels of network activity observed in vivo. Here we show that asynchronous background excitatory input increases neuronal gain and extends both temporal and spatial integration of stimulus-evoked synaptic input onto the dendritic tuft. Addition of fast and slow inhibitory synaptic conductances, with properties similar to those from dendritic targeting interneurons, that provided a 'balanced' background configuration, partially counteracted these effects, suggesting that inhibition can tune spatio-temporal integration in the tuft. Excitatory background input lowered the threshold for NMDA receptor-mediated dendritic spikes, extended their duration and increased the probability of additional regenerative events occurring in neighbouring branches. These effects were also observed in a passive model where all the non-synaptic voltage-gated conductances were removed. Our results show that glutamate-bound NMDA receptors arising from ongoing network activity can provide a powerful spatially distributed nonlinear dendritic conductance. This may enable L5 pyramidal cells to change their integrative properties as a function of local network activity, potentially allowing both clustered and spatially distributed synaptic inputs to be integrated over extended timescales.

Inhibition downunder: an update from the spinal cord

Inhibitory neurons in the spinal cord perform dedicated roles in processing somatosensory information and shaping motor behaviors that range from simple protective reflexes to more complex motor tasks such as locomotion, reaching and grasping. Recent efforts examining inhibition in the spinal cord have been directed toward determining how inhibitory cell types are specified and incorporated into the sensorimotor circuitry, identifying and characterizing molecularly defined cohorts of inhibitory neurons and interrogating the functional contribution these cells make to sensory processing and motor behaviors. Rapid progress is being made on all these fronts, driven in large part by molecular genetic and optogenetic approaches that are being creatively combined with neuroanatomical, electrophysiological and behavioral techniques.

Excitability and responsiveness of rat barrel cortex neurons in the presence and absence of spontaneous synaptic activity in vivo

The amplitude and temporal dynamics of spontaneous synaptic activity in the cerebral cortex vary as a function of brain states. To directly assess the impact of different ongoing synaptic activities on neocortical function, we performed in vivo intracellular recordings from barrel cortex neurons in rats under two pharmacological conditions generating either oscillatory or tonic synaptic drive. Cortical neurons membrane excitability and firing responses were compared, in the same neurons, before and after complete suppression of background synaptic drive following systemic injection of a high dose of anaesthetic. Compared to the oscillatory state, the tonic pattern resulted in a more depolarized and less fluctuating membrane potential (Vm), a lower input resistance (Rm) and steeper relations of firing frequency versus injected current (F-I). Whatever their temporal dynamics, suppression of background synaptic activities increased mean Vm, without affecting Rm, and induced a rightward shift of F-I curves. Both types of synaptic drive generated a high variability in current-induced firing rate and patterns in cortical neurons, which was much reduced after removal of spontaneous activity. These findings suggest that oscillatory and tonic synaptic patterns differentially facilitate the input-output function of cortical neurons but result in a similar moment-to-moment variability in spike responses to incoming depolarizing inputs.

Premotor spinal network with balanced excitation and inhibition during motor patterns has high resilience to structural division

Direct measurements of synaptic inhibition (I) and excitation (E) to spinal motoneurons can provide an important insight into the organization of premotor networks. Such measurements of flexor motoneurons participating in motor patterns in turtles have recently demonstrated strong concurrent E and I as well as stochastic membrane potentials and irregular spiking in the adult turtle spinal cord. These findings represent a departure from the widespread acceptance of feedforward reciprocal rate models for spinal motor function. The apparent discrepancy has been reviewed as an experimental artifact caused by the distortion of local networks in the transected turtle spinal cord. We tested this assumption in the current study by performing experiments to assess the integrity of motor functions in the intact spinal cord and the cord transected at segments D9/D10. Excitatory and inhibitory synaptic inputs to motoneurons were estimated during rhythmic motor activity and demonstrated primarily intense inputs that consisted of qualitatively similar mixed E/I before and after the transection. To understand this high functional resilience, we used mathematical modeling of networks with recurrent connectivity that could potentially explain the balanced E/I. Both experimental and modeling data support the concept of a locally balanced premotor network consisting of recurrent E/I connectivity, in addition to the well known reciprocal network activity. The multifaceted synaptic connections provide spinal networks with a remarkable ability to remain functional after structural divisions.

The log-dynamic brain: how skewed distributions affect network operations

We often assume that the variables of functional and structural brain parameters - such as synaptic weights, the firing rates of individual neurons, the synchronous discharge of neural populations, the number of synaptic contacts between neurons and the size of dendritic boutons - have a bell-shaped distribution. However, at many physiological and anatomical levels in the brain, the distribution of numerous parameters is in fact strongly skewed with a heavy tail, suggesting that skewed (typically lognormal) distributions are fundamental to structural and functional brain organization. This insight not only has implications for how we should collect and analyse data, it may also help us to understand how the different levels of skewed distributions - from synapses to cognition - are related to each other.

The impact of tonic GABAA receptor-mediated inhibition on neuronal excitability varies across brain region and cell type

The diversity of GABA_A receptor (GABA_AR) subunits and the numerous configurations during subunit assembly give rise to a variety of receptors with different functional properties. This heterogeneity results in variations in GABAergic conductances across numerous brain regions and cell types. Phasic inhibition is mediated by synaptically-localized receptors with a low affinity for GABA and results in a transient, rapidly desensitizing GABAergic conductance; whereas, tonic inhibition is mediated by extrasynaptic receptors with a high affinity for GABA and results in a persistent GABAergic conductance. The specific functions of tonic versus phasic GABAergic inhibition in different cell types and the impact on specific neural circuits are only beginning to be unraveled. Here we review the diversity in the magnitude of tonic GABAergic inhibition in various brain regions and cell types, and highlight the impact on neuronal excitability in different neuronal circuits. Further, we discuss the relevance of tonic inhibition in various physiological and pathological contexts as well as the potential of targeting these receptor subtypes for treatment of diseases, such as epilepsy.

Single neuron dynamics and computation

At the single neuron level, information processing involves the transformation of input spike trains into an appropriate output spike train. Building upon the classical view of a neuron as a threshold device, models have been developed in recent years that take into account the diverse electrophysiological make-up of neurons and accurately describe their input-output relations. Here, we review these recent advances and survey the computational roles that they have uncovered for various electrophysiological properties, for dendritic arbor anatomy as well as for short-term synaptic plasticity.

Sensory-evoked synaptic integration in cerebellar and cerebral cortical neurons

Neurons integrate synaptic inputs across time and space, a process that determines the transformation of input signals into action potential output. This article explores how synaptic integration contributes to the richness of sensory signalling in the cerebellar and cerebral cortices. Whether a neuron receives a few or a few thousand discrete inputs, most evoked synaptic activity generates only subthreshold membrane potential fluctuations. Sensory tuning of synaptic inputs is typically broad, but short-term dynamics and the interplay between excitation and inhibition restrict action potential firing to narrow windows of opportunity. We highlight the challenges and limitations of the use of somatic recordings in the study of synaptic integration and the importance of active dendritic mechanisms in sensory processing.

Interneuron cell types are fit to function

Understanding brain circuits begins with an appreciation of their component parts - the cells. Although GABAergic interneurons are a minority population within the brain, they are crucial for the control of inhibition. Determining the diversity of these interneurons has been a central goal of neurobiologists, but this amazing cell type has so far defied a generalized classification system. Interneuron complexity within the telencephalon could be simplified by viewing them as elaborations of a much more finite group of developmentally specified cardinal classes that become further specialized as they mature. Our perspective emphasizes that the ultimate goal is to dispense with classification criteria and directly define interneuron types by function.

Endogenous cannabinoid signaling at inhibitory interneurons

Significant progress has been made in our understanding of how endogenous cannabinoids (eCBs) signal at excitatory and inhibitory synapses in the central nervous system (CNS). This review discusses how eCBs regulate inhibitory interneurons, their synapses, and the networks in which they are embedded. eCB signaling plays a pivotal role in brain physiology by means of their synaptic signal transduction, spatiotemporal signaling profile, routing of information through inhibitory microcircuits, and experience-dependent plasticity. Understanding the normal processes underlying eCB signaling is beginning to shed light on how their dysregulation contributes to disease.

Cortically-controlled population stochastic facilitation as a plausible substrate for guiding sensory transfer across the thalamic gateway

The thalamus is the primary gateway that relays sensory information to the cerebral cortex. While a single recipient cortical cell receives the convergence of many principal relay cells of the thalamus, each thalamic cell in turn integrates a dense and distributed synaptic feedback from the cortex. During sensory processing, the influence of this functional loop remains largely ignored. Using dynamic-clamp techniques in thalamic slices in vitro, we combined theoretical and experimental approaches to implement a realistic hybrid retino-thalamo-cortical pathway mixing biological cells and simulated circuits. The synaptic bombardment of cortical origin was mimicked through the injection of a stochastic mixture of excitatory and inhibitory conductances, resulting in a gradable correlation level of afferent activity shared by thalamic cells. The study of the impact of the simulated cortical input on the global retinocortical signal transfer efficiency revealed a novel control mechanism resulting from the collective resonance of all thalamic relay neurons. We show here that the transfer efficiency of sensory input transmission depends on three key features: i) the number of thalamocortical cells involved in the many-to-one convergence from thalamus to cortex, ii) the statistics of the corticothalamic synaptic bombardment and iii) the level of correlation imposed between converging thalamic relay cells. In particular, our results demonstrate counterintuitively that the retinocortical signal transfer efficiency increases when the level of correlation across thalamic cells decreases. This suggests that the transfer efficiency of relay cells could be selectively amplified when they become simultaneously desynchronized by the cortical feedback. When applied to the intact brain, this network regulation mechanism could direct an attentional focus to specific thalamic subassemblies and select the appropriate input lines to the cortex according to the descending influence of cortically-defined “priors”.

Most of the sensory information in the early visual system is relayed from the retina to the primary visual cortex through principal relay cells in the thalamus. While relay cells receive ∼7–16% of their synapses from retina, they integrate the synaptic barrage of a dense cortical feedback, which accounts for more than 60% of their total input. This feedback is thought to carry some form of “prior” resulting from the computation performed in cortical areas, which influences the response of relay cells, presumably by regulating the transfer of sensory information to cortical areas. Nevertheless, its statistical nature (input synchronization, excitation/inhibition ratio, etc.) and the cellular mechanisms gating thalamic transfer are largely ignored. Here we implemented hybrid circuits (biological and modeled cells) reproducing the main features of the thalamic gate and explored the functional impact of various statistics of the cortical input. We found that the regulation of sensory information is critically determined by the statistical coherence of the cortical synaptic bombardment associated with a stochastic facilitation process. We propose that this tuning mechanism could operate in the intact brain to selectively filter the sensory information reaching cortical areas according to attended features predesignated by the cortical feedback.

Non-linear dynamics in parkinsonism

Over the last 30 years, the functions (and dysfunctions) of the sensory-motor circuitry have been mostly conceptualized using linear modelizations which have resulted in two main models: the “rate hypothesis” and the “oscillatory hypothesis.” In these two models, the basal ganglia data stream is envisaged as a random temporal combination of independent simple patterns issued from its probability distribution of interval interspikes or its spectrum of frequencies respectively. More recently, non-linear analyses have been introduced in the modelization of motor circuitry activities, and they have provided evidences that complex temporal organizations exist in basal ganglia neuronal activities. Regarding movement disorders, these complex temporal organizations in the basal ganglia data stream differ between conditions (i.e., parkinsonism, dyskinesia, healthy control) and are responsive to treatments (i.e., l-DOPA, deep brain stimulation). A body of evidence has reported that basal ganglia neuronal entropy (a marker for complexity/irregularity in time series) is higher in hypokinetic state. In line with these findings, an entropy-based model has been recently formulated to introduce basal ganglia entropy as a marker for the alteration of motor processing and a factor of motor inhibition. Importantly, non-linear features have also been identified as a marker of condition and/or treatment effects in brain global signals (EEG), muscular activities (EMG), or kinetic of motor symptoms (tremor, gait) of patients with movement disorders. It is therefore warranted that the non-linear dynamics of motor circuitry will contribute to a better understanding of the neuronal dysfunctions underlying the spectrum of parkinsonian motor symptoms including tremor, rigidity, and hypokinesia.

Restoring ionotropic inhibition as an analgesic strategy

Neuronal inhibition in nociceptive relays of the spinal cord is essential for the proper processing of nociceptive information. In the spinal cord dorsal horn, the activity of synaptic and extrasynaptic GABAA and glycine receptors generates rapid, Cl(-)-dependent neuronal inhibition. A loss of this ionotropic inhibition, particularly through the collapse of the inhibitory Cl(-)-gradient, is a key mechanism by which pathological pain conditions develop. This review summarizes the roles of ionotropic inhibition in the regulation of nociception, and explores recent evidence that the potentiation of GABAA or glycine receptor activity or the enhancement of inhibitory drive can reverse pathological pain.

Monitoring synaptic and neuronal activity in 3D with synthetic and genetic indicators using a compact acousto-optic lens two-photon microscope

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We expand the utility of acousto-optic lens (AOL) 3D 2P microscopy.

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We show rapid, simultaneous monitoring of synaptic inputs distributed in 3D.

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First use of genetically encoded indicators with AOL 3D functional imaging.

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Measurement of sensory-evoked neuronal population activity in 3D in vivo.

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Strategies for improving the measurement of the timing of neuronal signals.

Background

Two-photon microscopy is widely used to study brain function, but conventional microscopes are too slow to capture the timing of neuronal signalling and imaging is restricted to one plane. Recent development of acousto-optic-deflector-based random access functional imaging has improved the temporal resolution, but the utility of these technologies for mapping 3D synaptic activity patterns and their performance at the excitation wavelengths required to image genetically encoded indicators have not been investigated.

New method

Here, we have used a compact acousto-optic lens (AOL) two-photon microscope to make high speed [Ca²⁺] measurements from spines and dendrites distributed in 3D with different excitation wavelengths (800–920 nm).

Results

We show simultaneous monitoring of activity from many synaptic inputs distributed over the 3D arborisation of a neuronal dendrite using both synthetic as well as genetically encoded indicators. We confirm the utility of AOL-based imaging for fast in vivo recordings by measuring, simultaneously, visually evoked responses in 100 neurons distributed over a 150 μm focal depth range. Moreover, we explore ways to improve the measurement of timing of neuronal activation by choosing specific regions within the cell soma.

Comparison with existing methods

These results establish that AOL-based 3D random access two-photon microscopy has a wider range of neuroscience applications than previously shown.

Conclusions

Our findings show that the compact AOL microscope design has the speed, spatial resolution, sensitivity and wavelength flexibility to measure 3D patterns of synaptic and neuronal activity on individual trials.

Dopamine regulates two classes of primate prefrontal neurons that represent sensory signals

The lateral prefrontal cortex (PFC), a hub of higher-level cognitive processing, is strongly modulated by midbrain dopamine (DA) neurons. The cellular mechanisms have been comprehensively studied in the context of short-term memory, but little is known about how DA regulates sensory inputs to PFC that precede and give rise to such memory activity. By preparing recipient cortical circuits for incoming signals, DA could be a powerful determinant of downstream cognitive processing. Here, we tested the hypothesis that prefrontal DA regulates the representation of sensory signals that are required for perceptual decisions. In rhesus monkeys trained to report the presence or absence of visual stimuli at varying levels of contrast, we simultaneously recorded extracellular single-unit activity and applied DA to the immediate vicinity of the neurons by micro-iontophoresis. We found that DA modulation of prefrontal neurons is not uniform but tailored to specialized neuronal classes. In one population of neurons, DA suppressed activity with high temporal precision but preserved signal/noise ratio. Neurons in this group had short visual response latencies and comprised all recorded narrow-spiking, putative interneurons. In a distinct population, DA increased excitability and enhanced signal/noise ratio by reducing response variability. These neurons had longer visual response latencies and were composed exclusively of broad-spiking, putative pyramidal neurons. By gating sensory inputs to PFC and subsequently strengthening the representation of sensory signals, DA might play an important role in shaping how the PFC initiates appropriate behavior in response to changes in the sensory environment.

The contribution of synaptic location to inhibitory gain control in pyramidal cells

THE ACTIVITY OF PYRAMIDAL CELLS IS CONTROLLED BY TWO OPPOSING FORCES: synaptic inhibition and synaptic excitation. Interestingly, these synaptic inputs are not distributed evenly across the dendritic trees of cortical pyramidal cells. Excitatory synapses are densely packed along only the more peripheral dendrites, but are absent from the proximal stems and the soma. In contrast, inhibitory synapses are located throughout the dendritic tree, the soma, and the axon initial segment. Thus both excitatory and inhibitory inputs exist on the peripheral dendritic tree, while the proximal segments only receive inhibition. The functional consequences of this uneven organization remain unclear. We used both optogenetics and dynamic patch clamp techniques to simulate excitatory synaptic conductances in pyramidal cells, and then assessed how their firing output is modulated by gamma-amino-butyric acid type A (GABAA) receptor activation at different regions of the somatodendritic axis. We report here that activation of GABAA receptor on the same dendritic compartment as excitatory inputs causes a rightwards shift in the function relating firing rate to excitatory conductance (the input-output function). In contrast, GABAA receptor activation proximal to the soma causes both a rightwards shift and also a reduction in the maximal firing rate. The experimental data are well reproduced in a simple, four compartmental model of a neuron with inhibition either on the same compartment, or proximal, to the excitatory drive.

Real-time model predictive control using a self-organizing neural network

In this paper, a real-time model predictive control (RT-MPC) based on self-organizing radial basis function neural network (SORBFNN) is proposed for nonlinear systems. This RT-MPC has its simplicity in parallelism to model predictive control design and efficiency to deal with computational complexity. First, a SORBFNN with concurrent structure and parameter learning is developed as the predictive model of the nonlinear systems. The model performance can be significantly improved through SORBFNN, and the modeling error is uniformly ultimately bounded. Second, a fast gradient method (GM) is enhanced for the solution of optimal control problem. This proposed GM can reduce computational cost and suboptimize the RT-MPC online. Then, the conditions of the stability analysis and steady-state performance of the closed-loop systems are presented. Finally, numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance rejection performances. Experimental results demonstrate its effectiveness.

Directional hearing by linear summation of binaural inputs at the medial superior olive

Neurons in the medial superior olive (MSO) enable sound localization by their remarkable sensitivity to submillisecond interaural time differences (ITDs). Each MSO neuron has its own "best ITD" to which it responds optimally. A difference in physical path length of the excitatory inputs from both ears cannot fully account for the ITD tuning of MSO neurons. As a result, it is still debated how these inputs interact and whether the segregation of inputs to opposite dendrites, well-timed synaptic inhibition, or asymmetries in synaptic potentials or cellular morphology further optimize coincidence detection or ITD tuning. Using in vivo whole-cell and juxtacellular recordings, we show here that ITD tuning of MSO neurons is determined by the timing of their excitatory inputs. The inputs from both ears sum linearly, whereas spike probability depends nonlinearly on the size of synaptic inputs. This simple coincidence detection scheme thus makes accurate sound localization possible.

Synaptic inhibition and excitation estimated via the time constant of membrane potential fluctuations

When recording the membrane potential, V, of a neuron it is desirable to be able to extract the synaptic input. Critically, the synaptic input is stochastic and nonreproducible so one is therefore often restricted to single-trial data. Here, we introduce means of estimating the inhibition and excitation and their confidence limits from single sweep trials. The estimates are based on the mean membrane potential, V̄, and the membrane time constant, τ. The time constant provides the total conductance ( G = capacitance/τ) and is extracted from the autocorrelation of V. The synaptic conductances can then be inferred from V̄ when approximating the neuron as a single compartment. We further employ a stochastic model to establish limits of confidence. The method is verified on models and experimental data, where the synaptic input is manipulated pharmacologically or estimated by an alternative method. The method gives best results if the synaptic input is large compared with other conductances, the intrinsic conductances have little or no time dependence or are comparably small, the ligand-gated kinetics is faster than the membrane time constant, and the majority of synaptic contacts are electrotonically close to soma (recording site). Although our data are in current clamp, the method also works in V-clamp recordings, with some minor adaptations. All custom made procedures are provided in Matlab.

Mapping and cracking sensorimotor circuits in genetic model organisms

One central goal of systems neuroscience is to understand how neural circuits implement the computations that link sensory inputs to behavior. Work combining electrophysiological and imaging-based approaches to measure neural activity with pharmacological and electrophysiological manipulations has provided fundamental insights. More recently, genetic approaches have been used to monitor and manipulate neural activity, opening up new experimental opportunities and challenges. Here, we discuss issues associated with applying genetic approaches to circuit dissection in sensorimotor transformations, outlining important considerations for experimental design and considering how modeling can complement experimental approaches.

Coding and decoding with dendrites

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.

The coherent organization of mental life depends on mechanisms for context-sensitive gain-control that are impaired in schizophrenia

There is rapidly growing evidence that schizophrenia involves changes in context-sensitive gain-control and probabilistic inference. In addition to the well-known cognitive disorganization to which these changes lead, basic aspects of vision are also impaired, as discussed by other papers on this Frontiers Research Topic. The aim of this paper is to contribute to our understanding of such findings by examining five central hypotheses. First, context-sensitive gain-control is fundamental to brain function and mental life. Second, it occurs in many different regions of the cerebral cortex of many different mammalian species. Third, it has several computational functions, each with wide generality. Fourth, it is implemented by several neural mechanisms at cellular and circuit levels. Fifth, impairments of context-sensitive gain-control produce many of the well-known symptoms of schizophrenia and change basic processes of visual perception. These hypotheses suggest why disorders of vision in schizophrenia may provide insights into the nature and mechanisms of impaired reality testing and thought disorder in psychosis. They may also cast light on normal mental function and its neural bases. Limitations of these hypotheses, and ways in which they need further testing and development, are outlined.

An entropy-based model for basal ganglia dysfunctions in movement disorders

During this last decade, nonlinear analyses have been used to characterize the irregularity that exists in the neuronal data stream of the basal ganglia. In comparison to linear parameters for disparity (i.e., rate, standard deviation, and oscillatory activities), nonlinear analyses focus on complex patterns that are composed of groups of interspike intervals with matching lengths but not necessarily contiguous in the data stream. In light of recent animal and clinical studies, we present a review and commentary on the basal ganglia neuronal entropy in the context of movement disorders.

On the precision of neural computation with interaural level differences in the lateral superior olive

Interaural level difference (ILD) is one of the basic binaural clues in the spatial localization of a sound source. Due to the acoustic shadow cast by the head, a sound source out of the medial plane results in an increased sound level at the nearer ear and a decreased level at the distant ear. In the mammalian auditory brainstem, the ILD is processed by a neuronal circuit of binaural neurons in the lateral superior olive (LSO). These neurons receive major excitatory projections from the ipsilateral side and major inhibitory projections from the contralateral side. As the sound level is encoded predominantly by the neuronal discharge rate, the principal function of LSO neurons is to estimate and encode the difference between the discharge rates of the excitatory and inhibitory inputs. Two general mechanisms of this operation are biologically plausible: (1) subtraction of firing rates integrated over longer time intervals, and (2) detection of coincidence of individual spikes within shorter time intervals. However, the exact mechanism of ILD evaluation is not known. Furthermore, given the stochastic nature of neuronal activity, it is not clear how the circuit achieves the remarkable precision of ILD assessment observed experimentally. We employ a probabilistic model and complementary computer simulations to investigate whether the two general mechanisms are capable of the desired performance. Introducing the concept of an ideal observer, we determine the theoretical ILD accuracy expressed by means of the just-noticeable difference (JND) in dependence on the statistics of the interacting spike trains, the overall firing rate, detection time, the number of converging fibers, and on the neural mechanism itself. We demonstrate that the JNDs rely on the precision of spike timing; however, with an appropriate parameter setting, the lowest theoretical values are similar or better than the experimental values. Furthermore, a mechanism based on excitatory and inhibitory coincidence detection may give better results than the subtraction of firing rates. This article is part of a Special Issue entitled Neural Coding 2012.

Noise normalizes firing output of mouse lateral geniculate nucleus neurons

The output of individual neurons is dependent on both synaptic and intrinsic membrane properties. While it is clear that the response of an individual neuron can be facilitated or inhibited based on the summation of its constituent synaptic inputs, it is not clear whether subthreshold activity, (e.g. synaptic "noise"--fluctuations that do not change the mean membrane potential) also serve a function in the control of neuronal output. Here we studied this by making whole-cell patch-clamp recordings from 29 mouse thalamocortical relay (TC) neurons. For each neuron we measured neuronal gain in response to either injection of current noise, or activation of the metabotropic glutamate receptor-mediated cortical feedback network (synaptic noise). As expected, injection of current noise via the recording pipette induces shifts in neuronal gain that are dependent on the amplitude of current noise, such that larger shifts in gain are observed in response to larger amplitude noise injections. Importantly we show that shifts in neuronal gain are also dependent on the intrinsic sensitivity of the neuron tested, such that the gain of intrinsically sensitive neurons is attenuated divisively in response to current noise, while the gain of insensitive neurons is facilitated multiplicatively by injection of current noise- effectively normalizing the output of the dLGN as a whole. In contrast, when the cortical feedback network was activated, only multiplicative gain changes were observed. These network activation-dependent changes were associated with reductions in the slow afterhyperpolarization (sAHP), and were mediated at least in part, by T-type calcium channels. Together, this suggests that TC neurons have the machinery necessary to compute multiple output solutions to a given set of stimuli depending on the current level of network stimulation.

Modeling the generation of output by the cerebellar nuclei

Functional aspects of network integration in the cerebellar cortex have been studied experimentally and modeled in much detail ever since the early work by theoreticians such as Marr, Albus and Braitenberg more than 40 years ago. In contrast, much less is known about cerebellar processing at the output stage, namely in the cerebellar nuclei (CN). Here, input from Purkinje cells converges to control CN neuron spiking via GABAergic inhibition, before the output from the CN reaches cerebellar targets such as the brainstem and the motor thalamus. In this article we review modeling studies that address how the CN may integrate cerebellar cortical inputs, and what kind of signals may be transmitted. Specific hypotheses in the literature contrast rate coding and temporal coding of information in the spiking output from the CN. One popular hypothesis states that post-inhibitory rebound spiking may be an important mechanism by which Purkinje cell inhibition is turned into CN output spiking, but this hypothesis remains controversial. Rate coding clearly does take place, but in what way it may be augmented by temporal codes remains to be more clearly established. Several candidate mechanisms distinct from rebound spiking are discussed, such as the significance of spike time correlations between Purkinje cell pools to determine CN spike timing, irregularity of Purkinje cell spiking as a determinant of CN firing rate, and shared brief pauses between Purkinje cell pools that may trigger individual CN spikes precisely.

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.

Sensitivity of spinal neurons to GABA and glycine during voluntary movement in behaving monkeys

GABAergic and glycinergic inhibition play key roles in the function of spinal motor pathways. However, there is little direct information on the extent to which inhibition controls the activity of spinal neurons during behavior or the relative effectiveness of GABA and glycine on cell activity under normal conditions. These issues were investigated in three macaque monkeys trained to perform voluntary ramp-and-hold wrist movements and grip. Pipettes with an extracellular recording electrode and iontophoresis barrels were used to eject GABA, glycine, and/or their respective antagonists, bicuculline and strychnine, as the activity of single neurons was recorded in the C6-T1 spinal segments during hand movements. The firing rate of the vast majority of neurons decreased when an inhibitory neurotransmitter was ejected from the electrode, suggesting that most movement-related spinal neurons are sensitive to both GABA and glycine. Most movement-related neurons exhibited increased activity during iontophoresis of an antagonist, suggesting that both GABAergic and glycinergic inhibition actively regulate the majority of spinal neurons during movement. These conclusions were supported by the responses of neurons tested with both agonists or both antagonists. Bicuculline and strychnine produced the largest increases in firing rate during dynamic movements (ramp phase), smaller increases during maintained torque/force (hold phase), and the smallest increase during the rest period. Since excitatory inputs also tend to increase progressively from rest to static to dynamic muscle contractions, this result is consistent with coupled excitatory and inhibitory inputs to spinal neurons during movement.

Somatic and dendritic GABA(B) receptors regulate neuronal excitability via different mechanisms

GABA(B) receptors play a key role in regulating neuronal excitability in the brain. Whereas the impact of somatic GABA(B) receptors on neuronal excitability has been studied in some detail, much less is known about the role of dendritic GABA(B) receptors. Here, we investigate the impact of GABA(B) receptor activation on the somato-dendritic excitability of layer 5 pyramidal neurons in the rat barrel cortex. Activation of GABA(B) receptors led to hyperpolarization and a decrease in membrane resistance that was greatest at somatic and proximal dendritic locations. These effects were occluded by low concentrations of barium (100 μM), suggesting that they are mediated by potassium channels. In contrast, activation of dendritic GABA(B) receptors decreased the width of backpropagating action potential (APs) and abolished dendritic calcium electrogenesis, indicating that dendritic GABA(B) receptors regulate excitability, primarily via inhibition of voltage-dependent calcium channels. These distinct actions of somatic and dendritic GABA(B) receptors regulated neuronal output in different ways. Activation of somatic GABA(B) receptors led to a reduction in neuronal output, primarily by increasing the AP rheobase, whereas activation of dendritic GABA(B) receptors blocked burst firing, decreasing AP output in the absence of a significant change in somatic membrane properties. Taken together, our results show that GABA(B) receptors regulate somatic and dendritic excitability of cortical pyramidal neurons via different cellular mechanisms. Somatic GABA(B) receptors activate potassium channels, leading primarily to a subtractive or shunting form of inhibition, whereas dendritic GABA(B) receptors inhibit dendritic calcium electrogenesis, leading to a reduction in bursting firing.

STD-dependent and independent encoding of input irregularity as spike rate in a computational model of a cerebellar nucleus neuron

Neurons in the cerebellar nuclei (CN) receive inhibitory inputs from Purkinje cells in the cerebellar cortex and provide the major output from the cerebellum, but their computational function is not well understood. It has recently been shown that the spike activity of Purkinje cells is more regular than previously assumed and that this regularity can affect motor behaviour. We use a conductance-based model of a CN neuron to study the effect of the regularity of Purkinje cell spiking on CN neuron activity. We find that increasing the irregularity of Purkinje cell activity accelerates the CN neuron spike rate and that the mechanism of this recoding of input irregularity as output spike rate depends on the number of Purkinje cells converging onto a CN neuron. For high convergence ratios, the irregularity induced spike rate acceleration depends on short-term depression (STD) at the Purkinje cell synapses. At low convergence ratios, or for synchronised Purkinje cell input, the firing rate increase is independent of STD. The transformation of input irregularity into output spike rate occurs in response to artificial input spike trains as well as to spike trains recorded from Purkinje cells in tottering mice, which show highly irregular spiking patterns. Our results suggest that STD may contribute to the accelerated CN spike rate in tottering mice and they raise the possibility that the deficits in motor control in these mutants partly result as a pathological consequence of this natural form of plasticity.

Location-dependent excitatory synaptic interactions in pyramidal neuron dendrites

Neocortical pyramidal neurons (PNs) receive thousands of excitatory synaptic contacts on their basal dendrites. Some act as classical driver inputs while others are thought to modulate PN responses based on sensory or behavioral context, but the biophysical mechanisms that mediate classical-contextual interactions in these dendrites remain poorly understood. We hypothesized that if two excitatory pathways bias their synaptic projections towards proximal vs. distal ends of the basal branches, the very different local spike thresholds and attenuation factors for inputs near and far from the soma might provide the basis for a classical-contextual functional asymmetry. Supporting this possibility, we found both in compartmental models and electrophysiological recordings in brain slices that the responses of basal dendrites to spatially separated inputs are indeed strongly asymmetric. Distal excitation lowers the local spike threshold for more proximal inputs, while having little effect on peak responses at the soma. In contrast, proximal excitation lowers the threshold, but also substantially increases the gain of distally-driven responses. Our findings support the view that PN basal dendrites possess significant analog computing capabilities, and suggest that the diverse forms of nonlinear response modulation seen in the neocortex, including uni-modal, cross-modal, and attentional effects, could depend in part on pathway-specific biases in the spatial distribution of excitatory synaptic contacts onto PN basal dendritic arbors.

Pyramidal neurons (PNs) are the principal neurons of the cerebral cortex and therefore lie at the heart of the brain's higher sensory, motor, affective, memory, and executive functions. But how do they work? In particular, how do they manage interactions between the classical “driver” inputs that give rise to their basic response properties, and “contextual” inputs that nonlinearly modulate those responses? It is known that PNs are contacted by thousands of excitatory synapses scattered about their dendrites, but despite decades of research, the “rules” that govern how inputs at different locations in the dendritic tree combine to influence the cell's firing rate remain poorly understood. We show here that two excitatory inputs contacting the same dendrite interact in an asymmetric nonlinear way that depends on their absolute and relative locations, where the resulting spectrum of location-dependent synaptic interactions constitutes a previously unknown form of spatial analog computation. In addition to suggesting a possible substrate for classical-contextual interactions in PN dendrites, our results imply that the computing functions of cortical circuits can only be fully understood when the detailed map of synaptic connectivity – the cortical connectome – is known down to the subdendritic level.

Short term synaptic depression imposes a frequency dependent filter on synaptic information transfer

Depletion of synaptic neurotransmitter vesicles induces a form of short term depression in synapses throughout the nervous system. This plasticity affects how synapses filter presynaptic spike trains. The filtering properties of short term depression are often studied using a deterministic synapse model that predicts the mean synaptic response to a presynaptic spike train, but ignores variability introduced by the probabilistic nature of vesicle release and stochasticity in synaptic recovery time. We show that this additional variability has important consequences for the synaptic filtering of presynaptic information. In particular, a synapse model with stochastic vesicle dynamics suppresses information encoded at lower frequencies more than information encoded at higher frequencies, while a model that ignores this stochasticity transfers information encoded at any frequency equally well. This distinction between the two models persists even when large numbers of synaptic contacts are considered. Our study provides strong evidence that the stochastic nature neurotransmitter vesicle dynamics must be considered when analyzing the information flow across a synapse.

Location-dependent effects of inhibition on local spiking in pyramidal neuron dendrites

Cortical computations are critically dependent on interactions between pyramidal neurons (PNs) and a menagerie of inhibitory interneuron types. A key feature distinguishing interneuron types is the spatial distribution of their synaptic contacts onto PNs, but the location-dependent effects of inhibition are mostly unknown, especially under conditions involving active dendritic responses. We studied the effect of somatic vs. dendritic inhibition on local spike generation in basal dendrites of layer 5 PNs both in neocortical slices and in simple and detailed compartmental models, with equivalent results: somatic inhibition divisively suppressed the amplitude of dendritic spikes recorded at the soma while minimally affecting dendritic spike thresholds. In contrast, distal dendritic inhibition raised dendritic spike thresholds while minimally affecting their amplitudes. On-the-path dendritic inhibition modulated both the gain and threshold of dendritic spikes depending on its distance from the spike initiation zone. Our findings suggest that cortical circuits could assign different mixtures of gain vs. threshold inhibition to different neural pathways, and thus tailor their local computations, by managing their relative activation of soma- vs. dendrite-targeting interneurons.

Postnatal maturation of somatostatin-expressing inhibitory cells in the somatosensory cortex of GIN mice

Postnatal inhibitory neuron development affects mammalian brain function, and failure of this maturation process may underlie pathological conditions such as epilepsy, schizophrenia, and depression. Furthermore, understanding how physiological properties of inhibitory neurons change throughout development is critical to understanding the role(s) these cells play in cortical processing. One subset of inhibitory neurons that may be affected during postnatal development is somatostatin-expressing (SOM) cells. A subset of these cells is labeled with green-fluorescent protein (GFP) in a line of mice known as the GFP-positive inhibitory neurons (GIN) line. Here, we studied how intrinsic electrophysiological properties of these cells changed in the somatosensory cortex of GIN mice between postnatal ages P11 and P32+. GIN cells were targeted for whole-cell current-clamp recordings and ranges of positive and negative current steps were presented to each cell. The results showed that as the neocortical circuitry matured during this critical time period multiple intrinsic and firing properties of GIN inhibitory neurons, as well as those of excitatory (regular-spiking [RS]) cells, were altered. Furthermore, these changes were such that the output of GIN cells, but not RS cells, increased over this developmental period. We quantified changes in excitability by examining the input–output relationship of both GIN and RS cells. We found that the firing frequency of GIN cells increased with age, while the rheobase current remained constant across development. This created a multiplicative increase in the input–output relationship of the GIN cells, leading to increases in gain with age. The input–output relationship of the RS cells, on the other hand, showed primarily a subtractive shift with age, but no substantial change in gain. These results suggest that as the neocortex matures, inhibition coming from GIN cells may become more influential in the circuit and play a greater role in the modulation of neocortical activity.

Intrinsic and synaptic properties of vertical cells of the mouse dorsal cochlear nucleus

Multiple classes of inhibitory interneurons shape the activity of principal neurons of the dorsal cochlear nucleus (DCN), a primary target of auditory nerve fibers in the mammalian brain stem. Feedforward inhibition mediated by glycinergic vertical cells (also termed tuberculoventral or corn cells) is thought to contribute importantly to the sound-evoked response properties of principal neurons, but the cellular and synaptic properties that determine how vertical cells function are unclear. We used transgenic mice in which glycinergic neurons express green fluorescent protein (GFP) to target vertical cells for whole cell patch-clamp recordings in acute slices of DCN. We found that vertical cells express diverse intrinsic spiking properties and could fire action potentials at high, sustained spiking rates. Using paired recordings, we directly examined synapses made by vertical cells onto fusiform cells, a primary DCN principal cell type. Vertical cell synapses produced unexpectedly small-amplitude unitary currents in fusiform cells, and additional experiments indicated that multiple vertical cells must be simultaneously active to inhibit fusiform cell spike output. Paired recordings also revealed that a major source of inhibition to vertical cells comes from other vertical cells.

Decrease in tonic inhibition contributes to increase in dentate semilunar granule cell excitability after brain injury

Brain injury is an etiological factor for temporal lobe epilepsy and can lead to memory and cognitive impairments. A recently characterized excitatory neuronal class in the dentate molecular layer, semilunar granule cell (SGC), has been proposed to regulate dentate network activity patterns and working memory formation. Although SGCs, like granule cells, project to CA3, their typical sustained firing and associational axon collaterals suggest that they are functionally distinct from granule cells. We find that brain injury results in an enhancement of SGC excitability associated with an increase in input resistance 1 week after trauma. In addition to prolonging miniature and spontaneous IPSC interevent intervals, brain injury significantly reduces the amplitude of tonic GABA currents in SGCs. The postinjury decrease in SGC tonic GABA currents is in direct contrast to the increase observed in granule cells after trauma. Although our observation that SGCs express Prox1 indicates a shared lineage with granule cells, data from control rats show that SGC tonic GABA currents are larger and sIPSC interevent intervals shorter than in granule cells, demonstrating inherent differences in inhibition between these cell types. GABA(A) receptor antagonists selectively augmented SGC input resistance in controls but not in head-injured rats. Moreover, post-traumatic differences in SGC firing were abolished in GABA(A) receptor blockers. Our data show that cell-type-specific post-traumatic decreases in tonic GABA currents boost SGC excitability after brain injury. Hyperexcitable SGCs could augment dentate throughput to CA3 and contribute substantively to the enhanced risk for epilepsy and memory dysfunction after traumatic brain injury.

Tonic GABA(A) receptor-mediated signalling in temporal lobe epilepsy

The tonic activation of extrasynaptic GABAA receptors by extracellular GABA provides a powerful means of regulating neuronal excitability. A consistent finding from studies that have used various models of temporal lobe epilepsy is that tonic GABAA receptor-mediated conductances are largely preserved in epileptic brain (in contrast to synaptic inhibition which is often reduced). Tonic inhibition is therefore an attractive target for antiepileptic drugs. However, the network consequences of a commonly used approach to augment tonic GABAA receptor-mediated conductances by global manipulation of extracellular GABA are difficult to predict without understanding how epileptogenesis alters the pharmacology and GABA sensitivity of tonic inhibition, and how manipulation of tonic conductances modulates the output of individual neurons. Here we review the current literature on epilepsy-associated changes in tonic GABAA receptor-mediated signalling, and speculate about possible effects they have at the network level. This article is part of the Special Issue entitled 'New Targets and Approaches to the Treatment of Epilepsy'.

Microcircuits mediating feedforward and feedback synaptic inhibition in the piriform cortex

Local inhibition by GABA-releasing neurons is important for the operation of sensory cortices, but the details of these inhibitory circuits remain unclear. We addressed this question in the olfactory system by making targeted recordings from identified classes of inhibitory and glutamatergic neurons in the piriform cortex (PC) of mice. First, we looked for feedforward synaptic inhibition provided by interneurons located in the outermost layer of the PC, layer Ia, which is the unique recipient of afferent fibers from the olfactory bulb. We found two types of feedforward inhibition: a fast-rising, spatially restricted kind that was generated by horizontal cells, and a slow-rising, more diffuse kind generated by neurogliaform cells. Both cell types targeted the distal apical dendrites of layer II principal neurons. Next, we studied feedback synaptic inhibition in isolation by making a tissue cut across layer I to selectively remove feedforward inhibitory connections. We identified a powerful type of feedback inhibition of layer II neurons, mostly generated by soma-targeting fast-spiking multipolar cells in layer III, which in turn were driven by feedforward excitation from layer II semilunar cells. Dynamic clamp simulation of feedback inhibition revealed differential effects of this inhibition on the two main types of layer II principal neurons. Thus, our results articulate the connectivity and functions of two important classes of inhibitory microcircuits in the PC. Feedforward and feedback inhibition generated by these circuits is likely to be required for the operation of this sensory paleocortex during the processing of olfactory information.

Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

This article presents the results of an exploration of one two-parameter space of the Chay model of a cell excitable membrane. There are two main regions: a peripheral one, where the system dynamics will relax to an equilibrium point, and a central one where the expected dynamics is oscillatory. In the second region, we observe a variety of self-sustained oscillations including periodic oscillation, as well as bursting dynamics of different types. These oscillatory dynamics can be observed as periodic oscillations with different periodicities, and in some cases, as chaotic dynamics. These results, when displayed in bifurcation diagrams, result in complex bifurcation structures, which have been suggested as relevant to understand biological cell signaling.

Conductance-based neuron models and the slow dynamics of excitability

In recent experiments, synaptically isolated neurons from rat cortical culture, were stimulated with periodic extracellular fixed-amplitude current pulses for extended durations of days. The neuron’s response depended on its own history, as well as on the history of the input, and was classified into several modes. Interestingly, in one of the modes the neuron behaved intermittently, exhibiting irregular firing patterns changing in a complex and variable manner over the entire range of experimental timescales, from seconds to days. With the aim of developing a minimal biophysical explanation for these results, we propose a general scheme, that, given a few assumptions (mainly, a timescale separation in kinetics) closely describes the response of deterministic conductance-based neuron models under pulse stimulation, using a discrete time piecewise linear mapping, which is amenable to detailed mathematical analysis. Using this method we reproduce the basic modes exhibited by the neuron experimentally, as well as the mean response in each mode. Specifically, we derive precise closed-form input-output expressions for the transient timescale and firing rates, which are expressed in terms of experimentally measurable variables, and conform with the experimental results. However, the mathematical analysis shows that the resulting firing patterns in these deterministic models are always regular and repeatable (i.e., no chaos), in contrast to the irregular and variable behavior displayed by the neuron in certain regimes. This fact, and the sensitive near-threshold dynamics of the model, indicate that intrinsic ion channel noise has a significant impact on the neuronal response, and may help reproduce the experimentally observed variability, as we also demonstrate numerically. In a companion paper, we extend our analysis to stochastic conductance-based models, and show how these can be used to reproduce the details of the observed irregular and variable neuronal response.

Neural locus of color afterimages

After fixating on a colored pattern, observers see a similar pattern in complementary colors when the stimulus is removed [1-6]. Afterimages were important in disproving the theory that visual rays emanate from the eye, in demonstrating interocular interactions, and in revealing the independence of binocular vision from eye movements. Afterimages also prove invaluable in exploring selective attention, filling in, and consciousness. Proposed physiological mechanisms for color afterimages range from bleaching of cone photopigments to cortical adaptation [4-9], but direct neural measurements have not been reported. We introduce a time-varying method for evoking afterimages, which provides precise measurements of adaptation and a direct link between visual percepts and neural responses [10]. We then use in vivo electrophysiological recordings to show that all three classes of primate retinal ganglion cells exhibit subtractive adaptation to prolonged stimuli, with much slower time constants than those expected of photoreceptors. At the cessation of the stimulus, ganglion cells generate rebound responses that can provide afterimage signals for later neurons. Our results indicate that afterimage signals are generated in the retina but may be modified like other retinal signals by cortical processes, so that evidence presented for cortical generation of color afterimages is explainable by spatiotemporal factors that modify all signals.

The stochastic properties of input spike trains control neuronal arithmetic

In the nervous system, the representation of signals is based predominantly on the rate and timing of neuronal discharges. In most everyday tasks, the brain has to carry out a variety of mathematical operations on the discharge patterns. Recent findings show that even single neurons are capable of performing basic arithmetic on the sequences of spikes. However, the interaction of the two spike trains, and thus the resulting arithmetic operation may be influenced by the stochastic properties of the interacting spike trains. If we represent the individual discharges as events of a random point process, then an arithmetical operation is given by the interaction of two point processes. Employing a probabilistic model based on detection of coincidence of random events and complementary computer simulations, we show that the point process statistics control the arithmetical operation being performed and, particularly, that it is possible to switch from subtraction to division solely by changing the distribution of the inter-event intervals of the processes. Consequences of the model for evaluation of binaural information in the auditory brainstem are demonstrated. The results accentuate the importance of the stochastic properties of neuronal discharge patterns for information processing in the brain; further studies related to neuronal arithmetic should therefore consider the statistics of the interacting spike trains.

A theory of rate coding control by intrinsic plasticity effects

Intrinsic plasticity (IP) is a ubiquitous activity-dependent process regulating neuronal excitability and a cellular correlate of behavioral learning and neuronal homeostasis. Because IP is induced rapidly and maintained long-term, it likely represents a major determinant of adaptive collective neuronal dynamics. However, assessing the exact impact of IP has remained elusive. Indeed, it is extremely difficult disentangling the complex non-linear interaction between IP effects, by which conductance changes alter neuronal activity, and IP rules, whereby activity modifies conductance via signaling pathways. Moreover, the two major IP effects on firing rate, threshold and gain modulation, remain unknown in their very mechanisms. Here, using extensive simulations and sensitivity analysis of Hodgkin-Huxley models, we show that threshold and gain modulation are accounted for by maximal conductance plasticity of conductance that situate in two separate domains of the parameter space corresponding to sub- and supra-threshold conductance (i.e. activating below or above the spike onset threshold potential). Analyzing equivalent integrate-and-fire models, we provide formal expressions of sensitivities relating to conductance parameters, unraveling unprecedented mechanisms governing IP effects. Our results generalize to the IP of other conductance parameters and allow strong inference for calcium-gated conductance, yielding a general picture that accounts for a large repertoire of experimental observations. The expressions we provide can be combined with IP rules in rate or spiking models, offering a general framework to systematically assess the computational consequences of IP of pharmacologically identified conductance with both fine grain description and mathematical tractability. We provide an example of such IP loop model addressing the important issue of the homeostatic regulation of spontaneous discharge. Because we do not formulate any assumptions on modification rules, the present theory is also relevant to other neural processes involving excitability changes, such as neuromodulation, development, aging and neural disorders.

Over the past decades, experimental and theoretical studies of the cellular basis of learning and memory have mainly focused on synaptic plasticity, the experience-dependent modification of synapses. However, behavioral learning has also been correlated with experience-dependent changes of non-synaptic voltage-dependent ion channels. This intrinsic plasticity changes the neuron's propensity to fire action potentials in response to synaptic inputs. Thus a fundamental problem is to relate changes of the neuron input-output function with voltage-gated conductance modifications. Using a sensitivity analysis in biophysically realistic models, we depict a generic dichotomy between two classes of voltage-dependent ion channels. These two classes modify the threshold and the slope of the neuron input-output relation, allowing neurons to regulate the range of inputs they respond to and the gain of that response, respectively. We further provide analytical descriptions that enlighten the dynamical mechanisms underlying these effects and propose a concise and realistic framework for assessing the computational impact of intrinsic plasticity in neuron network models. Our results account for a large repertoire of empirical observations and may enlighten functional changes that characterize development, aging and several neural diseases, which also involve changes in voltage-dependent ion channels.

Microcircuits mediating feedforward and feedback synaptic inhibition in the piriform cortex

Local inhibition by GABA-releasing neurons is important for the operation of sensory cortices, but the details of these inhibitory circuits remain unclear. We addressed this question in the olfactory system by making targeted recordings from identified classes of inhibitory and glutamatergic neurons in the piriform cortex (PC) of mice. First, we looked for feedforward synaptic inhibition provided by interneurons located in the outermost layer of the PC, layer Ia, which is the unique recipient of afferent fibers from the olfactory bulb. We found two types of feedforward inhibition: a fast-rising, spatially restricted kind that was generated by horizontal cells, and a slow-rising, more diffuse kind generated by neurogliaform cells. Both cell types targeted the distal apical dendrites of layer II principal neurons. Next, we studied feedback synaptic inhibition in isolation by making a tissue cut across layer I to selectively remove feedforward inhibitory connections. We identified a powerful type of feedback inhibition of layer II neurons, mostly generated by soma-targeting fast-spiking multipolar cells in layer III, which in turn were driven by feedforward excitation from layer II semilunar cells. Dynamic clamp simulation of feedback inhibition revealed differential effects of this inhibition on the two main types of layer II principal neurons. Thus, our results articulate the connectivity and functions of two important classes of inhibitory microcircuits in the PC. Feedforward and feedback inhibition generated by these circuits is likely to be required for the operation of this sensory paleocortex during the processing of olfactory information.