Neuronal integration of synaptic input in the fluctuation-driven regime

Broadband coding with dynamic synapses

Short-term synaptic plasticity (STP) can significantly alter the amplitudes of synaptic responses in ways that depend on presynaptic history. Thus, it is widely assumed that STP acts as a filter for specific patterns of presynaptic inputs, and as a result can play key roles in neuronal information processing. To evaluate this assumption and directly quantify the effects of STP on information transmission, we consider a population of independent synaptic inputs to a model neuron. We show using standard information theoretic approaches that the changes in synaptic response amplitude resulting from STP interact with the related effects on fluctuations in membrane conductance, such that information transmission is broadband (no frequency-dependent filtering occurs), regardless of whether synaptic depression or facilitation dominates. Interestingly, this broadband transmission is preserved in the postsynaptic spike train as long as the postsynaptic neuron's baseline firing rate is relatively high; in contrast, low baseline firing rates lead to STP-dependent effects. Thus, background inputs that control the firing state of a postsynaptic neuron can gate the effects of STP on information transmission.

Signaling in large-scale neural networks

We examine the recent finding that neurons in spinal motor circuits enter a high conductance state during functional network activity. The underlying concomitant increase in random inhibitory and excitatory synaptic activity leads to stochastic signal processing. The possible advantages of this metabolically costly organization are analyzed by comparing with synaptically less intense networks driven by the intrinsic response properties of the network neurons.

Interpreting neurodynamics: concepts and facts

The dynamics of neuronal systems, briefly neurodynamics, has developed into an attractive and influential research branch within neuroscience. In this paper, we discuss a number of conceptual issues in neurodynamics that are important for an appropriate interpretation and evaluation of its results. We demonstrate their relevance for selected topics of theoretical and empirical work. In particular, we refer to the notions of determinacy and stochasticity in neurodynamics across levels of microscopic, mesoscopic and macroscopic descriptions. The issue of correlations between neural, mental and behavioral states is also addressed in some detail. We propose an informed discussion of conceptual foundations with respect to neurobiological results as a viable step to a fruitful future philosophy of neuroscience.

Dependence of neuronal correlations on filter characteristics and marginal spike train statistics

Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are. In this study, we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations. We demonstrate that correlation functions and statistical second-order measures like the variance, the covariance, and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains. We point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations. In many applications, the coherence allows a filter-independent quantification of correlated activity. In different network models, we discuss the estimation of network connectivity from the high-frequency coherence of simultaneous intracellular recordings of pairs of neurons.

Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model

Isolated feedforward networks (FFNs) of spiking neurons have been studied extensively for their ability to propagate transient synchrony and asynchronous firing rates, in the presence of activity independent synaptic background noise (Diesmann et al., 1999; van Rossum et al., 2002). In a biologically realistic scenario, however, the FFN should be embedded in a recurrent network, such that the activity in the FFN and the network activity may dynamically interact. Previously, transient synchrony propagating in an FFN was found to destabilize the dynamics of the embedding network (Mehring et al., 2003). Here, we show that by modeling synapses as conductance transients, rather than current sources, it is possible to embed and propagate transient synchrony in the FFN, without destabilizing the background network dynamics. However, the network activity has a strong impact on the type of activity that can be propagated in the embedded FFN. Global synchrony and high firing rates in the embedding network prohibit the propagation of both, synchronous and asynchronous spiking activity. In contrast, asynchronous low-rate network states support the propagation of both, synchronous spiking and asynchronous, but only low firing rates. In either case, spiking activity tends to synchronize as it propagates, challenging the feasibility to transmit information in asynchronous firing rates. Finally, asynchronous network activity allows to embed more than one FFN, with the amount of cross talk depending on the degree of overlap in the FFNs. This opens the possibility of computational mechanisms using transient synchrony among the activities in multiple FFNs.

The high-conductance state of cortical networks

We studied the dynamics of large networks of spiking neurons with conductance-based (nonlinear) synapses and compared them to networks with current-based (linear) synapses. For systems with sparse and inhibition-dominated recurrent connectivity, weak external inputs induced asynchronous irregular firing at low rates. Membrane potentials fluctuated a few millivolts below threshold, and membrane conductances were increased by a factor 2 to 5 with respect to the resting state. This combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo. Many aspects of the asynchronous irregular state in conductance-based networks could be sufficiently well characterized with a simple numerical mean field approach. In particular, it correctly predicted an intriguing property of conductance-based networks that does not appear to be shared by current-based models: they exhibit states of low-rate asynchronous irregular activity that persist for some period of time even in the absence of external inputs and without cortical pacemakers. Simulations of larger networks (up to 350,000 neurons) demonstrated that the survival time of self-sustained activity increases exponentially with network size.

Control of neuronal firing by dynamic parallel fiber feedback:implications for electrosensory reafference suppression

The cancellation of self-generated components of sensory inputs is a key function of sensory feedback pathways. In many systems, cerebellar parallel fiber feedback mediates this cancellation through anti-Hebbian plasticity,resulting in the generation of a negative image of the reafferent inputs. Parallel fiber feedback involves direct excitation and disynaptic inhibition as well as synaptic plasticity on multiple time scales. How the dynamics of these processes interact with anti-Hebbian plasticity to shape synaptic inputs and provide a cancellation mechanism remains unclear. In the present study, we investigated the influence of parallel fiber feedback onto pyramidal neurons of the electrosensory lateral line lobe (ELL) in weakly electric fish under open loop conditions. We mimicked naturalistic parallel fiber inputs in an ELL brain slice by implementing an experimentally based model of this synaptic pathway using dynamic clamp. We showed that as parallel fiber activity increases, the effective input to ELL pyramidal neurons changes from net excitation to net inhibition, resulting in a non-monotonic firing response. Using a model neuron, we found that this robust non-monotonic response is due to a shift from balanced excitation and inhibition at low parallel fiber input rates, to dominant inhibition at high input rates. We then showed that this non-monotonic response provides a simple basis for negative image generation. Through changes in the mean activation rate of parallel fibers, the feedback can switch roles between enhancement and suppression of sensory inputs in a manner that is directly determined by the slope of the non-monotonic response curve.

Characterizing synaptic conductance fluctuations in cortical neurons and their influence on spike generation

Cortical neurons are subject to sustained and irregular synaptic activity which causes important fluctuations of the membrane potential (V(m)). We review here different methods to characterize this activity and its impact on spike generation. The simplified, fluctuating point-conductance model of synaptic activity provides the starting point of a variety of methods for the analysis of intracellular V(m) recordings. In this model, the synaptic excitatory and inhibitory conductances are described by Gaussian-distributed stochastic variables, or "colored conductance noise". The matching of experimentally recorded V(m) distributions to an invertible theoretical expression derived from the model allows the extraction of parameters characterizing the synaptic conductance distributions. This analysis can be complemented by the matching of experimental V(m) power spectral densities (PSDs) to a theoretical template, even though the unexpected scaling properties of experimental PSDs limit the precision of this latter approach. Building on this stochastic characterization of synaptic activity, we also propose methods to qualitatively and quantitatively evaluate spike-triggered averages of synaptic time-courses preceding spikes. This analysis points to an essential role for synaptic conductance variance in determining spike times. The presented methods are evaluated using controlled conductance injection in cortical neurons in vitro with the dynamic-clamp technique. We review their applications to the analysis of in vivo intracellular recordings in cat association cortex, which suggest a predominant role for inhibition in determining both sub- and supra-threshold dynamics of cortical neurons embedded in active networks.

Detection psychophysics of intracortical microstimulation in rat primary somatosensory cortex

A problem of purposeful intracortical microstimulation is the long duration of neuronal integration time and the associated complex temporal interactions of effects to individual pulses in trains. Here we investigated the effects of repetitive stimuli on perception. We trained head-restraint rats to indicate the detection of cortical microstimulation in infragranular layers of barrel cortex. Three stimulus parameters: stimulus intensity, number of pulses and frequency were varied, and psychometric detection curves were assessed using the method of constant stimuli. The average psychophysical threshold of single pulses was 2.0 nC--a measure very close to what has been found earlier for the evocation of short-latency action potentials in neurons near the stimulation electrode. Detection of single-pulse stimulation always saturated at probabilities of about 0.8. In contrast, repetitive stimuli gave rise to lower thresholds (by a factor of two at 15 pulses, 320 Hz), and to saturation at probabilities close to 1. Interestingly, a large fraction of these perceptual benefits was observed already with double pulses. Moreover, the perceptual efficacy of individual pulses was higher using double pulses compared with longer sequences, i.e. double pulses were detected better than expected from the assumption of independence of single-pulse effects, while trains of 15 pulses fell well short of this expectation. The present results thus point to double-pulse stimulation as an optimal choice when trading economic stimulation against optimizing of the percept.

Inhibition determines membrane potential dynamics and controls action potential generation in awake and sleeping cat cortex

Intracellular recordings of cortical neurons in awake cat and monkey show a depolarized state, sustained firing, and intense subthreshold synaptic activity. It is not known what conductance dynamics underlie such activity and how neurons process information in such highly stochastic states. Here, we combine intracellular recordings in awake and naturally sleeping cats with computational models to investigate subthreshold dynamics of conductances and how conductance dynamics determine spiking activity. We show that during both wakefulness and the "up-states" of natural slow-wave sleep, membrane-potential activity stems from a diversity of combinations of excitatory and inhibitory synaptic conductances, with dominant inhibition in most of the cases. Inhibition also provides the largest contribution to membrane potential fluctuations. Computational models predict that in such inhibition-dominant states, spikes are preferentially evoked by a drop of inhibitory conductance, and that its signature is a transient drop of membrane conductance before the spike. This pattern of conductance change is indeed observed in estimates of spike-triggered averages of synaptic conductances during wakefulness and slow-wave sleep up states. These results show that activated states are defined by diverse combinations of excitatory and inhibitory conductances with pronounced inhibition, and that the dynamics of inhibition is particularly effective on spiking, suggesting an important role for inhibitory processes in both conscious and unconscious cortical states.

Spike timing and reliability in cortical pyramidal neurons: effects of EPSC kinetics, input synchronization and background noise on spike timing

In vivo studies have shown that neurons in the neocortex can generate action potentials at high temporal precision. The mechanisms controlling timing and reliability of action potential generation in neocortical neurons, however, are still poorly understood. Here we investigated the temporal precision and reliability of spike firing in cortical layer V pyramidal cells at near-threshold membrane potentials. Timing and reliability of spike responses were a function of EPSC kinetics, temporal jitter of population excitatory inputs, and of background synaptic noise. We used somatic current injection to mimic population synaptic input events and measured spike probability and spike time precision (STP), the latter defined as the time window (Δt) holding 80% of response spikes. EPSC rise and decay times were varied over the known physiological spectrum. At spike threshold level, EPSC decay time had a stronger influence on STP than rise time. Generally, STP was highest (≤2.45 ms) in response to synchronous compounds of EPSCs with fast rise and decay kinetics. Compounds with slow EPSC kinetics (decay time constants>6 ms) triggered spikes at lower temporal precision (≥6.58 ms). We found an overall linear relationship between STP and spike delay. The difference in STP between fast and slow compound EPSCs could be reduced by incrementing the amplitude of slow compound EPSCs. The introduction of a temporal jitter to compound EPSCs had a comparatively small effect on STP, with a tenfold increase in jitter resulting in only a five fold decrease in STP. In the presence of simulated synaptic background activity, precisely timed spikes could still be induced by fast EPSCs, but not by slow EPSCs.

Awaking and sleeping of a complex network

A network with a logistic-like local dynamics is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small, the dynamics is dissipated and there is no activity: the network is turned off. For a critical value of the coupling, a non-null stable synchronized state, which represents a turned on network, emerges. This global bifurcation is independent of the network topology. We characterize the bistability of the system by studying how to perform the transition, which is now topology dependent, from the active state to that with no activity, for the particular case of a scale-free network. This could be a naive model for the wakening and sleeping of a brain-like system, i.e., a multi-component system with two different dynamical behaviors.

Non-Gaussian membrane potential dynamics imply sparse, synchronous activity in auditory cortex

Many models of cortical dynamics have focused on the high-firing regime, in which neurons are driven near their maximal rate. Here we consider the responses of neurons in auditory cortex under typical low-firing rate conditions, when stimuli have not been optimized to drive neurons maximally. We used whole-cell patch-clamp recording in vivo to measure subthreshold membrane potential fluctuations in rat primary auditory cortex in both the anesthetized and awake preparations. By analyzing the subthreshold membrane potential dynamics on single trials, we made inferences about the underlying population activity. We found that, during both spontaneous and evoked responses, membrane potential was highly non-Gaussian, with dynamics consisting of occasional large excursions (sometimes tens of millivolts), much larger than the small fluctuations predicted by most random walk models that predict a Gaussian distribution of membrane potential. Thus, presynaptic inputs under these conditions are organized into quiescent periods punctuated by brief highly synchronous volleys, or "bumps." These bumps were typically so brief that they could not be well characterized as "up states" or "down states." We estimate that hundreds, perhaps thousands, of presynaptic neurons participate in the largest volleys. These dynamics suggest a computational scheme in which spike timing is controlled by concerted firing among input neurons rather than by small fluctuations in a sea of background activity.

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

Background

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

Results

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

Conclusion

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

Analytical integrate-and-fire neuron models with conductance-based dynamics for event-driven simulation strategies

Event-driven simulation strategies were proposed recently to simulate integrate-and-fire (IF) type neuronal models. These strategies can lead to computationally efficient algorithms for simulating large-scale networks of neurons; most important, such approaches are more precise than traditional clock-driven numerical integration approaches because the timing of spikes is treated exactly. The drawback of such event-driven methods is that in order to be efficient, the membrane equations must be solvable analytically, or at least provide simple analytic approximations for the state variables describing the system. This requirement prevents, in general, the use of conductance-based synaptic interactions within the framework of event-driven simulations and, thus, the investigation of network paradigms where synaptic conductances are important. We propose here a number of extensions of the classical leaky IF neuron model involving approximations of the membrane equation with conductance-based synaptic current, which lead to simple analytic expressions for the membrane state, and therefore can be used in the event-driven framework. These conductance-based IF (gIF) models are compared to commonly used models, such as the leaky IF model or biophysical models in which conductances are explicitly integrated. All models are compared with respect to various spiking response properties in the presence of synaptic activity, such as the spontaneous discharge statistics, the temporal precision in resolving synaptic inputs, and gain modulation under in vivo-like synaptic bombardment. Being based on the passive membrane equation with fixed-threshold spike generation, the proposed gIF models are situated in between leaky IF and biophysical models but are much closer to the latter with respect to their dynamic behavior and response characteristics, while still being nearly as computationally efficient as simple IF neuron models. gIF models should therefore provide a useful tool for efficient and precise simulation of large-scale neuronal networks with realistic, conductance-based synaptic interactions.

Dendritic amplification of inhibitory postsynaptic potentials in a model Purkinje cell

In neurons with large dendritic arbors, the postsynaptic potentials interact in a complex manner with active and passive membrane properties, causing not easily predictable transformations during the propagation from synapse to soma. Previous theoretical and experimental studies in both cerebellar Purkinje cells and neocortical pyramidal neurons have shown that voltage-dependent ion channels change the amplitude and time-course of postsynaptic potentials. We investigated the mechanisms involved in the propagation of inhibitory postsynaptic potentials (IPSPs) along active dendrites in a model of the Purkinje cell. The amplitude and time-course of IPSPs recorded at the soma were dependent on the synaptic distance from the soma, as predicted by passive cable theory. We show that the effect of distance on the amplitude and width of the IPSP was significantly reduced by the dendritic ion channels, whereas the rise time was not affected. Somatic IPSPs evoked by the activation of the most distal synapses were up to six times amplified owing to the presence of voltage-gated channels and the IPSP width became independent of the covered distance. A transient deactivation of the Ca(2+) channels and the Ca(2+)-dependent K(+) channels, triggered by the hyperpolarization following activation of the inhibitory synapse, was found to be responsible for these dynamics. Nevertheless, the position of activated synapses had a marked effect on the Purkinje cell firing pattern, making stellate cells and basket cells most suitable for controlling the firing rate and spike timing, respectively, of their target Purkinje cells.

Assessing Neuronal Coherence with Single-Unit, Multi-Unit, and Local Field Potentials

The purpose of this study was to obtain a better understanding of neuronal responses to correlated input, in particular focusing on the aspect of synchronization of neuronal activity. The first aim was to obtain an analytical expression for the coherence between the output spike train and correlated input and for the coherence between output spike trains of neurons with correlated input. For Poisson neurons, we could derive that the peak of the coherence between the correlated input and multi-unit activity increases proportionally with the square root of the number of neurons in the multi-unit recording. The coherence between two typical multi-unit recordings (2 to 10 single units) with partially correlated input increases proportionally with the number of units in the multi-unit recordings. The second aim of this study was to investigate to what extent the amplitude and signal-to-noise ratio of the coherence between input and output varied for single-unit versus multi-unit activity and how they are affected by the duration of the recording. The same problem was addressed for the coherence between two single-unit spike series and between two multi-unit spike series. The analytical results for the Poisson neuron and numerical simulations for the conductance-based leaky integrate-and-fire neuron and for the conductance-based Hodgkin-Huxley neuron show that the expectation value of the coherence function does not increase for a longer duration of the recording. The only effect of a longer duration of the spike recording is a reduction of the noise in the coherence function. The results of analytical derivations and computer simulations for model neurons show that the coherence for multi-unit activity is larger than that for single-unit activity. This is in agreement with the results of experimental data obtained from monkey visual cortex (V4). Finally, we show that multitaper techniques greatly contribute to a more accurate estimate of the coherence by reducing the bias and variance in the coherence estimate.

A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input

The integrate-and-fire neuron model is one of the most widely used models for analyzing the behavior of neural systems. It describes the membrane potential of a neuron in terms of the synaptic inputs and the injected current that it receives. An action potential (spike) is generated when the membrane potential reaches a threshold, but the actual changes associated with the membrane voltage and conductances driving the action potential do not form part of the model. The synaptic inputs to the neuron are considered to be stochastic and are described as a temporally homogeneous Poisson process. Methods and results for both current synapses and conductance synapses are examined in the diffusion approximation, where the individual contributions to the postsynaptic potential are small. The focus of this review is upon the mathematical techniques that give the time distribution of output spikes, namely stochastic differential equations and the Fokker-Planck equation. The integrate-and-fire neuron model has become established as a canonical model for the description of spiking neurons because it is capable of being analyzed mathematically while at the same time being sufficiently complex to capture many of the essential features of neural processing. A number of variations of the model are discussed, together with the relationship with the Hodgkin-Huxley neuron model and the comparison with electrophysiological data. A brief overview is given of two issues in neural information processing that the integrate-and-fire neuron model has contributed to - the irregular nature of spiking in cortical neurons and neural gain modulation.

Synaptic input statistics tune the variability and reproducibility of neuronal responses

Synaptic waveforms, constructed from excitatory and inhibitory presynaptic Poisson trains, are presented to living and computational neurons. We review how the average output of a neuron (e.g., the firing rate) is set by the difference between excitatory and inhibitory event rates while neuronal variability is set by their sum. We distinguish neuronal variability from reproducibility. Variability quantifies how much an output measure is expected to vary; for example, the interspike interval coefficient of variation quantifies the typical range of interspike intervals. Reproducibility quantifies the similarity of neuronal outputs in response to repeated presentations of identical stimuli. Although variability and reproducibility are conceptually distinct, we show that, for ideal current source synapses, reproducibility is defined entirely by variability. For physiologically realistic conductance-based synapses, however, reproducibility is distinct from variability and average output, set by the Poisson rate and the degree of synchrony within the synaptic waveform.

Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise

Neurons in the central nervous system, and in the cortex in particular, are subject to a barrage of pulses from their presynaptic populations. These synaptic pulses are mediated by conductance changes and therefore lead to increases or decreases of the neuronal membrane potential with amplitudes that are dependent on the voltage: synaptic noise is multiplicative. The statistics of the membrane potential are of experimental interest because the measurement of a single subthreshold voltage can be used to probe the activity occurring across the presynaptic population. Though the interpulse interval is not always significantly smaller than the characteristic decay time of the pulses, and so the fluctuations have the nature of shot noise, the majority of results available in the literature have been calculated in the diffusion limit, which is valid for high-rate pulses. Here the effects that multiplicative conductance noise and shot noise have on the voltage fluctuations are examined. It is shown that both these aspects of synaptic drive sculpt high-order features of the subthreshold voltage distribution, such as the skew. It is further shown that the diffusion approximation can only capture the effects arising from the multiplicative conductance noise, predicting a negative voltage skew for excitatory drive. Exact results for the full dynamics are derived from a master-equation approach, predicting positively skewed distributions with long tails in voltage ranges typical for action potential generation. It is argued that, although the skew is a high-order feature of subthreshold voltage distributions, the increased probability of reaching firing threshold suggests a potential role for shot noise in shaping the neuronal transfer function.

Multisynaptic activity in a pyramidal neuron model and neural code

The highly irregular firing of mammalian cortical pyramidal neurons is one of the most striking observation of the brain activity. This result affects greatly the discussion on the neural code, i.e. how the brain codes information transmitted along the different cortical stages. In fact it seems to be in favor of one of the two main hypotheses about this issue, named the rate code. But the supporters of the contrasting hypothesis, the temporal code, consider this evidence inconclusive. We discuss here a leaky integrate-and-fire model of a hippocampal pyramidal neuron intended to be biologically sound to investigate the genesis of the irregular pyramidal firing and to give useful information about the coding problem. To this aim, the complete set of excitatory and inhibitory synapses impinging on such a neuron has been taken into account. The firing activity of the neuron model has been studied by computer simulation both in basic conditions and allowing brief periods of over-stimulation in specific regions of its synaptic constellation. Our results show neuronal firing conditions similar to those observed in experimental investigations on pyramidal cortical neurons. In particular, the variation coefficient (CV) computed from the inter-spike intervals (ISIs) in our simulations for basic conditions is close to the unity as that computed from experimental data. Our simulation shows also different behaviors in firing sequences for different frequencies of stimulation.

Signal propagation and logic gating in networks of integrate-and-fire neurons

Transmission of signals within the brain is essential for cognitive function, but it is not clear how neural circuits support reliable and accurate signal propagation over a sufficiently large dynamic range. Two modes of propagation have been studied: synfire chains, in which synchronous activity travels through feedforward layers of a neuronal network, and the propagation of fluctuations in firing rate across these layers. In both cases, a sufficient amount of noise, which was added to previous models from an external source, had to be included to support stable propagation. Sparse, randomly connected networks of spiking model neurons can generate chaotic patterns of activity. We investigate whether this activity, which is a more realistic noise source, is sufficient to allow for signal transmission. We find that, for rate-coded signals but not for synfire chains, such networks support robust and accurate signal reproduction through up to six layers if appropriate adjustments are made in synaptic strengths. We investigate the factors affecting transmission and show that multiple signals can propagate simultaneously along different pathways. Using this feature, we show how different types of logic gates can arise within the architecture of the random network through the strengthening of specific synapses.

Simultaneous rate-synchrony codes in populations of spiking neurons

Firing rates and synchronous firing are often simultaneously relevant signals, and they independently or cooperatively represent external sensory inputs, cognitive events, and environmental situations such as body position. However, how rates and synchrony comodulate and which aspects of inputs are effectively encoded, particularly in the presence of dynamical inputs, are unanswered questions. We examine theoretically how mixed information in dynamic mean input and noise input is represented by dynamic population firing rates and synchrony. In a subthreshold regime, amplitudes of spatially uncorrelated noise are encoded up to a fairly high input frequency, but this requires both rate and synchrony output channels. In a suprathreshold regime, means and common noise amplitudes can be simultaneously and separately encoded by rates and synchrony, respectively, but the input frequency for which this is possible has a lower limit.

Short-term synaptic depression causes a non-monotonic response to correlated stimuli

Unreliability is a ubiquitous feature of synaptic transmission in the brain. The information conveyed in the discharges of an ensemble of cells (e.g., in the spike count or in the timing of synchronous events) may not be faithfully transmitted to the postsynaptic cell because a large fraction of the spikes fail to elicit a synaptic response. In addition, short-term depression increases the failure rate with the presynaptic activity. We use a simple neuron model with stochastic depressing synapses to understand the transformations undergone by the spatiotemporal patterns of incoming spikes as these are first converted into synaptic current and afterward into the cell response. We analyze the mean and SD of the current produced by different stimuli with spatiotemporal correlations. We find that the mean, which carries information only about the spike count, rapidly saturates as the input rate increases. In contrast, the current deviation carries information about the correlations. If the afferent action potentials are uncorrelated, it saturates monotonically, whereas if they are correlated it increases, reaches a maximum, and then decreases to the value produced by the uncorrelated stimulus. This means that, at high input rates, depression erases from the synaptic current any trace of the spatiotemporal structure of the input. The non-monotonic behavior of the deviation can be inherited by the response rate provided that the mean current saturates below the current threshold setting the cell in the fluctuation-driven regimen. Afferent correlations therefore enable the modulation of the response beyond the saturation of the mean current.

The Effect of NMDA Receptors on Gain Modulation

The ability of individual neurons to modulate the gain of their input-output function is important for information processing in the brain. In a recent study (Mitchell & Silver, 2003), shunting inhibition was found to modulate the gain of cerebellar granule cells subjected to simulated currents through AMPA receptor synapses. Here we investigate the effect on gain modulation resulting from adding the currents mediated by NMDA receptors to a compartmental model of the granule cell. With only AMPA receptors, the changes in gain induced by shunting inhibition decreased gradually with the average firing rate of the afferent mossy fibers. With NMDA receptors present, this decrease was more rapid, therefore narrowing the bandwidth of mossy fiber firing rates available for gain modulation. The deterioration of gain modulation was accompanied by a reduced variability of the input current and saturation of NMDA receptors. However, when the output of the granule cell was plotted as a function of the average input current instead of the input firing frequency, both models showed very similar response curves and comparable gain modulation. We conclude that NMDA receptors do not directly impair gain control by shunting inhibition, but the effective bandwidth decreases as a consequence of the increased total charge transfer.

Stimulus Competition by Inhibitory Interference

When two stimuli are present in the receptive field of a V4 neuron, the firing rate response is between the weakest and strongest response elicited by each of the stimuli when presented alone (Reynolds, Chelazzi, & Desimone, 1999). When attention is directed toward the stimulus eliciting the strongest response (the preferred stimulus), the response to the pair is increased, whereas the response decreases when attention is directed to the other stimulus (the poor stimulus). When attention is directed to either of the two stimuli presented alone, the firing rate remains the same or increases slightly, but the coherence between the neuron's spike train and the local field potential can increase (Fries, Reynolds, Rorie, & Desimone, 2001). These experimental results were reproduced in a model of a V4 neuron under the assumption that attention modulates the activity of local interneuron networks. The V4 model neuron received stimulus-specific excitation from V2 and synchronous inhibitory inputs from two local interneuron networks in V4. Each interneuron network was driven by stimulus-specific excitatory inputs from V2 and was modulated by the activity of the frontal eye fields. Stimulus competition was present because of a delay in arrival time of synchronous volleys from each interneuron network. For small delays, the firing rate was close to the rate elicited by the preferred stimulus alone, whereas for larger delays, it approached the firing rate of the poor stimulus. When either stimulus was presented alone, the neuron's response was not altered by the change in delay, but could change due to modulation of the degree of synchrony of the corresponding interneuron network. The model suggests that top-down attention biases the competition between V2 columns for control of V4 neurons primarily by changing the relative timing of inhibition, whereas changes in the degree of synchrony of interneuron networks modulate the response to a single stimulus. The new mechanism proposed here for attentional modulation of firing rate, gain modulation by inhibitory interference, is likely to have more general applicability to cortical information processing.

Coding of temporally varying signals in networks of spiking neurons with global delayed feedback

Oscillatory and synchronized neural activities are commonly found in the brain, and evidence suggests that many of them are caused by global feedback. Their mechanisms and roles in information processing have been discussed often using purely feedforward networks or recurrent networks with constant inputs. On the other hand, real recurrent neural networks are abundant and continually receive information-rich inputs from the outside environment or other parts of the brain. We examine how feedforward networks of spiking neurons with delayed global feedback process information about temporally changing inputs. We show that the network behavior is more synchronous as well as more correlated with and phase-locked to the stimulus when the stimulus frequency is resonant with the inherent frequency of the neuron or that of the network oscillation generated by the feedback architecture. The two eigenmodes have distinct dynamical characteristics, which are supported by numerical simulations and by analytical arguments based on frequency response and bifurcation theory. This distinction is similar to the class I versus class II classification of single neurons according to the bifurcation from quiescence to periodic firing, and the two modes depend differently on system parameters. These two mechanisms may be associated with different types of information processing.

Advancing the boundaries of high-connectivity network simulation with distributed computing

The availability of efficient and reliable simulation tools is one of the mission-critical technologies in the fast-moving field of computational neuroscience. Research indicates that higher brain functions emerge from large and complex cortical networks and their interactions. The large number of elements (neurons) combined with the high connectivity (synapses) of the biological network and the specific type of interactions impose severe constraints on the explorable system size that previously have been hard to overcome. Here we present a collection of new techniques combined to a coherent simulation tool removing the fundamental obstacle in the computational study of biological neural networks: the enormous number of synaptic contacts per neuron. Distributing an individual simulation over multiple computers enables the investigation of networks orders of magnitude larger than previously possible. The software scales excellently on a wide range of tested hardware, so it can be used in an interactive and iterative fashion for the development of ideas, and results can be produced quickly even for very large networks. In contrast to earlier approaches, a wide class of neuron models and synaptic dynamics can be represented.

Factors determining the precision of the correlated firing generated by a monosynaptic connection in the cat visual pathway

Across the visual pathway, strong monosynaptic connections generate a precise correlated firing between presynaptic and postsynaptic neurons. The precision of this correlated firing is not the same within thalamus and visual cortex. While retinogeniculate connections generate a very narrow peak in the correlogram (peak width < 1 ms), the peaks generated by geniculocortical and corticocortical connections have usually a time course of several milliseconds. Several factors could explain these differences in timing precision such as the amplitude of the monosynaptic EPSP (excitatory postsynaptic potential), its time course or the contribution of polysynaptic inputs. While it is difficult to isolate the contribution of each factor in physiological experiments, a first approximation can be done in modelling studies. Here, we simulated two monosynaptically connected neurons to measure changes in their correlated firing as we independently modified different parameters of the connection. Our results suggest that the precision of the correlated firing generated by strong monosynaptic connections is mostly determined by the EPSP time course of the connection and much less by other factors. In addition, we show that a polysynaptic pathway is unlikely to emulate the correlated firing generated by a monosynaptic connection unless it generates EPSPs with very small latency jitter.

Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductance-based synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Time-dependent activation of feed-forward inhibition in a looming-sensitive neuron

The lobula giant movement detector (LGMD) is an identified neuron in the locust visual system that responds preferentially to objects approaching on a collision course with the animal. For such looming stimuli, the LGMD firing rate gradually increases, peaks, and decays toward the end of approach. The LGMD receives both excitatory and feed-forward inhibitory inputs on distinct branches of its dendritic tree, but little is known about the contribution of feed-forward inhibition to its response properties. We used picrotoxin, a chloride channel blocker, to selectively block feed-forward inhibition to the LGMD. We then computed differences in firing rate and membrane potential between control and picrotoxin conditions to study the activation of feed-forward inhibition. For looming stimuli, a significant activation of inhibition was observed early, as objects exceeded on average approximately 23 degrees in angular extent at the retina. Inhibition then increased in parallel with excitation over the remainder of approach trials. Experiments in which the final angular size of the approaching objects was systematically varied revealed that the relative activation of excitation and inhibition remains well balanced over most of the course of looming trials. Feed-forward inhibition actively contributed to the termination of the response to approaching objects and was particularly effective for large or slowly moving objects. Suddenly appearing and receding objects activated excitation and feed-forward inhibition nearly simultaneously, in contrast to looming stimuli. Under these conditions, the activation of excitation and feed-forward inhibition was weaker than for approaching objects, suggesting that both are preferentially tuned to approaching objects. These results support a phenomenological model of multiplication within the LGMD and provide new constraints for biophysical models of its responses to looming and receding stimuli.

Controlling synaptic input patterns in vitro by dynamic photo stimulation

Recent experimental and theoretical work indicates that both the intensity and the temporal structure of synaptic activity strongly modulate the integrative properties of single neurons in the intact brain. However, studying these effects experimentally is complicated by the fact that, in experimental systems, network activity is either absent, as in the acute slice preparation, or difficult to monitor and to control, as in in vivo recordings. Here, we present a new implementation of neurotransmitter uncaging in acute brain slices that uses functional projections to generate tightly controlled, spatio-temporally structured synaptic input patterns in individual neurons. For that, a set of presynaptic neurons is activated in a precisely timed sequence through focal photolytic release of caged glutamate with the help of a fast laser scanning system. Integration of synaptic inputs can be studied in postsynaptic neurons that are not directly stimulated with the laser, but receive input from the targeted neurons through intact axonal projections. Our new approach of dynamic photo stimulation employs functional synapses, accounts for their spatial distribution on the dendrites, and thus allows study of the integrative properties of single neurons with physiologically realistic input. Data obtained with our new technique suggest that, not only the neuronal spike generator, but also synaptic transmission and dendritic integration in neocortical pyramidal cells, can be highly reliable.