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

The Roles of Potassium and Calcium Currents in the Bistable Firing Transition

Healthy brains display a wide range of firing patterns, from synchronized oscillations during slow-wave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking (RS) cells with frequency adaptation and do not exhibit bursts in current-clamp experiments (in vitro). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings (gsyn) and external current inputs (I). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to the bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold (IL) and low-threshold (IT) ion channels play a role in increasing and decreasing the parameter conditions (gsyn and I) in which bistable dynamics occur, respectively. For high values of IL conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance IT increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.

The Role of Potassium and Calcium Currents in the Bistable Firing Transition

Healthy brains display a wide range of firing patterns, from synchronized oscillations during slowwave sleep to desynchronized firing during movement. These physiological activities coexist with periods of pathological hyperactivity in the epileptic brain, where neurons can fire in synchronized bursts. Most cortical neurons are pyramidal regular spiking cells (RS) with frequency adaptation and do not exhibit bursts in current-clamp experiments ( in vitro ). In this work, we investigate the transition mechanism of spike-to-burst patterns due to slow potassium and calcium currents, considering a conductance-based model of a cortical RS cell. The joint influence of potassium and calcium ion channels on high synchronous patterns is investigated for different synaptic couplings ( g syn ) and external current inputs ( I ). Our results suggest that slow potassium currents play an important role in the emergence of high-synchronous activities, as well as in the spike-to-burst firing pattern transitions. This transition is related to bistable dynamics of the neuronal network, where physiological asynchronous states coexist with pathological burst synchronization. The hysteresis curve of the coefficient of variation of the inter-spike interval demonstrates that a burst can be initiated by firing states with neuronal synchronization. Furthermore, we notice that high-threshold ( I L ) and low-threshold ( I T ) ion channels play a role in increasing and decreasing the parameter conditions ( g syn and I ) in which bistable dynamics occur, respectively. For high values of I L conductance, a synchronous burst appears when neurons are weakly coupled and receive more external input. On the other hand, when the conductance I T increases, higher coupling and lower I are necessary to produce burst synchronization. In light of our results, we suggest that channel subtype-specific pharmacological interactions can be useful to induce transitions from pathological high bursting states to healthy states.

Large coefficient of variation of inter-spike intervals induced by noise current in the resonate-and-fire model neuron

Neuronal spike variability is a statistical property associated with the noise environment. Considering a linearised Hodgkin-Huxley model, we investigate how large spike variability can be induced in a typical stellate cell when submitted to constant and noise current amplitudes. For low noise current, we observe only periodic firing (active) or silence activities. For intermediate noise values, in addition to only active or inactive periods, we also identify a single transition from an initial spike-train (active) to silence dynamics over time, where the spike variability is low. However, for high noise current, we find intermittent active and silence periods with different values. The spike intervals during active and silent states follow the exponential distribution, which is similar to the Poisson process. For non-maximal noise current, we observe the highest values of inter-spike variability. Our results suggest sub-threshold oscillations as a possible mechanism for the appearance of high spike variability in a single neuron due to noise currents.

Disruptive effects of repeated stress on basolateral amygdala neurons and fear behavior across the estrous cycle in rats

Stress is a precipitating factor in depression and anxiety disorders. Patients with these disorders often show amygdala abnormalities. The basolateral amygdala (BLA) is integral in mood and emotion, and is sensitive to stress. While much is known about effects of stress on BLA neuron activity and morphology in males, less is known in females. We tested whether repeated stress exerts distinct effects on BLA in vivo neuronal activity and morphology of Golgi-stained BLA neurons [lateral (LAT) and basal (BA) nuclei] in adult female rats. Repeated restraint stress increased BLA neuronal firing and caused hypertrophy of BLA neurons in males, while it decreased LAT and BA neuronal firing and caused hypotrophy of neurons in the LAT of females. BLA neuronal activity and function, such as fear conditioning, shifts across the estrous cycle. Repeated stress disrupted this pattern of BLA activity and fear expression over the estrous cycle. The disruptive effects of stress on the pattern of BLA function across estrous may produce behavior that is non-optimal for a specific phase of the estrous cycle. The contrasting effects of stress may contribute to sex differences in the effects of stress on mood and psychiatric disorders.

Adult mouse sensory neurons on microelectrode arrays exhibit increased spontaneous and stimulus-evoked activity in the presence of interleukin-6

Following inflammation or injury, sensory neurons located in the dorsal root ganglia (DRG) may exhibit increased spontaneous and/or stimulus-evoked activity, contributing to chronic pain. Current treatment options for peripherally mediated chronic pain are highly limited, driving the development of cell- or tissue-based phenotypic (function-based) screening assays for peripheral analgesic and mechanistic lead discovery. Extant assays are often limited by throughput, content, use of tumorigenic cell lines, or tissue sources from immature developmental stages (i.e., embryonic or postnatal). Here, we describe a protocol for culturing adult mouse DRG neurons on substrate-integrated multiwell microelectrode arrays (MEAs). This approach enables multiplexed measurements of spontaneous as well as stimulus-evoked extracellular action potentials from large populations of cells. The DRG cultures exhibit stable spontaneous activity from 9 to 21 days in vitro. Activity is readily evoked by known chemical and physical agonists of sensory neuron activity such as capsaicin, bradykinin, PGE₂, heat, and electrical field stimulation. Most importantly, we demonstrate that both spontaneous and stimulus-evoked activity may be potentiated by incubation with the inflammatory cytokine interleukin-6 (IL-6). Acute responsiveness to IL-6 is inhibited by treatment with a MAPK-interacting kinase 1/2 inhibitor, cercosporamide. In total, these findings suggest that adult mouse DRG neurons on multiwell MEAs are applicable to ongoing efforts to discover peripheral analgesic and their mechanisms of action. NEW & NOTEWORTHY This work describes methodologies for culturing spontaneously active adult mouse dorsal root ganglia (DRG) sensory neurons on microelectrode arrays. We characterize spontaneous and stimulus-evoked adult DRG activity over durations consistent with pharmacological interventions. Furthermore, persistent hyperexcitability could be induced by incubation with inflammatory cytokine IL-6 and attenuated with cercosporamide, an inhibitor of the IL-6 sensitization pathway. This constitutes a more physiologically relevant, moderate-throughput in vitro model for peripheral analgesic screening as well as mechanistic lead discovery.

Propagation of Collective Temporal Regularity in Noisy Hierarchical Networks

Neuronal communication between different brain areas is achieved in terms of spikes. Consequently, spike-time regularity is closely related to many cognitive tasks and timing precision of neural information processing. A recent experiment on primate parietal cortex reports that spike-time regularity increases consistently from primary sensory to higher cortical regions. This observation conflicts with the influential view that spikes in the neocortex are fundamentally irregular. To uncover the underlying network mechanism, we construct a multilayered feedforward neural information transmission pathway and investigate how spike-time regularity evolves across subsequent layers. Numerical results reveal that despite the obviously irregular spiking patterns in previous several layers, neurons in downstream layers can generate rather regular spikes, which depends on the network topology. In particular, we find that collective temporal regularity in deeper layers exhibits resonance-like behavior with respect to both synaptic connection probability and synaptic weight, i.e., the optimal topology parameter maximizes the spike-timing regularity. Furthermore, it is demonstrated that synaptic properties, including inhibition, synaptic transient dynamics, and plasticity, have significant impacts on spike-timing regularity propagation. The emergence of the increasingly regular spiking (RS) patterns in higher parietal regions can, thus, be viewed as a natural consequence of spiking activity propagation between different brain areas. Finally, we validate an important function served by increased RS: promoting reliable propagation of spike-rate signals across downstream layers.

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.

A neuron is a tiny computer that transforms electrical inputs into electrical outputs. While neurons have been investigated and modeled for many decades, some aspects remain elusive. Recently, it was demonstrated that the membrane (voltage) state of a neuron determines its threshold to spiking. In the present study we asked, what are the consequences of this dependence for the computation the neuron performs. We find that this so called adaptive threshold allows neurons to be more focused on inputs which arrive close in time with other inputs. Also, it allows neurons to represent their information more robustly, such that a readout of their activity is less influenced by the state the brain is in. The present use of information theory provides a solid foundation for these results. We obtained the results primarily in detailed simulations, but performed neural recordings to verify these properties in real neurons. In summary, an adaptive spiking threshold allows neurons to specifically compute robustly with a focus on tight temporal correlations in their input.

Colored noise and memory effects on formal spiking neuron models

Simplified neuronal models capture the essence of the electrical activity of a generic neuron, besides being more interesting from the computational point of view when compared to higher-dimensional models such as the Hodgkin-Huxley one. In this work, we propose a generalized resonate-and-fire model described by a generalized Langevin equation that takes into account memory effects and colored noise. We perform a comprehensive numerical analysis to study the dynamics and the point process statistics of the proposed model, highlighting interesting new features such as (i) nonmonotonic behavior (emergence of peak structures, enhanced by the choice of colored noise characteristic time scale) of the coefficient of variation (CV) as a function of memory characteristic time scale, (ii) colored noise-induced shift in the CV, and (iii) emergence and suppression of multimodality in the interspike interval (ISI) distribution due to memory-induced subthreshold oscillations. Moreover, in the noise-induced spike regime, we study how memory and colored noise affect the coherence resonance (CR) phenomenon. We found that for sufficiently long memory, not only is CR suppressed but also the minimum of the CV-versus-noise intensity curve that characterizes the presence of CR may be replaced by a maximum. The aforementioned features allow to interpret the interplay between memory and colored noise as an effective control mechanism to neuronal variability. Since both variability and nontrivial temporal patterns in the ISI distribution are ubiquitous in biological cells, we hope the present model can be useful in modeling real aspects of neurons.

On how correlations between excitatory and inhibitory synaptic inputs maximize the information rate of neuronal firing

Cortical neurons receive barrages of excitatory and inhibitory inputs which are not independent, as network structure and synaptic kinetics impose statistical correlations. Experiments in vitro and in vivo have demonstrated correlations between inhibitory and excitatory synaptic inputs in which inhibition lags behind excitation in cortical neurons. This delay arises in feed-forward inhibition (FFI) circuits and ensures that coincident excitation and inhibition do not preclude neuronal firing. Conversely, inhibition that is too delayed broadens neuronal integration times, thereby diminishing spike-time precision and increasing the firing frequency. This led us to hypothesize that the correlation between excitatory and inhibitory synaptic inputs modulates the encoding of information of neural spike trains. We tested this hypothesis by investigating the effect of such correlations on the information rate (IR) of spike trains using the Hodgkin-Huxley model in which both synaptic and membrane conductances are stochastic. We investigated two different synaptic input regimes: balanced synaptic conductances and balanced currents. Our results show that correlations arising from the synaptic kinetics, τ, and millisecond lags, δ, of inhibition relative to excitation strongly affect the IR of spike trains. In the regime of balanced synaptic currents, for short time lags (δ ~ 1 ms) there is an optimal τ that maximizes the IR of the postsynaptic spike train. Given the short time scales for monosynaptic inhibitory lags and synaptic decay kinetics reported in cortical neurons under physiological contexts, we propose that FFI in cortical circuits is poised to maximize the rate of information transfer between cortical neurons. Our results also provide a possible explanation for how certain drugs and genetic mutations affecting the synaptic kinetics can deteriorate information processing in the brain.

Impact of correlated inputs to neurons: modeling observations from in vivo intracellular recordings

In vivo recordings in rat somatosensory cortex suggest that excitatory and inhibitory inputs are often correlated during spontaneous and sensory-evoked activity. Using a computational approach, we study how the interplay of input correlations and timing observed in experiments controls the spiking probability of single neurons. Several correlation-based mechanisms are identified, which can effectively switch a neuron on and off. In addition, we investigate the transfer of input correlation to output correlation in pairs of neurons, at the spike train and the membrane potential levels, by considering spike-driving and non-spike-driving inputs separately. In particular, we propose a plausible explanation for the in vivo finding that membrane potentials in neighboring neurons are correlated, but the spike-triggered averages of membrane potentials preceding a spike are not: Neighboring neurons possibly receive an ongoing bombardment of correlated subthreshold background inputs, and occasionally uncorrelated spike-driving inputs.

Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel

A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen-Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV(t))((ISI)) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.

Response of Integrate-and-Fire Neurons to Noisy Inputs Filtered by Synapses with Arbitrary Timescales: Firing Rate and Correlations

Delivery of neurotransmitter produces on a synapse a current that flows through the membrane and gets transmitted into the soma of the neuron, where it is integrated. The decay time of the current depends on the synaptic receptor's type and ranges from a few (e.g., AMPA receptors) to a few hundred milliseconds (e.g., NMDA receptors). The role of the variety of synaptic timescales, several of them coexisting in the same neuron, is at present not understood. A prime question to answer is which is the effect of temporal filtering at different timescales of the incoming spike trains on the neuron's response. Here, based on our previous work on linear synaptic filtering, we build a general theory for the stationary firing response of integrate-and-fire (IF) neurons receiving stochastic inputs filtered by one, two, or multiple synaptic channels, each characterized by an arbitrary timescale. The formalism applies to arbitrary IF model neurons and arbitrary forms of input noise (i.e., not required to be gaussian or to have small amplitude), as well as to any form of synaptic filtering (linear or nonlinear). The theory determines with exact analytical expressions the firing rate of an IF neuron for long synaptic time constants using the adiabatic approach. The correlated spiking (cross-correlations function) of two neurons receiving common as well as independent sources of noise is also described. The theory is illustrated using leaky, quadratic, and noise-thresholded IF neurons. Although the adiabatic approach is exact when at least one of the synaptic timescales is long, it provides a good prediction of the firing rate even when the timescales of the synapses are comparable to that of the leak of the neuron; it is not required that the synaptic time constants are longer than the mean interspike intervals or that the noise has small variance. The distribution of the potential for general IF neurons is also characterized. Our results provide powerful analytical tools that can allow a quantitative description of the dynamics of neuronal networks with realistic synaptic dynamics.

Effects of synaptic synchrony on the neuronal input-output relationship

The firing rate of individual neurons depends on the firing frequency of their distributed synaptic inputs, with linear and nonlinear relations subserving different computational functions. This letter explores the relationship between the degree of synchrony among excitatory synapses and the linearity of the response using detailed compartmental models of cortical pyramidal cells. Synchronous input resulted in a linear input-output relationship, while asynchronous stimulation yielded sub- and supraproportional outputs at low and high frequencies, respectively. The dependence of input-output linearity on synchrony was sigmoidal and considerably robust with respect to dendritic location, stimulus irregularity, and alteration of active and synaptic properties. Moreover, synchrony affected firing rate differently at lower and higher input frequencies. A reduced integrate-and-fire model suggested a mechanism explaining these results based on spatiotemporal integration, with fundamental implications relating synchrony to memory encoding.

A first-order nonhomogeneous Markov model for the response of spiking neurons stimulated by small phase-continuous signals

We present a first-order nonhomogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval density to be expressed as products of two separate functions, one of which describes only the neuron characteristics and the other of which describes only the signal characteristics. The approximation shows particularly clearly that signal autocorrelations and cross-correlations arise as natural features of the interspike-interval density and are particularly clear for small signals and moderate noise. We show that this model simplifies the design of spiking neuron cross-correlation systems and describe a four-neuron mutual inhibition network that generates a cross-correlation output for two input signals.

Relating neuronal firing patterns to functional differentiation of cerebral cortex

It has been empirically established that the cerebral cortical areas defined by Brodmann one hundred years ago solely on the basis of cellular organization are closely correlated to their function, such as sensation, association, and motion. Cytoarchitectonically distinct cortical areas have different densities and types of neurons. Thus, signaling patterns may also vary among cytoarchitectonically unique cortical areas. To examine how neuronal signaling patterns are related to innate cortical functions, we detected intrinsic features of cortical firing by devising a metric that efficiently isolates non-Poisson irregular characteristics, independent of spike rate fluctuations that are caused extrinsically by ever-changing behavioral conditions. Using the new metric, we analyzed spike trains from over 1,000 neurons in 15 cortical areas sampled by eight independent neurophysiological laboratories. Analysis of firing-pattern dissimilarities across cortical areas revealed a gradient of firing regularity that corresponded closely to the functional category of the cortical area; neuronal spiking patterns are regular in motor areas, random in the visual areas, and bursty in the prefrontal area. Thus, signaling patterns may play an important role in function-specific cerebral cortical computation.

Neurons, or nerve cells in the brain, communicate with each other using stereotyped electric pulses, called spikes. It is believed that neurons convey information mainly through the frequency of the transmitted spikes, called the firing rate. In addition, neurons may communicate some information through the finer temporal patterns of the spikes. Neuronal firing patterns may depend on cellular organization, which varies among the regions of the brain, according to the roles they play, such as sensation, association, and motion. In order to examine the relationship among signals, structure, and function, we devised a metric to detect firing irregularity intrinsic and specific to individual neurons and analyzed spike sequences from over 1,000 neurons in 15 different cortical areas. Here we report two results of this study. First, we found that neurons exhibit stable firing patterns that can be characterized as “regular”, “random”, and “bursty”. Second, we observed a strong correlation between the type of signaling pattern exhibited by neurons in a given area and the function of that area. This suggests that, in addition to reflecting the cellular organization of the brain, neuronal signaling patterns may also play a role in specific types of neuronal computations.

The response of cortical neurons to in vivo-like input current: theory and experiment : I. Noisy inputs with stationary statistics

The study of several aspects of the collective dynamics of interacting neurons can be highly simplified if one assumes that the statistics of the synaptic input is the same for a large population of similarly behaving neurons (mean field approach). In particular, under such an assumption, it is possible to determine and study all the equilibrium points of the network dynamics when the neuronal response to noisy, in vivo-like, synaptic currents is known. The response function can be computed analytically for simple integrate-and-fire neuron models and it can be measured directly in experiments in vitro. Here we review theoretical and experimental results about the neural response to noisy inputs with stationary statistics. These response functions are important to characterize the collective neural dynamics that are proposed to be the neural substrate of working memory, decision making and other cognitive functions. Applications to the case of time-varying inputs are reviewed in a companion paper (Giugliano et al. in Biol Cybern, 2008). We conclude that modified integrate-and-fire neuron models are good enough to reproduce faithfully many of the relevant dynamical aspects of the neuronal response measured in experiments on real neurons in vitro.

Interspike interval statistics of a leaky integrate-and-fire neuron driven by Gaussian noise with large correlation times

We analytically investigate the interspike interval (ISI) density, the Fano factor, and the coefficient of variation of a leaky integrate-and-fire neuron model driven by exponentially correlated Gaussian noise with a large correlation time tau . We find a burstinglike behavior of the spike train, which is revealed by a dominant peak of the ISI density at small intraburst intervals and a slow power-law decay of long interburst intervals. The large, power-law distributed ISIs give rise to a coefficient of variation which diverges as square root [tau] . This leads to the paradoxical effect that ISI correlations, as expressed by the serial correlation coefficient, vanish for large correlation times. This is in contrast to findings of previous works on a simpler neuron model where the effect of noise correlations appeared in higher-order statistical measures.

Efficient evaluation of neuron populations receiving colored-noise current based on a refractory density method

The expected firing probability of a stochastic neuron is approximated by a function of the expected subthreshold membrane potential, for the case of colored noise. We propose this approximation in order to extend the recently proposed white noise model [A. V. Chizhov and L. J. Graham, Phys. Rev. E 75, 011924 (2007)] to the case of colored noise, applying a refractory density approach to conductance-based neurons. The uncoupled neurons of a single population receive a common input and are dispersed by the noise. Within the framework of the model the effect of noise is expressed by the so-called hazard function, which is the probability density for a single neuron to fire given the average membrane potential in the presence of a noise term. To derive the hazard function we solve the Kolmogorov-Fokker-Planck equation for a mean voltage-driven neuron fluctuating due to colored noisy current. We show that a sum of both a self-similar solution for the case of slow changing mean voltage and a frozen stationary solution for fast changing mean voltage gives a satisfactory approximation for the hazard function in the arbitrary case. We demonstrate the quantitative effect of a temporal correlation of noisy input on the neuron dynamics in the case of leaky integrate-and-fire and detailed conductance-based neurons in response to an injected current step.

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.

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.

Multiple time scales of temporal response in pyramidal and fast spiking cortical neurons

Neural dynamic processes correlated over several time scales are found in vivo, in stimulus-evoked as well as spontaneous activity, and are thought to affect the way sensory stimulation is processed. Despite their potential computational consequences, a systematic description of the presence of multiple time scales in single cortical neurons is lacking. In this study, we injected fast spiking and pyramidal (PYR) neurons in vitro with long-lasting episodes of step-like and noisy, in-vivo-like current. Several processes shaped the time course of the instantaneous spike frequency, which could be reduced to a small number (1-4) of phenomenological mechanisms, either reducing (adapting) or increasing (facilitating) the neuron's firing rate over time. The different adaptation/facilitation processes cover a wide range of time scales, ranging from initial adaptation (<10 ms, PYR neurons only), to fast adaptation (<300 ms), early facilitation (0.5-1 s, PYR only), and slow (or late) adaptation (order of seconds). These processes are characterized by broad distributions of their magnitudes and time constants across cells, showing that multiple time scales are at play in cortical neurons, even in response to stationary stimuli and in the presence of input fluctuations. These processes might be part of a cascade of processes responsible for the power-law behavior of adaptation observed in several preparations, and may have far-reaching computational consequences that have been recently described.

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.

Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model

After the report of Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350], leaky integrate-and-fire models have been investigated to explain high coefficient of variation (CV) of interspike intervals (ISIs) at high firing rates observed in the cortex. The purpose of this paper is to study the effect of the position of a lower boundary of membrane potential on the possible value of CV of ISIs based on the diffusional leaky integrate-and-fire models with and without reversal potentials. Our result shows that the irregularity of ISIs for the diffusional leaky integrate-and-fire neuron significantly changes by imposing a lower boundary of membrane potential, which suggests the importance of the position of the lower boundary as well as that of the firing threshold when we study the statistical properties of leaky integrate-and-fire neuron models. It is worth pointing out that the mean-CV plot of ISIs for the diffusional leaky integrate-and-fire neuron with reversal potentials shows a close similarity to the experimental result obtained in Softky and Koch [Softky, W.R., Koch, C., 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci. 13, 334-350].

Measurement of time-dependent changes in the irregularity of neural spiking

Irregularity of firing in spike trains has been associated with coding processes and information transfer or alternatively treated as noise. Previous studies of irregularity have mainly used the coefficient of variation (CV) of the interspike interval distribution. Proper estimation of CV requires a constant underlying firing rate, a condition that most experimental situations do not fulfill either within or across trials. Here we introduce a novel irregularity metric based on the ratio of adjacent intervals in the spike train. The new metric is not affected by firing rate and is very localized in time so that it can be used to examine the time course of irregularity relative to an alignment marker. We characterized properties of the new metric with simulated spike trains of known characteristics and then applied it to data recorded from 108 single neurons in the motor cortex of two monkeys during performance of a precision grip task. Fifty-six cells were antidromically identified as pyramidal tract neurons (PTNs). Sixty-one cells (30 PTNs) exhibited significant temporal modulation of their irregularity during task performance with the contralateral hand. The irregularity modulations generally differed in sign and latency from the modulations of firing rate. High irregularity tended to occur during the task phases requiring the most detailed control of movement, whereas neural firing became more regular during the steady hold phase. Such irregularity modulation could have important consequences for the response of downstream neurons and may provide insight into the nature of the cortical code.

Relation between single neuron and population spiking statistics and effects on network activity

To simplify theoretical analyses of neural networks, individual neurons are often modeled as Poisson processes. An implicit assumption is that even if the spiking activity of each neuron is non-Poissonian, the composite activity obtained by summing many spike trains limits to a Poisson process. Here, we show analytically and through simulations that this assumption is invalid. Moreover, we show with Fokker-Planck equations that the behavior of feedforward networks is reproduced accurately only if the tendency of neurons to fire periodically is incorporated by using colored noise whose autocorrelation has a negative component.

Auto- and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses

An analytical description of the response properties of simple but realistic neuron models in the presence of noise is still lacking. We determine completely up to the second order the firing statistics of a single and a pair of leaky integrate-and-fire neurons receiving some common slowly filtered white noise. In particular, the auto- and cross-correlation functions of the output spike trains of pairs of cells are obtained from an improvement of the adiabatic approximation introduced previously by Moreno-Bote and Parga [Phys. Rev. Lett. 92, 028102 (2004)10.1103/PhysRevLett.92.028102]. These two functions define the firing variability and firing synchronization between neurons, and are of much importance for understanding neuron communication.

Computational and in vitro studies of persistent activity: edging towards cellular and synaptic mechanisms of working memory

Persistent neural activity selective to features of an extinct stimulus has been identified as the neural correlate of working memory processes. The precise nature of the physiological substrate for this self-sustained activity is still unknown. In the last few years, this problem has gathered experimental together with computational neuroscientists in a quest to identify the cellular and network mechanisms involved. I introduce here the attractor theory framework within which current persistent activity computational models are built, and I then review the main physiological mechanisms that have been linked thereby to persistent activity and working memory. Open computational and physiological issues with these models are discussed, together with their potential experimental validation in current in vitro models of persistent activity.

Pooled spike trains of correlated presynaptic inputs as realizations of cluster point processes

The pooled spike trains of correlated presynaptic terminals acting synchronously upon a single neuron are realizations of cluster point processes: the notions of spikes synchronizing in bursts and of points bunching in clusters are conceptually identical. The primary processes constituent specifies the timing of the cluster series; subsidiary processes and poolings specify burst structure and tightness. This representation and the Poisson process representation of independent terminals complete the formal approach to pooled trains. The notion's usefulness was illustrated by expressing physiological questions in terms of those constituents, each possessing a clear biological embodiment; constituents provided the control variables in simulations using leaky integrate-and-fire postsynaptic neurons excited by multiple weak terminals. Regular or irregular primary processes and bursts series determined low or high postsynaptic dispersions. When convergent set synchrony increased, its postsynaptic consequences approached those of single powerful synapses; concomitantly, output spike trains approached periodic, quasiperiodic, or aperiodic behaviors. The sequence in which terminals fired within bursts affected the predictee and predictor roles of presynaptic and postsynaptic spikes; when inhibition was added, EPSP and IPSP delays and order were influential (summation was noncommutative). Outputs to different correlations were heterogeneous; heterogeneity was accentuated by conditioning by variables such as DC biases.

Modulation power and phase spectrum of natural sounds enhance neural encoding performed by single auditory neurons

We examined the neural encoding of synthetic and natural sounds by single neurons in the auditory system of male zebra finches by estimating the mutual information in the time-varying mean firing rate of the neuronal response. Using a novel parametric method for estimating mutual information with limited data, we tested the hypothesis that song and song-like synthetic sounds would be preferentially encoded relative to other complex, but non-song-like synthetic sounds. To test this hypothesis, we designed two synthetic stimuli: synthetic songs that matched the power of spectral-temporal modulations but lacked the modulation phase structure of zebra finch song and noise with uniform band-limited spectral-temporal modulations. By defining neural selectivity as relative mutual information, we found that the auditory system of songbirds showed selectivity for song-like sounds. This selectivity increased in a hierarchical manner along ascending processing stages in the auditory system. Midbrain neurons responded with highest information rates and efficiency to synthetic songs and thus were selective for the spectral-temporal modulations of song. Primary forebrain neurons showed increased information to zebra finch song and synthetic song equally over noise stimuli. Secondary forebrain neurons responded with the highest information to zebra finch song relative to other stimuli and thus were selective for its specific modulation phase relationships. We also assessed the relative contribution of three response properties to this selectivity: (1) spiking reliability, (2) rate distribution entropy, and (3) bandwidth. We found that rate distribution and bandwidth but not reliability were responsible for the higher average information rates found for song-like sounds.

The relationship between oscillatory activity and motor reaction time in the parkinsonian subthalamic nucleus

Averaging techniques have demonstrated that movement preparatory cues and movement itself are associated with marked reductions in the oscillatory synchrony of local neuronal populations in the area of the human parkinsonian subthalamic nucleus (STN), as indexed by 8-30 Hz local field potential (LFP) activity. In order to examine the detailed nature and strength of the relationship between reductions in oscillatory activity and movement we examined single-trial LFP activity recorded from the STN area of parkinsonian subjects engaged in a choice reaction task. In this task an initial warning cue was either fully predictive or non-predictive of the hand required to make a later motor response. This motor response was elicited by a second go cue to which data were aligned. We observed a significant linear relationship between the onset time of oscillation reduction after go cues and subsequent motor response time across single trials within subjects. Consistent with this observation we also found a positive correlation of power with response time following go cues. In addition, we observed shorter durations of suppression in fully predictive trials where selection of the response could precede go cue presentation. The results are consistent with the hypothesis that reductions in 8-30 Hz population synchrony in the STN area are related to the processing required for motor preparation, particularly response selection.

Control of neuronal discharge timing by afferent fiber number and the temporal pattern of afferent impulses

We employ computer simulations to explore the effect of different temporal patterns of afferent impulses on the evoked discharge of a model cerebellar Purkinje cell. We show that the frequency and temporal correlation of impulses across afferent fibers determines which of four regimes of discharge activity is evoked. In the uncorrelated, here Poissonian, case, (i) cell discharge is determined by the total stimulation rate and temporal patterns of discharge are the same for different combinations of afferent fiber number and mean impulse rate per fiber giving the same total stimulation. Alternatively, if temporal correlations are present in the stimulus, (ii) for stimulation frequencies of 4 to at least 64 Hz there is a narrow range of afferent fiber number for which every stimulus pulse (composed of a single impulse on each afferent fiber) evokes a single action potential. In this case cell discharge is frequency locked to the stimulus with a concomitant reduction in discharge variability. (iii) For lower fiber numbers and thus discharge frequencies lower than the locking frequency, the variability of cell discharge is typically independent of afferent impulse timing, whereas, (iv) at higher fiber numbers and thus higher discharge frequencies, the reverse is true. We conclude that in case (iii) the cell acts as an integrator and discharge is determined by the stimulation rate, whereas in case (iv) the cell acts as a coincidence detector and the timing of discharge is determined by the temporal pattern of afferent stimulation. We discuss our results in terms of their significance for neuronal activity at the network level and suggest that the reported effects of varying stimulus timing and afferent convergence can be expected to obtain also with other principal cell types within the central nervous system.

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

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

Spike-Timing-Dependent Plasticity: The Relationship to Rate-Based Learning for Models with Weight Dynamics Determined by a Stable Fixed Point

Experimental evidence indicates that synaptic modification depends on the timing relationship between the presynaptic inputs and the output spikes that they generate. In this letter, results are presented for models of spike-timing-dependent plasticity (STDP) whose weight dynamics is determined by a stable fixed point. Four classes of STDP are identified on the basis of the time extent of their input-output interactions. The effect on the potentiation of synapses with different rates of input is investigated to elucidate the relationship of STDP with classical studies of long-term potentiation and depression and rate-based Hebbian learning. The selective potentiation of higher-rate synaptic inputs is found only for models where the time extent of the input-output interactions is input restricted (i.e., restricted to time domains delimited by adjacent synaptic inputs) and that have a time-asymmetric learning window with a longer time constant for depression than for potentiation. The analysis provides an account of learning dynamics determined by an input-selective stable fixed point. The effect of suppressive interspike interactions on STDP is also analyzed and shown to modify the synaptic dynamics.

Single-neuron discharge properties and network activity in dissociated cultures of neocortex

Cultures of neurons from rat neocortex exhibit spontaneous, temporally patterned, network activity. Such a distributed activity in vitro constitutes a possible framework for combining theoretical and experimental approaches, linking the single-neuron discharge properties to network phenomena. In this work, we addressed the issue of closing the loop, from the identification of the single-cell discharge properties to the prediction of collective network phenomena. Thus, we compared these predictions with the spontaneously emerging network activity in vitro, detected by substrate arrays of microelectrodes. Therefore, we characterized the single-cell discharge properties to Gauss-distributed noisy currents, under pharmacological blockade of the synaptic transmission. Such stochastic currents emulate a realistic input from the network. The mean (m) and variance (s(2)) of the injected current were varied independently, reminiscent of the extended mean-field description of a variety of possible presynaptic network organizations and mean activity levels, and the neuronal response was evaluated in terms of the steady-state mean firing rate (f). Experimental current-to-spike-rate responses f(m, s(2)) were similar to those of neurons in brain slices, and could be quantitatively described by leaky integrate-and-fire (IF) point neurons. The identified model parameters were then used in numerical simulations of a network of IF neurons. Such a network reproduced a collective activity, matching the spontaneous irregular population bursting, observed in cultured networks. We finally interpret such a collective activity and its link with model details by the mean-field theory. We conclude that the IF model is an adequate minimal description of synaptic integration and neuronal excitability, when collective network activities are considered in vitro.

Recurrent biological neural networks: the weak and noisy limit

A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak synaptic connectivity. The terms of the series can be interpreted as loops of interactions between neurons, so the technique is called a loop expansion. A diagrammatic method is introduced that allows for construction of analytic expressions for the parameter dependencies of the spike-probability function and correlation functions. An analytic expression is obtained to predict the effect of the surrounding network on a neuron during an intracellular current injection. The analytic results are compared with simulations to test the range of their validity and significant effects of the the recurrent connections in network are accurately predicted by the loop expansion.

Role of synaptic filtering on the firing response of simple model neurons

During active states of the brain neurons process their afferent currents with an effective membrane time constant much shorter than its value at rest. This fact, together with the existence of several synaptic time scales, determines to which aspects of the input the neuron responds best. Here we present a solution to the response of a leaky integrate-and-fire neuron with synaptic filters when long synaptic times are present, and predict the firing rate for all values of the synaptic time constant. We also discuss under which conditions this neuron becomes a coincidence detector.

Synaptic transmission of chaotic spike trains between primary afferent fiber and spinal dorsal horn neuron in the rat

Primary sensory neurons can generate irregular burst firings in which the existence of significant deterministic behaviors of chaotic dynamics has been proved with nonlinear time series analysis. But how well the deterministic characteristics and neural information of presynaptic chaotic spike trains were transmitted into postsynaptic spike trains is still an open question. Here we investigated the synaptic transmission of chaotic spike trains between primary Adelta afferent fiber and spinal dorsal horn neuron. Two kinds of basic stimulus unit, brief burst and single pulse, were employed by us to comprise chaotic stimulus trains. For time series analysis, we defined "events" as the longest sequences of spikes with all interspike intervals less than or equal to a certain threshold and extracted the interevent intervals (IEIs) from spike trains. Return map analysis of the IEI series showed that the main temporal structure of chaotic input trains could be detected in postsynaptic output trains, especially under brief-burst stimulation. Using correlation dimension and nonlinear prediction methods, we found that synaptic transmission could influence the nonlinear characteristics of chaotic trains, such as fractal dimension and short-term predictability, with greater influence made under single-pulse stimulation. By calculating the mutual information between input and output trains, we found the information carried by presynaptic spike trains could not be completely transmitted at primary afferent synapses, and that brief bursts could more reliably transmit the information carried by chaotic input trains across synapses. These results indicate that although unreliability exists during synaptic transmission, the main deterministic characteristics of chaotic burst trains can be transmitted across primary afferent synapses. Moreover, brief bursts that come from the periphery can more reliably transmit neural information between primary afferent fibers and spinal dorsal horn neurons.

Firing properties of spinal interneurons during voluntary movement. I. State-dependent regularity of firing

The firing properties of single spinal interneurons (INs) were studied in five awake, behaving monkeys performing isometric or auxotonic flexion-extension torques at the wrist. INs tended to fire tonically at rest (mean rate, 14 spikes (sp)/sec) and during generation of static torque (mean rate, 19 sp/sec in flexion, 24 sp/sec in extension). INs exhibited regular firing, with autocorrelation functions showing clear periodic features and a mean coefficient of variation of interspike intervals (CV) of 0.55 during production of static torque. For the population, there was an inverse correlation between CV and mean rate. However, 46% of the INs had task-dependent changes in regularity that were not predicted by changes in firing rate, suggesting that their firing pattern is determined not only by the intrinsic properties of the neurons but also by the properties of its synaptic inputs. INs showed two main response types to passive wrist displacement: biphasic and coactivation. Cells with these sensory responses had different, stereotypical temporal activity profiles and firing regularity during active movement. However, INs having correlational linkages with forearm muscles, identified as features in spike-triggered averages of electromyographic activity, did not exhibit unique responses or firing properties, although they tended to fire more regularly than other INs. This suggests the lack of a precise mapping of inputs to outputs for the spinal premotor network.

Firing properties of spinal interneurons during voluntary movement. I. State-dependent regularity of firing

The firing properties of single spinal interneurons (INs) were studied in five awake, behaving monkeys performing isometric or auxotonic flexion-extension torques at the wrist. INs tended to fire tonically at rest (mean rate, 14 spikes (sp)/sec) and during generation of static torque (mean rate, 19 sp/sec in flexion, 24 sp/sec in extension). INs exhibited regular firing, with autocorrelation functions showing clear periodic features and a mean coefficient of variation of interspike intervals (CV) of 0.55 during production of static torque. For the population, there was an inverse correlation between CV and mean rate. However, 46% of the INs had task-dependent changes in regularity that were not predicted by changes in firing rate, suggesting that their firing pattern is determined not only by the intrinsic properties of the neurons but also by the properties of its synaptic inputs. INs showed two main response types to passive wrist displacement: biphasic and coactivation. Cells with these sensory responses had different, stereotypical temporal activity profiles and firing regularity during active movement. However, INs having correlational linkages with forearm muscles, identified as features in spike-triggered averages of electromyographic activity, did not exhibit unique responses or firing properties, although they tended to fire more regularly than other INs. This suggests the lack of a precise mapping of inputs to outputs for the spinal premotor network.

Effects of fatigue on the catchlike property in a turtle hindlimb muscle

The purpose of this report was to test for the possibility that a catchlike, force-enhancing property, attributable to a particular stimulation pattern, could be evoked in non-mammalian turtle muscle, just as it has been shown in mammalian muscle. We tested for the presence of this property in dynamic lengthening and shortening contractions, as well as in the more commonly studied isometric contractions. A second aim was to note the effects of fatigue on the catchlike property, if the latter was present. The force response of the external gastrocnemius muscle in the adult turtle, Pseudemys ( Trachemys) scripta elegans, was compared for a control, constant-frequency 10 Hz, 1-s duration stimulation pattern using 0.1-ms pulses vs. the same pattern, but with two additional pulses within the first 100-ms interspike interval of the control stimulus train. This latter train produced a pronounced and prolonged enhancement of muscle force, which was attributed to a catchlike effect. It was greatly increased when the muscle was in a fatigued state. The extent of this force enhancement was significantly different for the three contraction types, and generally in the order: isometric>lengthening>shortening contraction. These differences were greater in fatigued vs. fresh muscle. Comparative aspects and potential mechanisms underlying the catchlike effect are discussed.

The discharge variability of neocortical neurons during high-conductance states

In vivo recordings have shown that the discharge of cortical neurons is often highly variable and can have statistics similar to a Poisson process with a coefficient of variation around unity. To investigate the determinants of this high variability, we analyzed the spontaneous discharge of Hodgkin-Huxley type models of cortical neurons, in which in vivo-like synaptic background activity was modeled by random release events at excitatory and inhibitory synapses. By using compartmental models with active dendrites, or single compartment models with fluctuating conductances and fluctuating currents, we found that a high discharge variability was always paralleled with a high-conductance state, while some active and passive cellular properties had only a minor impact. Furthermore, a balance between excitation and inhibition was not a necessary condition for high discharge variability. We conclude that the fluctuating high-conductance state caused by the ongoing activity in the cortical network in vivo may be viewed as a natural determinant of the highly variable discharges of these neurons.

Coherent oscillations in neuronal activity of the supplementary motor area during a visuomotor task

Neural activity recorded in behaving animals is nonstationary, making it difficult to determine factors influencing its temporal patterns. In the present study, rhesus monkeys were trained to produce a series of visually guided hand movements according to the changes in target locations, and multichannel single-neuron activity was recorded from the caudal supplementary motor area. Coherent oscillations in neural activity were analyzed using the wavelet cross-spectrum, and its statistical significance was evaluated using various methods based on surrogate spike trains and trial shuffling. A population-averaged wavelet cross-spectrum displayed a strong tendency for oscillatory activity in the gamma frequency range (30 approximately 50 Hz) to synchronize immediately before and after the onset of movement target. The duration of synchronized oscillations in the gamma frequency range increased when the onset of the next target was delayed. In addition, analysis of individual neuron pairs revealed that many neuron pairs also displayed coherent oscillations in the beta frequency range (15-30 Hz). Coherent beta frequency oscillations were less likely to be synchronized than gamma frequency oscillations, consistent with the fact that coherent beta frequency oscillations were not clearly seen in the population-averaged cross-spectrum. For a given neuron pair, the time course and phase of coherent oscillations were often similar across different movements. These results are consistent with the proposal that synchronized oscillations in the gamma frequency range might be related to the anticipation of behaviorally relevant events and the contextual control of cortical information flow.

Coherent oscillations in neuronal activity of the supplementary motor area during a visuomotor task

Neural activity recorded in behaving animals is nonstationary, making it difficult to determine factors influencing its temporal patterns. In the present study, rhesus monkeys were trained to produce a series of visually guided hand movements according to the changes in target locations, and multichannel single-neuron activity was recorded from the caudal supplementary motor area. Coherent oscillations in neural activity were analyzed using the wavelet cross-spectrum, and its statistical significance was evaluated using various methods based on surrogate spike trains and trial shuffling. A population-averaged wavelet cross-spectrum displayed a strong tendency for oscillatory activity in the gamma frequency range (30 approximately 50 Hz) to synchronize immediately before and after the onset of movement target. The duration of synchronized oscillations in the gamma frequency range increased when the onset of the next target was delayed. In addition, analysis of individual neuron pairs revealed that many neuron pairs also displayed coherent oscillations in the beta frequency range (15-30 Hz). Coherent beta frequency oscillations were less likely to be synchronized than gamma frequency oscillations, consistent with the fact that coherent beta frequency oscillations were not clearly seen in the population-averaged cross-spectrum. For a given neuron pair, the time course and phase of coherent oscillations were often similar across different movements. These results are consistent with the proposal that synchronized oscillations in the gamma frequency range might be related to the anticipation of behaviorally relevant events and the contextual control of cortical information flow.

Influence of subthreshold nonlinearities on signal-to-noise ratio and timing precision for small signals in neurons: minimal model analysis

Subthreshold voltage- and time-dependent conductances can subserve different roles in signal integration and action potential generation. Here, we use minimal models to demonstrate how a non-inactivating low-threshold outward current (I(KLT)) can enhance the precision of small-signal integration. Our integrate-and-fire models have only a few biophysical parameters, enabling a parametric study of I(KLT) effects. I(KLT) increases the signal-to-noise ratio (SNR) for firing when a subthreshold 'signal' EPSP is delivered in the presence of weak random input. The increased SNR is due to the suppression of spontaneous firings to random input. In accordance, SNR grows as the EPSP amplitude increases. SNR also grows as the unitary synaptic current's time constant increases, leading to more effective suppression of spontaneous activity. Spike-triggered reverse correlation of the injected current indicates that, to reach spike threshold, a cell with I(KLT) requires a briefer time course of injected current. Consistent with this narrowed integration time window, I(KI.T) enhances phase-locking. measured as vector strength, to a weak noisy and periodically modulated stimulus. Thus subthreshold negative feedback mediated by I(KLT) enhances temporal processing. An alternative suppression mechanism is voltage- and time-dependent inactivation of a low-threshold inward current. This feature in an integrate-and-fire model also shows SNR enhancement, in comparison with a case when the inward current is non-inactivating. Small-signal detection can be significantly improved in noisy neuronal systems by subthreshold negative feedback, serving to suppress false positives.

Synaptic background noise controls the input/output characteristics of single cells in an in vitro model of in vivo activity

In vivo, in vitro and computational studies were used to investigate the impact of the synaptic background activity observed in neocortical neurons in vivo. We simulated background activity in vitro using two stochastic Ornstein-Uhlenbeck processes describing glutamatergic and GABAergic synaptic conductances, which were injected into a cell in real time using the dynamic clamp technique. With parameters chosen to mimic in vivo conditions, layer 5 rat prefrontal cortex cells recorded in vitro were depolarized by about 15 mV, their membrane fluctuated with a S.D. of about 4 mV, their input resistances decreased five-fold, their spontaneous firing had a high coefficient of variation and an average firing rate of about 5-10 Hz. Brief changes in the variance of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synaptic conductance fluctuations induced time-locked spiking without significantly changing the average membrane potential of the cell. These transients mimicked increases in the correlation of excitatory inputs. Background activity was highly effective in modulating the firing-rate/current curve of the cell: the variance of the simulated gamma-aminobutyric acid (GABA) and AMPA conductances individually set the input/output gain, the mean excitatory and inhibitory conductances set the working point, and the mean inhibitory conductance controlled the input resistance. An average ratio of inhibitory to excitatory mean conductances close to 4 was optimal in generating membrane potential fluctuations with high coefficients of variation. We conclude that background synaptic activity can dynamically modulate the input/output properties of individual neocortical neurons in vivo.

Higher-order statistics of input ensembles and the response of simple model neurons

Pairwise correlations among spike trains recorded in vivo have been frequently reported. It has been argued that correlated activity could play an important role in the brain, because it efficiently modulates the response of a postsynaptic neuron. We show here that a neuron's output firing rate critically depends on the higher-order statistics of the input ensemble. We constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations, but differed with regard to the higher-order interactions within the population. The first ensemble was characterized by clusters of spikes synchronized over the whole population. In the second ensemble, the size of spike clusters was, on average, proportional to the pairwise correlation. For both input models, we assessed the role of the size of the population, the firing rate, and the pairwise correlation on the output rate of two simple model neurons: a continuous firing-rate model and a conductance-based leaky integrate-and-fire neuron. An approximation to the mean output rate of the firing-rate neuron could be derived analytically with the help of shot noise theory. Interestingly, the essential features of the mean response of the two neuron models were similar. For both neuron models, the three input parameters played radically different roles with respect to the postsynaptic firing rate, depending on the interaction structure of the input. For instance, in the case of an ensemble with small and distributed spike clusters, the output firing rate was efficiently controlled by the size of the input population. In addition to the interaction structure, the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate.