Fast global oscillations in networks of integrate-and-fire neurons with low firing rates

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to infinity,the network exhibits a sharp transition between a stationary and an oscillatory global activity regime where neurons are weakly synchronized. The activity becomes oscillatory when the inhibitory feedback is strong enough. The period of the global oscillation is found to be mainly controlled by synaptic times, but depends also on the characteristics of the external input. In large but finite networks, the analysis shows that global oscillations of finite coherence time generically exist both above and below the critical inhibition threshold. Their characteristics are determined as functions of systems parameters, in these two different regimes. The results are found to be in good agreement with numerical simulations.Comment: 45 pages, 11 figures, to be published in Neural Computatio

Transient Information Flow in a Network of Excitatory and Inhibitory Model Neurons: Role of Noise and Signal Autocorrelation

We investigate the performance of sparsely-connected networks of integrate-and-fire neurons for ultra-short term information processing. We exploit the fact that the population activity of networks with balanced excitation and inhibition can switch from an oscillatory firing regime to a state of asynchronous irregular firing or quiescence depending on the rate of external background spikes. We find that in terms of information buffering the network performs best for a moderate, non-zero, amount of noise. Analogous to the phenomenon of stochastic resonance the performance decreases for higher and lower noise levels. The optimal amount of noise corresponds to the transition zone between a quiescent state and a regime of stochastic dynamics. This provides a potential explanation on the role of non-oscillatory population activity in a simplified model of cortical micro-circuits.Comment: 27 pages, 7 figures, to appear in J. Physiology (Paris) Vol. 9

One-Dimensional Population Density Approaches to Recurrently Coupled Networks of Neurons with Noise

Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential (AdEx) and quartic integrate and fire (QIF), among others. Unfortunately, the mean-field systems have a degree of frequency error and the networks analyzed often do not include noise when there is adaptation. Here, we derive a one-dimensional partial differential equation (PDE) approximation for the marginal voltage density under a first order moment closure for coupled networks of integrate-and-fire neurons with white noise inputs. The PDE has substantially less frequency error than the mean-field system, and provides a great deal more information, at the cost of analytical tractability. The convergence properties of the mean-field system in the low noise limit are elucidated. A novel method for the analysis of the stability of the asynchronous tonic firing solution is also presented and implemented. Unlike previous attempts at stability analysis with these network types, information about the marginal densities of the adaptation variables is used. This method can in principle be applied to other systems with nonlinear partial differential equations.Comment: 26 Pages, 6 Figure

A mean-field model for conductance-based networks of adaptive exponential integrate-and-fire neurons

Voltage-sensitive dye imaging (VSDi) has revealed fundamental properties of neocortical processing at mesoscopic scales. Since VSDi signals report the average membrane potential, it seems natural to use a mean-field formalism to model such signals. Here, we investigate a mean-field model of networks of Adaptive Exponential (AdEx) integrate-and-fire neurons, with conductance-based synaptic interactions. The AdEx model can capture the spiking response of different cell types, such as regular-spiking (RS) excitatory neurons and fast-spiking (FS) inhibitory neurons. We use a Master Equation formalism, together with a semi-analytic approach to the transfer function of AdEx neurons. We compare the predictions of this mean-field model to simulated networks of RS-FS cells, first at the level of the spontaneous activity of the network, which is well predicted by the mean-field model. Second, we investigate the response of the network to time-varying external input, and show that the mean-field model accurately predicts the response time course of the population. One notable exception was that the "tail" of the response at long times was not well predicted, because the mean-field does not include adaptation mechanisms. We conclude that the Master Equation formalism can yield mean-field models that predict well the behavior of nonlinear networks with conductance-based interactions and various electrophysiolgical properties, and should be a good candidate to model VSDi signals where both excitatory and inhibitory neurons contribute.Comment: 21 pages, 7 figure

Decision time, slow inhibition, and theta rhythm

In this paper, we examine decision making in a spiking neuronal network and show that longer time constants for the inhibitory neurons can decrease the reaction times and produce theta rhythm.We analyze the mechanism and find that the spontaneous firing rate before the decision cues are applied can drift, and thereby influence the speed of the reaction time when the decision cues are applied. The drift of the firing rate in the population that will win the competition is larger if the time constant of the inhibitory interneurons is increased from 10 to 33 ms, and even larger if there are two populations of inhibitory neurons with time constants of 10 and 100 ms. Of considerable interest is that the decision that will be made can be influenced by the noise-influenced drift of the spontaneous firing rate over many seconds before the decision cues are applied. The theta rhythm associated with the longer time constant networks mirrors the greater integration in the firing rate drift produced by the recurrent connections over long time periods in the networks with slow inhibition. The mechanism for the effect of slow waves in the theta and delta range on decision times is suggested to be increased neuronal spiking produced by depolarization of the membrane potential on the positive part of the slow waves when the neuron’s membrane potential is close to the firing threshold

Locking of correlated neural activity to ongoing oscillations

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spike synchrony and in how far these channels can be considered separate. Experiments indeed showed that correlated spiking co-modulates with the static firing rate and is also tightly locked to the phase of beta-oscillations. While the dependence of correlations on the mean rate is well understood in feed-forward networks, it remains unclear why and by which mechanisms correlations tightly lock to an oscillatory cycle. We here demonstrate that such correlated activation of pairs of neurons is qualitatively explained by periodically-driven random networks. We identify the mechanisms by which covariances depend on a driving periodic stimulus. Mean-field theory combined with linear response theory yields closed-form expressions for the cyclostationary mean activities and pairwise zero-time-lag covariances of binary recurrent random networks. Two distinct mechanisms cause time-dependent covariances: the modulation of the susceptibility of single neurons (via the external input and network feedback) and the time-varying variances of single unit activities. For some parameters, the effectively inhibitory recurrent feedback leads to resonant covariances even if mean activities show non-resonant behavior. Our analytical results open the question of time-modulated synchronous activity to a quantitative analysis.Comment: 57 pages, 12 figures, published versio

Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity

We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate-and-fire spiking model. The synaptic strength is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between pre- and post-synaptic activity. We store multiple patterns and study the network capacity. For the analog model, we find that the network capacity scales linearly with the network size, and that both capacity and the oscillation frequency of the retrieval state depend on the asymmetry of the learning time window. In addition to fully-connected networks, we study sparse networks, where each neuron is connected only to a small number z << N of other neurons. Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase. Also in the spiking integrate and fire model the crucial result of storing and retrieval of multiple phase-coded patterns is observed. The capacity of the fully-connected spiking network is investigated, together with the relation between oscillation frequency of retrieval state and window asymmetry