Nicolas Brunel

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.

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 , 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.

Erratum to: Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition

Experimental evidence suggests that the maintenance of an item in working memory is achieved through persistent activity in selective neural assemblies of the cortex. To understand the mechanisms underlying this phenomenon, it is essential to investigate how persistent activity is affected by external inputs or neuromodulation. We have addressed these questions using a recurrent network model of object working memory. Recurrence is dominated by inhibition, although persistent activity is generated through recurrent excitation in small subsets of excitatory neurons. Our main findings are as follows. (1) Because of the strong feedback inhibition, persistent activity shows an inverted U shape as a function of increased external drive to the network. (2) A transient external excitation can switch off a network from a selective persistent state to its spontaneous state. (3) The maintenance of the sample stimulus in working memory is not affected by intervening stimuli (distractors) during the delay period, provided the stimulation intensity is not large. On the other hand, if stimulation intensity is large enough, distractors disrupt sample-related persistent activity, and the network is able to maintain a memory only of the last shown stimulus. (4) A concerted modulation of GABA(A) and NMDA conductances leads to a decrease of spontaneous activity but an increase of persistent activity; the enhanced signal-to-noise ratio is shown to increase the resistance of the network to distractors. (5) Two mechanisms are identified that produce an inverted U shaped dependence of persistent activity on modulation. The present study therefore points to several mechanisms that enhance the signal-to-noise ratio in working memory states. These mechanisms could be implemented in the prefrontal cortex by dopaminergic projections from the midbrain.

Sensory neural codes using multiplexed temporal scales

Determining how neuronal activity represents sensory information is central for understanding perception. Recent work shows that neural responses at different timescales can encode different stimulus attributes, resulting in a temporal multiplexing of sensory information. Multiplexing increases the encoding capacity of neural responses, enables disambiguation of stimuli that cannot be discriminated at a single response timescale, and makes sensory representations stable to the presence of variability in the sensory world. Thus, as we discuss here, temporal multiplexing could be a key strategy used by the brain to form an information-rich and stable representation of the environment.

Mutual information, Fisher information, and population coding

In the context of parameter estimation and model selection, it is only quite recently that a direct link between the Fisher information and information-theoretic quantities has been exhibited. We give an interpretation of this link within the standard framework of information theory. We show that in the context of population coding, the mutual information between the activity of a large array of neurons and a stimulus to which the neurons are tuned is naturally related to the Fisher information. In the light of this result, we consider the optimization of the tuning curves parameters in the case of neurons responding to a stimulus represented by an angular variable.

Encoding of Naturalistic Stimuli by Local Field Potential Spectra in Networks of Excitatory and Inhibitory Neurons

Recordings of local field potentials (LFPs) reveal that the sensory cortex displays rhythmic activity and fluctuations over a wide range of frequencies and amplitudes. Yet, the role of this kind of activity in encoding sensory information remains largely unknown. To understand the rules of translation between the structure of sensory stimuli and the fluctuations of cortical responses, we simulated a sparsely connected network of excitatory and inhibitory neurons modeling a local cortical population, and we determined how the LFPs generated by the network encode information about input stimuli. We first considered simple static and periodic stimuli and then naturalistic input stimuli based on electrophysiological recordings from the thalamus of anesthetized monkeys watching natural movie scenes. We found that the simulated network produced stimulus-related LFP changes that were in striking agreement with the LFPs obtained from the primary visual cortex. Moreover, our results demonstrate that the network encoded static input spike rates into gamma-range oscillations generated by inhibitory–excitatory neural interactions and encoded slow dynamic features of the input into slow LFP fluctuations mediated by stimulus–neural interactions. The model cortical network processed dynamic stimuli with naturalistic temporal structure by using low and high response frequencies as independent communication channels, again in agreement with recent reports from visual cortex responses to naturalistic movies. One potential function of this frequency decomposition into independent information channels operated by the cortical network may be that of enhancing the capacity of the cortical column to encode our complex sensory environment.

Optimal Information Storage and the Distribution of Synaptic Weights: Perceptron versus Purkinje Cell

It is widely believed that synaptic modifications underlie learning and memory. However, few studies have examined what can be deduced about the learning process from the distribution of synaptic weights. We analyze the perceptron, a prototypical feedforward neural network, and obtain the optimal synaptic weight distribution for a perceptron with excitatory synapses. It contains more than 50% silent synapses, and this fraction increases with storage reliability: silent synapses are therefore a necessary byproduct of optimizing learning and reliability. Exploiting the classical analogy between the perceptron and the cerebellar Purkinje cell, we fitted the optimal weight distribution to that measured for granule cell-Purkinje cell synapses. The two distributions agreed well, suggesting that the Purkinje cell can learn up to 5 kilobytes of information, in the form of 40,000 input-output associations.

Dynamics of the firing probability of noisy integrate-and-fire neurons

Cortical neurons in vivo undergo a continuous bombardment due to synaptic activity, which acts as a major source of noise. Here, we investigate the effects of the noise filtering by synapses with various levels of realism on integrate-and-fire neuron dynamics. The noise input is modeled by white (for instantaneous synapses) or colored (for synapses with a finite relaxation time) noise. Analytical results for the modulation of firing probability in response to an oscillatory input current are obtained by expanding a Fokker-Planck equation for small parameters of the problemwhen both the amplitude of the modulation is small compared to the background firing rate and the synaptic time constant is small compared to the membrane time constant. We report here the detailed calculations showing that if a synaptic decay time constant is included in the synaptic current model, the firing-rate modulation of the neuron due to an oscillatory input remains finite in the high-frequency limit with no phase lag. In addition, we characterize the low-frequency behavior and the behavior of the high-frequency limit for intermediate decay times. We also characterize the effects of introducing a rise time to the synaptic currents and the presence of several synaptic receptors with different kinetics. In both cases, we determine, using numerical simulations, an effective decay time constant that describes the neuronal response completely.

Dynamics of a recurrent network of spiking neurons before and following learning

Extensive simulations of large recurrent networks of integrate-and-fire excitatory and inhibitory neurons in realistic cortical conditions (before and after Hebbian unsupervised learning of uncorrelated stimuli) exhibit a rich phenomenology of stochastic neural spike dynamics and, in particular, coexistence between two types of stable states: spontaneous activity upon stimulation by an unlearned stimulus, and ‘working memory’ states strongly correlated with learned stimuli. Firing rates have very wide distributions, due to the variability in the connectivity from neuron to neuron. ISI histograms are exponential, except for small intervals. Thus the spike emission processes are well approximated by a Poisson process. The variability of the spike emission process is effectively controlled by the magnitude of the post-spike reset potential relative to the mean depolarization of the cell. Cross-correlations (CC) exhibit a central peak near zero delay, flanked by damped oscillations. The magnitude of the centr...

Calcium-based plasticity model explains sensitivity of synaptic changes to spike pattern, rate, and dendritic location

Multiple stimulation protocols have been found to be effective in changing synaptic efficacy by inducing long-term potentiation or depression. In many of those protocols, increases in postsynaptic calcium concentration have been shown to play a crucial role. However, it is still unclear whether and how the dynamics of the postsynaptic calcium alone determine the outcome of synaptic plasticity. Here, we propose a calcium-based model of a synapse in which potentiation and depression are activated above calcium thresholds. We show that this model gives rise to a large diversity of spike timing-dependent plasticity curves, most of which have been observed experimentally in different systems. It accounts quantitatively for plasticity outcomes evoked by protocols involving patterns with variable spike timing and firing rate in hippocampus and neocortex. Furthermore, it allows us to predict that differences in plasticity outcomes in different studies are due to differences in parameters defining the calcium dynamics. The model provides a mechanistic understanding of how various stimulation protocols provoke specific synaptic changes through the dynamics of calcium concentration and thresholds implementing in simplified fashion protein signaling cascades, leading to long-term potentiation and long-term depression. The combination of biophysical realism and analytical tractability makes it the ideal candidate to study plasticity at the synapse, neuron, and network levels.