Partial synchronous output of a neuronal population under weak common noise: Analytical approaches to the correlation statistics

Information transmission in recurrent networks: Consequences of network noise for synchronous and asynchronous signal encoding

Information about natural time-dependent stimuli encoded by the sensory periphery or communication between cortical networks may span a large frequency range or be localized to a smaller frequency band. Biological systems have been shown to multiplex such disparate broadband and narrow-band signals and then discriminate them in later populations by employing either an integration (low-pass) or coincidence detection (bandpass) encoding strategy. Analytical expressions have been developed for both encoding methods in feedforward populations of uncoupled neurons and confirm that the integration of a population's output low-pass filters the information, whereas synchronous output encodes less information overall and retains signal information in a selected frequency band. The present study extends the theory to recurrent networks and shows that recurrence may sharpen the synchronous bandpass filter. The frequency of the pass band is significantly influenced by the synaptic strengths, especially for inhibition-dominated networks. Synchronous information transfer is also increased when network models take into account heterogeneity that arises from the stochastic distribution of the synaptic weights.

How single neuron properties shape chaotic dynamics and signal transmission in random neural networks

While most models of randomly connected neural networks assume single-neuron models with simple dynamics, neurons in the brain exhibit complex intrinsic dynamics over multiple timescales. We analyze how the dynamical properties of single neurons and recurrent connections interact to shape the effective dynamics in large randomly connected networks. A novel dynamical mean-field theory for strongly connected networks of multi-dimensional rate neurons shows that the power spectrum of the network activity in the chaotic phase emerges from a nonlinear sharpening of the frequency response function of single neurons. For the case of two-dimensional rate neurons with strong adaptation, we find that the network exhibits a state of "resonant chaos", characterized by robust, narrow-band stochastic oscillations. The coherence of stochastic oscillations is maximal at the onset of chaos and their correlation time scales with the adaptation timescale of single units. Surprisingly, the resonance frequency can be predicted from the properties of isolated neurons, even in the presence of heterogeneity in the adaptation parameters. In the presence of these internally-generated chaotic fluctuations, the transmission of weak, low-frequency signals is strongly enhanced by adaptation, whereas signal transmission is not influenced by adaptation in the non-chaotic regime. Our theoretical framework can be applied to other mechanisms at the level of single neurons, such as synaptic filtering, refractoriness or spike synchronization. These results advance our understanding of the interaction between the dynamics of single units and recurrent connectivity, which is a fundamental step toward the description of biologically realistic neural networks.

Detecting single-cell stimulation in a large network of integrate-and-fire neurons

Several experiments have shown that the stimulation of a single neuron in the cortex can influence the local network activity and even the behavior of an animal. From the theoretical point of view, it is not clear how stimulating a single cell in a cortical network can evoke a statistically significant change in the activity of a large population. Our previous study considered a random network of integrate-and-fire neurons and proposed a way of detecting the stimulation of a single neuron in the activity of a local network: a threshold detector biased toward a specific subset of neurons. Here, we revisit this model and extend it by introducing a second network acting as a readout. In the simplest scenario, the readout consists of a collection of integrate-and-fire neurons with no recurrent connections. In this case, the ability to detect the stimulus does not improve. However, a readout network with both feed-forward and local recurrent inhibition permits detection with a very small bias, if compared to the readout scheme introduced previously. The crucial role of inhibition is to reduce global input cross correlations, the main factor limiting detectability. Finally, we show that this result is robust if recurrent excitatory connections are included or if a different kind of readout bias (in the synaptic amplitudes instead of connection probability) is used.

Measuring spike timing distance in the Hindmarsh-Rose neurons

In the present paper, a simple spike timing distance is defined which can be used to measure the degree of synchronization with the information only encoded in the precise timing of the spike trains. Via calculating the spike timing distance defined in this paper, the spike train similarity of uncoupled Hindmarsh-Rose neurons in bursting or spiking states with different initial conditions is investigated and the results are compared with other spike train distance measures. Later, the spike timing distance measure is applied to study the synchronization of coupled or common noise-stimulated neurons. Counterintuitively, the addition of weak coupling or common noise doesn't enhance the degree of synchronization although after critical values, both of them can induce complete synchronizations. More interestingly, the common noise plays opposite roles for weak and strong enough couplings. Finally, it should be noted that the measure defined in this paper can be extended to measure large neuronal ensembles and the lag synchronization.

Synchronous spikes are necessary but not sufficient for a synchrony code in populations of spiking neurons

Synchronous activity in populations of neurons potentially encodes special stimulus features. Selective readout of either synchronous or asynchronous activity allows formation of two streams of information processing. Theoretical work predicts that such a synchrony code is a fundamental feature of populations of spiking neurons if they operate in specific noise and stimulus regimes. Here we experimentally test the theoretical predictions by quantifying and comparing neuronal response properties in tuberous and ampullary electroreceptor afferents of the weakly electric fish Apteronotus leptorhynchus These related systems show similar levels of synchronous activity, but only in the more irregularly firing tuberous afferents a synchrony code is established, whereas in the more regularly firing ampullary afferents it is not. The mere existence of synchronous activity is thus not sufficient for a synchrony code. Single-cell features such as the irregularity of spiking and the frequency dependence of the neuron's transfer function determine whether synchronous spikes possess a distinct meaning for the encoding of time-dependent signals.