Spike-count distribution in a neuronal population under weak common stimulation

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.

Quantifying encoding redundancy induced by rate correlations in Poisson neurons

Temporal correlations in neuronal spike trains are known to introduce redundancy to stimulus encoding. However, exact methods to describe how these correlations impact neural information transmission quantitatively are lacking. Here, we provide a general measure for the information carried by correlated rate modulations only, neglecting other spike correlations, and use it to investigate the effect of rate correlations on encoding redundancy. We derive it analytically by calculating the mutual information between a time-correlated, rate modulating signal and the resulting spikes of Poisson neurons. Whereas this information is determined by spike autocorrelations only, the redundancy in information encoding due to rate correlations depends on both the distribution and the autocorrelation of the rate histogram. We further demonstrate that at very small signal strengths the information carried by rate correlated spikes becomes identical to that of independent spikes, in effect measuring the signal modulation depth. In contrast, a vanishing signal correlation time maximizes information but does not generally yield the information of independent spikes. Overall, our study sheds light on the role of signal-induced temporal correlations for neural coding, by providing insight into how signal features shape redundancy and by establishing mathematical links between existing methods.

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.

From the statistics of connectivity to the statistics of spike times in neuronal networks

An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending on the spatial scales of recurrent and feedforward connectivity. We close by showing how these ideas, together with plasticity rules, can help to close the loop between network structure and activity statistics.

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

We consider a homogeneous population of stochastic neurons that are driven by weak common noise (stimulus). To capture and analyze the joint firing events within the population, we introduce the partial synchronous output of the population. This is a time series defined by the events that at least a fixed fraction γ∈[0,1] of the population fires simultaneously within a small time interval. For this partial synchronous output we develop two analytical approaches to the correlation statistics. In the Gaussian approach we represent the synchronous output as a nonlinear transformation of the summed population activity and approximate the latter by a Gaussian process. In the combinatorial approach the synchronous output is represented by products of box-filtered spike trains of the single neurons. In both approaches we use linear-response theory to derive approximations for statistical measures that hold true for weak common noise. In particular, we calculate the mean value and power spectrum of the synchronous output and the cross-spectrum between synchronous output and common noise. We apply our results to the leaky integrate-and-fire neuron model and compare them to numerical simulations. The combinatorial approach is shown to provide a more accurate description of the statistics for small populations, whereas the Gaussian approximation yields compact formulas that work well for a sufficiently large population size. In particular, in the Gaussian approximation all statistical measures reveal a symmetry in the synchrony threshold γ around the mean value of the population activity. Our results may contribute to a better understanding of the role of coincidence detection in neural signal processing.

The mechanics of state-dependent neural correlations

Simultaneous recordings from large neural populations are becoming increasingly common. An important feature of population activity is the trial-to-trial correlated fluctuation of spike train outputs from recorded neuron pairs. Similar to the firing rate of single neurons, correlated activity can be modulated by a number of factors, from changes in arousal and attentional state to learning and task engagement. However, the physiological mechanisms that underlie these changes are not fully understood. We review recent theoretical results that identify three separate mechanisms that modulate spike train correlations: changes in input correlations, internal fluctuations and the transfer function of single neurons. We first examine these mechanisms in feedforward pathways and then show how the same approach can explain the modulation of correlations in recurrent networks. Such mechanistic constraints on the modulation of population activity will be important in statistical analyses of high-dimensional neural data.