Theory of oscillatory firing induced by spatially correlated noise and delayed inhibitory feedback

Abstract

A network of leaky integrate-and-fire neurons with global inhibitory feedback and under the influence of spatially correlated noise is studied. We calculate the spectral statistics of the network (power spectrum of the population activity, cross spectrum between spike trains of different neurons) as well as of a single neuron (power spectrum of spike train, cross spectrum between external noise and spike train) within the network. As shown by comparison with numerical simulations, our theory works well for arbitrary network size if the feedback is weak and the amount of external noise does not exceed that of the internal noise. By means of our analytical results we discuss the quality of the correlation-induced oscillation in a large network as a function of the transmission delay and the internal noise intensity. It is shown that the strongest oscillation is obtained in a system with zero internal noise and adiabatically long delay (i.e., the delay period is longer than any other time scale in the system). For a neuron with a strong intrinsic frequency, the oscillation becomes strongly anharmonic in the case of a long delay time. We also discuss briefly the kind of synchrony introduced by the feedback-induced oscillation.

Effect of inhibitory feedback on correlated firing of spiking neural network

“…6. With the increase in s D , a monotonically increasing degree of q is obtained for all values of G. That the correlation coefficient becomes bigger with increasing transmission delay is mainly due to the pronounced oscillation in the network (Lindner et al 2005). At short delay, no sharp delayed activity, with little effects on neuronal firing, is received by the network due to the effect of the a function.…”

“…How correlations of population responses are shaped in neural systems remains unclear. It has been observed, both in experimental systems and in computational models of varying complexity, that the correlations within a population of neurons are influenced by the magnitude and correlations of the external stimuli (Tetzlaff et al 2008;Lindner et al 2005). Pairwise correlations in feed-forward circuits generally increase with firing rate (Tetzlaff et al 2008).…”

“…The network correlations are critically dependent on the value of the transmission of the feedback loop. However, for small delay, no network oscillation would be present (Lindner et al 2005), Therefore, s D = 1 is selected to be the start point for simulations. Correlation coefficient is plotted against inhibitory feedback strength and transmission delay in Fig.…”

“…Especially, gamma oscillations, thought to be fundamental for transmitting information, rely on inhibitory interneurons, and arise from oscillatory, synchronized firing of these interneurons onto pyramidal cells (Bartos et al 2007;Borgers and Kopell 2003;Brunel and Wang 2003;Mazzoni et al 2008;Wang and Buzsaki 1996). In the electrosensory system, inhibition is linked to oscillations via global delayed inhibitory feedback (Lindner et al 2005;Marinazzo et al 2007;Doiron et al 2003Doiron et al , 2004), which will be our focus here. By using numerical simulations of a spiking neural network of noise leaky integrate-and-fire (LIF) neurons with delayed inhibitory feedback under the influence of partially correlated input, we obtain the curves of intensity of oscillation, mean firing rate and correlation coefficient with the increase of feedback strength.…”

“…By using numerical simulations of a spiking neural network of noise leaky integrate-and-fire (LIF) neurons with delayed inhibitory feedback under the influence of partially correlated input, we obtain the curves of intensity of oscillation, mean firing rate and correlation coefficient with the increase of feedback strength. This model, directly inspired by studies of the lateral line lobe of electric, possesses detailed spatio-temporal correlations, and provides insight into the structure of the neural activity (Lindner et al 2005;Doiron et al 2003Doiron et al , 2004Maler 2007). To further explicate how inhibitory feedback circuit modulates correlations, computational simulations that increase G while concomitantly increasing the bias to maintain a constant firing rate or increasing the external noise to destroy the network oscillations are employed.…”