Correlations in population dynamics in multi-component networks

Abstract

This is a theoretical study of correlations in spiking activity between neuronal populations. We focus on the spike firing of entire local populations without regard to the identities of the neurons that fire the spikes, and show that such a population-level metric is more robust than correlations between pairs of neurons. Between any source and target populations, there is an intrinsic response time characterized by the phase-shift that maximizes the correlation between their spiking. We find that the alignment of gamma-band rhythms contributes significantly to the positive correlations between populations. Hence, the correlation metric sheds light on the transference of gamma rhythms between populations; the effectiveness of such transference has been hypothesized to be connected to communication between brain regions. We investigate the dependence of correlations on connectivity and degree of synchrony, and consider multi-component network motifs with configurations known to occur in real cortex, studying the correlations between components that are directly or indirectly connected, by single or multiple pathways, with or without feedback. Mechanistic explanations are offered for many of the phenomena observed.

Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

“…To identify how information can be encoded in the input, transmitted and represented in the output of the firing rate of the E-cells, we consider periodic inputs with different amplitudes modulated by the parameter A (when A = 0, the stimulus is not present) and we measure the changes in the firing rate of the post-synpatic group, either on the average firing rate or in the spike synchronization, as suggested in [ 21 ]. If inputs with different amplitudes generate different output responses, then the information encoded in the amplitude of the input will be detected at the output and communication will occur.…”

“…There are also several modeling studies approaching different aspects of the CTC hypothesis. These studies are based either on computational simulations of spiking networks [ 17 – 21 ] or models that admit an analytically more tractable approach such as single neuron models [ 22 , 23 ], or firing rate models [ 10 , 24 ]. There are also studies that compare different modeling approaches [ 10 , 25 ], but when both spiking and mean firing rate models are considered [ 10 ], the latter are not an exact derivation of the former.…”

Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

“…We acknowledge the fact that gamma-band rhythms observed in experimental data do not show regular oscillatory behavior, but they are rather irregular and episodic [46,47]. In [21] the authors consider an E-I network showing irregular and episodic gamma rhythms and observe that this assumption enables a target population to be correlated to two independent sources that differ either in frequency or in phase. Notice that in this case correlations are used to measure entrainment and synchronization between neural populations.…”

“…In our previous work [24], we considered only the factor ∆α, but the quantities ∆ᾱ and ∆γ allow us to complement the information about the changes in the firing rate. In particular, we can explore whether "communication" means that the target network shows higher firing rates and/or higher coherence, that is, enhancement of synchronization in spiking neurons within the target population [21].…”

“…There are also several modeling studies approaching different aspects of the CTC hypothesis. These studies are based either on computational simulations of spiking networks [17,18,19,20,21] or models that admit an analytically more tractable approach such as single neuron models [22,23], or firing rate models [10,24]. Other studies compare different approaches such as in [10,25].…”