Self-Consistent Scheme for Spike-Train Power Spectra in Heterogeneous Sparse Networks

Author(s)

Pena, Rodrigo F. O. ^[1] ; Vellmer, Sebastian ^{[2, 3]} ; Bernardi, Davide ^{[2, 3]} ; Roque, Antonio C. ^[1] ; Lindner, Benjamin ^{[2, 3]}

Affiliation

^[1] Univ Sao Paulo, Sch Philosophy Sci & Letters Ribeirao Preto, Dept Phys, Lab Sistemas Neurais, Sao Paulo - Brazil

^[2] Humboldt Univ, Dept Phys, Berlin - Germany

^[3] Bernstein Ctr Computat Neurosci, Theory Complex Syst & Neurophys, Berlin - Germany

• Document type: Journal article
• Source: FRONTIERS IN COMPUTATIONAL NEUROSCIENCE; v. 12, MAR 2 2018.
• Web of Science Citations: 3

Abstract

Recurrent networks of spiking neurons can be in an asynchronous state characterized by low or absent cross-correlations and spike statistics which resemble those of cortical neurons. Although spatial correlations are negligible in this state, neurons can show pronounced temporal correlations in their spike trains that can be quantified by the autocorrelation function or the spike-train power spectrum. Depending on cellular and network parameters, correlations display diverse patterns (ranging from simple refractory-period effects and stochastic oscillations to slow fluctuations) and it is generally not well-understood how these dependencies come about. Previous work has explored how the single-cell correlations in a homogeneous network (excitatory and inhibitory integrate-and-fire neurons with nearly balanced mean recurrent input) can be determined numerically from an iterative single-neuron simulation. Such a scheme is based on the fact that every neuron is driven by the network noise (i.e., the input currents from all its presynaptic partners) but also contributes to the network noise, leading to a self-consistency condition for the input and output spectra. Here we first extend this scheme to homogeneous networks with strong recurrent inhibition and a synaptic filter, in which instabilities of the previous scheme are avoided by an averaging procedure. We then extend the scheme to heterogeneous networks in which (i) different neural subpopulations (e.g., excitatory and inhibitory neurons) have different cellular or connectivity parameters; (ii) the number and strength of the input connections are random (Erdos-Renyi topology) and thus different among neurons. In all heterogeneous cases, neurons are lumped in different classes each of which is represented by a single neuron in the iterative scheme; in addition, we make a Gaussian approximation of the input current to the neuron. These approximations seem to be justified over a broad range of parameters as indicated by comparison with simulation results of large recurrent networks. Our method can help to elucidate how network heterogeneity shapes the asynchronous state in recurrent neural networks. (AU)

• FAPESP's process: 15/50122-0 - Dynamic phenomena in complex networks: basics and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support type: Research Projects - Thematic Grants
• FAPESP's process: 13/25667-8 - Mechanisms of propagation of epileptiform activity in a large-scale cortical model
• Grantee: Rodrigo Felipe de Oliveira Pena
• Support type: Scholarships in Brazil - Doctorate (Direct)
• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Jefferson Antonio Galves
• Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC