Emergence of Irregular Activity in Networks of Strongly Coupled Conductance-Based Neurons.

M. H. Histed,A. Sanzeni,N. Brunel

doi:10.1103/physrevx.12.011044

M. H. Histed, A. Sanzeni

Open Access

https://doi.org/10.1103/physrevx.12.011044

Copy DOI

Abstract

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive firing. In networks of neurons with current-based synapses, the balanced state emerges dynamically if coupling is strong, i.e., if the mean number of synapses per neuron K is large and synaptic efficacy is of the order of . When synapses are conductance-based, current fluctuations are suppressed when coupling is strong, questioning the applicability of the balanced state idea to biological neural networks. We analyze networks of strongly coupled conductance-based neurons and show that asynchronous irregular activity and broad distributions of rates emerge if synaptic efficacy is of the order of 1/ log(K). In such networks, unlike in the standard balanced state model, current fluctuations are small and firing is maintained by a drift-diffusion balance. This balance emerges dynamically, without fine-tuning, if inputs are smaller than a critical value, which depends on synaptic time constants and coupling strength, and is significantly more robust to connection heterogeneities than the classical balanced state model. Our analysis makes experimentally testable predictions of how the network response properties should evolve as input increases.

Highlights

To explain the observed irregularity, it has been proposed that neural networks operate in a balanced state, where strong feed forward and recurrent excitatory inputs are canceled by recurrent inhibition and firing is driven by fluctuations [5,6]
We study the dynamics of networks of leaky integrateand-fire (LIF) neurons with conductance-based synaptic inputs
We examine the effect of a finite synaptic time constant on network response

Summary

INTRODUCTION

Each neuron in the cortex receives inputs from hundreds to thousands of presynaptic neurons. It has been shown that the balanced state emerges dynamically (without fine-tuning) in randomly connected networks of binary units [7,8] and networks of currentbased spiking neurons [9,10], provided that coupling is strong, and recurrent inhibition is powerful enough to counterbalance instabilities due to recurrent excitation. These results are all derived assuming that the firing of a presynaptic neuron produces a fixed amount of synaptic current, neglecting the dependence of synaptic current on the membrane potential, a key aspect of neuronal biophysics. The model generates qualitatively different predictions compared to the current-based model, which could be tested experimentally

Membrane potential dynamics

Diffusion and effective time constant approximations

Current-based model

BEHAVIOR OF SINGLE-NEURON RESPONSE FOR LARGE K

A SCALING RELATION THAT PRESERVES SINGLE-NEURON RESPONSE FOR LARGE K

ASYNCHRONOUS IRREGULAR ACTIVITY IN NETWORK RESPONSE AT STRONG COUPLING

ROBUST LOG-NORMAL DISTRIBUTION OF FIRING RATES IN NETWORKS WITH HETEROGENEOUS CONNECTIVITY

COMPARISON WITH EXPERIMENTAL DATA

VIII. EFFECTS OF FINITE SYNAPTIC TIME CONSTANTS

DISCUSSION

Equations for arbitrary drift and diffusion terms

Equations for conductance-based LIF neurons