## Biologically realistic mean-field models of conductance-based
networks of spiking neurons with adaptation.

#### Matteo di Volo, Alberto Romagnoni, Cristiano Capone and Alain
Destexhe

*Neural Computation* 31: 653-680, 2019.

## Abstract

Accurate population models are needed to build very large scale
neural models, but their derivation is difficult for realistic
networks of neurons, in particular when nonlinear properties are
involved such as conductance-based interactions and spike-frequency
adaptation. Here, we consider such models based on networks of
Adaptive exponential Integrate and fire excitatory and inhibitory
neurons. Using a Master Equation formalism, we derive a mean-field
model of such networks and compare it to the full network dynamics.
The mean-field model is capable to correctly predict the average
spontaneous activity levels in asynchronous irregular regimes
similar to in vivo activity. It also captures the transient
temporal response of the network to complex external inputs.
Finally, the mean-field model is also able to quantitatively
describe regimes where high and low activity states alternate
(UP-DOWN state dynamics), leading to slow oscillations. We conclude
that such mean-field models are "biologically realistic" in the
sense that they can capture both spontaneous and evoked activity,
and they naturally appear as candidates to build very large scale
models involving multiple brain areas.

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