A state-dependent mean-field formalism to model different activity states in conductance-based networks of spiking neurons

Cristiano Capone, Matteo di Volo, Alberto Romagnoni, Maurizio Mattia and Alain Destexhe

bioRxiv preprint: https://www.biorxiv.org/content/10.1101/565127v1

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Abstract

Higher and higher interest has been shown in the recent years to large scale spiking simulations of cerebral neuronal networks, coming both from the presence of high performance computers and increasing details in the experimental observations. In this context it is important to understand how population dynamics are generated by the designed parameters of the networks, that is the question addressed by mean field theories. Despite analytic solutions for the mean field dynamics has already been proposed generally for current based neurons (CUBA), the same for more realistic neural properties, such as conductance based (COBA) network of adaptive exponential neurons (AdEx), a complete analytic model has not been achieved yet. Here, we propose a novel principled approach to map a COBA on a CUBA. Such approach provides a state-dependent approximation capable to reliably predict the firing rate properties of an AdEx neuron with non-instantaneous COBA integration. We also applied our theory to population dynamics, predicting the dynamical properties of the network in very different regimes, such as asynchronous irregular (AI) and synchronous irregular (SI) (slow oscillations, SO). This results show that a state-dependent approximation can be successfully introduced in order to take into account the subtle effects of COBA integration and to deal with a theory capable to correctly predicts the activity in regimes of alternating states like slow oscillations.
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