Eur. Phys. J. Special Topics 227, 1015–1028 (2018)
https://doi.org/10.1140/epjst/e2018-800072-1

Regular Article

Neuronal devices: understanding neuronal cultures through percolation helps prepare for the next step

¹ Laboratoire Matière et Systèmes Complexes, UMR 7057 CNRS, Université Denis Diderot-Paris 7, 10 rue A. Domon et L. Duquet, 75013 Paris Cedex, France
² Université d’Evry-Val d’Essonne, 23 Boulevard François Mitterrand, 91000 Evry, France

^a e-mail: samuel.bottani@univ-paris-diderot.fr

Received: 26 April 2018
Received in final form: 2 July 2018
Published online: 12 December 2018

Abstract

Cultures of dissociated neurons are an invaluable experimental tool in studying neuronal networks at an intermediate scale in an in vitro controlled physico-chemical environment. Moreover, current micro-fabrication techniques allow the design of a custom connectivity between subpopulations, which could make it possible to carry out computations with devices involving living cells. The quorum percolation (QP) model has been designed in the context of neurobiology to describe bursts of activity occurring in neuronal cultures from the point of view of collective phenomena rather than from a dynamical synchronization approach. Such a model is well suited to describe triggered activity in neuronal devices, and its generic character points at the necessity of heavily structured devices to go beyond collective bursting. We derive a continuous extension of the QP model, seen as information propagation on a non-metric directed graph, and discuss how its critical behavior might give insight on the connectivity of neuronal networks. The link with metric graphs, embedded in a two-dimensional space, is tackled by the introduction of a geometrical model based upon a random walk, where axon growth is constrained by obstacles such as walls and channels. This provides a starting point for the construction of neuronal devices in vitro capable of more complex behaviors. Lastly, we show how simulations of bursts with a dynamical adaptive integrate-and-fire model can be interpreted in terms of QP, confirming the robustness of this synchronized behavior.