title: Stability of Neuronal Networks with Homeostatic Regulation.
abstract: Neurons are equipped with homeostatic mechanisms that counteract long-term perturbations of their average activity and thereby keep neurons in a healthy and information-rich operating regime. While homeostasis is believed to be crucial for neural function, a systematic analysis of homeostatic control has largely been lacking. The analysis presented here analyses the necessary conditions for stable homeostatic control. We consider networks of neurons with homeostasis and show that homeostatic control that is stable for single neurons, can destabilize activity in otherwise stable recurrent networks leading to strong non-abating oscillations in the activity. This instability can be prevented by slowing down the homeostatic control. The stronger the network recurrence, the slower the homeostasis has to be. Next, we consider how non-linearities in the neural activation function affect these constraints. Finally, we consider the case that homeostatic feedback is mediated via a cascade of multiple intermediate stages. Counter-intuitively, the addition of extra stages in the homeostatic control loop further destabilizes activity in single neurons and networks. Our theoretical framework for homeostasis thus reveals previously unconsidered constraints on homeostasis in biological networks, and identifies conditions that require the slow time-constants of homeostatic regulation observed experimentally.
authors.affiliation: School of Informatics, University of Edinburgh, Edinburgh, United Kingdom.
authors.forename: Daniel
authors.initials: D
authors.lastname: Harnack
authors.affiliation: School of Informatics, University of Edinburgh, Edinburgh, United Kingdom.
authors.forename: Miha
authors.initials: M
authors.lastname: Pelko
authors.affiliation: L2S-Univ. Paris Sud-CentraleSupélec, Gif sur Yvette, France.
authors.forename: Antoine
authors.initials: A
authors.lastname: Chaillet
authors.affiliation: L2S-Univ. Paris Sud-CentraleSupélec, Gif sur Yvette, France.
authors.forename: Yacine
authors.initials: Y
authors.lastname: Chitour
authors.affiliation: School of Informatics, University of Edinburgh, Edinburgh, United Kingdom.
authors.forename: Mark C W
authors.initials: MC
authors.lastname: van Rossum
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology*; D006706:Homeostasis / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*