Stability of neuronal networks with homeostatic regulation

Harnack, Daniel and Pelko, Miha and Chaillet, Antoine and Chitour, Yacine and van Rossum, Mark C.W. (2015) Stability of neuronal networks with homeostatic regulation. PLoS computational biology, 11 (7). e1004357. ISSN 1553-7358

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
University of Nottingham, UK > Faculty of Science > School of Psychology
Identification Number: 10.1371/journal.pcbi.1004357
Depositing User: Van Rossum, Mark
Date Deposited: 08 Feb 2018 12:02
Last Modified: 08 Feb 2018 12:07
URI: http://eprints.nottingham.ac.uk/id/eprint/49630

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