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Stability of neuronal networks with homeostatic regulation

Harnack, Daniel; Pelko, Miha; Chaillet, Antoine; Chitour, Yacine; van Rossum, Mark C.W.


Daniel Harnack

Miha Pelko

Antoine Chaillet

Yacine Chitour

Mark C.W. van Rossum


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.


Harnack, D., Pelko, M., Chaillet, A., Chitour, Y., & van Rossum, M. C. (2015). Stability of neuronal networks with homeostatic regulation. PLoS Computational Biology, 11(7), Article e1004357.

Journal Article Type Article
Acceptance Date May 28, 2015
Publication Date Jul 8, 2015
Deposit Date Feb 8, 2018
Publicly Available Date Feb 8, 2018
Journal PLoS computational biology
Print ISSN 1553-734X
Electronic ISSN 1553-7358
Publisher Public Library of Science
Peer Reviewed Peer Reviewed
Volume 11
Issue 7
Article Number e1004357
Public URL
Publisher URL


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