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Stability of neuronal networks with homeostatic regulation

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

Authors

Daniel Harnack

Miha Pelko

Antoine Chaillet

Yacine Chitour

Mark C.W. van Rossum



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.

Journal Article Type Article
Publication Date Jul 8, 2015
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
APA6 Citation 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), https://doi.org/10.1371/journal.pcbi.1004357
DOI https://doi.org/10.1371/journal.pcbi.1004357
Publisher URL http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004357
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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