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Stability of Neuronal Networks with Homeostatic Regulation.

Harnack D, Pelko M, Chaillet A, Chitour Y, van Rossum MC - PLoS Comput. Biol. (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Informatics, University of Edinburgh, Edinburgh, United Kingdom.

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.

No MeSH data available.


Related in: MedlinePlus

Parallel controllers do not lead to increased stability.The maximal recurrence is plotted against the time-constant of the second feedback loop. The τ3 time-constant of the system with single feedback is indicated by the arrow. The system with the extra feedback loop (solid curve) is always less stable than the system with a single feedback loop (dashed line), even if the additional feedback is much slower than the original one. The control loop is shown in the inset.
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pcbi.1004357.g006: Parallel controllers do not lead to increased stability.The maximal recurrence is plotted against the time-constant of the second feedback loop. The τ3 time-constant of the system with single feedback is indicated by the arrow. The system with the extra feedback loop (solid curve) is always less stable than the system with a single feedback loop (dashed line), even if the additional feedback is much slower than the original one. The control loop is shown in the inset.

Mentions: One can wonder if stability can be rescued in another way. For instance, it is not unreasonable to assume that biology uses multiple, parallel homeostatic regulators. While a general theory of such systems is lacking, some cases can be incorporated in our framework, for instance if multiple feed-backs use the same error signal, stability is determined by the quickest feedback. An addition of a parallel feedback, even if it is slower can only destabilize the system. The stability can be analyzed using the above techniques, adding the extra controller to the feedback-loop. As a technicality, because the system is invariant to the division of labor between the two feedback loops, the stability matrix gains a zero eigenvalue, which can be safely ignored. The system with parallel controllers is always less stable than the system with a single controller, even if the second controller is slower than the first one, Fig 6.


Stability of Neuronal Networks with Homeostatic Regulation.

Harnack D, Pelko M, Chaillet A, Chitour Y, van Rossum MC - PLoS Comput. Biol. (2015)

Parallel controllers do not lead to increased stability.The maximal recurrence is plotted against the time-constant of the second feedback loop. The τ3 time-constant of the system with single feedback is indicated by the arrow. The system with the extra feedback loop (solid curve) is always less stable than the system with a single feedback loop (dashed line), even if the additional feedback is much slower than the original one. The control loop is shown in the inset.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4495932&req=5

pcbi.1004357.g006: Parallel controllers do not lead to increased stability.The maximal recurrence is plotted against the time-constant of the second feedback loop. The τ3 time-constant of the system with single feedback is indicated by the arrow. The system with the extra feedback loop (solid curve) is always less stable than the system with a single feedback loop (dashed line), even if the additional feedback is much slower than the original one. The control loop is shown in the inset.
Mentions: One can wonder if stability can be rescued in another way. For instance, it is not unreasonable to assume that biology uses multiple, parallel homeostatic regulators. While a general theory of such systems is lacking, some cases can be incorporated in our framework, for instance if multiple feed-backs use the same error signal, stability is determined by the quickest feedback. An addition of a parallel feedback, even if it is slower can only destabilize the system. The stability can be analyzed using the above techniques, adding the extra controller to the feedback-loop. As a technicality, because the system is invariant to the division of labor between the two feedback loops, the stability matrix gains a zero eigenvalue, which can be safely ignored. The system with parallel controllers is always less stable than the system with a single controller, even if the second controller is slower than the first one, Fig 6.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: School of Informatics, University of Edinburgh, Edinburgh, United Kingdom.

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.

No MeSH data available.


Related in: MedlinePlus