Minimal requirements for a neuron to co-regulate many properties and the implications for ion channel correlations and robustness

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Abstract

Neurons regulate their excitability by adjusting their ion channel levels. Degeneracy - achieving equivalent outcomes (excitability) using different solutions (channel combinations) - facilitates this regulation by enabling a disruptive change in one channel to be offset by compensatory changes in other channels. But neurons must co-regulate many properties. Pleiotropy - the impact of one channel on more than one property - complicates regulation because a compensatory ion channel change that restores one property to its target value often disrupts other properties. How then does a neuron simultaneously regulate multiple properties? Here we demonstrate that of the many channel combinations producing the target value for one property (the single-output solution set), few combinations produce the target value for other properties. Combinations producing the target value for two or more properties (the multi-output solution set) correspond to the intersection between single-output solution sets. Properties can be effectively co-regulated only if the number of adjustable channels (n_in) exceeds the number of regulated properties (n_out). Ion channel correlations emerge during homeostatic regulation when the dimensionality of solution space (n_in- n_out) is low. Even if each property can be regulated to its target value when considered in isolation, regulation as a whole fails if single-output solution sets do not intersect. Our results also highlight that ion channels must be co-adjusted with different ratios to regulate different properties, which suggests that each error signal drives modulatory changes independently, despite those changes ultimately affecting the same ion channels.

Data availability

All computer code is available at http://modeldb.yale.edu/267309 and at http://prescottlab.ca/code-for-models. Key parameter values are provided in Supplementary File 1. Other parameter values are identified in the Methods. Source data is provided for Figure 2.

Article and author information

Author details

Jane Yang

Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Canada

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0003-0114-5503
Husain Shakil

Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Canada

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0003-3995-6811
Stéphanie Ratté

Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Canada

Competing interests
The authors declare that no competing interests exist.
Steven Alec Prescott

Neurosciences and Mental Health, The Hospital for Sick Children, Toronto, Canada

For correspondence
steve.prescott@sickkids.ca

Competing interests
The authors declare that no competing interests exist.

"This ORCID iD identifies the author of this article:" 0000-0002-3827-4512

Funding

Canadian Institutes of Health Research (Foundation Grant 167276)

Steven Alec Prescott

Natural Sciences and Engineering Research Council of Canada (Discovery Grant RGPIN 436168)

Steven Alec Prescott

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Ethics

Animal experimentation: All experimental procedures were approved by The Hospital for Sick Children Animal Care Committee (protocol #53451) and were conducted in accordance with guidelines from the Canadian Council on Animal Care

Copyright

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.