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

Abstract

Different ion channel combinations can yield equivalent neuronal excitability. This degeneracy facilitates robust regulation of excitability by enabling a disruptive change in one channel to be offset by compensatory changes in other channels. But various aspects of excitability plus other cellular properties require regulation. Coordinately regulating multiple properties via control of overlapping sets of ion channels is no easy task. Here we demonstrate that of the many ion 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. We demonstrate that for multi-output solution sets to be degenerate, the number of controllable ion channels (nin) must exceed the number of regulated properties (nout). We further demonstrate how the dimensionality of solution space shapes ion channel correlations that emerge during homeostatic regulation and how homeostatic regulation may fail given the heightened challenge of simultaneously regulating many properties.SIGNIFICANCE STATEMENTNeurons, like other cells, must continue functioning despite variations in their operating conditions. In particular, they must adjust their intrinsic excitability to maintain their information processing capabilities. Neurons homeostatically regulate their excitability and other properties by up- or down-regulating, or otherwise modulating, myriad different ion channels. But each ion channel tends to affect several properties; consequently, adjusting an ion channel to regulate one property is liable to disrupt another property. Instead, multiple ion channels must be adjusted. Specifically, we show that in order to regulate n properties, n+1 ion channels must be adjustable. This has a simple mathematical explanation but important biological implications. The need to simultaneously regulate many properties may help account for ion channel diversity.

Pareto optimality, economy–effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons

“…Likewise, ion channel expression data from fast-spiking neurons in the vestibular nucleus suggest that co-regulation of ion channels supports optimal balance between high firing rates and their energy efficiency [119]. Other recent computational work using biophysically simple single-compartment models has explored as to when homeostatic co-regulation of ion channels leads to ion channel correlations [124]. Intriguingly, Yang et al .…”

“…Thus, homeostatic co-tuning of multiple tasks seems possible only with sufficiently large ion channel diversity (see also [36]). In addition, ion channel correlations seem to arise if the solution space (defined as a difference between the number of dimensions of parameter space and the number of dimensions of performance space) is low-dimensional [124]. It would be interesting to compare these predictions to experiments accompanied by simulations in biophysically and morphologically more complex models complemented by Pareto analysis.…”

“…Intriguingly, Yang et al . [124] have addressed this question in the context of ion channel degeneracy and multi-objective optimization. The authors predict that homeostatic ion channel co-regulation can lead to many (degenerate) multi-objective solutions if the number of available ion channels is higher than the number of objectives.…”

Multiscale computer model of the spinal dorsal horn reveals changes in network processing associated with chronic pain

“…It is important to reserve certain constraints for model validation, rather than applying them during the fitting process. In this respect, the degree of degeneracy could be overestimated and would be revised down in light of additional constraints (Yang et al, 2021). The remaining degeneracy underlies biological variability (see above) and often prevents simple conclusions whose validity hinges on a certain context; in other words, a molecule or cell type may be "necessary" in some circuits but not others contingent on synaptic weights.…”