Minimal requirements for a neuron to coregulate many properties and the implications for ion channel correlations and robustness

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 (nin) exceeds the number of regulated properties (nout). Ion channel correlations emerge during homeostatic regulation when the dimensionality of solution space (nin - nout) 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.

Biological complexity facilitates tuning of the neuronal parameter space

“…A homeostatic mechanism based on a single feedback signal (O’Leary et al ., 2013, 2014) that has been suggested to play a role in model robustness was not compatible with our model in our hands since it decreased ion channel degeneracy. This is in agreement with a recent study (Yang et al ., 2022) that provided new insights into the complex relationship between ion channel diversity and homeostatic co-regulation of ion channel densities. The study by Yang et al (2022) suggested the necessity of more than one master feedback regulator (i.e.…”

“…This is in agreement with a recent study (Yang et al ., 2022) that provided new insights into the complex relationship between ion channel diversity and homeostatic co-regulation of ion channel densities. The study by Yang et al (2022) suggested the necessity of more than one master feedback regulator (i.e. more regulators than just global calcium) for homeostatic feedback loops, which must co-tune numerous degenerate and pleiotropic ion channels to achieve multiple regulated functions or objectives (cf.…”

“…The reason is that the topology of the high-dimensional space increases the likelihood of neurons returning into functional subspaces by random ion channel parameter adjustments. An interesting extension would be to compare the efficiency of activity-dependent regulation (O’Leary et al ., 2014; Franci et al ., 2020; Yang et al ., 2022) implemented with single or multiple homeostatic error signals (Yang et al ., 2022), with the multi-objective optimisation (Druckmann, 2007; Van Geit et al ., 2008; Pallasdies et al ., 2021; Jedlicka et al ., 2022) that arises naturally from stochastically exploring high-dimensional parameter spaces.…”

“…Experimental as well as theoretical studies from the last decades revealed that pharmacological manipulations like the blockage or upregulation of intrinsic or synaptic mechanisms, resulting in a pathological cellular activity on a short timescale, can be compensated by up-and downregulation of the remaining conductances on a long timescale (MacLean et al, 2003;Swensen, 2005;O'Leary et al, 2014;Drion et al, 2015;Guo et al, 2005;Nerbonne et al, 2008;Stegen et al, 2012;MacLean et al, 2005). Interestingly, not all manipulations can be compensated by mechanisms of homeostatic regulation (Zhang et al, 2003;Yang et al, 2022), indicating differences in the capability of homeostatic compensation between ion channels as well as types of neurons. As opposed to other studies using biophysically realistic mechanisms of homeostatic intrinsic plasticity based on calcium signals (O'Leary et al, 2013(O'Leary et al, , 2014Abbott and LeMasson, 1993;Golowasch et al, 1999;Liu et al, 1998;Franci et al, 2020; see also Yang et al, 2022), we decided to use a gradient 20/52 descent approach to investigate the large and complex parameter space of possible intrinsic compensations.…”

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

“…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.…”