Ion Channel Degeneracy: Understanding Function-Energy Trade-Offs in CA1 Pyramidal Cells

Abstract

Introduction

In recent years, there has been an advent of interest in the phenomenon of ion channel degeneracy and the explanations for its emergence [1], [2], [3]. Ion channel degeneracy is defined as a functional many-to-one relationship in which distinct combinations of ion channels elicit similar functional or electrophysiological features. Despite the recent progress in the illumination of this phenomenon, there is still a multitude of open questions, i.e., what are the constraints on ion channel degeneracy; is there a guiding principle; are there functional trade-offs?

In this thesis, we ask how far ion channel degeneracy is moderated by function-energy trade-offs and show Pareto-optimal behavior. Precisely, we hypothesized that CA1 pyramidal cells express trade-offs between spatial coding (function) and energy efficiency and obey Pareto-optimal principles. Pareto optimality is defined as a trade-off in which it is not possible to improve in one objective without worsening in another.

Methodology

We applied a stochastic-search strategy on a full-morphological conductance-based CA1 pyramidal cell model [3], which provided us with valid models that fulfill biophysical constraints of intrinsic somatodendritic measurements, spatial coding, and ATP consumption in a biologically plausible parameter range. Thereafter, we investigated ion-channel co-expression as correlation plots between our 22 active and passive model parameters to see if we could observe degeneracy. We used graphical analysis tools to inquire if Pareto fronts guide the trade-off between our valid models, i.e., fit functions for the respective objectives. Furthermore, we checked for spike moderations.

Results

We found no specific correlations in ion-channel co-expression, indicating degeneracy. Moreover, we observed weak correlations between ATP consumption and spatial coding (MI) in our model population (r=-0.1), which was non-significant (p=0.26). Post-hoc tests revealed no significant correlation between spatial coding and spike counts (r=0.03, p=0.68), but a positive correlation between ATP consumption and spike count (r=0.21, p=0.01). 

Discussion

We didn't observe any significant trade-offs between energy and function in our model population. Moreover, we found a moderate correlation between energy and spike count, which makes intuitive sense if we expect ATP as the energy currency of spike activity. However, our biophysical constraints, in particular, the tuning curve limitations of the place fields, i.e., frequency range and full-width half-maximum size, might have been too strict to allow energy-function trade-offs to appear.

In this thesis, we tried to elucidate a basic principle in neuroscience by combining methods from machine learning, computational modelling, and neuroscience to find out about fundamental principles guiding biological function.

References

[1] E. Marder and J.-M. Goaillard, “Variability, compensation and homeostasis in neuron and network function,” Nat Rev Neurosci, vol. 7, no. 7, pp. 563–574, Jul. 2006. doi: 10.1038/nrn1949.

[2] P. Jedlicka, A. D. Bird, and H. Cuntz, “Pareto optimality, economy–effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons,” Open Biol., vol. 12, no. 7, p. 220073, Jul. 2022. doi: 10.1098/rsob.220073.

[3] A. Roy and R. Narayanan, “Spatial information transfer in hippocampal place cells depends on trial-to-trial variability, symmetry of place-field firing, and biophysical heterogeneities,” Neural Networks, vol. 142, pp. 636–660, Oct. 2021. doi: 10.1016/j.neunet.2021.07.026.