Computational modelling of dentate granule cells reveals Pareto optimal trade-off between pattern separation and energy efficiency (economy)

Hippocampal granule cell (GC) models exhibit degeneracy with different ion channel parameters resulting in comparable functional behaviour [1,2]. However, it is unknown how the degenerate models are further constrained by energetic considerations and known computational functions of GCs. Here, we use Pareto optimality to investigate this question. The Pareto perspective is particularly useful for multi-objective optimisation with multiple trade-offs [3]. We assume that evolution constrains and simplifies the ion channel parameter space by favouring Pareto optimal neurons, which cannot improve their performance in one objective without reducing their effectiveness in another [3,6].
The first cost we consider in the investigation of two-objective optimality for GC models is pattern separation [4]. GCs are thought to facilitate this function of the dentate circuit by reducing the similarity between their inputs and outputs. Previous measures of pattern separation have neglected the information content between input and output, potentially leading to biased estimates of pattern separation when the input information or pattern is nearly destroyed. Therefore, here we use information-theoretic measures (such as relative redundancy reduction and mutual information) to make the assessment of pattern separation more reliable (see our pattern separation toolbox in [5]). The second cost we include in the analysis of the two-objective optimality of GC models is energy efficiency (economy), estimated by converting ion currents to ATP [6].
Using biophysically realistic compartmental GC models, we show that GCs with ion channel distributions taken from the experimental literature [7] are close to Pareto optimal when compared to a set of randomly generated GC models. The random GC models still have realistic spiking properties but different ion channel combinations [2]. In addition, we simulate the role of adult-born immature GCs in pattern separation, as adult GC neurogenesis affects hippocampal memory function [8]. Compared to mature GCs, the young immature GCs (simulated using their known biophysics) can effectively separate patterns with a tendency towards higher economy with respect to mature GC models. Taken together, we demonstrate in this work that the Pareto perspective is a useful tool for the simultaneous analysis of multiple GC objectives.