Fast reconstruction of degenerate populations of conductance-based neuron models from spike times

TL;DR

This approach first maps spike times to DIC densities at threshold using a neural network that learns a low-dimensional representation of neuronal activity, which is used to generate degenerate CBM populations via an iterative compensation algorithm, ensuring compatibility with the intermediate target DICs.

Abstract

Inferring the biophysical parameters of conductance-based models (CBMs) from experimentally accessible recordings remains a central challenge in computational neuroscience. Spike times are the most widely available data, yet they reveal little about which combinations of ion channel conductances generate the observed activity. This inverse problem is further complicated by neuronal degeneracy, where multiple distinct conductance sets yield similar spiking patterns. We introduce a method that addresses this challenge by combining deep learning with Dynamic Input Conductances (DICs), a theoretical framework that reduces complex CBMs to three interpretable feedback components governing excitability and firing patterns. Our approach first maps spike times to DIC densities at threshold using a neural network that learns a low-dimensional representation of neuronal activity. The predicted DIC values are then used to generate degenerate CBM populations via an iterative compensation algorithm, ensuring compatibility with the intermediate target DICs, and thereby reproducing the corresponding firing patterns, even in high-dimensional models. Applied to two models, this algorithmic pipeline reconstructs spiking and bursting regimes with high accuracy and robustness to variability, including spike trains generated under noisy current injection mimicking physiological stochasticity. It produces diverse degenerate populations within milliseconds on standard hardware, enabling scalable and efficient inference from spike recordings alone. Together, this work positions DICs as a practical and interpretable link between experimentally observed activity and mechanistic models. By enabling fast and scalable reconstruction of degenerate populations directly from spike times, our approach provides a powerful way to investigate how neurons exploit conductance variability to achieve reliable computation.

Figures (6)

• Figure 1: Our proposed approach. Spike time sequences are processed by a deep learning model that predicts DICs, a compact representation of the high-dimensional conductance space. These predicted DIC values serve as targets for an iterative compensation algorithm, which explores the degenerate solution space to generate multiple conductance configurations $\bar{g}$ that reproduce the input spike pattern. This two-step strategy (i) reduces the dimensionality of the inference problem, and (ii) leverages compensation to recover diverse biologically plausible parameter sets consistent with the observed activity.
• Figure 2: Activity descriptors vary smoothly across the DIC space. Heatmaps show how individual activity metrics vary across the DIC space, revealing clear gradients that reflect a nonlinear yet structured relationship between DIC constraints and neuronal firing patterns. (A) Representative example traces of a spiking neuron (top) and a bursting neuron (bottom), with annotations highlighting the descriptors extracted from each regime: mean spiking frequency for the spiking case, and mean burst duration, mean intra-burst frequency, mean inter-burst frequency, and mean number of spikes per burst for the bursting case. (B) Spiking metrics summarized by mean firing rate. (C) Bursting metrics including intra-burst frequency, inter-burst frequency, burst duration, and spikes per burst. These smooth gradients support the learnability of the inverse mapping from spike trains to DICs, and position DICs as meaningful low-dimensional intermediates for characterizing neuronal activity.
• Figure 3: Backbone pipeline output for the STG neuron model.(A) Target spike trains (dark green, top) compared with three representative generated spike trains for spiking (red, right) and bursting (purple, left) regimes, showing accurate reproduction of activity patterns. (B) Distributions of maximal conductances across 500 generated neurons in spiking (red, right) and bursting (purple, left) regimes, demonstrating broad parameter variability despite similar dynamics.
• Figure 4: Quantitative comparison of input and generated populations. Four target DIC values (green dots) are selected in the $(g_\text{s}, g_\text{u})$ plane, spanning spiking and bursting regimes. For each target, an input population of $256$ degenerate neurons is generated via iterative compensation. Spike times from each input neuron are passed through the full pipeline: the deep learning architecture infers a conditional density over DICs (shown as contour plots), from which one pair of DIC targets is sampled and used to generate one neuron each via iterative compensation. Violin plots compare distributions of key activity metrics between the input population (left, green) and the output population (right, colored) for each target point, demonstrating faithful reproduction of firing statistics across regimes.
• Figure 5: Performance of the adapted pipeline on the DA neuron model.(A) Two target DIC values (green dots) are selected in the DA $(g_\text{s}, g_\text{u})$ plane, one for each tested activity regime: slow pacemaking and bursting. For each target, the pipeline infers a conditional density over DICs (contour plots), from which DIC targets are sampled to generate output populations. Violin plots compare input and output activity descriptors across regimes. (B) Target spike trains (dark green, top) compared with three representative generated spike trains for slow pacemaking (right) and bursting (left), showing accurate reproduction of activity patterns. (C) Distributions of maximal conductances across generated neurons for both regimes, demonstrating broad parameter variability despite similar dynamics.