Estimation of HH-model parameters from membrane potential and steady-state current profiles.

Given the membrane potential responses (V) and steady-state current profiles (IV) of a neuron, the task is to predict biophysical parameters of Hodgkin-Huxley type neuron model (Left). We use Encoder-Generator approach to predict the parameters (Right)

EP-GAN (32k) predictions on simulated neurons.

A: EP-GAN predicted membrane potential traces and steady-state currents (Red) overlaid on top of groundtruth counterparts (black) for Transient outward rectifier neuron type. B: Outward rectifier neuron type. C: Bistable neuron type.

Bar plot showing the mean RMSE errors for membrane potential responses (pre-, mid-, post-activation periods, averaged error) and steady-state currents for 9 experimental neurons.

A: Membrane potential responses (left) and steady-state currents (right) diagrams showing the time and voltage intervals of which the RMSE errors are computed. B: Bar plots showing RMSE errors for membrane potential responses and steady-state currents for small HH-model scenarios (Top) and Large HH-model prediction scenarios (Bottom). All methods use 32k sample size for both scenarios.

Small HH-model scenarios RMSE errors for predicted membrane potential responses and steady-state currents.

Each method is tested with 32k or 64k total sample sizes where the top row shows membrane potential responses RMSE errors averaged across pre-activation, mid-activation, post-activation periods and the bottom row shows steady-state currents RMSE errors across 18 voltage values.

EP-GAN (32k) Prediction on experimental neurons (small HH-model).

A: EP-GAN predicted membrane potential traces and steady-state currents (Red) overlaid on top of groundtruth counterparts (black) for Transient outward rectifier neuron type (RIM, DVC, HSN). B: Outward rectifier neuron type (AIY, URX, RIS). C: Bistable neuron type (AFD, AWB, AWC).

Large HH-model scenarios RMSE errors for predicted membrane potential responses and steady-state currents.

Each method is tested with 32k or 64k total sample sizes where the top row shows membrane potential responses RMSE errors averaged across pre-activation, mid-activation, post-activation periods and the bottom row shows steady-state currents RMSE errors across 18 voltage values.

EP-GAN (32k) Prediction on experimental neurons (large HH-model).

A: EP-GAN predicted membrane potential traces and steady-state currents (Red) overlaid on top of groundtruth counterparts (black) for Transient outward rectifier neuron type (RIM, DVC, HSN). B: Outward rectifier neuron type (AIY, URX, RIS). C: Bistable neuron type (AFD, AWB, AWC).

Ablation studies.

Top: membrane potential responses and steady-state current errors achieved for EP-GAN (32k) when provided with incomplete input data. Bottom: membrane potential responses and steady-state current errors achieved for EP-GAN upon using only adversarial loss (Adv) and using adversarial + current reconstruction loss (Adv + Steady state) and all three loss components (Adv + Steady state + Membrane potential)

Input data ablation on EP-GAN (32k).

Left: Reconstructed membrane potential responses for RIM, AIY and AFD when given with incomplete membrane potential responses data. Percentages in parenthesis represent the remaining portion of input membrane potential responses trajectories. Right: Reconstructed membrane potential responses for RIM, AIY, and AFD when given with incomplete steady-state current input.

Architecture of EP-GAN.

The architecture consists of an Encoder, Generator and Discriminator. Encoder compresses the membrane potential responses into a 1D vector (i.e., latent space) which is then concatenated with 1D steady-state current profile to be used as an input to both generator and discriminator. Generator translates the latent space vector into a vector of parameters and the Discriminator outputs a scalar measuring the similarity between generated parameters and ground truths . The Generator is trained with adversarial loss supplemented by reconstruction losses for both membrane potential responses and steady-state current profiles. The Discriminator is trained with discriminator adversarial loss only. Generator and Discriminator follow the architecture of Wasserstein GAN with gradient penalty (WGAN-GP) for more stable learning. During training, random masking is applied to input membrane potential responses which gradually decreases toward as the training continues.

Description of membrane potential responses and current reconstruction losses for the Generator.

Generated parameter vector is used to evaluate membrane potential responses derivatives dV/dt at n time points sampled with fixed interval given the ground truth at those time points. The evaluated membrane potential responses derivatives are then used to reconstruct using the forward integration operation ∇−1. The reconstructed is then compared with ground truth to evaluate the membrane potential responses reconstruction loss . Current reconstruction is computed in a similar way via evaluating the currents at defined membrane potential responses steps V given generated parameters as inputs.

Training data generation.

In Step 1, each parameter is initially sampled from biologically plausible ranges using both skewed gaussian (channel conductance) and uniform sampling. A parameter set consists of 175 parameters spanning 16 known ion channels in C. elegans and similar organisms. In Step 2 and 3, steady-state currents and membrane potential responses are evaluated for each set to ensure they satisfy the predefined constraints such as bifurcation structure represented by dI/dV bounds and minimum-maximum membrane potential across current-clamp protocols. Only parameter sets that meet both constraints are included in the training set.

Simulation protocols for simulated and experimental neurons.