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)

The lowest membrane potential responses errors achieved by each method for experimental validation scenarios.

# of simulations represents the total number of synthetic neuron simulations each method used during optimization. For all scenarios, the error represents the average RMSE between ground truth and predicted membrane potential responses in each time point across all membrane potential responses traces.

Comparison of membrane potential responses reconstructed from predicted parameters (experimental validation scenarios).

Each row and column corresponds to predicted neuron and method respectively. For each neuron we show ground truth membrane potential responses (Black) against the reconstructed membrane potential responses (red) from the predicted parameters.

Ablation studies.

Top: membrane potential responses errors achieved for EP-GAN when provided with incomplete input data. Bottom: membrane potential responses errors achieved for EP-GAN upon using only adversarial loss (A) and using adversarial + current reconstruction loss (A, IV) and all three loss components (A, IV, V)

The lowest membrane potential responses errors achieved by each method for prediction scenarios.

# of simulations represents the total number of synthetic neuron simulations each method used during optimization.

Input data ablation on EP-GAN.

A: Reconstructed membrane potential responses when given with incomplete membrane potential responses data. Percentages in parenthesis represent the remaining portion of input membrane potential responses trajectories. B: Reconstructed membrane potential responses when given with incomplete current profile.

Illustration of membrane potential responses reconstructed from predicted parameters (prediction scenarios).

Membrane potential responses trajectories reconstructed from EP-GAN predicted parameters (red) overlaid on top of the ground truth recording membrane potential responses (black).

Inference Time Comparison between methods for validation scenarios.

For EP-GAN, a training consists of 100 epochs.

Percentages of predicted membrane potential trajectories within empirical range.

The predicted membrane potential at time t is considered acceptable if it falls within < 2 standard deviations from experimental mean voltage at that time point. All methods use identical setups as Table 3.

Simulation protocol for neurons.

Both neuron groups (training/testing) in synthetic neurons used identical protocol. Neurons modeled with EP-GAN-E are marked with (Ext) where simulation duration and stimulation periods are extended by 5 seconds to ensure stability of resting membrane potentials

Predicted individual membrane potentials compared to ground truths with confidence bands for EP-GAN baseline (Top) vs EP-GAN-E (Bottom).

Each column represents an individual membrane potential trajectory associated with a current stimulus. Membrane potential responses trajectories reconstructed from predicted parameters (red) are overlaid on top of the ground truth recording membrane potential responses (black) where the grey shade represents the confidence band of 2 standard deviations obtained from ground truth experimental recordings (n = 3).

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.

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 inverse gradient 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.

Generating training data.

Each parameter is initially sampled from biologically plausible ranges using uniform sampling. A parameter set consists of 176 parameters spanning 15 known ion channels in C. elegans. Once parameter sets are generated, membrane potential responses and current profiles are evaluated for each set to ensure they satisfy the predefined constraints such as minimum offset between membrane potential responses traces and minimum and maximum bounds for steady-state current traces. Only parameter sets that meet the constraints are included in the training set.