1. Neuroscience

Generation of biophysical neuron model parameters from recorded electrophysiological responses

  1. Jimin Kim
  2. Minxian Peng
  3. Shuqi Chen
  4. Qiang Liu  Is a corresponding author
  5. Eli Shlizerman  Is a corresponding author
  1. Department of Electrical and Computer Engineering, University of Washington, United States
  2. Department of Neuroscience, City University of Hong Kong, Hong Kong
  3. Department of Applied Mathematics, University of Washington, United States
https://doi.org/10.7554/eLife.95607.4
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Cite this article
  1. Jimin Kim
  2. Minxian Peng
  3. Shuqi Chen
  4. Qiang Liu
  5. Eli Shlizerman
(2025)
Generation of biophysical neuron model parameters from recorded electrophysiological responses
eLife 13:RP95607.
https://doi.org/10.7554/eLife.95607.4
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9 figures, 8 tables and 2 additional files

Figures

Figure 1
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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 the Hodgkin–Huxley-type neuron model (left). We use the Encoder-Generator approach to predict the parameters (right).

Figure 2 with 1 supplement
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ElectroPhysiomeGAN (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.

Figure 2—figure supplement 1
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Root mean square error (RMSE) error distribution (averaged over pre-, mid-, post-activation time periods) for the simulated neurons (n=200) in test set.
Figure 3 with 1 supplement
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ElectroPhysiomeGAN (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).

Figure 3—figure supplement 1
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Small HH-model GDE3, NSDE, DEMO, NSGA2 predictions (sample size = 32k) on experimental neurons.

(A) Predicted membrane potential traces (red) overlaid on top of ground truth (black) for all nine experimental neurons. (B) Predicted steady-state current traces (red) overlaid on top of ground truth (black) for all nine experimental neurons.

Figure 4 with 1 supplement
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ElectroPhysiomeGAN (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).

Figure 4—figure supplement 1
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Large HH-model GDE3, NSDE, DEMO, NSGA2 predictions (sample size = 32k) on experimental neurons.

(A) Predicted membrane potential traces (red) overlaid on top of ground truth (black) for all nine experimental neurons. (B) Predicted steady-state current traces (red) overlaid on top of ground truth (black) for all nine experimental neurons.

Figure 5
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Bar plot showing the average root mean square error (RMSE) errors for membrane potential responses (pre-, mid-, post-activation periods, mean error) and steady-state currents for nine 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 (n = 9, 95% confidence level using t-test) for membrane potential responses and steady-state currents for small HH-model prediction scenarios (top) and large HH-model prediction scenarios (bottom). All methods use a 32k sample size for both scenarios.

Figure 6 with 1 supplement
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Input data ablation on ElectroPhysiomeGAN (EP-GAN) (32k, Large HH-model).

Left: reconstructed membrane potential responses for RIM, AIY, and AFD when given with incomplete membrane potential responses data. Percentages in parentheses 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.

Figure 6—figure supplement 1
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Input data ablation on ElectroPhysiomeGAN (EP-GAN) (32k, Large HH-model).

Left: reconstructed steady-state currents when given with incomplete membrane potential responses data. Percentages in parentheses represent the remaining portion of input membrane potential responses trajectories. Right: reconstructed steady-state currents when given with incomplete steady-state current input.

Figure 7
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Architecture of ElectroPhysiomeGAN (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) that 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 p~→ and the Discriminator outputs a scalar measuring the similarity between generated parameters (p~→) and ground truths (p→). 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 where its masking rate gradually decreases as the training continues.

Figure 8
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Description of membrane potential responses and steady-state current reconstruction losses for the Generator.

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

Figure 9
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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 Steps 2 and 3, steady-state currents and membrane potential responses are evaluated for each parameter 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.

Tables

Table 1
Small HH-model scenarios root mean square error (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. The lowest membrane potential responses RMSE error is marked bold for each neuron.

MethodSample sizeMedian errorRIMDVCHSNAIYURXRISAFDAWBAWC
GDE332k16.9 mV20.958.18.913.016.925.46.332.54.7
5.9 pA5.85.819.84.82.45.919.17.211.9
64k6.0 mV11.524.113.76.05.17.14.15.63.6
7.9 pA7.54.66.87.218.77.942.117.646.7
NSDE32k7.1 mV38.78.320.25.77.111.05.56.36.6
13.6 pA3.121.59.713.614.25.724.79.614.5
64k5.5 mV15.48.720.213.55.25.54.94.94.0
9.7 pA2.65.99.73.411.73.264.412.419.0
DEMO32k6.7 mV35.914.15.813.29.06.75.04.93.8
11.5 pA6.513.814.65.25.49.723.811.518.7
64k4.8 mV12.310.55.810.24.84.73.14.42.9
14.6 pA4.46.514.64.115.210.341.023.117.8
NSGA232k7.5 mV12.415.42.69.86.16.47.59.46.6
10 pA4.07.414.34.616.65.014.411.910.0
64k4.3 mV10.519.05.213.33.53.24.24.33.1
8.4 pA8.41.85.22.321.26.526.612.649.4
EP-GAN
(ours)		32k2.5 mV3.42.41.62.53.21.74.92.52.0
13.8 pA4.013.810.310.738.916.848.09.628.9
64k2.4 mV3.42.41.62.42.91.43.42.52.1
13.1 pA3.213.92.59.816.513.149.711.627.9
Table 2
Large HH-model scenarios root mean square error (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. The lowest membrane potential responses RMSE error is marked bold for each neuron.

MethodSample sizeMedian errorRIMDVCHSNAIYURXRISAFDAWBAWC
GDE332k12.8 mV14.012.512.819.49.015.229.410.89.2
9.6 pA3.223.512.810.26.36.07.918.19.6
64k10.5 mV14.011.010.511.712.49.05.09.54.7
4.9 pA3.26.57.43.84.84.016.914.84.9
NSDE32k16.1 mV31.519.08.712.18.623.89.827.116.1
7.2 pA7.88.09.66.85.14.218.27.26.2
64k8.6 mV33.98.612.45.98.68.016.612.54.6
8.1 pA4.029.68.14.75.14.39.115.014.9
DEMO32k16.6 mV28.017.816.610.222.918.16.013.15.1
11.9 pA7.611.921.47.211.16.818.211.930.9
64k10.5 mV10.529.511.010.26.818.46.013.14.4
8.0 pA7.42.621.37.28.07.051.111.99.8
NSGA232k13.4 mV13.416.129.211.38.613.58.211.213.6
7.6 pA6.67.65.88.75.12.724.110.97.6
64k7.5 mV10.616.022.57.54.613.45.46.96.6
4.9 pA4.93.23.71.29.53.124.713.76.9
EP-GAN
(ours)		32k2.7 mV3.22.53.02.73.01.84.52.62.1
12.4 pA3.212.417.410.536.621.943.29.38.4
64k2.6 mV3.22.92.52.63.41.84.42.62.2
8.6 pA3.68.63.34.937.99.231.85.110.2
Table 3
Ablation studies.

Top: membrane potential responses and steady-state current errors achieved for EP-GAN (32k, Large HH-model) when provided with incomplete input data. Bottom: membrane potential responses and steady-state current errors achieved for EP-GAN (32k, Large HH-model) 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 AblationSample sizeMedian ErrorRIMAIYAFD
EP-GAN (25% membrane potential)32k5.4 mV
14.9 pA		3.8
2.8		5.4
14.9		8.9
34.4
EP-GAN (75% steady-state)32k3.5 mV
15.6 pA		3.3
3.7		3.5
15.6		5.1
68.9
EP-GAN (50% steady-state)32k3.5 mV
15.5 pA		3.3
3.7		3.5
15.5		5.1
68.9
EP-GAN (25% steady-state)32k3.5 mV
15.6 pA		3.3
3.7		3.5
15.6		5.1
68.9
EP-GAN (75% membrane potential)32k3.4 mV
11.3 pA		3.4
3.6		2.7
11.3		4.9
44.0
EP-GAN (full)32k3.3 mV
10.5 pA		3.3
3.2		2.7
10.5		5.2
39.5
EP-GAN (50% membrane potential)32k3.3 mV
13.5 pA		3.3
3.4		2.9
13.5		4.5
43.2
Loss ablationSample sizeMedian ErrorRIMAIYAFD
EP-GAN (Adv)32k14.4 mV
20.3 pA		14.4
3.1		6.1
20.3		24.5
75.4
EP-GAN (Adv + steady state)32k6.0 mV
19.1 pA		5.7
2.8		6.0
19.1		3.9
23.1
EP-GAN (Adv + steady state + membrane potential)32k3.3 mV
10.5 pA		3.3
3.2		2.7
10.5		5.2
39.5
Table 4
Simulation protocols for simulated and experimental neurons.
NeuronDuration (s)Current-clamp (min:step:max)Stimulation period (s)Voltage-clamp (min:step:max)
Simulated15–15 pA:5 pA:35 pA5–10–120 mV:10 mV:50 mV
RIM15–15 pA:5 pA:35 pA5–10–120 mV:10 mV:50 mV
DVC15–2 pA:1 pA:8 pA5–10–120 mV:10 mV:50 mV
HSN15–2 pA:1 pA:8 pA5–10–120 mV:10 mV:50 mV
AIY15–15 pA:5 pA:35 pA5–10–120 mV:10 mV:50 mV
URX15–4 pA:2 pA:16 pA5–10–120 mV:10 mV:50 mV
RIS15–4 pA:2 pA:16 pA5–10–120 mV:10 mV:50 mV
AFD15–15 pA:5 pA:35 pA5–10–120 mV:10 mV:50 mV
AWB15–4 pA:2 pA:16 pA5–10–120 mV:10 mV:50 mV
AWC15–4 pA:2 pA:16 pA5–10–120 mV:10 mV:50 mV
Table 5
List of ion channels included in the estimated HH-models.

Ion selectivity for each channel and the number of ElectroPhysiomeGAN (EP-GAN) trained parameters (not including reversal potentials) for both small and large HH-models are listed.

Ion channelIon selectivity# of parameters(small HH-model)# of parameters(large HH-model)
SHL1K+422
SHK1K+314
EGL2K+28
IRK1/3K+210
UNC103K+315
KQT1K+317
EXP2K+315
SLO1K+22
SLO1-CaVK+33
SLO2K+22
SLO2-CaVK+33
EGL19Ca+323
UNC2Ca+318
CCA1Ca+315
LeakLeak11
NCANa+11
Appendix 1—table 1
Root mean square error (RMSE) errors for membrane potential responses (top) and steady-state currents (bottom) for test neurons (n=200) considered in prediction on simulated neurons scenario.

Membrane potential responses errors are ordered as pre-activation error [4–5 s), mid-activation error [5–10 s], and post-activation periods error (10–11 s].

MethodSimulation #Test neurons
EPGAN32k1.33 mV | 3.63 mV | 2.15 mV
8.41 pA
Appendix 1—table 2
Small HH-model root mean square error (RMSE) errors (sample size = 32k) for membrane potential responses and steady-state currents for predictions on small HH-model scenarios.

For each neuron, top row shows the RMSE errors for three time intervals – pre-activation [4–5s), mid-activation [5–10s], and post-activation (10–11s] and bottom row shows the RMSE error for steady-state currents across 18 voltage points.

MethodNeurons
GDE3RIMDVCHSN
5.63 mV53.09 mV3.92 mV47.39 mV79.42 mV47.34 mV2.8 mV14.76 mV8.98 mV
5.78 pA5.78 pA19.84 pA
AIYURXRIS
9.75 mV17.41 mV11.75 mV14.89 mV25.19 mV10.61 mV28.39 mV19.52 mV28.18 mV
4.82 pA2.42 pA5.94 pA
AFDAWBAWC
0.66 mV17.37 mV0.93 mV36.72 mV26.7 mV34.21 mV0.56 mV12.42 mV1.2 mV
19.13 pA7.22 pA11.92 pA
NSDERIMDVCHSN
33.29 mV51.33 mV31.54 mV0.86 mV19.88 mV4.29 mV9.76 mV41.66 mV9.22 mV
3.14 pA21.47 pA9.7 pA
AIYURXRIS
0.46 mV11.84 mV4.69 mV1.35 mV15.19 mV4.61 mV5.86 mV21.26 mV5.96 mV
13.63 pA14.2 pA5.68 pA
AFDAWBAWC
1.74 mV13.16 mV1.49 mV0.5 mV15.88 mV2.39 mV0.74 mV17.47 mV
24.73 pA9.55 pA14.49 pA
DEMORIMDVCHSN
32.73 mV43.2 mV31.84 mV7.92 mV27.06 mV7.24 mV1.18 mV14.5 mV1.59 mV
6.52 pA13.77 pA14.63 pA
AIYURXRIS
7.26 mV26.04 mV6.27 mV1.7 mV22.14 mV3.09 mV1.29 mV15.55 mV3.26 mV
5.16 pA5.39 pA9.68 pA
AFDAWBAWC
0.85 mV13.06 mV1.08 mV0.05 mV14.41 mV0.21 mV0.8 mV9.44 mV1.23 mV
23.84 pA11.47 pA18.7 pA
NSGA2RIMDVCHSN
3.1 mV26.28 mV7.88 mV16.15 mV21.63 mV8.39 mV0.48 mV6.67 mV0.64 mV
3.97 pA7.39 pA14.29 pA
AIYURXRIS
3.58 mV22.2 mV3.71 mV2.36 mV10.37 mV5.46 mV2.88 mV13.94 mV2.36 mV
4.59 pA16.555.01
AFDAWBAWC
2.24 mV17.99 mV2.37 mV0.52 mV19.49 mV8.32 mV1.9 mV14.82 mV2.98 mV
14.38 pA11.86 pA9.98 pA
EP-GANRIMDVCHSN
0.33 mV8.23 mV1.52 mV0.19 mV5.74 mV1.22 mV0.18 mV4.02 mV0.49 mV
4.03 pA13.8 pA10.29 pA
AIYURXRIS
0.66 mV6.41 mV0.55 mV1.66 mV5.07 mV2.82 mV0.74 mV3.77 mV0.59 mV
10.7 pA16.84 pA13.8 pA
AFDAWBAWC
3.15 mV8.66 mV2.87 mV0.04 mV7.23 mV0.33 mV0.66 mV4.71 mV0.72 mV
47.97 pA9.64 pA28.86 pA
Appendix 1—table 3
Large HH-model root mean square error (RMSE) errors (sample size = 32k) for membrane potential responses and steady-state currents for predictions on large HH-model scenarios.

For each neuron, the top row shows the RMSE errors for three time intervals – pre-activation [4–5s), mid-activation [5–10s], and post-activation (10–11s], and the bottom row shows the RMSE error for steady-state currents across 18 voltage points.

MethodNeurons
GDE3RIMDVCHSN
2.31 mV30.01 mV9.71 mV3.08 mV27.0 mV7.54 mV3.4 mV31.0 mV4.09 mV
3.15 pA23.53 pA12.75 pA
AIYURXRIS
16.88 mV25.85 mV15.51 mV3.79 mV20.27 mV2.97 mV6.54 mV32.36 mV6.61 mV
10.24 pA6.32 pA5.99 pA
AFDAWBAWC
33.71 mV20.5 mV33.86 mV3.8 mV24.56 mV4.14 mV8.05 mV11.58 mV8.04 mV
7.85 pA18.08 pA9.55 pA
NSDERIMDVCHSN
27.97 mV40.68 mV25.98 mV13.33 mV30.91 mV12.46 mV5.03 mV15.31 mV5.73 mV
7.75 pA8.03 pA9.58 pA
AIYURXRIS
6.81 mV22.46 mV7.05 mV0.19 mV21.14 mV4.45 mV24.54 mV22.72 mV24.22 mV
6.82 pA5.06 pA4.17 pA
AFDAWBAWC
24.96 mV2.09 mV18.19 mV31.41 mV21.6 mV28.39 mV12.25 mV22.77 mV13.38 mV
14.73 pA7.24 pA6.18 pA
DEMORIMDVCHSN
8.91 mV63.94 mV11.11 mV16.01 mV21.32 mV15.96 mV11.8 mV26.0 mV12.11 mV
7.57 pA11.89 pA21.4 pA
AIYURXRIS
1.46 mV25.9 mV3.21 mV23.15 mV18.16 mV27.24 mV19.32 mV15.3 mV19.8 mV
7.24 pA11.14 pA6.81 pA
AFDAWBAWC
2.29 mV11.92 mV3.79 mV7.0 mV24.03 mV8.3 mV1.03 mV10.97 mV3.22 mV
18.17 pA11.9 pA30.85 pA
NSGA2RIMDVCHSN
3.58 mV32.89 mV3.63 mV7.55 mV33.6 mV7.06 mV31.5 mV24.36 mV31.81 mV
6.57 pA7.63 pA5.75 pA
AIYURXRIS
0.38 mV14.99 mV18.39 mV3.61 mV20.4 mV1.87 mV11.87 mV17.09 mV11.45 mV
8.68 pA5.13 pA2.74 pA
AFDAWBAWC
0.8 mV22.68 mV1.14 mV1.14 mV30.38 mV2.11 mV5.12 mV32.47 mV3.17 mV
24.07 pA10.9 pA7.55 pA
EP-GANRIMDVCHSN
0.24 mV7.78 mV1.65 mV0.30 mV5.90 mV1.39 mV0.46 mV6.62 mV2.02 mV
3.21 pA12.35 pA17.44 pA
AIYURXRIS
0.43 mV6.57 mV1.12 mV0.74 mV4.58 mV3.78 mV0.27 mV3.42 mV1.78 mV
10.52 pA36.64 pA21.86 pA
AFDAWBAWC
1.68 mV9.99 mV1.86 mV0.37 mV7.24 mV0.31 mV0.57 mV4.93 mV0.84 mV
43.20 pA9.27 pA8.35 pA

Additional files

MDAR checklist
https://cdn.elifesciences.org/articles/95607/elife-95607-mdarchecklist1-v1.pdf
Supplementary file 1

Table of EP-GAN(32k) generated parameters (Small, Large).

https://cdn.elifesciences.org/articles/95607/elife-95607-supp1-v1.zip

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  1. Jimin Kim
  2. Minxian Peng
  3. Shuqi Chen
  4. Qiang Liu
  5. Eli Shlizerman
(2025)
Generation of biophysical neuron model parameters from recorded electrophysiological responses
eLife 13:RP95607.
https://doi.org/10.7554/eLife.95607.4