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Identifying multi-compartment Hodgkin-Huxley models with high-density extracellular voltage recordings
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Infers membrane voltages, channel states, conductances and cell-probe geometry from dense extracellular voltage recordings by combining an Extended Kalman Filter (diagonal and block-diagonal variants) with marginal-likelihood maximization over differentiable Jaxley HH simulations.
Problem
Fitting multi-compartment Hodgkin-Huxley models requires intracellular voltage recordings, which are hard to obtain in vivo; the paper asks whether biophysical parameters and neuron position can be inferred from extracellular voltages alone.
Approach
Treat the multi-compartment HH model as a nonlinear state-space model with process noise, infer latent voltages and gating states with an EKF whose covariances are approximated as diagonal or block-diagonal (BD(K)) for scalability, and learn conductances and geometry by gradient-based maximization of the EKF marginal likelihood.
Key results
- On a 10-compartment single branch with 40 recordings at 1 µV noise, EKF-based inference recovered maximum conductances with negligible bias and variance, and MSE minimization achieved nearly identical estimates.
- On a 2D retinal ganglion cell with 122 compartments (latent dimension 610), the diagonal EKF failed while the block-diagonal EKF recovered the marginal likelihood optimum, voltages and conductances.
- On a CA1 pyramidal C10 model discretized into 60 compartments (latent dimension 360), the block-diagonal EKF recovered the spatial configuration and most of 24 conductances, with some degeneracy.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an EKF rather than deterministic MSE minimization under omitted ion channels | Single-branch HH neuron · Misspecified channels: omitted M-type K+ and CaL | membrane voltage reconstruction accuracy | Helped |
| Use an EKF rather than deterministic MSE minimization with perturbed gating kinetics | Single-branch HH neuron · Perturbed gating dynamics | membrane voltage and channel-state reconstruction accuracy | Helped |
| Use a diagonal covariance approximation instead of the full covariance (ablation) | EKF on a single-branch neuron · Single-branch neuron | conductance recovery | Hurt |
| Use a block-diagonal covariance approximation instead of the full covariance (ablation) | EKF on a single-branch neuron · Single-branch neuron | conductance recovery | No clear effect |
| Use a diagonal covariance approximation instead of a block-diagonal covariance (ablation) | EKF on a three-branch neuron · Three-branch neuron | conductance recovery | Hurt |
| Use a diagonal covariance approximation instead of a block-diagonal covariance (ablation) | EKF on a retinal ganglion cell · Retinal ganglion cell | membrane voltage reconstruction accuracy | Hurt |
| Use a block-diagonal covariance approximation | EKF on a retinal ganglion cell · Retinal ganglion cell | membrane voltage reconstruction accuracy | Helped |
| Infer with a block-diagonal EKF | C10 CA1 pyramidal neuron · CA1 pyramidal neuron | membrane voltage reconstruction accuracy | Helped |
| Increase observation noise | Conductance inference for a single-branch neuron · Single-branch neuron | variance of conductance estimates | Hurt |
| Increase the distance between the cell and recording site | Conductance inference for a single-branch neuron · Single-branch neuron | variance of conductance estimates | Hurt |
Surprising findings
- The diagonal EKF performed poorly on the RGC because dense electrode arrays make the measurement information matrix strongly non-diagonal.
- MSE minimization diverged under omitted-channel misspecification while the EKF remained accurate.
Limitations
- EKF is more computationally expensive than MSE minimization, especially for large models.
- Diagonal approximation is unreliable for certain cell-probe geometries with dense electrodes.
- Parameter degeneracy limits identifiability of conductances (e.g., CA1 model).
Experimental setup
Datasets: simulated extracellular recordings from synthetic single-branch, multi-branch, RGC and C10 CA1 morphologies
Metrics: parameter bias and variance marginal log-likelihood voltage reconstruction accuracy recovered compartment position
Baselines: MSE minimization (Jaxley) standard EKF diagonal EKF
Builds on: Jaxley Dynamax SparseJac Extended Kalman Filter
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