Identifying multi-compartment Hodgkin-Huxley models with high-density extracellular voltage recordings

Multi-compartment Hodgkin-Huxley models are biophysical models of how electrical signals propagate throughout a neuron, and they form the basis of our knowledge of neural computation at the cellular level. However, these models have many free parameters that must be estimated for each cell, and existing fitting methods rely on intracellular voltage measurements that are highly challenging to obtain in vivo. Recent advances in neural recording technology with high-density probes and arrays enable dense sampling of extracellular voltage from many sites surrounding a neuron, allowing indirect measurement of many compartments of a cell simultaneously. Here, we propose a method for inferring the underlying membrane voltage, biophysical parameters, and the neuron's position relative to the probe, using extracellular measurements alone. We use an Extended Kalman Filter to infer membrane voltage and channel states using efficient, differentiable simulators. Then, we learn the model parameters by maximizing the marginal likelihood using gradient-based methods. We demonstrate the performance of this approach using simulated data and real neuron morphologies.