A self-organizing state-space-model approach for parameter estimation in Hodgkin-Huxley-type models of single neurons

TL;DR

This paper introduces a novel parameter estimation method for Hodgkin-Huxley neuron models using a self-organizing state-space approach, which effectively handles noisy data and high-dimensional inference without explicit cost functions.

Contribution

The study applies Kitagawa's self-organizing state-space model to neuron models, enabling robust, high-dimensional parameter inference from noisy electrophysiological data without needing explicit cost functions.

Findings

Successfully estimated multiple parameters including conductances and kinetics.

Operated effectively with noisy and limited data.

Reduced variance of estimates using adaptive sampling.

Abstract

Traditionally, parameter estimation in biophysical neuron and neural network models usually adopts a global search algorithm, often combined with a local search method in order to minimize the value of a cost function, which measures the discrepancy between various features of the available experimental data and model output. In this study, we approach the problem of parameter estimation in conductance-based models of single neurons from a different perspective. By adopting a hidden-dynamical-systems formalism, we expressed parameter estimation as an inference problem in these systems, which can then be tackled using well-established statistical inference methods. The particular method we used was Kitagawa's self-organizing state-space model, which was applied on a number of Hodgkin-Huxley models using simulated or actual electrophysiological data. We showed that the algorithm can be used to estimate a large number of parameters, including maximal conductances, reversal potentials, kinetics of ionic currents and measurement noise, based on low-dimensional experimental data and sufficiently informative priors in the form of pre-defined constraints imposed on model parameters. The algorithm remained operational even when very noisy experimental data were used. Importantly, by combining the self-organizing state-space model with an adaptive sampling algorithm akin to the Covariance Matrix Adaptation Evolution Strategy we achieved a significant reduction in the variance of parameter estimates. The algorithm did not require the explicit formulation of a cost function and it was straightforward to apply on compartmental models and multiple data sets. Overall, the proposed methodology is particularly suitable for resolving high-dimensional inference problems based on noisy electrophysiological data and, therefore, a potentially useful tool in the construction of biophysical neuron models.