A Self-Organizing State-Space-Model Approach for Parameter Estimation in Hodgkin-Huxley-Type Models of Single Neurons

Traditional approaches to the problem of parameter estimation in biophysical models of neurons and neural networks usually adopt a global search algorithm (for example, an evolutionary algorithm), often in combination with a local search method (such as gradient descent) 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 a range of 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-type 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, measurement and intrinsic 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. Author Summary: Parameter estimation is a problem of central importance and, perhaps, the most laborious task in biophysical modeling of neurons and neural networks. An emerging trend is to treat parameter estimation in this context as yet another statistical inference problem, which can be tackled using well-established methods from Computational Statistics. Inspired by these recent advances, we adopted a self-organizing state-space-model approach augmented with an adaptive sampling algorithm akin to the Covariance Matrix Adaptation Evolution Strategy in order to estimate a large number of parameters in a number of Hodgkin-Huxley-type models of single neurons. Parameter estimation was based on noisy electrophysiological data and involved the maximal conductances, reversal potentials, levels of noise and, unlike most mainstream work, the kinetics of ionic currents in the examined models. Our main conclusion was that parameters in complex, conductance-based neuron models can be inferred using the aforementioned methodology, if sufficiently informative priors regarding the unknown model parameters are available. Importantly, the use of an adaptive algorithm for sampling new parameter vectors significantly reduced the variance of parameter estimates. Flexibility and scalability are additional advantages of the proposed method, which is particularly suited to resolve high-dimensional inference problems.