Multimodal parameter spaces of a complex multi-channel neuron model - Wang, Y. Curtis; Rudi, Johann; Velasco, James; Sinha, Nirvik; Idumah, Gideon; Powers, Randall K.; Heckman, Charles J.; Chardon, Matthieu K. (Frontiers in Systems Neuroscience, 2022)
One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin--Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce the same output for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness poses a challenge for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe nonlinearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in a eight-channel HH model, which we analyze in detail. We demonstrate the effects on inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show the complex multimodality, they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities. These solution maps can enable experimentalists to improve the design of future experiments and increase scientific productivity.