Multimodal parameter spaces of a complex multi-channel neuron model

Area of Science:

• Computational Neuroscience
• Biophysics
• Systems Biology

Background:

• Hodgkin-Huxley (HH) models are fundamental for understanding neuron behavior but face parameter non-uniqueness challenges.
• Multiple parameter sets can yield similar model outputs, creating multimodal objective functions problematic for standard optimization.
• Severe non-linearities in HH models further complicate algorithmic parameter inference.

Purpose of the Study:

• To develop a tractable method for inferring parameters in high-dimensional HH models.
• To address the challenge of multimodal solutions in inverse problems using a Bayesian framework.
• To analyze complex parameter relationships and sensitivities in an eight-channel HH model.

Main Methods:

• Application of a specific Markov chain Monte Carlo (MCMC) algorithm within a Bayesian inference framework.
• Demonstration on a three-channel HH model, followed by detailed analysis of a nine-parameter, eight-channel HH model.
• Utilizing five injected current levels to explore parameter space and generating nine-dimensional posterior distributions.

Main Results:

• The MCMC algorithm successfully inferred parameters and uncovered complex relationships between them.
• Visualized 'solution maps' revealed intricate structures within multimodal posterior distributions.
• These maps facilitated the selection of optimal parameter sets and highlighted parameter sensitivities.

Conclusions:

• The proposed Bayesian MCMC approach effectively handles parameter non-uniqueness and non-linearities in HH models.
• Solution maps provide valuable insights into parameter robustness and model behavior.
• This methodology can enhance experimental design, scientific productivity, and model ideation in neuroscience research.