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Multimodal parameter spaces of a complex multi-channel neuron model

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 similar output...

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Autores principales: Wang, Y. Curtis, Rudi, Johann, Velasco, James, Sinha, Nirvik, Idumah, Gideon, Powers, Randall K., Heckman, Charles J., Chardon, Matthieu K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9632740/
https://www.ncbi.nlm.nih.gov/pubmed/36341477
http://dx.doi.org/10.3389/fnsys.2022.999531
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author Wang, Y. Curtis
Rudi, Johann
Velasco, James
Sinha, Nirvik
Idumah, Gideon
Powers, Randall K.
Heckman, Charles J.
Chardon, Matthieu K.
author_facet Wang, Y. Curtis
Rudi, Johann
Velasco, James
Sinha, Nirvik
Idumah, Gideon
Powers, Randall K.
Heckman, Charles J.
Chardon, Matthieu K.
author_sort Wang, Y. Curtis
collection PubMed
description 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 similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, 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 an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between 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 new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.
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spelling pubmed-96327402022-11-04 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. Front Syst Neurosci Neuroscience 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 similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, 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 an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between 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 new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data. Frontiers Media S.A. 2022-10-20 /pmc/articles/PMC9632740/ /pubmed/36341477 http://dx.doi.org/10.3389/fnsys.2022.999531 Text en Copyright © 2022 Wang, Rudi, Velasco, Sinha, Idumah, Powers, Heckman and Chardon. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Neuroscience
Wang, Y. Curtis
Rudi, Johann
Velasco, James
Sinha, Nirvik
Idumah, Gideon
Powers, Randall K.
Heckman, Charles J.
Chardon, Matthieu K.
Multimodal parameter spaces of a complex multi-channel neuron model
title Multimodal parameter spaces of a complex multi-channel neuron model
title_full Multimodal parameter spaces of a complex multi-channel neuron model
title_fullStr Multimodal parameter spaces of a complex multi-channel neuron model
title_full_unstemmed Multimodal parameter spaces of a complex multi-channel neuron model
title_short Multimodal parameter spaces of a complex multi-channel neuron model
title_sort multimodal parameter spaces of a complex multi-channel neuron model
topic Neuroscience
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9632740/
https://www.ncbi.nlm.nih.gov/pubmed/36341477
http://dx.doi.org/10.3389/fnsys.2022.999531
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