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Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods.

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Title: Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods.
Authors: Kostuk, Mark1, Toth, Bryan1, Meliza, C.2 dmeliza@uchicago.edu, Margoliash, Daniel2, Abarbanel, Henry3 habarbanel@ucsd.edu
Source: Biological Cybernetics. Mar2012, Vol. 106 Issue 3, p155-167. 13p. 3 Charts, 4 Graphs.
Subjects: Computer networks, Monte Carlo method software, Nonlinear differential equations, Ion channels, Electric noise, Error analysis in mathematics, Electrophysiology
Abstract: Hodgkin-Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron's electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (<50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known. [ABSTRACT FROM AUTHOR]
Copyright of Biological Cybernetics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Biological+Cybernetics%22&quot;&gt;Biological Cybernetics&lt;/searchLink&gt;. Mar2012, Vol. 106 Issue 3, p155-167. 13p. 3 Charts, 4 Graphs.
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  Data: Hodgkin-Huxley (HH) models of neuronal membrane dynamics consist of a set of nonlinear differential equations that describe the time-varying conductance of various ion channels. Using observations of voltage alone we show how to estimate the unknown parameters and unobserved state variables of an HH model in the expected circumstance that the measurements are noisy, the model has errors, and the state of the neuron is not known when observations commence. The joint probability distribution of the observed membrane voltage and the unobserved state variables and parameters of these models is a path integral through the model state space. The solution to this integral allows estimation of the parameters and thus a characterization of many biological properties of interest, including channel complement and density, that give rise to a neuron&#39;s electrophysiological behavior. This paper describes a method for directly evaluating the path integral using a Monte Carlo numerical approach. This provides estimates not only of the expected values of model parameters but also of their posterior uncertainty. Using test data simulated from neuronal models comprising several common channels, we show that short (&lt;50 ms) intracellular recordings from neurons stimulated with a complex time-varying current yield accurate and precise estimates of the model parameters as well as accurate predictions of the future behavior of the neuron. We also show that this method is robust to errors in model specification, supporting model development for biological preparations in which the channel expression and other biophysical properties of the neurons are not fully known. [ABSTRACT FROM AUTHOR]
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  Data: &lt;i&gt;Copyright of Biological Cybernetics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00422-012-0487-5
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 155
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      – SubjectFull: Computer networks
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      – SubjectFull: Monte Carlo method software
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      – SubjectFull: Nonlinear differential equations
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      – SubjectFull: Ion channels
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      – SubjectFull: Electric noise
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      – SubjectFull: Error analysis in mathematics
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      – SubjectFull: Electrophysiology
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      – TitleFull: Dynamical estimation of neuron and network properties II: path integral Monte Carlo methods.
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              Text: Mar2012
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