A Bayesian Restoration of an Ion Channel Signal

Hodgson, M. E. A.

doi:10.1111/1467-9868.00165

Cited by 26 publications

(23 citation statements)

References 19 publications

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“…Therefore, it is advantageous to fit directly to the single-channel record. Fredkin and Rice (1992), Ball et al (1999), Hodgson (1999) and Rosales et al (2001) have developed methods by which one can reconstruct the sequence of open and closed events directly from the raw single-channel record to give a reconstruction of the open and closed time distributions along with estimation of the Markov model rate constants. In other words, in this more powerful approach, not only does the fit determine the rate constants of the Markov model, it also reconstructs the single-channel record by determining the best-fit positions of the openings and closings.…”

Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

Gin

Falcke

Wagner

et al. 2009

Journal of Theoretical Biology

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Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

Gin

Falcke

Wagner

et al. 2009

Journal of Theoretical Biology

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“…Hidden Markov models (HMM) are specific latent variable models where the completed model is directed by an unobserved Markov process S. When the state space of S is continuous, these models are usually called state space models such as in econometrics, in stochastic volatility models (Shephard and Pitt (1997), Hamilton (1989), Chib (1996)) or in signal processing (Hodgson (1999), Rabiner (1989)). HMM's also have a large ranging number of applications, when the state space of S is discrete : in Genetics as DNA sequence modeling (Rabiner (1989), Durbin et al (1998), Muri (1998)) and in medicine (Guihenneuc et al (2000), Kirby and Spiegelhalter (1994) In this paper we assume that we have N observations X = (X 1 , ..., X N ) and that conditionally on some vector S they are independent with distribution whose density with respect to Lebesgue measure is denoted f (X i |θ S , S), i = 1, ..., N .…”

Section: Discussionmentioning

confidence: 99%

Laplace Expansions in Markov chain Monte Carlo Algorithms

Guihenneuc‐Jouyaux¹,

Rousseau²

2005

Journal of Computational and Graphical Statistics

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SummaryComplex hierarchical models lead to a complicated likelihood and then, in a Bayesian analysis, to complicated posterior distributions. To obtain Bayes estimates such as the posterior mean or Bayesian confidence regions, it is therefore necessary to simulate the posterior distribution using a method such as an MCMC algorithm. These algorithms often get slower as the number of observations increases, especially when the latent variables are considered. To improve the convergence of the algorithm, we propose to decrease the number of parameters to simulate at each iteration by using a Laplace approximation on the nuisance parameters. We provide a theoretical study of the impact that such an approximation has on the target posterior distribution. We prove that the distance between the true target distribution and the approximation becomes of order O(N −a ) with a ∈ (0, 1), a close to 1, as the number of observations N increases. A simulation study illustrates the theoretical results.The approximated MCMC algorithm behaves extremely well on an example which is driven by a study on HIV patients.

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“…Therefore, the open times and closed times are not fixed for the entire fitting procedure, eliminating any inherent error in first obtaining the times. These such methods have been developed by Fredkin and Rice, 52 Ball et al, 51 Hodgson, 53 and Rosales et al 54 Fredkin and Rice 52 do this in a maximum likelihood framework while Ball et al, 51 Hodgson, 53 and Rosales et al 54 use Bayesian inference and MCMC techniques.…”

Section: B Fitting the Noisy Single-channel Record Not The Open Timmentioning

confidence: 99%

Inositol trisphosphate receptor and ion channel models based on single-channel data

Gin

Wagner²,

Yule³

et al. 2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The inositol trisphosphate receptor ͑IPR͒ plays an important role in controlling the dynamics of intracellular Ca 2+ . Single-channel patch-clamp recordings are a typical way to study these receptors as well as other ion channels. Methods for analyzing and using this type of data have been developed to fit Markov models of the receptor. The usual method of parameter fitting is based on maximum-likelihood techniques. However, Bayesian inference and Markov chain Monte Carlo techniques are becoming more popular. We describe the application of the Bayesian methods to real experimental single-channel data in three ion channels: the ryanodine receptor, the K + channel, and the IPR. One of the main aims of all three studies was that of model selection with different approaches taken. We also discuss the modeling implications for single-channel data that display different levels of channel activity within one recording. © 2009 American Institute of Physics. ͓DOI: 10.1063/1.3184540͔In this review we focus on an intracellular Ca 2+ channel, the inositol trisphosphate receptor (IPR), and describe the use of single-channel data in constructing a Markov model of the receptor. We discuss parameter fitting from the point of view of Bayesian inference and Markov chain Monte Carlo (MCMC) techniques and discuss a simple Markov model for the IPR fitted using these techniques. We also discuss models of two other ion channels: the ryanodine receptor (RyR) and a K + channel. Model selection is an important issue and the three ion channels discussed take different approaches to addressing this problem. We also look at the modeling aspects for modal gating behavior.

show abstract

A Bayesian Restoration of an Ion Channel Signal

Cited by 26 publications

References 19 publications

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors

Laplace Expansions in Markov chain Monte Carlo Algorithms

Inositol trisphosphate receptor and ion channel models based on single-channel data

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