MCMC Estimation of Markov Models for Ion Channels

Auckland Bioengineering Institute, The University of Auckland, Auckland, New Zealand.
Biophysical Journal (Impact Factor: 3.97). 04/2011; 100(8):1919-29. DOI: 10.1016/j.bpj.2011.02.059
Source: PubMed


Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time series of open and closed channels to a CTMM remains a challenge. Bayesian statistics combined with Markov chain Monte Carlo (MCMC) sampling provide means for estimating the rate constants of a CTMM directly from single channel data. In this article, different approaches for the MCMC sampling of Markov models are combined. This method, new to our knowledge, detects overparameterizations and gives more accurate results than existing MCMC methods. It shows similar performance as QuB-MIL, which indicates that it also compares well with maximum likelihood estimators. Data collected from an inositol trisphosphate receptor is used to demonstrate how the best model for a given data set can be found in practice.

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Available from: Colin Fox, Sep 30, 2015
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    • "Here, we focus on the problem of idealization, as it is called in this field, of ion channel current traces, i.e., on the reconstruction or estimation of the channel's conductivity over time without noise; one may also call that denoising or signal detection. This is an important step in the analysis of an ion channel's traces as many of its characteristics can be decuced from idealized traces: number of states, open and closed times, transition rates between states [5], or the Nernst potential [6]. Many idealization methods are based on specific models for the channel's behavior [7], e.g., that there is a Markov chain of states, each with its associated conductance. "
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    ABSTRACT: Based on a combination of jump segmentation and statistical multiresolution analysis for dependent data, a new approach called J-SMURF to idealize ion channel recordings has been developed. It is model-free in the sense that no a-priori assumptions about the channel's characteristics have to be made; it thus complements existing methods which assume a model for the channel's dynamics, like hidden Markov models. The method accounts for the effect of an analog filter being applied before the data analysis, which results in colored noise, by adapting existing muliresolution statistics to this situation. J-SMURF's ability to denoise the signal without missing events even when the signal-tonoise ratio is low is demonstrated on simulations as well as on ion current traces obtained from gramicidin A channels reconstituted into solvent-free planar membranes. When analyzing a newly synthesized acylated system of a fatty acid modified gramicidin channel, we are able to give statistical evidence for unknown gating characteristics such as subgating.
    IEEE transactions on nanobioscience 11/2013; 12(4). DOI:10.1109/TNB.2013.2284063 · 2.31 Impact Factor
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    • "Improved version of the algorithm by Siekmann et al. (2011) The main difference to the algorithm described in Siekmann et al. (2) is that the complicated likelihood function presented there (which requires sampling a sequence of Markov states) is replaced by a simpler version, see Eq. A12. More details can be found in Siekmann et al. (3). "
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    • "The JIPR flux also requires that we incorporate sensitivity to IP3 binding and Ca2+ feedback. In the initial version of the model, this was achieved by using a model of the IP3R developed by De Young and Keizer (1992), although more recent work uses more modern IP3R models (Gin et al., 2009a,b,c; Siekmann et al., 2011). The RyR is modeled using the model of Keizer and Levine (1996). "
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    ABSTRACT: Airway hyperresponsiveness (AHR), a characteristic of asthma that involves an excessive reduction in airway caliber, is a complex mechanism reflecting multiple processes that manifest over a large range of length and time scales. At one extreme, molecular interactions determine the force generated by airway smooth muscle (ASM). At the other, the spatially distributed constriction of the branching airways leads to breathing difficulties. Similarly, asthma therapies act at the molecular scale while clinical outcomes are determined by lung function. These extremes are linked by events operating over intermediate scales of length and time. Thus, AHR is an emergent phenomenon that limits our understanding of asthma and confounds the interpretation of studies that address physiological mechanisms over a limited range of scales. A solution is a modular computational model that integrates experimental and mathematical data from multiple scales. This includes, at the molecular scale, kinetics, and force production of actin-myosin contractile proteins during cross-bridge and latch-state cycling; at the cellular scale, Ca(2+) signaling mechanisms that regulate ASM force production; at the tissue scale, forces acting between contracting ASM and opposing viscoelastic tissue that determine airway narrowing; at the organ scale, the topographic distribution of ASM contraction dynamics that determine mechanical impedance of the lung. At each scale, models are constructed with iterations between theory and experimentation to identify the parameters that link adjacent scales. This modular model establishes algorithms for modeling over a wide range of scales and provides a framework for the inclusion of other responses such as inflammation or therapeutic regimes. The goal is to develop this lung model so that it can make predictions about bronchoconstriction and identify the pathophysiologic mechanisms having the greatest impact on AHR and its therapy.
    Frontiers in Physiology 06/2012; 3:191. DOI:10.3389/fphys.2012.00191 · 3.53 Impact Factor
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