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Probability distributions of molecular observables computed from Markov models. II. Uncertainties in observables and their time-evolution

Please always quote using this URN:urn:nbn:de:0296-matheon-10913
  • Discrete-state Markov (or master equation) models provide a useful simplified representation for characterizing the long-time statistical evolution of biomolecules in a manner that allows direct comparison with experiments as well as the elucidation of mechanistic pathways for an inherently stochastic process. A vital part of meaningful comparison with experiment is the characterization of the statistical uncertainty in the predicted experimental measurement, which may take the form of an equilibrium measurement of some spectroscopic signal, the time-evolution of this signal following a perturbation, or the observation of some statistic (such as the correlation function) of the equilib- rium dynamics of a single molecule. Without meaningful error bars (which arise due to the finite quantity of data used to construct the model), there is no way to determine whether the deviations between model and experiment are statistically meaningful. Previous work has demonstrated that a Bayesian method that enforces microscopic reversibility can be used to characterize the correlated uncertainties in state-to-state transition probabilities (and functions thereof) for a model inferred from molecular simulation data. Here, we extend this approach to include the uncertainty in observables that are functions of molecular conformation (such as surrogate spectroscopic signals) characteriz- ing each state, permitting the full statistical uncertainty in computed spectroscopic experiments to be assessed. We test the approach in a simple model system to demonstrate that the computed uncer- tainties provide a useful indictor of statistical variation, and then apply it to the computation of the fluorescence autocorrelation function measured for a dye-labeled peptide previously studied by both experiment and simulation.

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Metadaten
Author:John D. Chodera, Frank Noe
URN:urn:nbn:de:0296-matheon-10913
Referee:Christof Schütte
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/02/27
Release Date:2012/02/27
Tag:Bayesian error analysis; Markov models; molecular dynamics; statistical error
Institute:Research Center Matheon
Freie Universität Berlin
MSC-Classification:62-XX STATISTICS / 62Mxx Inference from stochastic processes / 62M05 Markov processes: estimation
Preprint Number:935
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