De-Noising Single Molecule FRET Trajectories using Wavelent and Bayesian Techniques

Abstract

Extracting quantitative information from low signal-to-noise single molecule FRET trajectories remains a significant challenge. In particular, biological systems that derive their function from shallowly defined or continua of states are not amenable to recent Markovian analysis algorithms. A method to de-noise single-molecule fluorescence resonance energy (smFRET) trajectories using wavelet detail thresholding and Bayesian inference is presented. Bayesian methods are developed to identify fluorophore photoblinks in the time trajectories. Simulated data are used to quantify the improvement in static and dynamic data analysis. Application of the method to experimental smFRET data shows that it distinguishes photoblinks from large shifts in smFRET efficiency while maintaining the important advantage of an unbiased approach. Known sources of experimental noise are examined and quantified as a means to remove their contributions via soft thresholding of wavelet coefficients. A wavelet decomposition algorithm is described, and thresholds are produced through the knowledge of noise parameters in the discrete-time photon signals. Reconstruction of the signals from thresholded coefficients produces signals that contain noise arising only from unquantifiable parameters. The method is applied to simulated and observed smFRET data, and it is found that the denoised data retain their underlying dynamical properties, but with increased resolution.