Fast Step Transition and State Identification (STaSI) for Discrete Single-Molecule Data Analysis

Abstract

We introduce a step transition and state identification (STaSI) method for piecewise constant single-molecule data with a newly derived minimum description length equation as the objective function. We detect the step transitions using the Student’s t test and group the segments into states by hierarchical clustering. The optimum number of states is determined based on the minimum description length equation. This method provides comprehensive, objective analysis of multiple traces requiring few user inputs about the underlying physical models and is faster and more precise in determining the number of states than established and cutting-edge methods for single-molecule data analysis. Perhaps most importantly, the method does not require either time-tagged photon counting or photon counting in general and thus can be applied to a broad range of experimental setups and analytes.

Conformational Transitions in the Glycine-Bound GluN1 NMDA Receptor LBD via Single-Molecule FRET

“…More importantly, we introduce a model-free step transition and state identification method (STaSI) to identify additional cleft states in the isolated LBD that are too wide to be observed in the full hetero-tetramer. Using STaSI and recent advances in extending smFRET trajectories (50)(51)(52)(53), transition analysis confirms that interstate conversions follow equilibrium statistics. Although it is unclear how these long-lived states relate to channel function in the full receptor, the states identified by smFRET correlate well to the broad distribution of states identified in umbrella sampling models of the LBD cleft in both NMDA and AMPA receptors (38,54).…”

“…The seven states are located at FRET efficiency values of 0.96, 0.87, 0.79, 0.68, 0.53, 0.43, and 0.28 (Table 1). To determine the number, location, and state-to-state transition points, we first reduced the noise of each smFRET trajectory with the wavelet denoising method (58,59), then analyzed the trajectories using the STaSI method (51), which was specifically developed to work with binned smFRET data (details are explained in Materials and Methods and in the Supporting Material). Based on state determination methods for single-photon counting and the MDL principle (62,63), STaSI was tested for validity with simulated trajectories with similar levels of noise to our data (see Fig.…”

“…The MDL equation considers both the goodness of fit and the complexity of the fitting model. Simulation tests show MDL avoids overfitting and underfitting even with high noise level (51). More detailed explanation of STaSI can be found in the Supporting Material.…”

“…The step-transition-and-state-identification (STaSI) method was developed to help cluster FRET traces into the optimum number of states with minimal user input (51), as opposed to other methods such as hidden Markov modeling or change point analysis, which require either foreknowledge of the number of expected states or the data to be raw-time-tagged rather than binned (60)(61)(62). STaSI combines the advantages of the bias-free approach of an information theoretic analysis method with the ability to analyze binned data to allow for unbiased conformational state determination.…”

Quantifying the Assembly of Multicomponent Molecular Machines by Single-Molecule Total Internal Reflection Fluorescence Microscopy

“…When the thresholding method is insufficient, for example, due to the presence of multiple, poorly separated states, or to the noise in the recording, other methods allow better quality idealization, and thereby a more accurate identification of the states and extraction of dwell times (Watkins and Yang, 2005, Bronson et al, 2009, Shuang et al, 2014). A powerful set of methods for extracting kinetic information from noisy trajectories or in the presence of multiple ill-defined states is based on Hidden Markov modelling (HMM) (Chung et al, 1990, Talaga, 2007, Blanco and Walter, 2010, Liu et al, 2010).…”