Joint Statistical Analysis of Multichannel Time Series from Single Quantum Dot−(Cy5)n Constructs

Fluorescence Intermittency of Quantum Dot-Organic Dye Conjugates: Implications for Alternative Energy and Biological Imaging

Quantum dot (QD)-organic dye couple chromophores are topical due to their applications in biology, catalysis, and energy. The maximization of energy transfer efficiency can be guided by the underlying Förster or Dexter mechanisms; however, the impact of fluorescence intermittency must also be considered. Here we demonstrate that the average ⟨t_on⟩ and ⟨t_off⟩ times of dye acceptors in coupled QD-dye chromophores are substantially affected by the donors' blinking behavior. With regard to biological imaging, this effect beneficially minimizes the photobleaching of the acceptor dye. The implications for alternative energy are less encouraging as the acceptors' capacity to store energy, using ⟨t_on⟩/⟨t_off⟩ as a metric, was reduced by as much as ∼95%. These detrimental effects can be mitigated by suppressing QD blinking via surface treatment. This study also demonstrates several instances of the nonconformity of QD blinking dynamics to a power law distribution, as a robust examination of the off times reveals log-normal behavior that is consistent with the Albery model.

Statistical Learning of Discrete States in Time Series

Time series obtained from time-dependent experiments contain rich information on kinetics and dynamics of the system under investigation. This work describes an unsupervised learning framework, along with the derivation of the necessary analytical expressions, for the analysis of Gaussian-distributed time series that exhibit discrete states. After the time series has been partitioned into segments in a model-free manner using the previously developed change-point (CP) method, this protocol starts with an agglomerative hierarchical clustering algorithm to classify the detected segments into possible states. The initial state clustering is further refined using an expectation-maximization (EM) procedure, and the number of states is determined by a Bayesian information criterion (BIC). Also introduced here is an achievement scalarization function, usually seen in artificial intelligence literature, for quantitatively assessing the performance of state determination. The statistical learning framework, which is comprised of three stages, detection of signal change, clustering, and number-of-state determination, was thoroughly characterized using simulated trajectories with random intensity segments that have no underlying kinetics, and its performance was critically evaluated. The application to experimental data is also demonstrated. The results suggested that this general framework, the implementation of which is based on firm theoretical foundations and does not require the imposition of any kinetics model, is powerful in determining the number of states, the parameters contained in each state, as well as the associated statistical significance.

State transition identification in multivariate time series (STIMTS) applied to rotational jump trajectories from single molecules

Time resolved data from single molecule experiments often suffer from contamination with noise due to a low signal level. Identifying a proper model to describe the data thus requires an approach with sufficient model parameters without misinterpreting the noise as relevant data. Here, we report on a generalized data evaluation process to extract states with piecewise constant signal level from simultaneously recorded multivariate data, typical for multichannel single molecule experiments. The method employs the minimum description length principle to avoid overfitting the data by using an objective function, which is based on a tradeoff between fitting accuracy and model complexity. We validate our method with synthetic data from Monte Carlo simulations modeling fluorescence resonance energy transfer and rotational jumps, respectively. The method is applied to quantify rotational jump dynamics of single terrylene diimide (TDI) molecules deposited on a solid substrate. Depending on the substitution pattern of the TDI molecules and the chosen substrate materials, we find significant differences in time scale and geometry of molecular reorientation. From an additional application of our state transition identification in multivariate time series approach, a significant correlation between shifts of emission spectra and the occurrence of rotational jumps was found.

SOLVING SINGLE BIOMOLECULES BY ADVANCED FRET-BASED SINGLE-MOLECULE FLUORESCENCE TECHNIQUES

The use of Förster resonance energy transfer (FRET) has undergone a renaissance in the last two decades, especially in the study of structure of biomolecules, biomolecular interactions, and dynamics. Thanks to powerful advances in single-molecule fluorescence (SMF) techniques, seeing molecules at work is a reality, which has helped to build up the mindset of molecular machines. In the last few years, many technical developments have broadened the applications of SMF-FRET, expanding the amount of information that can be recovered from individual molecules. Here, we focus on the non-standard SMF-FRET techniques, such as two-color coincidence detection (TCCD), alternating laser excitation (ALEX), multiparameter fluorescence detection (MFD); the addition of fluorescence lifetime as an orthogonal dimension in single-molecule experiments; or the development of novel and improved methods of analysis constituting to a set of advanced methodologies that may become routine tools in a close future.

[Formula: see text]Special Issue Comment: This review about advanced single-molecule FRET techniques is specially related to the review by Jørgensen and Hatzakis,6 who detail experimetal strategies to solve the activity of single enzymes. The advanced techniques described in our paper may serve as interesting alternatives when applied to enzyme studies. Our manuscript is also related to the reviews in this Special Issue that deal with model solving.22,130

Variational Bayes analysis of a photon-based hidden Markov model for single-molecule FRET trajectories

Single-molecule fluorescence resonance energy transfer (smFRET) measurement is a powerful technique for investigating dynamics of biomolecules, for which various efforts have been made to overcome significant stochastic noise. Time stamp (TS) measurement has been employed experimentally to enrich information within the signals, while data analyses such as the hidden Markov model (HMM) have been successfully applied to recover the trajectories of molecular state transitions from time-binned photon counting signals or images. In this article, we introduce the HMM for TS-FRET signals, employing the variational Bayes (VB) inference to solve the model, and demonstrate the application of VB-HMM-TS-FRET to simulated TS-FRET data. The same analysis using VB-HMM is conducted for other models and the previously reported change point detection scheme. The performance is compared to other analysis methods or data types and we show that our VB-HMM-TS-FRET analysis can achieve the best performance and results in the highest time resolution. Finally, an smFRET experiment was conducted to observe spontaneous branch migration of Holliday-junction DNA. VB-HMM-TS-FRET was successfully applied to reconstruct the state transition trajectory with the number of states consistent with the nucleotide sequence. The results suggest that a single migration process frequently involves rearrangement of multiple basepairs.

Identification of intensity ratio break points from photon arrival trajectories in ratiometric single molecule spectroscopy

We describe a statistical method to analyze dual-channel photon arrival trajectories from single molecule spectroscopy model-free to identify break points in the intensity ratio. Photons are binned with a short bin size to calculate the logarithm of the intensity ratio for each bin. Stochastic photon counting noise leads to a near-normal distribution of this logarithm and the standard student t-test is used to find statistically significant changes in this quantity. In stochastic simulations we determine the significance threshold for the t-test's p-value at a given level of confidence. We test the method's sensitivity and accuracy indicating that the analysis reliably locates break points with significant changes in the intensity ratio with little or no error in realistic trajectories with large numbers of small change points, while still identifying a large fraction of the frequent break points with small intensity changes. Based on these results we present an approach to estimate confidence intervals for the identified break point locations and recommend a bin size to choose for the analysis. The method proves powerful and reliable in the analysis of simulated and actual data of single molecule reorientation in a glassy matrix.

Combining MFD and PIE for accurate single-pair Förster resonance energy transfer measurements

Single-pair Förster resonance energy transfer (spFRET) experiments using single-molecule burst analysis on a confocal microscope are an ideal tool to measure inter- and intramolecular distances and dynamics on the nanoscale. Different techniques have been developed to maximize the amount of information available in spFRET burst analysis experiments. Multiparameter fluorescence detection (MFD) is used to monitor a variety of fluorescence parameters simultaneously and pulsed interleaved excitation (PIE) employs direct excitation of the acceptor to probe its presence and photoactivity. To calculate accurate FRET efficiencies from spFRET experiments with MFD or PIE, several calibration measurements are usually required. Herein, we demonstrate that by combining MFD with PIE information regarding all calibration factors as well as an accurate determination of spFRET histograms can be performed in a single measurement. In addition, the quality of overlap of the different detection volumes as well as the detection of acceptor photophysics can be investigated with MFD-PIE. Bursts containing acceptor photobleaching can be identified and excluded from further investigation while bursts that contain FRET dynamics are unaffected by this analysis. We have employed MFD-PIE to accurately analyze the effects of nucleotides and substrate on the interdomain separation in DnaK, the major bacterial heat shock protein 70 (Hsp70). The interdomain distance increases from 47 Å in the ATP-bound state to 84 Å in the ADP-bound state and slightly contracts to 77 Å when a substrate is bound. This is in contrast to what was observed for the mitochondrial member of the Hsp70s, Ssc1, supporting the notion of evolutionary specialization of Hsp70s for different cellular functions in different organisms and cell organelles.

Changepoint analysis for single-molecule polarized total internal reflection fluorescence microscopy experiments

The experimental study of individual macromolecules has opened a door to determining the details of their mechanochemical operation. Motor enzymes such as the myosin family have been particularly attractive targets for such study, in part because some of them are highly processive and their "product" is spatial motion. But single-molecule resolution comes with its own costs and limitations. Often, the observations rest on single fluorescent dye molecules, which emit a limited number of photons before photobleaching and are subject to complex internal dynamics. Thus, it is important to develop methods that extract the maximum useful information from a finite set of detected photons. We have extended an experimental technique, multiple polarization illumination in total internal reflection fluorescence microscopy (polTIRF), to record the arrival time and polarization state of each individual detected photon. We also extended an analysis technique, previously applied to FRET experiments, that optimally determines times of changes in photon emission rates. Combining these improvements allows us to identify the structural dynamics of a molecular motor (myosin V) with unprecedented detail and temporal resolution.