Simulated data sets for single molecule kinetics: some limitations and complications of data analysis

INSIGHTS IN ENZYME FUNCTIONAL DYNAMICS AND ACTIVITY REGULATION BY SINGLE MOLECULE STUDIES

The advent of advanced single molecule measurements heralded the arrival of a wealth of dynamic information revolutionizing our understanding of protein dynamics and behavior in ways not deducible by conventional bulk assays. They offered the direct observation and quantification of the abundance and life time of multiple states and transient intermediates in the energy landscape that are typically averaged out in non-synchronized ensemble measurements, thus providing unprecedented insights into complex biological processes. Here we survey the current state of the art in single-molecule fluorescence microscopy methodology for studying the mechanism of enzymatic activity and the insights on protein functional dynamics. We will initially discuss the strategies employed to date, their limitations and possible ways to overcome them, and finally how single enzyme kinetics can advance our understanding on mechanisms underlying function and regulation of proteins.

[Formula: see text]Special Issue Comment: This review focuses on functional dynamics of individual enzymes and is related to the review on ion channels by Lu,44 the reviews on mathematical treatment of Flomenbom45 and Sach et al.,46 and review on FRET by Ruedas-Rama et al.41

Single-molecule photon stamping FRET spectroscopy study of enzymatic conformational dynamics

The fluorescence resonant energy transfer (FRET) from a donor to an acceptor via transition dipole-dipole interactions decreases the donor's fluorescent lifetime. The donor's fluorescent lifetime decreases as the FRET efficiency increases, following the equation: E(FRET) = 1 - τ(DA)/τ(D), where τ(D) and τ(DA) are the donor fluorescence lifetime without FRET and with FRET. Accordingly, the FRET time trajectories associated with single-molecule conformational dynamics can be recorded by measuring the donor's lifetime fluctuations. In this article, we report our work on the use of a Cy3/Cy5-labeled enzyme, HPPK to demonstrate probing single-molecule conformational dynamics in an enzymatic reaction by measuring single-molecule FRET donor lifetime time trajectories. Compared with single-molecule fluorescence intensity-based FRET measurements, single-molecule lifetime-based FRET measurements are independent of fluorescence intensity. The latter has an advantage in terms of eliminating the analysis background noise from the acceptor fluorescence detection leak through noise, excitation light intensity noise, or light scattering noise due to local environmental factors, for example, in a AFM-tip correlated single-molecule FRET measurements. Furthermore, lifetime-based FRET also supports simultaneous single-molecule fluorescence anisotropy.

Dynamic disorder in single-enzyme experiments: facts and artifacts

Using a single-molecule fluorescence approach, the time series of catalytic events of an enzymatic reaction can be monitored, yielding a sequence of fluorescent "on"- and "off"-states. An accurate on/off-assignment is complicated by the intrinsic and extrinsic noise in every single-molecule fluorescence experiment. Using simulated data, the performance of the most widely employed binning and thresholding approach was systematically compared to change point analysis. It is shown that the underlying on- and off-histograms as well as the off-autocorrelation are not necessarily extracted from the "signal'' buried in noise. The shapes of the on- and off-histograms are affected by artifacts introduced by the analysis procedure and depend on the signal-to-noise ratio and the overall fluorescence intensity. For experimental data where the background intensity is not constant over time we consider change point analysis to be more accurate. When using change point analysis for data of the enzyme α-chymotrypsin, no characteristics of dynamic disorder was found. In light of these results, dynamic disorder might not be a general sign of enzymatic reactions.

Probing single-molecule enzyme active-site conformational state intermittent coherence

The relationship between protein conformational dynamics and enzymatic reactions has been a fundamental focus in modern enzymology. Using single-molecule fluorescence resonance energy transfer (FRET) with a combined statistical data analysis approach, we have identified the intermittently appearing coherence of the enzymatic conformational state from the recorded single-molecule intensity-time trajectories of enzyme 6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) in catalytic reaction. The coherent conformational state dynamics suggests that the enzymatic catalysis involves a multistep conformational motion along the coordinates of substrate-enzyme complex formation and product releasing, presenting as an extreme dynamic behavior intrinsically related to the time bunching effect that we have reported previously. The coherence frequency, identified by statistical results of the correlation function analysis from single-molecule FRET trajectories, increases with the increasing substrate concentrations. The intermittent coherence in conformational state changes at the enzymatic reaction active site is likely to be common and exist in other conformation regulated enzymatic reactions. Our results of HPPK interaction with substrate support a multiple-conformational state model, being consistent with a complementary conformation selection and induced-fit enzymatic loop-gated conformational change mechanism in substrate-enzyme active complex formation.

Revealing time bunching effect in single-molecule enzyme conformational dynamics

In this perspective, we focus our discussion on how the single-molecule spectroscopy and statistical analysis are able to reveal enzyme hidden properties, taking the study of T4 lysozyme as an example. Protein conformational fluctuations and dynamics play a crucial role in biomolecular functions, such as in enzymatic reactions. Single-molecule spectroscopy is a powerful approach to analyze protein conformational dynamics under physiological conditions, providing dynamic perspectives on a molecular-level understanding of protein structure-function mechanisms. Using single-molecule fluorescence spectroscopy, we have probed T4 lysozyme conformational motions under the hydrolysis reaction of a polysaccharide of E. coli B cell walls by monitoring the fluorescence resonant energy transfer (FRET) between a donor-acceptor probe pair tethered to T4 lysozyme domains involving open-close hinge-bending motions. Based on the single-molecule spectroscopic results, molecular dynamics simulation, a random walk model analysis, and a novel 2D statistical correlation analysis, we have revealed a time bunching effect in protein conformational motion dynamics that is critical to enzymatic functions. Bunching effect implies that conformational motion times tend to bunch in a finite and narrow time window. We show that convoluted multiple Poisson rate processes give rise to the bunching effect in the enzymatic reaction dynamics. Evidently, the bunching effect is likely common in protein conformational dynamics involving in conformation-gated protein functions. In this perspective, we will also discuss a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anti-correlated fluctuations under a non-correlated noise background. Using this new method, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anti-correlated, or non-correlated; after which, a cross correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis.

2D regional correlation analysis of single-molecule time trajectories

We report a new approach of 2D regional correlation analysis capable of analyzing fluctuation dynamics of complex multiple correlated and anticorrelated fluctuations under a noncorrelated noise background. Using this new method, by changing and scanning the start time and end time along a pair of fluctuation trajectories, we are able to map out any defined segments along the fluctuation trajectories and determine whether they are correlated, anticorrelated, or noncorrelated; after which, a cross-correlation analysis can be applied for each specific segment to obtain a detailed fluctuation dynamics analysis. We specifically discuss an application of this approach to analyze single-molecule fluorescence resonance energy transfer (FRET) fluctuation dynamics where the fluctuations are often complex, although this approach can be useful for analyzing other types of fluctuation dynamics of various physical variables as well.