Unraveling multi-state molecular dynamics in single-molecule FRET experiments. I. Theory of FRET-lines

Abstract

Conformational dynamics of biomolecules are of fundamental importance for their function. Single-molecule studies of Förster Resonance Energy Transfer (smFRET) between a tethered donor and acceptor dye pair are a powerful tool to investigate the structure and dynamics of labeled molecules. However, capturing and quantifying conformational dynamics in intensity-based smFRET experiments remains challenging when the dynamics occur on the sub-millisecond timescale. The method of multiparameter fluorescence detection addresses this challenge by simultaneously registering fluorescence intensities and lifetimes of the donor and acceptor. Together, two FRET observables, the donor fluorescence lifetime τD and the intensity-based FRET efficiency E, inform on the width of the FRET efficiency distribution as a characteristic fingerprint for conformational dynamics. We present a general framework for analyzing dynamics that relates average fluorescence lifetimes and intensities in two-dimensional burst frequency histograms. We present parametric relations of these observables for interpreting the location of FRET populations in E–τ D diagrams, called FRET-lines. To facilitate the analysis of complex exchange equilibria, FRET-lines serve as reference curves for a graphical interpretation of experimental data to (i) identify conformational states, (ii) resolve their dynamic connectivity, (iii) compare different kinetic models, and (iv) infer polymer properties of unfolded or intrinsically disordered proteins. For a simplified graphical analysis of complex kinetic networks, we derive a moment-based representation of the experimental data that decouples the motion of the fluorescence labels from the conformational dynamics of the biomolecule. Importantly, FRET-lines facilitate exploring complex dynamic models via easily computed experimental observables. We provide extensive computational tools to facilitate applying FRET-lines.

Reliability and accuracy of single-molecule FRET studies for characterization of structural dynamics and distances in proteins

“…(b) In the E - τ plot, the intensity-based FRET efficiency E is plotted against the intensity-weighted average donor fluorescence lifetime, 〈 τ ( D ( A ) 〉 F . Molecules undergoing dynamics are shifted from the static line (black) and follow a dynamic FRET-line (red, see text) 59 . For a given population, the dynamic shift is defined as the displacement of the population orthogonal to the static FRET-line.…”

“…To estimate the magnitude of the conformational fluctuations necessary to generate the observed dynamic shifts (Fig. 4f and Supplementary Table 8), we assume that the dynamics occur between two nearby states with interdye distances of R 〈 E 〉 , ± δR , where δ R is the amplitude of the fluctuation 59 (Fig. 5g, Supplementary Note 12 and Supplementary Table 8).…”

Identification and Quantification of Within-Burst Dynamics in Singly-Labeled Single-Molecule Fluorescence Lifetime Experiments

“…This deviation occurs due to the dynamics, where the high FRET state has not only lower donor lifetime than the lower FRET state, but also less donor fluorescence photons -a situation analogous to the changes in both fluorescence lifetime and quantum yield in PIFE. Understanding the sources of these differences paved the way for Seidel and co-workers to develop an analytical framework dubbed FRET-Lines 44 to retrieve the underlying FRET dynamics from multi-parameter fluorescence detection (MFD) time-resolved smFRET measurements [45][46][47] . In parallel to this approach, we provide the mpH 2 MM approach for analyzing and quantifying within-burst 15 dynamics in such confocal-based single-molecule measurements that refer to ratiometric FRET efficiency, donor and acceptor fluorescence lifetimes, fluorescence anisotropies and other parameters.…”

Multisite Phosphorylation and Binding Alter Conformational Dynamics of the 4E-BP2 Protein

“…For each FRET construct, a family of τ DA /τ vs E curves were generated based on a WLC model with stiffness parameters κ between 0.01 and 1 using the FRETlines Python library(52). The chain stiffness for given dataset was selected as the κ value of the τ DA /τ vs E curve passing through the centroid of a 2D Gaussian fit of the experimental τ DA /τ vs E histogram.…”

“…A linear relation is expected for a static structure, with conformations that are rigid or fluctuate on a timescale slower than ~100 µs; in contrast, a nonlinear relation is expected for IDPs, as the burst duration (~1 ms) is much longer than typical chain reconfiguration times (~100 ns) (51). A family of dynamic τ vs. E lines based on a worm-like chain (WLC) model with variable stiffness κ (or persistence length) was generated using a method described by Barth et al (52) The center of the experimental 2D FRET histogram was best matched to a WLC curve to infer the average stiffness for different regions of 4E-BP2 in different phospho/binding states (Table 3). = 0.25 ± 0.10 upon phosphorylation, and even more significantly, to 𝜅𝜅 32−91 𝑁𝑁𝑁𝑁+4𝐸𝐸 = 0.66 ± 0.17 upon binding to eIF4E (Fig.…”