Complete Kinetic Theory of FRET

FRET mechanism to enhance the quantum yield of the PCz/gC3N4 nanocomposite, an emissive material for OLED applications

Conjugated polymers such as polycarbazole (PCz) have captivated more attention than other carbazole-based derivatives due to their superior electrical and optical properties. Accordingly, we synthesized PCz/gC3N4 nanocomposites via the in situ polymerization method using FeCl3 as the oxidative reagent. The synthesized nanocomposites were subjected to characterization techniques to examine their optical and electrical parameters and decide whether the materials were suitable as emissive materials. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) were carried out to ascertain the crystalline or amorphous nature, surface interactions, and functional groups present in them. The surface microstructural and topographical investigations were conducted using field-emission scanning electron microscopy (FESEM) and transmission electron microscopy (HRTEM) techniques. Optical parameters, such as refractive index ∼2.06, optical absorbance, optical band energy ∼2.77 eV, and the photoluminescence emission range, were studied using UV-Visible and photoluminescence spectrometry. The theoretical relative emission quantum yield of ∼67.9% and 87.7% energy transfer from the donor to the acceptor ion via the Förster energy transfer mechanism are illustrated by the PL data. The Förster energy transfer mechanism has been elaborated. The carrier mobility ∼32.03 m2 V-1 S-1, sheet resistance ∼1.6977 × 102 Ω m, carrier density ∼11.96 × 1014 cm-3 and conductivity ∼5.90 × 10-3 S cm-1 were computed using Hall effect measurements. The dielectric constant, dielectric loss, and IV characteristic curve were estimated by the LCR and Four-probe IV measurement methods. The high PL emission intensity, CIE coordinates in the blue emission region, and the CCT value indicate that it is a suitable emissive layer material for OLED applications.

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

Single-molecule Förster-resonance energy transfer (smFRET) experiments allow the study of biomolecular structure and dynamics in vitro and in vivo. We performed an international blind study involving 19 laboratories to assess the uncertainty of FRET experiments for proteins with respect to the measured FRET efficiency histograms, determination of distances, and the detection and quantification of structural dynamics. Using two protein systems with distinct conformational changes and dynamics, we obtained an uncertainty of the FRET efficiency ≤0.06, corresponding to an interdye distance precision of ≤2 Å and accuracy of ≤5 Å. We further discuss the limits for detecting fluctuations in this distance range and how to identify dye perturbations. Our work demonstrates the ability of smFRET experiments to simultaneously measure distances and avoid the averaging of conformational dynamics for realistic protein systems, highlighting its importance in the expanding toolbox of integrative structural biology.

Diffusion-Enhanced Förster Resonance Energy Transfer in Flexible Peptides: From the Haas-Steinberg Partial Differential Equation to a Closed Analytical Expression

In the huge field of polymer structure and dynamics, including intrinsically disordered peptides, protein folding, and enzyme activity, many questions remain that cannot be answered by methodology based on artificial intelligence, X-ray, or NMR spectroscopy but maybe by fluorescence spectroscopy. The theory of Förster resonance energy transfer (FRET) describes how an optically excited fluorophore transfers its excitation energy through space to an acceptor moiety-with a rate that depends on the distance between donor and acceptor. When the donor and acceptor moiety are conjugated to different sites of a flexible peptide chain or any other linear polymer, the pair could in principle report on chain structure and dynamics, on the site-to-site distance distribution, and on the diffusion coefficient of mutual site-to-site motion of the peptide chain. However, the dependence of FRET on distance distribution and diffusion is not defined by a closed analytical expression but by a partial differential equation (PDE), by the Haas-Steinberg equation (HSE), which can only be solved by time-consuming numerical methods. As a second complication, time-resolved FRET measurements have thus far been deemed necessary. As a third complication, the evaluation requires a computationally demanding but indispensable global analysis of an extended experimental data set. These requirements have made the method accessible to only a few experts. Here, we show how the Haas-Steinberg equation leads to a closed analytical expression (CAE), the Haas-Steinberg-Jacob equation (HSJE), which relates a diffusion-diagnosing parameter, the effective donor-acceptor distance, to the augmented diffusion coefficient, J, composed of the diffusion coefficient, D, and the photophysical parameters that characterize the used FRET method. The effective donor-acceptor distance is easily retrieved either through time-resolved or steady-state fluorescence measurements. Any global fit can now be performed in seconds and minimizes the sum-of-square difference between the experimental values of the effective distance and the values obtained from the HSJE. In summary, the HSJE can give a decisive advantage in applying the speed and sensitivity of FRET spectroscopy to standing questions of polymer structure and dynamics.

Structural dynamics of DNA strand break sensing by PARP-1 at a single-molecule level

Single-stranded breaks (SSBs) are the most frequent DNA lesions threatening genomic integrity. A highly kinked DNA structure in complex with human PARP-1 domains led to the proposal that SSB sensing in Eukaryotes relies on dynamics of both the broken DNA double helix and PARP-1's multi-domain organization. Here, we directly probe this process at the single-molecule level. Quantitative smFRET and structural ensemble calculations reveal how PARP-1's N-terminal zinc fingers convert DNA SSBs from a largely unperturbed conformation, via an intermediate state into the highly kinked DNA conformation. Our data suggest an induced fit mechanism via a multi-domain assembly cascade that drives SSB sensing and stimulates an interplay with the scaffold protein XRCC1 orchestrating subsequent DNA repair events. Interestingly, a clinically used PARP-1 inhibitor Niraparib shifts the equilibrium towards the unkinked DNA conformation, whereas the inhibitor EB47 stabilizes the kinked state.

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

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-τD 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.

Resolving distance variations by single-molecule FRET and EPR spectroscopy using rotamer libraries

Förster resonance energy transfer (FRET) and electron paramagnetic resonance (EPR) spectroscopy are complementary techniques for quantifying distances in the nanometer range. Both approaches are commonly employed for probing the conformations and conformational changes of biological macromolecules based on site-directed fluorescent or paramagnetic labeling. FRET can be applied in solution at ambient temperature and thus provides direct access to dynamics, especially if used at the single-molecule level, whereas EPR requires immobilization or work at cryogenic temperatures but provides data that can be more reliably used to extract distance distributions. However, a combined analysis of the complementary data from the two techniques has been complicated by the lack of a common modeling framework. Here, we demonstrate a systematic analysis approach based on rotamer libraries for both FRET and EPR labels to predict distance distributions between two labels from a structural model. Dynamics of the fluorophores within these distance distributions are taken into account by diffusional averaging, which improves the agreement with experiment. Benchmarking this methodology with a series of surface-exposed pairs of sites in a structured protein domain reveals that the lowest resolved distance differences can be as small as ∼0.25 nm for both techniques, with quantitative agreement between experimental and simulated transfer efficiencies within a range of ±0.045. Rotamer library analysis thus establishes a coherent way of treating experimental data from EPR and FRET and provides a basis for integrative structural modeling, including studies of conformational distributions and dynamics of biological macromolecules using both techniques.

FRET-based dynamic structural biology: Challenges, perspectives and an appeal for open-science practices

Single-molecule FRET (smFRET) has become a mainstream technique for studying biomolecular structural dynamics. The rapid and wide adoption of smFRET experiments by an ever-increasing number of groups has generated significant progress in sample preparation, measurement procedures, data analysis, algorithms and documentation. Several labs that employ smFRET approaches have joined forces to inform the smFRET community about streamlining how to perform experiments and analyze results for obtaining quantitative information on biomolecular structure and dynamics. The recent efforts include blind tests to assess the accuracy and the precision of smFRET experiments among different labs using various procedures. These multi-lab studies have led to the development of smFRET procedures and documentation, which are important when submitting entries into the archiving system for integrative structure models, PDB-Dev. This position paper describes the current 'state of the art' from different perspectives, points to unresolved methodological issues for quantitative structural studies, provides a set of 'soft recommendations' about which an emerging consensus exists, and lists openly available resources for newcomers and seasoned practitioners. To make further progress, we strongly encourage 'open science' practices.

Advanced FRET normalization allows quantitative analysis of protein interactions including stoichiometries and relative affinities in living cells

FRET (Fluorescence Resonance Energy Transfer) measurements are commonly applied to proof protein-protein interactions. However, standard methods of live cell FRET microscopy and signal normalization only allow a principle assessment of mutual binding and are unable to deduce quantitative information of the interaction. We present an evaluation and normalization procedure for 3-filter FRET measurements, which reflects the process of complex formation by plotting FRET-saturation curves. The advantage of this approach relative to traditional signal normalizations is demonstrated by mathematical simulations. Thereby, we also identify the contribution of critical parameters such as the total amount of donor and acceptor molecules and their molar ratio. When combined with a fitting procedure, this normalization facilitates the extraction of key properties of protein complexes such as the interaction stoichiometry or the apparent affinity of the binding partners. Finally, the feasibility of our method is verified by investigating three exemplary protein complexes. Altogether, our approach offers a novel method for a quantitative analysis of protein interactions by 3-filter FRET microscopy, as well as flow cytometry. To facilitate the application of this method, we created macros and routines for the programs ImageJ, R and MS-Excel, which we make publicly available.